From e8569c197f9ef7c369a6aa3d055c9d500407ad4a Mon Sep 17 00:00:00 2001 From: jasonaebischerGIT Date: Thu, 10 Feb 2022 11:51:02 +0100 Subject: [PATCH 1/7] full LEFT beta function added --- wilson/run/smeft/betaleft.py | 269 +++++++++++++++++++++++++++++++++++ 1 file changed, 269 insertions(+) create mode 100644 wilson/run/smeft/betaleft.py diff --git a/wilson/run/smeft/betaleft.py b/wilson/run/smeft/betaleft.py new file mode 100644 index 0000000..0024691 --- /dev/null +++ b/wilson/run/smeft/betaleft.py @@ -0,0 +1,269 @@ +from numpy import pi +from wilson.run.smeft.beta import my_einsum +from collections import OrderedDict + + +Nc = 3 +# Eq. (3.42) +CA = Nc +CF = (Nc**2-1)/(2*Nc) +C1 = (Nc**2-1)/(4*Nc**2) +Cd = (Nc**2-4)/Nc + + +qu = 0.6666666666666666 +qd = -0.3333333333333333 +qe = -1 +nu = 2 +nd = 3 +ne = 3 +b0g = (11*Nc - 2*(nd + nu))/3. +b0e = (-4*(Nc*nd*qd**2 + ne*qe**2 + Nc*nu*qu**2))/3. + + +def betaLEFT(C): + e = C["e"] + g = C["gs"] + + + # Eq. (3.41) + zetae = (8/3)*(2*my_einsum("wv,wv",C["nugamma"],C["nugamma"].conj())+my_einsum("wv,wv",C["egamma"],C["egamma"].conj())+Nc*my_einsum("wv,wv",C["ugamma"],C["ugamma"].conj())+Nc*my_einsum("wv,wv",C["dgamma"],C["dgamma"].conj())) + zetag = (4/3)*(my_einsum("wv,wv",C["uG"],C["uG"].conj())+my_einsum("wv,wv",C["dG"],C["dG"].conj())) + + + Beta = OrderedDict() + + + # Dimension 3: Masses + + Beta["Mnu"] = 24*my_einsum("vwrs,wv",C["SnunuLL"],C["Mnu"].conj().T @ C["Mnu"] @ C["Mnu"].conj().T) + 16*my_einsum("wrvs,wv",C["VnunuLL"],C["Mnu"] @ C["Mnu"].conj().T @ C["Mnu"]) + 8*my_einsum("rsvw,wv",C["SnueLL"],C["Me"].conj().T @ C["Me"] @ C["Me"].conj().T) + 8*my_einsum("rsvw,wv",C["SnueLR"],C["Me"] @ C["Me"].conj().T @ C["Me"]) + 8*Nc*my_einsum("rsvw,wv",C["SnuuLL"],C["Mu"].conj().T @ C["Mu"] @ C["Mu"].conj().T) + 8*Nc*my_einsum("rsvw,wv",C["SnuuLR"],C["Mu"] @ C["Mu"].conj().T @ C["Mu"]) + 8*Nc*my_einsum("rsvw,wv",C["SnudLL"],C["Md"].conj().T @ C["Md"] @ C["Md"].conj().T) + 8*Nc*my_einsum("rsvw,wv",C["SnudLR"],C["Md"] @ C["Md"].conj().T @ C["Md"]) - 48*my_einsum("rw,uv,wv,us",C["nugamma"],C["nugamma"].conj(),C["Mnu"].conj().T @ C["Mnu"],C["Mnu"]) + 16*my_einsum("rw,vw,vs",C["nugamma"],C["nugamma"].conj(),C["Mnu"] @ C["Mnu"].conj().T @ C["Mnu"]) - 48*my_einsum("wu,vs,wv,ru",C["nugamma"].conj(),C["nugamma"],C["Mnu"] @ C["Mnu"].conj().T,C["Mnu"]) + 16*my_einsum("wv,ws,rv",C["nugamma"].conj(),C["nugamma"],C["Mnu"] @ C["Mnu"].conj().T @ C["Mnu"]) - 96*my_einsum("rv,ws,vw",C["nugamma"],C["nugamma"],C["Mnu"].conj().T @ C["Mnu"] @ C["Mnu"].conj().T) + + Beta["Me"] = - 6*qe**2*e**2*my_einsum("rs",C["Me"]) + 12*qe*e*my_einsum("vr,vs",C["egamma"].conj(),C["Me"].conj().T @ C["Me"]) + 12*qe*e*my_einsum("sv,rv",C["egamma"].conj(),C["Me"] @ C["Me"].conj().T) + 4*my_einsum("vwrs,wv",C["SnueLL"],C["Mnu"].conj().T @ C["Mnu"] @ C["Mnu"].conj().T) + 4*my_einsum("wvsr,wv",C["SnueLR"].conj(),C["Mnu"] @ C["Mnu"].conj().T @ C["Mnu"]) + (8*my_einsum("srwv,wv",C["SeeRR"].conj(),C["Me"].conj().T @ C["Me"] @ C["Me"].conj().T) - 4*my_einsum("wrsv,wv",C["SeeRR"].conj(),C["Me"].conj().T @ C["Me"] @ C["Me"].conj().T)) - 8*my_einsum("vsrw,wv",C["VeeLR"],C["Me"] @ C["Me"].conj().T @ C["Me"]) + 4*Nc*my_einsum("srwv,wv",C["SeuRR"].conj(),C["Mu"].conj().T @ C["Mu"] @ C["Mu"].conj().T) + 4*Nc*my_einsum("srwv,wv",C["SeuRL"].conj(),C["Mu"] @ C["Mu"].conj().T @ C["Mu"]) + 4*Nc*my_einsum("srwv,wv",C["SedRR"].conj(),C["Md"].conj().T @ C["Md"] @ C["Md"].conj().T) + 4*Nc*my_einsum("srwv,wv",C["SedRL"].conj(),C["Md"] @ C["Md"].conj().T @ C["Md"]) - 12*my_einsum("wr,vu,wv,us",C["egamma"].conj(),C["egamma"],C["Me"].conj().T @ C["Me"],C["Me"]) + 4*my_einsum("wr,wv,vs",C["egamma"].conj(),C["egamma"],C["Me"] @ C["Me"].conj().T @ C["Me"]) - 12*my_einsum("uw,sv,wv,ru",C["egamma"],C["egamma"].conj(),C["Me"] @ C["Me"].conj().T,C["Me"]) + 4*my_einsum("vw,sw,rv",C["egamma"],C["egamma"].conj(),C["Me"] @ C["Me"].conj().T @ C["Me"]) - 24*my_einsum("vr,sw,vw",C["egamma"].conj(),C["egamma"].conj(),C["Me"].conj().T @ C["Me"] @ C["Me"].conj().T) + + Beta["Mu"] = - 6*(CF*g**2 + qu**2*e**2)*my_einsum("rs",C["Mu"]) + 12*(CF*g*my_einsum("vr,vs",C["uG"].conj(),C["Mu"].conj().T @ C["Mu"]) + qu*e*my_einsum("vr,vs",C["ugamma"].conj(),C["Mu"].conj().T @ C["Mu"])) + 12*(CF*g*my_einsum("sv,rv",C["uG"].conj(),C["Mu"] @ C["Mu"].conj().T) + qu*e*my_einsum("sv,rv",C["ugamma"].conj(),C["Mu"] @ C["Mu"].conj().T)) + 4*my_einsum("vwrs,wv",C["SnuuLL"],C["Mnu"].conj().T @ C["Mnu"] @ C["Mnu"].conj().T) + 4*my_einsum("wvsr,wv",C["SnuuLR"].conj(),C["Mnu"] @ C["Mnu"].conj().T @ C["Mnu"]) + 4*my_einsum("wvsr,wv",C["SeuRR"].conj(),C["Me"].conj().T @ C["Me"] @ C["Me"].conj().T) + 4*my_einsum("vwrs,wv",C["SeuRL"],C["Me"] @ C["Me"].conj().T @ C["Me"]) + (8*Nc*my_einsum("srwv,wv",C["S1uuRR"].conj(),C["Mu"].conj().T @ C["Mu"] @ C["Mu"].conj().T) - 4*my_einsum("svwr,wv",C["S1uuRR"].conj(),C["Mu"].conj().T @ C["Mu"] @ C["Mu"].conj().T) - 4*CF*my_einsum("svwr,wv",C["S8uuRR"].conj(),C["Mu"].conj().T @ C["Mu"] @ C["Mu"].conj().T)) - 8*(my_einsum("vsrw,wv",C["V1uuLR"],C["Mu"] @ C["Mu"].conj().T @ C["Mu"]) + CF*my_einsum("vsrw,wv",C["V8uuLR"],C["Mu"] @ C["Mu"].conj().T @ C["Mu"])) + (4*Nc*my_einsum("srwv,wv",C["S1udRR"].conj(),C["Md"].conj().T @ C["Md"] @ C["Md"].conj().T) - 2*my_einsum("svwr,wv",C["S1udduRR"].conj(),C["Md"].conj().T @ C["Md"] @ C["Md"].conj().T) - 2*CF*my_einsum("svwr,wv",C["S8udduRR"].conj(),C["Md"].conj().T @ C["Md"] @ C["Md"].conj().T)) - 8*(my_einsum("svwr,wv",C["V1udduLR"].conj(),C["Md"] @ C["Md"].conj().T @ C["Md"]) + CF*my_einsum("svwr,wv",C["V8udduLR"].conj(),C["Md"] @ C["Md"].conj().T @ C["Md"])) - 12*my_einsum("wr,vu,wv,us",C["ugamma"].conj(),C["ugamma"],C["Mu"].conj().T @ C["Mu"],C["Mu"]) + 4*my_einsum("wr,wv,vs",C["ugamma"].conj(),C["ugamma"],C["Mu"] @ C["Mu"].conj().T @ C["Mu"]) - 12*my_einsum("uw,sv,wv,ru",C["ugamma"],C["ugamma"].conj(),C["Mu"] @ C["Mu"].conj().T,C["Mu"]) + 4*my_einsum("vw,sw,rv",C["ugamma"],C["ugamma"].conj(),C["Mu"] @ C["Mu"].conj().T @ C["Mu"]) - 12*CF*my_einsum("wr,vu,wv,us",C["uG"].conj(),C["uG"],C["Mu"].conj().T @ C["Mu"],C["Mu"]) + 4*CF*my_einsum("wr,wv,vs",C["uG"].conj(),C["uG"],C["Mu"] @ C["Mu"].conj().T @ C["Mu"]) - 12*CF*my_einsum("uw,sv,wv,ru",C["uG"],C["uG"].conj(),C["Mu"] @ C["Mu"].conj().T,C["Mu"]) + 4*CF*my_einsum("vw,sw,rv",C["uG"],C["uG"].conj(),C["Mu"] @ C["Mu"].conj().T @ C["Mu"]) - 24*my_einsum("vr,sw,vw",C["ugamma"].conj(),C["ugamma"].conj(),C["Mu"].conj().T @ C["Mu"] @ C["Mu"].conj().T) - 24*CF*my_einsum("vr,sw,vw",C["uG"].conj(),C["uG"].conj(),C["Mu"].conj().T @ C["Mu"] @ C["Mu"].conj().T) + + Beta["Md"] = - 6*(CF*g**2 + qd**2*e**2)*my_einsum("rs",C["Md"]) + 12*(CF*g*my_einsum("vr,vs",C["dG"].conj(),C["Md"].conj().T @ C["Md"]) + qd*e*my_einsum("vr,vs",C["dgamma"].conj(),C["Md"].conj().T @ C["Md"])) + 12*(CF*g*my_einsum("sv,rv",C["dG"].conj(),C["Md"] @ C["Md"].conj().T) + qd*e*my_einsum("sv,rv",C["dgamma"].conj(),C["Md"] @ C["Md"].conj().T)) + 4*my_einsum("vwrs,wv",C["SnudLL"],C["Mnu"].conj().T @ C["Mnu"] @ C["Mnu"].conj().T) + 4*my_einsum("wvsr,wv",C["SnudLR"].conj(),C["Mnu"] @ C["Mnu"].conj().T @ C["Mnu"]) + 4*my_einsum("wvsr,wv",C["SedRR"].conj(),C["Me"].conj().T @ C["Me"] @ C["Me"].conj().T) + 4*my_einsum("vwrs,wv",C["SedRL"],C["Me"] @ C["Me"].conj().T @ C["Me"]) + (4*Nc*my_einsum("wvsr,wv",C["S1udRR"].conj(),C["Mu"].conj().T @ C["Mu"] @ C["Mu"].conj().T) - 2*my_einsum("wrsv,wv",C["S1udduRR"].conj(),C["Mu"].conj().T @ C["Mu"] @ C["Mu"].conj().T) - 2*CF*my_einsum("wrsv,wv",C["S8udduRR"].conj(),C["Mu"].conj().T @ C["Mu"] @ C["Mu"].conj().T)) - 8*(my_einsum("vsrw,wv",C["V1udduLR"],C["Mu"] @ C["Mu"].conj().T @ C["Mu"]) + CF*my_einsum("vsrw,wv",C["V8udduLR"],C["Mu"] @ C["Mu"].conj().T @ C["Mu"])) + (8*Nc*my_einsum("wvsr,wv",C["S1ddRR"].conj(),C["Md"].conj().T @ C["Md"] @ C["Md"].conj().T) - 4*my_einsum("wrsv,wv",C["S1ddRR"].conj(),C["Md"].conj().T @ C["Md"] @ C["Md"].conj().T) - 4*CF*my_einsum("wrsv,wv",C["S8ddRR"].conj(),C["Md"].conj().T @ C["Md"] @ C["Md"].conj().T)) - 8*(my_einsum("vsrw,wv",C["V1ddLR"],C["Md"] @ C["Md"].conj().T @ C["Md"]) + CF*my_einsum("vsrw,wv",C["V8ddLR"],C["Md"] @ C["Md"].conj().T @ C["Md"])) - 12*my_einsum("wr,vu,wv,us",C["dgamma"].conj(),C["dgamma"],C["Md"].conj().T @ C["Md"],C["Md"]) + 4*my_einsum("wr,wv,vs",C["dgamma"].conj(),C["dgamma"],C["Md"] @ C["Md"].conj().T @ C["Md"]) - 12*my_einsum("uw,sv,wv,ru",C["dgamma"],C["dgamma"].conj(),C["Md"] @ C["Md"].conj().T,C["Md"]) + 4*my_einsum("vw,sw,rv",C["dgamma"],C["dgamma"].conj(),C["Md"] @ C["Md"].conj().T @ C["Md"]) - 12*CF*my_einsum("wr,vu,wv,us",C["dG"].conj(),C["dG"],C["Md"].conj().T @ C["Md"],C["Md"]) + 4*CF*my_einsum("wr,wv,vs",C["dG"].conj(),C["dG"],C["Md"] @ C["Md"].conj().T @ C["Md"]) - 12*CF*my_einsum("uw,sv,wv,ru",C["dG"],C["dG"].conj(),C["Md"] @ C["Md"].conj().T,C["Md"]) + 4*CF*my_einsum("vw,sw,rv",C["dG"],C["dG"].conj(),C["Md"] @ C["Md"].conj().T @ C["Md"]) - 24*my_einsum("vr,sw,vw",C["dgamma"].conj(),C["dgamma"].conj(),C["Md"].conj().T @ C["Md"] @ C["Md"].conj().T) - 24*CF*my_einsum("vr,sw,vw",C["dG"].conj(),C["dG"].conj(),C["Md"].conj().T @ C["Md"] @ C["Md"].conj().T) + + # Dimension 4: Gauge Couplings + + Beta["e"] = - b0e*e**3 - 8*e**2*qe*(my_einsum("rs,sr",C["egamma"],C["Me"]) + my_einsum("rs,rs",C["Me"].conj().T,C["egamma"].conj())) - 8*e**2*Nc*qu*(my_einsum("rs,sr",C["ugamma"],C["Mu"]) + my_einsum("rs,rs",C["Mu"].conj().T,C["ugamma"].conj())) - 8*e**2*Nc*qd*(my_einsum("rs,sr",C["dgamma"],C["Md"]) + my_einsum("rs,rs",C["Md"].conj().T,C["dgamma"].conj())) + 8*e*(2*my_einsum("ts,sr,rp,pt",C["Mnu"].conj().T,C["nugamma"],C["Mnu"].conj().T,C["nugamma"]) + 2*my_einsum("pr,sr,st,pt",C["Mnu"],C["nugamma"].conj(),C["Mnu"],C["nugamma"].conj()) + my_einsum("ts,sr,rp,pt",C["Me"],C["egamma"],C["Me"],C["egamma"]) + my_einsum("pr,sr,st,pt",C["Me"].conj().T,C["egamma"].conj(),C["Me"].conj().T,C["egamma"].conj()) + Nc*my_einsum("ts,sr,rp,pt",C["Mu"],C["ugamma"],C["Mu"],C["ugamma"]) + Nc*my_einsum("pr,sr,st,pt",C["Mu"].conj().T,C["ugamma"].conj(),C["Mu"].conj().T,C["ugamma"].conj()) + Nc*my_einsum("ts,sr,rp,pt",C["Md"],C["dgamma"],C["Md"],C["dgamma"]) + Nc*my_einsum("pr,sr,st,pt",C["Md"].conj().T,C["dgamma"].conj(),C["Md"].conj().T,C["dgamma"].conj())) + + Beta["g"] = - b0g*g**3 - 4*g**2*(my_einsum("rs,sr",C["uG"],C["Mu"]) + my_einsum("rs,rs",C["Mu"].conj().T,C["uG"].conj())) - 4*g**2*(my_einsum("rs,sr",C["dG"],C["Md"]) + my_einsum("rs,rs",C["Md"].conj().T,C["dG"].conj())) + 4*g*(my_einsum("ts,sr,rp,pt",C["Mu"],C["uG"],C["Mu"],C["uG"]) + my_einsum("pr,sr,st,pt",C["Mu"].conj().T,C["uG"].conj(),C["Mu"].conj().T,C["uG"].conj()) + my_einsum("ts,sr,rp,pt",C["Md"],C["dG"],C["Md"],C["dG"]) + my_einsum("pr,sr,st,pt",C["Md"].conj().T,C["dG"].conj(),C["Md"].conj().T,C["dG"].conj())) + + Beta["thetaQCD"] = ((64*pi**2)/(g))*(1j*my_einsum("rs,sr",C["uG"],C["Mu"]) - 1j*my_einsum("rs,rs",C["Mu"].conj().T,C["uG"].conj())) + ((64*pi**2)/(g))*(1j*my_einsum("rs,sr",C["dG"],C["Md"]) - 1j*my_einsum("rs,rs",C["Md"].conj().T,C["dG"].conj())) + ((32*pi**2)/(g**2))*2j*( - my_einsum("ts,sr,rp,pt",C["Mu"],C["uG"],C["Mu"],C["uG"]) + my_einsum("ts,sr,rp,pt",C["Mu"].conj(),C["uG"].conj(),C["Mu"].conj(),C["uG"].conj()) - my_einsum("ts,sr,rp,pt",C["Md"],C["dG"],C["Md"],C["dG"]) + my_einsum("ts,sr,rp,pt",C["Md"].conj(),C["dG"].conj(),C["Md"].conj(),C["dG"].conj())) + + Beta["thetaQED"] = ((128*pi**2*qe)/(e))*(1j*my_einsum("rs,sr",C["egamma"],C["Me"]) - 1j*my_einsum("rs,rs",C["Me"].conj().T,C["egamma"].conj())) + ((128*Nc*pi**2*qu)/(e))*(1j*my_einsum("rs,sr",C["ugamma"],C["Mu"]) - 1j*my_einsum("rs,rs",C["Mu"].conj().T,C["ugamma"].conj())) + ((128*Nc*pi**2*qd)/(e))*(1j*my_einsum("rs,sr",C["dgamma"],C["Md"]) - 1j*my_einsum("rs,rs",C["Md"].conj().T,C["dgamma"].conj())) + ((32*pi**2)/(e**2))*4j*(2*my_einsum("ts,sr,rp,pt",C["Mnu"].conj().T,C["nugamma"],C["Mnu"].conj().T,C["nugamma"]) - 2*my_einsum("pr,sr,st,pt",C["Mnu"],C["nugamma"].conj(),C["Mnu"],C["nugamma"].conj()) - my_einsum("ts,sr,rp,pt",C["Me"],C["egamma"],C["Me"],C["egamma"]) + my_einsum("pr,sr,st,pt",C["Me"].conj().T,C["egamma"].conj(),C["Me"].conj().T,C["egamma"].conj()) - Nc*my_einsum("ts,sr,rp,pt",C["Mu"],C["ugamma"],C["Mu"],C["ugamma"]) + Nc*my_einsum("pr,sr,st,pt",C["Mu"].conj().T,C["ugamma"].conj(),C["Mu"].conj().T,C["ugamma"].conj()) - Nc*my_einsum("ts,sr,rp,pt",C["Md"],C["dgamma"],C["Md"],C["dgamma"]) + Nc*my_einsum("pr,sr,st,pt",C["Md"].conj().T,C["dgamma"].conj(),C["Md"].conj().T,C["dgamma"].conj())) + + # Dimension 5: Dipole Operators + + Beta["nugamma"] = - b0e*e**2*my_einsum("rs",C["nugamma"]) - 8*e*qe*(my_einsum("rs,vw,wv",C["nugamma"],C["egamma"],C["Me"]) + my_einsum("rs,vw,vw",C["nugamma"],C["Me"].conj().T,C["egamma"].conj())) - 8*e*Nc*qu*(my_einsum("rs,vw,wv",C["nugamma"],C["ugamma"],C["Mu"]) + my_einsum("rs,vw,vw",C["nugamma"],C["Mu"].conj().T,C["ugamma"].conj())) - 8*e*Nc*qd*(my_einsum("rs,vw,wv",C["nugamma"],C["dgamma"],C["Md"]) + my_einsum("rs,vw,vw",C["nugamma"],C["Md"].conj().T,C["dgamma"].conj())) + + Beta["egamma"] = (10*qe**2 - b0e)*e**2*my_einsum("rs",C["egamma"]) - 8*e*Nc*qd*my_einsum("wv,rsvw",C["Md"],C["TedRR"]) - 8*e*Nc*qu*my_einsum("wv,rsvw",C["Mu"],C["TeuRR"]) + 2*e*qe*my_einsum("wv,rwvs",C["Me"],C["SeeRR"]) - 12*e*qe*my_einsum("rw,wv,vs",C["egamma"],C["Me"],C["egamma"]) - 8*e*qe*(my_einsum("vw,rw,vs",C["egamma"].conj(),C["egamma"],C["Me"].conj().T) + my_einsum("vw,vs,rw",C["egamma"].conj(),C["egamma"],C["Me"].conj().T)) - 8*e*qe*(my_einsum("rs,vw,wv",C["egamma"],C["egamma"],C["Me"]) + my_einsum("rs,vw,vw",C["egamma"],C["Me"].conj().T,C["egamma"].conj())) - 8*e*Nc*qu*(my_einsum("rs,vw,wv",C["egamma"],C["ugamma"],C["Mu"]) + my_einsum("rs,vw,vw",C["egamma"],C["Mu"].conj().T,C["ugamma"].conj())) - 8*e*Nc*qd*(my_einsum("rs,vw,wv",C["egamma"],C["dgamma"],C["Md"]) + my_einsum("rs,vw,vw",C["egamma"],C["Md"].conj().T,C["dgamma"].conj())) + + Beta["ugamma"] = (2*CF*g**2 + (10*qu**2 - b0e)*e**2)*my_einsum("rs",C["ugamma"]) + 8*CF*e*g*qu*my_einsum("rs",C["uG"]) - 8*e*qe*my_einsum("wv,vwrs",C["Me"],C["TeuRR"]) + 2*e*qu*my_einsum("wv,rwvs",C["Mu"],C["S1uuRR"]) + 2*e*CF*qu*my_einsum("wv,rwvs",C["Mu"],C["S8uuRR"]) + e*qd*my_einsum("wv,rwvs",C["Md"],C["S1udduRR"]) + e*CF*qd*my_einsum("wv,rwvs",C["Md"],C["S8udduRR"]) - (4*g*CF*my_einsum("rw,vw,vs",C["ugamma"],C["uG"].conj(),C["Mu"].conj().T) + 8*e*qu*my_einsum("rw,vw,vs",C["ugamma"],C["ugamma"].conj(),C["Mu"].conj().T)) - (4*g*CF*my_einsum("rw,vw,vs",C["Mu"].conj().T,C["uG"].conj(),C["ugamma"]) + 8*e*qu*my_einsum("rw,vw,vs",C["Mu"].conj().T,C["ugamma"].conj(),C["ugamma"])) - 8*e*qe*(my_einsum("rs,vw,wv",C["ugamma"],C["egamma"],C["Me"]) + my_einsum("rs,vw,vw",C["ugamma"],C["Me"].conj().T,C["egamma"].conj())) - 8*e*Nc*qu*(my_einsum("rs,vw,wv",C["ugamma"],C["ugamma"],C["Mu"]) + my_einsum("rs,vw,vw",C["ugamma"],C["Mu"].conj().T,C["ugamma"].conj())) - 8*e*Nc*qd*(my_einsum("rs,vw,wv",C["ugamma"],C["dgamma"],C["Md"]) + my_einsum("rs,vw,vw",C["ugamma"],C["Md"].conj().T,C["dgamma"].conj())) - 12*e*qu*my_einsum("rw,wv,vs",C["ugamma"],C["Mu"],C["ugamma"]) - 4*e*qu*CF*my_einsum("wv,rw,vs",C["Mu"],C["uG"],C["uG"]) - 4*g*CF*(my_einsum("wv,rw,vs",C["Mu"],C["ugamma"],C["uG"]) + my_einsum("wv,rw,vs",C["Mu"],C["uG"],C["ugamma"])) - 4*CF*e*qu*my_einsum("wv,ws,rv",C["uG"].conj(),C["uG"],C["Mu"].conj().T) - 4*CF*e*qu*my_einsum("rw,vw,vs",C["uG"],C["uG"].conj(),C["Mu"].conj().T) + + Beta["dgamma"] = (2*CF*g**2 + (10*qd**2 - b0e)*e**2)*my_einsum("rs",C["dgamma"]) + 8*CF*e*g*qd*my_einsum("rs",C["dG"]) - 8*e*qe*my_einsum("wv,vwrs",C["Me"],C["TedRR"]) + 2*e*qd*my_einsum("wv,rwvs",C["Md"],C["S1ddRR"]) + 2*e*CF*qd*my_einsum("wv,rwvs",C["Md"],C["S8ddRR"]) + e*qu*my_einsum("wv,vsrw",C["Mu"],C["S1udduRR"]) + e*CF*qu*my_einsum("wv,vsrw",C["Mu"],C["S8udduRR"]) - (4*g*CF*my_einsum("rw,vw,vs",C["dgamma"],C["dG"].conj(),C["Md"].conj().T) + 8*e*qd*my_einsum("rw,vw,vs",C["dgamma"],C["dgamma"].conj(),C["Md"].conj().T)) - (4*g*CF*my_einsum("rw,vw,vs",C["Md"].conj().T,C["dG"].conj(),C["dgamma"]) + 8*e*qd*my_einsum("rw,vw,vs",C["Md"].conj().T,C["dgamma"].conj(),C["dgamma"])) - 8*e*qe*(my_einsum("rs,vw,wv",C["dgamma"],C["egamma"],C["Me"]) + my_einsum("rs,vw,vw",C["dgamma"],C["Me"].conj().T,C["egamma"].conj())) - 8*e*Nc*qu*(my_einsum("rs,vw,wv",C["dgamma"],C["ugamma"],C["Mu"]) + my_einsum("rs,vw,vw",C["dgamma"],C["Mu"].conj().T,C["ugamma"].conj())) - 8*e*Nc*qd*(my_einsum("rs,vw,wv",C["dgamma"],C["dgamma"],C["Md"]) + my_einsum("rs,vw,vw",C["dgamma"],C["Md"].conj().T,C["dgamma"].conj())) - 12*e*qd*my_einsum("rw,wv,vs",C["dgamma"],C["Md"],C["dgamma"]) - 4*e*qd*CF*my_einsum("wv,rw,vs",C["Md"],C["dG"],C["dG"]) - 4*g*CF*(my_einsum("wv,rw,vs",C["Md"],C["dgamma"],C["dG"]) + my_einsum("wv,rw,vs",C["Md"],C["dG"],C["dgamma"])) - 4*CF*e*qd*my_einsum("wv,ws,rv",C["dG"].conj(),C["dG"],C["Md"].conj().T) - 4*CF*e*qd*my_einsum("rw,vw,vs",C["dG"],C["dG"].conj(),C["Md"].conj().T) + + Beta["uG"] = ((10*CF - 4*CA - b0g)*g**2 + 2*e**2*qu**2)*my_einsum("rs",C["uG"]) + 8*e*g*qu*my_einsum("rs",C["ugamma"]) + 3*g**2*CA*my_einsum("rs",C["Mu"].conj().T)*(C["G"] + 1j*C["Gtilde"]) + 2*g*my_einsum("wv,rwvs",C["Mu"],C["S1uuRR"]) + 2*g*(CF - ((1)/(2))*CA)*my_einsum("wv,rwvs",C["Mu"],C["S8uuRR"]) + g*my_einsum("wv,rwvs",C["Md"],C["S1udduRR"]) + g*(CF - ((1)/(2))*CA)*my_einsum("wv,rwvs",C["Md"],C["S8udduRR"]) - ((8*CF - 2*CA)*g*my_einsum("rw,vw,vs",C["uG"],C["uG"].conj(),C["Mu"].conj().T) + 4*e*qu*my_einsum("rw,vw,vs",C["uG"],C["ugamma"].conj(),C["Mu"].conj().T)) - ((8*CF - 2*CA)*g*my_einsum("rw,vw,vs",C["Mu"].conj().T,C["uG"].conj(),C["uG"]) + 4*e*qu*my_einsum("rw,vw,vs",C["Mu"].conj().T,C["ugamma"].conj(),C["uG"])) - 4*g*(my_einsum("rs,vw,wv",C["uG"],C["uG"],C["Mu"]) + my_einsum("rs,vw,vw",C["uG"],C["Mu"].conj().T,C["uG"].conj())) - 4*g*(my_einsum("rs,vw,wv",C["uG"],C["dG"],C["Md"]) + my_einsum("rs,vw,vw",C["uG"],C["Md"].conj().T,C["dG"].conj())) + (10*CA - 12*CF)*g*my_einsum("rw,wv,vs",C["uG"],C["Mu"],C["uG"]) - 4*e*qu*(my_einsum("wv,rw,vs",C["Mu"],C["ugamma"],C["uG"]) + my_einsum("wv,rw,vs",C["Mu"],C["uG"],C["ugamma"])) - 4*g*my_einsum("wv,rw,vs",C["Mu"],C["ugamma"],C["ugamma"]) - 4*g*my_einsum("wv,ws,rv",C["ugamma"].conj(),C["ugamma"],C["Mu"].conj().T) - 4*g*my_einsum("rw,vw,vs",C["ugamma"],C["ugamma"].conj(),C["Mu"].conj().T) + + Beta["dG"] = ((10*CF - 4*CA - b0g)*g**2 + 2*e**2*qd**2)*my_einsum("rs",C["dG"]) + 8*e*g*qd*my_einsum("rs",C["dgamma"]) + 3*g**2*CA*my_einsum("rs",C["Md"].conj().T)*(C["G"] + 1j*C["Gtilde"]) + 2*g*my_einsum("wv,rwvs",C["Md"],C["S1ddRR"]) + 2*g*(CF - ((1)/(2))*CA)*my_einsum("wv,rwvs",C["Md"],C["S8ddRR"]) + g*my_einsum("wv,vsrw",C["Mu"],C["S1udduRR"]) + g*(CF - ((1)/(2))*CA)*my_einsum("wv,vsrw",C["Mu"],C["S8udduRR"]) - ((8*CF - 2*CA)*g*my_einsum("rw,vw,vs",C["dG"],C["dG"].conj(),C["Md"].conj().T) + 4*e*qd*my_einsum("rw,vw,vs",C["dG"],C["dgamma"].conj(),C["Md"].conj().T)) - ((8*CF - 2*CA)*g*my_einsum("rw,vw,vs",C["Md"].conj().T,C["dG"].conj(),C["dG"]) + 4*e*qd*my_einsum("rw,vw,vs",C["Md"].conj().T,C["dgamma"].conj(),C["dG"])) - 4*g*(my_einsum("rs,vw,wv",C["dG"],C["uG"],C["Mu"]) + my_einsum("rs,vw,vw",C["dG"],C["Mu"].conj().T,C["uG"].conj())) - 4*g*(my_einsum("rs,vw,wv",C["dG"],C["dG"],C["Md"]) + my_einsum("rs,vw,vw",C["dG"],C["Md"].conj().T,C["dG"].conj())) + (10*CA - 12*CF)*g*my_einsum("rw,wv,vs",C["dG"],C["Md"],C["dG"]) - 4*e*qd*(my_einsum("wv,rw,vs",C["Md"],C["dgamma"],C["dG"]) + my_einsum("wv,rw,vs",C["Md"],C["dG"],C["dgamma"])) - 4*g*my_einsum("wv,rw,vs",C["Md"],C["dgamma"],C["dgamma"]) - 4*g*my_einsum("wv,ws,rv",C["dgamma"].conj(),C["dgamma"],C["Md"].conj().T) - 4*g*my_einsum("rw,vw,vs",C["dgamma"],C["dgamma"].conj(),C["Md"].conj().T) + + # X^3 + + Beta["G"] = (12*CA - 3*b0g)*g**2*C["G"] + + Beta["Gtilde"] =(12*CA - 3*b0g)*g**2*C["Gtilde"] + + # \psi^4: (\overline L L)*(\overline L L) + + Beta["VnunuLL"] = 0 + + Beta["VeeLL"] = 12*e**2*qe**2*my_einsum("prst",C["VeeLL"]) + ((1)/(3))*e**2*qe*(Nc*qd*my_einsum("pr,stww",C["delta"],C["VedLL"]) + Nc*qd*my_einsum("pr,stww",C["delta"],C["VedLR"]) + Nc*qu*my_einsum("pr,stww",C["delta"],C["VeuLL"]) + Nc*qu*my_einsum("pr,stww",C["delta"],C["VeuLR"]) + qe*(4*my_einsum("pr,stww",C["delta"],C["VeeLL"]) + my_einsum("pr,stww",C["delta"],C["VeeLR"]))) + ((1)/(3))*e**2*qe*(Nc*qd*my_einsum("st,prww",C["delta"],C["VedLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VedLR"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VeuLL"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VeuLR"]) + qe*(4*my_einsum("st,prww",C["delta"],C["VeeLL"]) + my_einsum("st,prww",C["delta"],C["VeeLR"]))) + ((1)/(3))*e**2*qe*(Nc*qd*my_einsum("pt,srww",C["delta"],C["VedLL"]) + Nc*qd*my_einsum("pt,srww",C["delta"],C["VedLR"]) + Nc*qu*my_einsum("pt,srww",C["delta"],C["VeuLL"]) + Nc*qu*my_einsum("pt,srww",C["delta"],C["VeuLR"]) + qe*(4*my_einsum("pt,srww",C["delta"],C["VeeLL"]) + my_einsum("pt,srww",C["delta"],C["VeeLR"]))) + ((1)/(3))*e**2*qe*(Nc*qd*my_einsum("sr,ptww",C["delta"],C["VedLL"]) + Nc*qd*my_einsum("sr,ptww",C["delta"],C["VedLR"]) + Nc*qu*my_einsum("sr,ptww",C["delta"],C["VeuLL"]) + Nc*qu*my_einsum("sr,ptww",C["delta"],C["VeuLR"]) + qe*(4*my_einsum("sr,ptww",C["delta"],C["VeeLL"]) + my_einsum("sr,ptww",C["delta"],C["VeeLR"]))) + ((26)/(3))*e**2*qe**2*(my_einsum("pw,rw,st",C["egamma"],C["egamma"].conj(),C["delta"]) + my_einsum("sw,tw,pr",C["egamma"],C["egamma"].conj(),C["delta"]) + my_einsum("pw,tw,sr",C["egamma"],C["egamma"].conj(),C["delta"]) + my_einsum("sw,rw,pt",C["egamma"],C["egamma"].conj(),C["delta"])) + e**2*qe**2*zetae*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["VnueLL"] = ((4)/(3))*e**2*qe*(Nc*qu*my_einsum("st,prww",C["delta"],C["VnuuLL"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VnuuLR"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VnudLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VnudLR"]) + qe*(my_einsum("st,prww",C["delta"],C["VnueLL"]) + my_einsum("st,prww",C["delta"],C["VnueLR"]))) + 96*e**2*qe**2*my_einsum("wr,wp,st",C["nugamma"],C["nugamma"].conj(),C["delta"]) + + Beta["VnuuLL"] = ((4)/(3))*e**2*qu*(Nc*qu*my_einsum("st,prww",C["delta"],C["VnuuLL"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VnuuLR"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VnudLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VnudLR"]) + qe*(my_einsum("st,prww",C["delta"],C["VnueLL"]) + my_einsum("st,prww",C["delta"],C["VnueLR"]))) + 96*e**2*qu**2*my_einsum("wr,wp,st",C["nugamma"],C["nugamma"].conj(),C["delta"]) + + Beta["VnudLL"] = ((4)/(3))*e**2*qd*(Nc*qu*my_einsum("st,prww",C["delta"],C["VnuuLL"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VnuuLR"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VnudLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VnudLR"]) + qe*(my_einsum("st,prww",C["delta"],C["VnueLL"]) + my_einsum("st,prww",C["delta"],C["VnueLR"]))) + 96*e**2*qd**2*my_einsum("wr,wp,st",C["nugamma"],C["nugamma"].conj(),C["delta"]) + + Beta["VeuLL"] = ((4)/(3))*e**2*qe*(Nc*qd*my_einsum("pr,stww",C["delta"],C["V1udLL"]) + Nc*qd*my_einsum("pr,stww",C["delta"],C["V1udLR"]) + Nc*qu*(2*my_einsum("pr,stww",C["delta"],C["VuuLL"]) + my_einsum("pr,stww",C["delta"],C["V1uuLR"])) + qe*my_einsum("pr,wwst",C["delta"],C["VeuLL"]) + qe*my_einsum("pr,stww",C["delta"],C["VueLR"]) + 2*qu*my_einsum("pr,swwt",C["delta"],C["VuuLL"])) + ((4)/(3))*e**2*qu*(Nc*qd*my_einsum("st,prww",C["delta"],C["VedLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VedLR"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VeuLL"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VeuLR"]) + qe*(4*my_einsum("st,prww",C["delta"],C["VeeLL"]) + my_einsum("st,prww",C["delta"],C["VeeLR"]))) + 12*e**2*qe*qu*my_einsum("prst",C["VeuLL"]) - ((16)/(3))*CF*e**2*qe*qu*my_einsum("sw,tw,pr",C["uG"],C["uG"].conj(),C["delta"]) + 8*CF*e*g*qe*(my_einsum("sw,tw,pr",C["uG"],C["ugamma"].conj(),C["delta"]) + my_einsum("sw,tw,pr",C["ugamma"],C["uG"].conj(),C["delta"])) + e**2*(24*qu**2 + ((32)/(3))*qe*qu)*my_einsum("pw,rw,st",C["egamma"],C["egamma"].conj(),C["delta"]) + e**2*(24*qe**2 + ((32)/(3))*qe*qu)*my_einsum("sw,tw,pr",C["ugamma"],C["ugamma"].conj(),C["delta"]) + 2*e**2*qe*qu*zetae*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["VedLL"] = ((4)/(3))*e**2*qe*(Nc*qu*my_einsum("pr,wwst",C["delta"],C["V1udLL"]) + Nc*qu*my_einsum("pr,stww",C["delta"],C["V1duLR"]) + Nc*qd*(2*my_einsum("pr,stww",C["delta"],C["VddLL"]) + my_einsum("pr,stww",C["delta"],C["V1ddLR"])) + qe*my_einsum("pr,wwst",C["delta"],C["VedLL"]) + qe*my_einsum("pr,stww",C["delta"],C["VdeLR"]) + 2*qd*my_einsum("pr,swwt",C["delta"],C["VddLL"])) + ((4)/(3))*e**2*qd*(Nc*qd*my_einsum("st,prww",C["delta"],C["VedLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VedLR"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VeuLL"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VeuLR"]) + qe*(4*my_einsum("st,prww",C["delta"],C["VeeLL"]) + my_einsum("st,prww",C["delta"],C["VeeLR"]))) + 12*e**2*qd*qe*my_einsum("prst",C["VedLL"]) - ((16)/(3))*CF*e**2*qe*qd*my_einsum("sw,tw,pr",C["dG"],C["dG"].conj(),C["delta"]) + 8*CF*e*g*qe*(my_einsum("sw,tw,pr",C["dG"],C["dgamma"].conj(),C["delta"]) + my_einsum("sw,tw,pr",C["dgamma"],C["dG"].conj(),C["delta"])) + e**2*(24*qd**2 + ((32)/(3))*qe*qd)*my_einsum("pw,rw,st",C["egamma"],C["egamma"].conj(),C["delta"]) + e**2*(24*qe**2 + ((32)/(3))*qe*qd)*my_einsum("sw,tw,pr",C["dgamma"],C["dgamma"].conj(),C["delta"]) + 2*e**2*qe*qd*zetae*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["VnueduLL"] = 6*e**2*qe*qu*my_einsum("prst",C["VnueduLL"]) + + Beta["VuuLL"] = ((2)/(3))*e**2*qu*(Nc*qd*my_einsum("pr,stww",C["delta"],C["V1udLL"]) + Nc*qd*my_einsum("pr,stww",C["delta"],C["V1udLR"]) + Nc*qu*(2*my_einsum("pr,stww",C["delta"],C["VuuLL"]) + my_einsum("pr,stww",C["delta"],C["V1uuLR"])) + qe*my_einsum("pr,wwst",C["delta"],C["VeuLL"]) + qe*my_einsum("pr,stww",C["delta"],C["VueLR"]) + 2*qu*my_einsum("pr,swwt",C["delta"],C["VuuLL"])) + ((2)/(3))*e**2*qu*(Nc*qd*my_einsum("st,prww",C["delta"],C["V1udLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["V1udLR"]) + Nc*qu*(2*my_einsum("st,prww",C["delta"],C["VuuLL"]) + my_einsum("st,prww",C["delta"],C["V1uuLR"])) + qe*my_einsum("st,wwpr",C["delta"],C["VeuLL"]) + qe*my_einsum("st,prww",C["delta"],C["VueLR"]) + 2*qu*my_einsum("st,pwwr",C["delta"],C["VuuLL"])) + ((g**2)/(6*Nc))*(Nc*(my_einsum("pt,srww",C["delta"],C["V8udLL"]) + my_einsum("pt,srww",C["delta"],C["V8udLR"]) + 4*my_einsum("pt,swwr",C["delta"],C["VuuLL"]) + my_einsum("pt,srww",C["delta"],C["V8uuLR"])) + Nc*(my_einsum("rs,ptww",C["delta"],C["V8udLL"]) + my_einsum("rs,ptww",C["delta"],C["V8udLR"]) + 4*my_einsum("rs,pwwt",C["delta"],C["VuuLL"]) + my_einsum("rs,ptww",C["delta"],C["V8uuLR"])) - (my_einsum("pr,stww",C["delta"],C["V8udLL"]) + my_einsum("pr,stww",C["delta"],C["V8udLR"]) + 4*my_einsum("pr,swwt",C["delta"],C["VuuLL"]) + my_einsum("pr,stww",C["delta"],C["V8uuLR"])) - (my_einsum("st,prww",C["delta"],C["V8udLL"]) + my_einsum("st,prww",C["delta"],C["V8udLR"]) + 4*my_einsum("st,pwwr",C["delta"],C["VuuLL"]) + my_einsum("st,prww",C["delta"],C["V8uuLR"]))) + (12*e**2*qu**2 - ((6*g**2)/(Nc)))*my_einsum("prst",C["VuuLL"]) + 6*g**2*my_einsum("ptsr",C["VuuLL"]) - ((8)/(3))*CF*e**2*qu**2*(my_einsum("pw,rw,st",C["uG"],C["uG"].conj(),C["delta"]) + my_einsum("sw,tw,pr",C["uG"],C["uG"].conj(),C["delta"])) - ((1)/(2*Nc))*(((16)/(3))*CF + 3*Cd - 5*CA - 24*Nc*C1)*g**2*(my_einsum("pw,rw,st",C["uG"],C["uG"].conj(),C["delta"]) + my_einsum("sw,tw,pr",C["uG"],C["uG"].conj(),C["delta"])) + ((1)/(2))*(((16)/(3))*CF + 3*Cd - 5*CA)*g**2*(my_einsum("pw,tw,sr",C["uG"],C["uG"].conj(),C["delta"]) + my_einsum("sw,rw,pt",C["uG"],C["uG"].conj(),C["delta"])) + 4*(CF - ((2)/(Nc)))*e*g*qu*(my_einsum("pw,rw,st",C["ugamma"],C["uG"].conj(),C["delta"]) + my_einsum("pw,rw,st",C["uG"],C["ugamma"].conj(),C["delta"])) + 4*(CF - ((2)/(Nc)))*e*g*qu*(my_einsum("sw,tw,pr",C["ugamma"],C["uG"].conj(),C["delta"]) + my_einsum("sw,tw,pr",C["uG"],C["ugamma"].conj(),C["delta"])) + 8*e*g*qu*(my_einsum("pw,tw,sr",C["ugamma"],C["uG"].conj(),C["delta"]) + my_einsum("pw,tw,sr",C["uG"],C["ugamma"].conj(),C["delta"])) + 8*e*g*qu*(my_einsum("sw,rw,pt",C["ugamma"],C["uG"].conj(),C["delta"]) + my_einsum("sw,rw,pt",C["uG"],C["ugamma"].conj(),C["delta"])) + (((52)/(3))*e**2*qu**2 + ((4)/(3*Nc))*g**2)*(my_einsum("pw,rw,st",C["ugamma"],C["ugamma"].conj(),C["delta"]) + my_einsum("sw,tw,pr",C["ugamma"],C["ugamma"].conj(),C["delta"])) - ((4)/(3))*g**2*(my_einsum("pw,tw,sr",C["ugamma"],C["ugamma"].conj(),C["delta"]) + my_einsum("sw,rw,pt",C["ugamma"],C["ugamma"].conj(),C["delta"])) + e**2*qu**2*zetae*my_einsum("pr,st",C["delta"],C["delta"]) - ((1)/(2*Nc))*g**2*zetag*my_einsum("pr,st",C["delta"],C["delta"]) + ((1)/(2))*g**2*zetag*my_einsum("pt,sr",C["delta"],C["delta"]) + + Beta["VddLL"] = ((2)/(3))*e**2*qd*(Nc*qd*2*my_einsum("pr,stww",C["delta"],C["VddLL"]) + Nc*qd*my_einsum("pr,stww",C["delta"],C["V1ddLR"]) + Nc*qu*(my_einsum("pr,wwst",C["delta"],C["V1udLL"]) + my_einsum("pr,stww",C["delta"],C["V1duLR"])) + qe*my_einsum("pr,wwst",C["delta"],C["VedLL"]) + qe*my_einsum("pr,stww",C["delta"],C["VdeLR"]) + 2*qd*my_einsum("pr,swwt",C["delta"],C["VddLL"])) + ((2)/(3))*e**2*qd*(Nc*qd*2*my_einsum("st,prww",C["delta"],C["VddLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["V1ddLR"]) + Nc*qu*(my_einsum("st,wwpr",C["delta"],C["V1udLL"]) + my_einsum("st,prww",C["delta"],C["V1duLR"])) + qe*my_einsum("st,wwpr",C["delta"],C["VedLL"]) + qe*my_einsum("st,prww",C["delta"],C["VdeLR"]) + 2*qd*my_einsum("st,pwwr",C["delta"],C["VddLL"])) + ((g**2)/(6*Nc))*(Nc*(4*my_einsum("pt,swwr",C["delta"],C["VddLL"]) + my_einsum("pt,wwsr",C["delta"],C["V8udLL"]) + my_einsum("pt,srww",C["delta"],C["V8duLR"]) + my_einsum("pt,srww",C["delta"],C["V8ddLR"])) + Nc*(4*my_einsum("rs,pwwt",C["delta"],C["VddLL"]) + my_einsum("rs,wwpt",C["delta"],C["V8udLL"]) + my_einsum("rs,ptww",C["delta"],C["V8duLR"]) + my_einsum("rs,ptww",C["delta"],C["V8ddLR"])) - (4*my_einsum("pr,swwt",C["delta"],C["VddLL"]) + my_einsum("pr,wwst",C["delta"],C["V8udLL"]) + my_einsum("pr,stww",C["delta"],C["V8duLR"]) + my_einsum("pr,stww",C["delta"],C["V8ddLR"])) - (4*my_einsum("st,pwwr",C["delta"],C["VddLL"]) + my_einsum("st,wwpr",C["delta"],C["V8udLL"]) + my_einsum("st,prww",C["delta"],C["V8duLR"]) + my_einsum("st,prww",C["delta"],C["V8ddLR"]))) + (12*e**2*qd**2 - ((6*g**2)/(Nc)))*my_einsum("prst",C["VddLL"]) + 6*g**2*my_einsum("ptsr",C["VddLL"]) - ((8)/(3))*CF*e**2*qd**2*(my_einsum("pw,rw,st",C["dG"],C["dG"].conj(),C["delta"]) + my_einsum("sw,tw,pr",C["dG"],C["dG"].conj(),C["delta"])) - ((1)/(2*Nc))*(((16)/(3))*CF + 3*Cd - 5*CA - 24*Nc*C1)*g**2*(my_einsum("pw,rw,st",C["dG"],C["dG"].conj(),C["delta"]) + my_einsum("sw,tw,pr",C["dG"],C["dG"].conj(),C["delta"])) + ((1)/(2))*(((16)/(3))*CF + 3*Cd - 5*CA)*g**2*(my_einsum("pw,tw,sr",C["dG"],C["dG"].conj(),C["delta"]) + my_einsum("sw,rw,pt",C["dG"],C["dG"].conj(),C["delta"])) + 4*(CF - ((2)/(Nc)))*e*g*qd*(my_einsum("pw,rw,st",C["dgamma"],C["dG"].conj(),C["delta"]) + my_einsum("pw,rw,st",C["dG"],C["dgamma"].conj(),C["delta"])) + 4*(CF - ((2)/(Nc)))*e*g*qd*(my_einsum("sw,tw,pr",C["dgamma"],C["dG"].conj(),C["delta"]) + my_einsum("sw,tw,pr",C["dG"],C["dgamma"].conj(),C["delta"])) + 8*e*g*qd*(my_einsum("pw,tw,sr",C["dgamma"],C["dG"].conj(),C["delta"]) + my_einsum("pw,tw,sr",C["dG"],C["dgamma"].conj(),C["delta"])) + 8*e*g*qd*(my_einsum("sw,rw,pt",C["dgamma"],C["dG"].conj(),C["delta"]) + my_einsum("sw,rw,pt",C["dG"],C["dgamma"].conj(),C["delta"])) + (((52)/(3))*e**2*qd**2 + ((4)/(3*Nc))*g**2)*(my_einsum("pw,rw,st",C["dgamma"],C["dgamma"].conj(),C["delta"]) + my_einsum("sw,tw,pr",C["dgamma"],C["dgamma"].conj(),C["delta"])) - ((4)/(3))*g**2*(my_einsum("pw,tw,sr",C["dgamma"],C["dgamma"].conj(),C["delta"]) + my_einsum("sw,rw,pt",C["dgamma"],C["dgamma"].conj(),C["delta"])) + e**2*qd**2*zetae*my_einsum("pr,st",C["delta"],C["delta"]) - ((1)/(2*Nc))*g**2*zetag*my_einsum("pr,st",C["delta"],C["delta"]) + ((1)/(2))*g**2*zetag*my_einsum("pt,sr",C["delta"],C["delta"]) + + Beta["V1udLL"] = ((4)/(3))*e**2*qd*(Nc*qd*my_einsum("st,prww",C["delta"],C["V1udLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["V1udLR"]) + Nc*qu*(2*my_einsum("st,prww",C["delta"],C["VuuLL"]) + my_einsum("st,prww",C["delta"],C["V1uuLR"])) + qe*my_einsum("st,wwpr",C["delta"],C["VeuLL"]) + qe*my_einsum("st,prww",C["delta"],C["VueLR"]) + 2*qu*my_einsum("st,pwwr",C["delta"],C["VuuLL"])) + ((4)/(3))*e**2*qu*(Nc*qd*2*my_einsum("pr,stww",C["delta"],C["VddLL"]) + Nc*qd*my_einsum("pr,stww",C["delta"],C["V1ddLR"]) + Nc*qu*(my_einsum("pr,wwst",C["delta"],C["V1udLL"]) + my_einsum("pr,stww",C["delta"],C["V1duLR"])) + qe*my_einsum("pr,wwst",C["delta"],C["VedLL"]) + qe*my_einsum("pr,stww",C["delta"],C["VdeLR"]) + 2*qd*my_einsum("pr,swwt",C["delta"],C["VddLL"])) + 12*e**2*qd*qu*my_einsum("prst",C["V1udLL"]) + 6*g**2*((CF)/(Nc))*my_einsum("prst",C["V8udLL"]) - (((16)/(3))*CF*e**2*qu*qd - 24*g**2*C1)*(my_einsum("pw,rw,st",C["uG"],C["uG"].conj(),C["delta"]) + my_einsum("sw,tw,pr",C["dG"],C["dG"].conj(),C["delta"])) + 8*CF*e*g*qd*(my_einsum("pw,rw,st",C["uG"],C["ugamma"].conj(),C["delta"]) + my_einsum("pw,rw,st",C["ugamma"],C["uG"].conj(),C["delta"])) + 8*CF*e*g*qu*(my_einsum("sw,tw,pr",C["dG"],C["dgamma"].conj(),C["delta"]) + my_einsum("sw,tw,pr",C["dgamma"],C["dG"].conj(),C["delta"])) + e**2*(24*qd**2 + ((32)/(3))*qu*qd)*my_einsum("pw,rw,st",C["ugamma"],C["ugamma"].conj(),C["delta"]) + e**2*(24*qu**2 + ((32)/(3))*qu*qd)*my_einsum("sw,tw,pr",C["dgamma"],C["dgamma"].conj(),C["delta"]) + 2*e**2*qu*qd*zetae*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["V8udLL"] = ((2)/(3))*g**2*(4*my_einsum("pr,swwt",C["delta"],C["VddLL"]) + my_einsum("pr,wwst",C["delta"],C["V8udLL"]) + my_einsum("pr,stww",C["delta"],C["V8duLR"]) + my_einsum("pr,stww",C["delta"],C["V8ddLR"])) + ((2)/(3))*g**2*(my_einsum("st,prww",C["delta"],C["V8udLL"]) + my_einsum("st,prww",C["delta"],C["V8udLR"]) + 4*my_einsum("st,pwwr",C["delta"],C["VuuLL"]) + my_einsum("st,prww",C["delta"],C["V8uuLR"])) + 12*g**2*my_einsum("prst",C["V1udLL"]) + (12*e**2*qd*qu - ((12*g**2)/(Nc)))*my_einsum("prst",C["V8udLL"]) + (((32)/(3))*CF + 6*Cd - 10*CA)*g**2*(my_einsum("pw,rw,st",C["uG"],C["uG"].conj(),C["delta"]) + my_einsum("sw,tw,pr",C["dG"],C["dG"].conj(),C["delta"])) + 8*e*g*(qu + 3*qd)*(my_einsum("pw,rw,st",C["ugamma"],C["uG"].conj(),C["delta"]) + my_einsum("pw,rw,st",C["uG"],C["ugamma"].conj(),C["delta"])) + 8*e*g*(qd + 3*qu)*(my_einsum("sw,tw,pr",C["dgamma"],C["dG"].conj(),C["delta"]) + my_einsum("sw,tw,pr",C["dG"],C["dgamma"].conj(),C["delta"])) - ((16)/(3))*g**2*(my_einsum("pw,rw,st",C["ugamma"],C["ugamma"].conj(),C["delta"]) + my_einsum("sw,tw,pr",C["dgamma"],C["dgamma"].conj(),C["delta"])) + 2*g**2*zetag*my_einsum("pr,st",C["delta"],C["delta"]) + + # \psi^4: (\overline R R)*(\overline R R) + + Beta["VeeRR"] = 12*e**2*qe**2*my_einsum("prst",C["VeeRR"]) + ((1)/(3))*e**2*qe*(Nc*qd*my_einsum("pr,wwst",C["delta"],C["VdeLR"]) + Nc*qd*my_einsum("pr,stww",C["delta"],C["VedRR"]) + Nc*qu*my_einsum("pr,wwst",C["delta"],C["VueLR"]) + Nc*qu*my_einsum("pr,stww",C["delta"],C["VeuRR"]) + qe*(my_einsum("pr,wwst",C["delta"],C["VeeLR"]) + 4*my_einsum("pr,stww",C["delta"],C["VeeRR"]))) + ((1)/(3))*e**2*qe*(Nc*qd*my_einsum("st,wwpr",C["delta"],C["VdeLR"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VedRR"]) + Nc*qu*my_einsum("st,wwpr",C["delta"],C["VueLR"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VeuRR"]) + qe*(my_einsum("st,wwpr",C["delta"],C["VeeLR"]) + 4*my_einsum("st,prww",C["delta"],C["VeeRR"]))) + ((1)/(3))*e**2*qe*(Nc*qd*my_einsum("pt,wwsr",C["delta"],C["VdeLR"]) + Nc*qd*my_einsum("pt,srww",C["delta"],C["VedRR"]) + Nc*qu*my_einsum("pt,wwsr",C["delta"],C["VueLR"]) + Nc*qu*my_einsum("pt,srww",C["delta"],C["VeuRR"]) + qe*(my_einsum("pt,wwsr",C["delta"],C["VeeLR"]) + 4*my_einsum("pt,srww",C["delta"],C["VeeRR"]))) + ((1)/(3))*e**2*qe*(Nc*qd*my_einsum("sr,wwpt",C["delta"],C["VdeLR"]) + Nc*qd*my_einsum("sr,ptww",C["delta"],C["VedRR"]) + Nc*qu*my_einsum("sr,wwpt",C["delta"],C["VueLR"]) + Nc*qu*my_einsum("sr,ptww",C["delta"],C["VeuRR"]) + qe*(my_einsum("sr,wwpt",C["delta"],C["VeeLR"]) + 4*my_einsum("sr,ptww",C["delta"],C["VeeRR"]))) + ((26)/(3))*e**2*qe**2*(my_einsum("wp,wr,st",C["egamma"].conj(),C["egamma"],C["delta"]) + my_einsum("ws,wt,pr",C["egamma"].conj(),C["egamma"],C["delta"]) + my_einsum("wp,wt,sr",C["egamma"].conj(),C["egamma"],C["delta"]) + my_einsum("ws,wr,pt",C["egamma"].conj(),C["egamma"],C["delta"])) + e**2*qe**2*zetae*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["VeuRR"] = ((4)/(3))*e**2*qe*(Nc*qd*my_einsum("pr,wwst",C["delta"],C["V1duLR"]) + Nc*qd*my_einsum("pr,stww",C["delta"],C["V1udRR"]) + Nc*qu*(my_einsum("pr,wwst",C["delta"],C["V1uuLR"]) + 2*my_einsum("pr,stww",C["delta"],C["VuuRR"])) + qe*my_einsum("pr,wwst",C["delta"],C["VeuLR"]) + qe*my_einsum("pr,wwst",C["delta"],C["VeuRR"]) + 2*qu*my_einsum("pr,swwt",C["delta"],C["VuuRR"])) + ((4)/(3))*e**2*qu*(Nc*qd*my_einsum("st,wwpr",C["delta"],C["VdeLR"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VedRR"]) + Nc*qu*my_einsum("st,wwpr",C["delta"],C["VueLR"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VeuRR"]) + qe*(my_einsum("st,wwpr",C["delta"],C["VeeLR"]) + 4*my_einsum("st,prww",C["delta"],C["VeeRR"]))) + 12*e**2*qe*qu*my_einsum("prst",C["VeuRR"]) - ((16)/(3))*CF*e**2*qe*qu*my_einsum("ws,wt,pr",C["uG"].conj(),C["uG"],C["delta"]) + 8*CF*e*g*qe*(my_einsum("ws,wt,pr",C["uG"].conj(),C["ugamma"],C["delta"]) + my_einsum("ws,wt,pr",C["ugamma"].conj(),C["uG"],C["delta"])) + e**2*(24*qu**2 + ((32)/(3))*qe*qu)*my_einsum("wp,wr,st",C["egamma"].conj(),C["egamma"],C["delta"]) + e**2*(24*qe**2 + ((32)/(3))*qe*qu)*my_einsum("ws,wt,pr",C["ugamma"].conj(),C["ugamma"],C["delta"]) + 2*e**2*qe*qu*zetae*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["VedRR"] = ((4)/(3))*e**2*qe*(Nc*qd*my_einsum("pr,wwst",C["delta"],C["V1ddLR"]) + 2*Nc*qd*my_einsum("pr,stww",C["delta"],C["VddRR"]) + Nc*qu*(my_einsum("pr,wwst",C["delta"],C["V1udLR"]) + my_einsum("pr,wwst",C["delta"],C["V1udRR"])) + qe*my_einsum("pr,wwst",C["delta"],C["VedLR"]) + qe*my_einsum("pr,wwst",C["delta"],C["VedRR"]) + 2*qd*my_einsum("pr,swwt",C["delta"],C["VddRR"])) + ((4)/(3))*e**2*qd*(Nc*qd*my_einsum("st,wwpr",C["delta"],C["VdeLR"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VedRR"]) + Nc*qu*my_einsum("st,wwpr",C["delta"],C["VueLR"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VeuRR"]) + qe*(my_einsum("st,wwpr",C["delta"],C["VeeLR"]) + 4*my_einsum("st,prww",C["delta"],C["VeeRR"]))) + 12*e**2*qd*qe*my_einsum("prst",C["VedRR"]) - ((16)/(3))*CF*e**2*qe*qd*my_einsum("ws,wt,pr",C["dG"].conj(),C["dG"],C["delta"]) + 8*CF*e*g*qe*(my_einsum("ws,wt,pr",C["dG"].conj(),C["dgamma"],C["delta"]) + my_einsum("ws,wt,pr",C["dgamma"].conj(),C["dG"],C["delta"])) + e**2*(24*qd**2 + ((32)/(3))*qe*qd)*my_einsum("wp,wr,st",C["egamma"].conj(),C["egamma"],C["delta"]) + e**2*(24*qe**2 + ((32)/(3))*qe*qd)*my_einsum("ws,wt,pr",C["dgamma"].conj(),C["dgamma"],C["delta"]) + 2*e**2*qe*qd*zetae*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["VuuRR"] = ((2)/(3))*e**2*qu*(Nc*qd*my_einsum("pr,wwst",C["delta"],C["V1duLR"]) + Nc*qd*my_einsum("pr,stww",C["delta"],C["V1udRR"]) + Nc*qu*(my_einsum("pr,wwst",C["delta"],C["V1uuLR"]) + 2*my_einsum("pr,stww",C["delta"],C["VuuRR"])) + qe*my_einsum("pr,wwst",C["delta"],C["VeuLR"]) + qe*my_einsum("pr,wwst",C["delta"],C["VeuRR"]) + 2*qu*my_einsum("pr,swwt",C["delta"],C["VuuRR"])) + ((2)/(3))*e**2*qu*(Nc*qd*my_einsum("st,wwpr",C["delta"],C["V1duLR"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["V1udRR"]) + Nc*qu*(my_einsum("st,wwpr",C["delta"],C["V1uuLR"]) + 2*my_einsum("st,prww",C["delta"],C["VuuRR"])) + qe*my_einsum("st,wwpr",C["delta"],C["VeuLR"]) + qe*my_einsum("st,wwpr",C["delta"],C["VeuRR"]) + 2*qu*my_einsum("st,pwwr",C["delta"],C["VuuRR"])) + ((g**2)/(6*Nc))*(Nc*(my_einsum("pt,wwsr",C["delta"],C["V8duLR"]) + my_einsum("pt,srww",C["delta"],C["V8udRR"]) + my_einsum("pt,wwsr",C["delta"],C["V8uuLR"]) + 4*my_einsum("pt,swwr",C["delta"],C["VuuRR"])) + Nc*(my_einsum("rs,wwpt",C["delta"],C["V8duLR"]) + my_einsum("rs,ptww",C["delta"],C["V8udRR"]) + my_einsum("rs,wwpt",C["delta"],C["V8uuLR"]) + 4*my_einsum("rs,pwwt",C["delta"],C["VuuRR"])) - (my_einsum("pr,wwst",C["delta"],C["V8duLR"]) + my_einsum("pr,stww",C["delta"],C["V8udRR"]) + my_einsum("pr,wwst",C["delta"],C["V8uuLR"]) + 4*my_einsum("pr,swwt",C["delta"],C["VuuRR"])) - (my_einsum("st,wwpr",C["delta"],C["V8duLR"]) + my_einsum("st,prww",C["delta"],C["V8udRR"]) + my_einsum("st,wwpr",C["delta"],C["V8uuLR"]) + 4*my_einsum("st,pwwr",C["delta"],C["VuuRR"]))) + (12*e**2*qu**2 - ((6*g**2)/(Nc)))*my_einsum("prst",C["VuuRR"]) + 6*g**2*my_einsum("ptsr",C["VuuRR"]) - ((8)/(3))*CF*e**2*qu**2*(my_einsum("wp,wr,st",C["uG"].conj(),C["uG"],C["delta"]) + my_einsum("ws,wt,pr",C["uG"].conj(),C["uG"],C["delta"])) - ((1)/(2*Nc))*(((16)/(3))*CF + 3*Cd - 5*CA - 24*Nc*C1)*g**2*(my_einsum("wp,wr,st",C["uG"].conj(),C["uG"],C["delta"]) + my_einsum("ws,wt,pr",C["uG"].conj(),C["uG"],C["delta"])) + ((1)/(2))*(((16)/(3))*CF + 3*Cd - 5*CA)*g**2*(my_einsum("wp,wt,sr",C["uG"].conj(),C["uG"],C["delta"]) + my_einsum("ws,wr,pt",C["uG"].conj(),C["uG"],C["delta"])) + 4*(CF - ((2)/(Nc)))*e*g*qu*(my_einsum("wp,wr,st",C["ugamma"].conj(),C["uG"],C["delta"]) + my_einsum("wp,wr,st",C["uG"].conj(),C["ugamma"],C["delta"])) + 4*(CF - ((2)/(Nc)))*e*g*qu*(my_einsum("ws,wt,pr",C["ugamma"].conj(),C["uG"],C["delta"]) + my_einsum("ws,wt,pr",C["uG"].conj(),C["ugamma"],C["delta"])) + 8*e*g*qu*(my_einsum("wp,wt,sr",C["ugamma"].conj(),C["uG"],C["delta"]) + my_einsum("wp,wt,sr",C["uG"].conj(),C["ugamma"],C["delta"])) + 8*e*g*qu*(my_einsum("ws,wr,pt",C["ugamma"].conj(),C["uG"],C["delta"]) + my_einsum("ws,wr,pt",C["uG"].conj(),C["ugamma"],C["delta"])) + (((52)/(3))*e**2*qu**2 + ((4)/(3*Nc))*g**2)*(my_einsum("wp,wr,st",C["ugamma"].conj(),C["ugamma"],C["delta"]) + my_einsum("ws,wt,pr",C["ugamma"].conj(),C["ugamma"],C["delta"])) - ((4)/(3))*g**2*(my_einsum("wp,wt,sr",C["ugamma"].conj(),C["ugamma"],C["delta"]) + my_einsum("ws,wr,pt",C["ugamma"].conj(),C["ugamma"],C["delta"])) + e**2*qu**2*zetae*my_einsum("pr,st",C["delta"],C["delta"]) - ((1)/(2*Nc))*g**2*zetag*my_einsum("pr,st",C["delta"],C["delta"]) + ((1)/(2))*g**2*zetag*my_einsum("pt,sr",C["delta"],C["delta"]) + + Beta["VddRR"] = ((2)/(3))*e**2*qd*(Nc*qd*my_einsum("pr,wwst",C["delta"],C["V1ddLR"]) + 2*Nc*qd*my_einsum("pr,stww",C["delta"],C["VddRR"]) + Nc*qu*(my_einsum("pr,wwst",C["delta"],C["V1udLR"]) + my_einsum("pr,wwst",C["delta"],C["V1udRR"])) + qe*my_einsum("pr,wwst",C["delta"],C["VedLR"]) + qe*my_einsum("pr,wwst",C["delta"],C["VedRR"]) + 2*qd*my_einsum("pr,swwt",C["delta"],C["VddRR"])) + ((2)/(3))*e**2*qd*(Nc*qd*my_einsum("st,wwpr",C["delta"],C["V1ddLR"]) + 2*Nc*qd*my_einsum("st,prww",C["delta"],C["VddRR"]) + Nc*qu*(my_einsum("st,wwpr",C["delta"],C["V1udLR"]) + my_einsum("st,wwpr",C["delta"],C["V1udRR"])) + qe*my_einsum("st,wwpr",C["delta"],C["VedLR"]) + qe*my_einsum("st,wwpr",C["delta"],C["VedRR"]) + 2*qd*my_einsum("st,pwwr",C["delta"],C["VddRR"])) + ((g**2)/(6*Nc))*(Nc*(my_einsum("pt,wwsr",C["delta"],C["V8udLR"]) + my_einsum("pt,wwsr",C["delta"],C["V8ddLR"]) + 4*my_einsum("pt,swwr",C["delta"],C["VddRR"]) + my_einsum("pt,wwsr",C["delta"],C["V8udRR"])) + Nc*(my_einsum("rs,wwpt",C["delta"],C["V8udLR"]) + my_einsum("rs,wwpt",C["delta"],C["V8ddLR"]) + 4*my_einsum("rs,pwwt",C["delta"],C["VddRR"]) + my_einsum("rs,wwpt",C["delta"],C["V8udRR"])) - (my_einsum("pr,wwst",C["delta"],C["V8udLR"]) + my_einsum("pr,wwst",C["delta"],C["V8ddLR"]) + 4*my_einsum("pr,swwt",C["delta"],C["VddRR"]) + my_einsum("pr,wwst",C["delta"],C["V8udRR"])) - (my_einsum("st,wwpr",C["delta"],C["V8udLR"]) + my_einsum("st,wwpr",C["delta"],C["V8ddLR"]) + 4*my_einsum("st,pwwr",C["delta"],C["VddRR"]) + my_einsum("st,wwpr",C["delta"],C["V8udRR"]))) + (12*e**2*qd**2 - ((6*g**2)/(Nc)))*my_einsum("prst",C["VddRR"]) + 6*g**2*my_einsum("ptsr",C["VddRR"]) - ((8)/(3))*CF*e**2*qd**2*(my_einsum("wp,wr,st",C["dG"].conj(),C["dG"],C["delta"]) + my_einsum("ws,wt,pr",C["dG"].conj(),C["dG"],C["delta"])) - ((1)/(2*Nc))*(((16)/(3))*CF + 3*Cd - 5*CA - 24*Nc*C1)*g**2*(my_einsum("wp,wr,st",C["dG"].conj(),C["dG"],C["delta"]) + my_einsum("ws,wt,pr",C["dG"].conj(),C["dG"],C["delta"])) + ((1)/(2))*(((16)/(3))*CF + 3*Cd - 5*CA)*g**2*(my_einsum("wp,wt,sr",C["dG"].conj(),C["dG"],C["delta"]) + my_einsum("ws,wr,pt",C["dG"].conj(),C["dG"],C["delta"])) + 4*(CF - ((2)/(Nc)))*e*g*qd*(my_einsum("wp,wr,st",C["dgamma"].conj(),C["dG"],C["delta"]) + my_einsum("wp,wr,st",C["dG"].conj(),C["dgamma"],C["delta"])) + 4*(CF - ((2)/(Nc)))*e*g*qd*(my_einsum("ws,wt,pr",C["dgamma"].conj(),C["dG"],C["delta"]) + my_einsum("ws,wt,pr",C["dG"].conj(),C["dgamma"],C["delta"])) + 8*e*g*qd*(my_einsum("wp,wt,sr",C["dgamma"].conj(),C["dG"],C["delta"]) + my_einsum("wp,wt,sr",C["dG"].conj(),C["dgamma"],C["delta"])) + 8*e*g*qd*(my_einsum("ws,wr,pt",C["dgamma"].conj(),C["dG"],C["delta"]) + my_einsum("ws,wr,pt",C["dG"].conj(),C["dgamma"],C["delta"])) + (((52)/(3))*e**2*qd**2 + ((4)/(3*Nc))*g**2)*(my_einsum("wp,wr,st",C["dgamma"].conj(),C["dgamma"],C["delta"]) + my_einsum("ws,wt,pr",C["dgamma"].conj(),C["dgamma"],C["delta"])) - ((4)/(3))*g**2*(my_einsum("wp,wt,sr",C["dgamma"].conj(),C["dgamma"],C["delta"]) + my_einsum("ws,wr,pt",C["dgamma"].conj(),C["dgamma"],C["delta"])) + e**2*qd**2*zetae*my_einsum("pr,st",C["delta"],C["delta"]) - ((1)/(2*Nc))*g**2*zetag*my_einsum("pr,st",C["delta"],C["delta"]) + ((1)/(2))*g**2*zetag*my_einsum("pt,sr",C["delta"],C["delta"]) + + Beta["V1udRR"] = ((4)/(3))*e**2*qu*(Nc*qd*my_einsum("pr,wwst",C["delta"],C["V1ddLR"]) + 2*Nc*qd*my_einsum("pr,stww",C["delta"],C["VddRR"]) + Nc*qu*(my_einsum("pr,wwst",C["delta"],C["V1udLR"]) + my_einsum("pr,wwst",C["delta"],C["V1udRR"])) + qe*my_einsum("pr,wwst",C["delta"],C["VedLR"]) + qe*my_einsum("pr,wwst",C["delta"],C["VedRR"]) + 2*qd*my_einsum("pr,swwt",C["delta"],C["VddRR"])) + ((4)/(3))*e**2*qd*(Nc*qd*my_einsum("st,wwpr",C["delta"],C["V1duLR"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["V1udRR"]) + Nc*qu*(my_einsum("st,wwpr",C["delta"],C["V1uuLR"]) + 2*my_einsum("st,prww",C["delta"],C["VuuRR"])) + qe*my_einsum("st,wwpr",C["delta"],C["VeuLR"]) + qe*my_einsum("st,wwpr",C["delta"],C["VeuRR"]) + 2*qu*my_einsum("st,pwwr",C["delta"],C["VuuRR"])) + 12*e**2*qd*qu*my_einsum("prst",C["V1udRR"]) + 6*g**2*((CF)/(Nc))*my_einsum("prst",C["V8udRR"]) - (((16)/(3))*CF*e**2*qu*qd - 24*g**2*C1)*(my_einsum("wp,wr,st",C["uG"].conj(),C["uG"],C["delta"]) + my_einsum("ws,wt,pr",C["dG"].conj(),C["dG"],C["delta"])) + 8*CF*e*g*qd*(my_einsum("wp,wr,st",C["uG"].conj(),C["ugamma"],C["delta"]) + my_einsum("wp,wr,st",C["ugamma"].conj(),C["uG"],C["delta"])) + 8*CF*e*g*qu*(my_einsum("ws,wt,pr",C["dG"].conj(),C["dgamma"],C["delta"]) + my_einsum("ws,wt,pr",C["dgamma"].conj(),C["dG"],C["delta"])) + e**2*(24*qd**2 + ((32)/(3))*qu*qd)*my_einsum("wp,wr,st",C["ugamma"].conj(),C["ugamma"],C["delta"]) + e**2*(24*qu**2 + ((32)/(3))*qu*qd)*my_einsum("ws,wt,pr",C["dgamma"].conj(),C["dgamma"],C["delta"]) + 2*e**2*qu*qd*zetae*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["V8udRR"] = ((2)/(3))*g**2*(my_einsum("pr,wwst",C["delta"],C["V8udLR"]) + my_einsum("pr,wwst",C["delta"],C["V8ddLR"]) + 4*my_einsum("pr,swwt",C["delta"],C["VddRR"]) + my_einsum("pr,wwst",C["delta"],C["V8udRR"])) + ((2)/(3))*g**2*(my_einsum("st,wwpr",C["delta"],C["V8duLR"]) + my_einsum("st,prww",C["delta"],C["V8udRR"]) + my_einsum("st,wwpr",C["delta"],C["V8uuLR"]) + 4*my_einsum("st,pwwr",C["delta"],C["VuuRR"])) + 12*g**2*my_einsum("prst",C["V1udRR"]) + (12*e**2*qd*qu - ((12*g**2)/(Nc)))*my_einsum("prst",C["V8udRR"]) + g**2*(((32)/(3))*CF + 6*Cd - 10*CA)*(my_einsum("wp,wr,st",C["uG"].conj(),C["uG"],C["delta"]) + my_einsum("ws,wt,pr",C["dG"].conj(),C["dG"],C["delta"])) + 8*e*g*(qu + 3*qd)*(my_einsum("wp,wr,st",C["ugamma"].conj(),C["uG"],C["delta"]) + my_einsum("wp,wr,st",C["uG"].conj(),C["ugamma"],C["delta"])) + 8*e*g*(qd + 3*qu)*(my_einsum("ws,wt,pr",C["dgamma"].conj(),C["dG"],C["delta"]) + my_einsum("ws,wt,pr",C["dG"].conj(),C["dgamma"],C["delta"])) - ((16)/(3))*g**2*(my_einsum("wp,wr,st",C["ugamma"].conj(),C["ugamma"],C["delta"]) + my_einsum("ws,wt,pr",C["dgamma"].conj(),C["dgamma"],C["delta"])) + 2*g**2*zetag*my_einsum("pr,st",C["delta"],C["delta"]) + + # \psi^4: (\overline L L)*(\overline R R) + + Beta["VnueLR"] = ((4)/(3))*e**2*qe*(Nc*qd*my_einsum("st,prww",C["delta"],C["VnudLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VnudLR"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VnuuLL"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VnuuLR"]) + qe*(my_einsum("st,prww",C["delta"],C["VnueLL"]) + my_einsum("st,prww",C["delta"],C["VnueLR"]))) - 96*e**2*qe**2*my_einsum("wr,wp,st",C["nugamma"],C["nugamma"].conj(),C["delta"]) + + Beta["VeeLR"] = ((4)/(3))*e**2*qe*(Nc*qd*my_einsum("pr,wwst",C["delta"],C["VdeLR"]) + Nc*qd*my_einsum("pr,stww",C["delta"],C["VedRR"]) + Nc*qu*my_einsum("pr,wwst",C["delta"],C["VueLR"]) + Nc*qu*my_einsum("pr,stww",C["delta"],C["VeuRR"]) + qe*(my_einsum("pr,wwst",C["delta"],C["VeeLR"]) + 4*my_einsum("pr,stww",C["delta"],C["VeeRR"]))) + ((4)/(3))*e**2*qe*(Nc*qd*my_einsum("st,prww",C["delta"],C["VedLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VedLR"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VeuLL"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VeuLR"]) + qe*(4*my_einsum("st,prww",C["delta"],C["VeeLL"]) + my_einsum("st,prww",C["delta"],C["VeeLR"]))) - 12*e**2*qe**2*my_einsum("prst",C["VeeLR"]) - ((40)/(3))*e**2*qe**2*(my_einsum("pw,rw,st",C["egamma"],C["egamma"].conj(),C["delta"]) + my_einsum("ws,wt,pr",C["egamma"].conj(),C["egamma"],C["delta"])) + 96*e**2*qe**2*my_einsum("pt,rs",C["egamma"],C["egamma"].conj()) + 2*e**2*qe**2*zetae*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["VnuuLR"] = ((4)/(3))*e**2*qu*(Nc*qd*my_einsum("st,prww",C["delta"],C["VnudLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VnudLR"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VnuuLL"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VnuuLR"]) + qe*(my_einsum("st,prww",C["delta"],C["VnueLL"]) + my_einsum("st,prww",C["delta"],C["VnueLR"]))) - 96*e**2*qu**2*my_einsum("wr,wp,st",C["nugamma"],C["nugamma"].conj(),C["delta"]) + + Beta["VnudLR"] = ((4)/(3))*e**2*qd*(Nc*qd*my_einsum("st,prww",C["delta"],C["VnudLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VnudLR"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VnuuLL"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VnuuLR"]) + qe*(my_einsum("st,prww",C["delta"],C["VnueLL"]) + my_einsum("st,prww",C["delta"],C["VnueLR"]))) - 96*e**2*qd**2*my_einsum("wr,wp,st",C["nugamma"],C["nugamma"].conj(),C["delta"]) + + Beta["VeuLR"] = ((4)/(3))*e**2*qe*(Nc*qd*my_einsum("pr,wwst",C["delta"],C["V1duLR"]) + Nc*qd*my_einsum("pr,stww",C["delta"],C["V1udRR"]) + Nc*qu*(my_einsum("pr,wwst",C["delta"],C["V1uuLR"]) + 2*my_einsum("pr,stww",C["delta"],C["VuuRR"])) + qe*my_einsum("pr,wwst",C["delta"],C["VeuLR"]) + qe*my_einsum("pr,wwst",C["delta"],C["VeuRR"]) + 2*qu*my_einsum("pr,swwt",C["delta"],C["VuuRR"])) + ((4)/(3))*e**2*qu*(Nc*qd*my_einsum("st,prww",C["delta"],C["VedLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VedLR"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VeuLL"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VeuLR"]) + qe*(4*my_einsum("st,prww",C["delta"],C["VeeLL"]) + my_einsum("st,prww",C["delta"],C["VeeLR"]))) - 12*e**2*qe*qu*my_einsum("prst",C["VeuLR"]) - ((16)/(3))*CF*e**2*qe*qu*my_einsum("ws,wt,pr",C["uG"].conj(),C["uG"],C["delta"]) + 8*CF*e*g*qe*(my_einsum("ws,wt,pr",C["uG"].conj(),C["ugamma"],C["delta"]) + my_einsum("ws,wt,pr",C["ugamma"].conj(),C["uG"],C["delta"])) + e**2*(((32)/(3))*qe*qu - 24*qu**2)*my_einsum("pw,rw,st",C["egamma"],C["egamma"].conj(),C["delta"]) + e**2*(((32)/(3))*qe*qu - 24*qe**2)*my_einsum("ws,wt,pr",C["ugamma"].conj(),C["ugamma"],C["delta"]) + 2*e**2*qu*qe*zetae*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["VedLR"] = ((4)/(3))*e**2*qe*(Nc*qd*my_einsum("pr,wwst",C["delta"],C["V1ddLR"]) + 2*Nc*qd*my_einsum("pr,stww",C["delta"],C["VddRR"]) + Nc*qu*(my_einsum("pr,wwst",C["delta"],C["V1udLR"]) + my_einsum("pr,wwst",C["delta"],C["V1udRR"])) + qe*my_einsum("pr,wwst",C["delta"],C["VedLR"]) + qe*my_einsum("pr,wwst",C["delta"],C["VedRR"]) + 2*qd*my_einsum("pr,swwt",C["delta"],C["VddRR"])) + ((4)/(3))*e**2*qd*(Nc*qd*my_einsum("st,prww",C["delta"],C["VedLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VedLR"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VeuLL"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VeuLR"]) + qe*(4*my_einsum("st,prww",C["delta"],C["VeeLL"]) + my_einsum("st,prww",C["delta"],C["VeeLR"]))) - 12*e**2*qd*qe*my_einsum("prst",C["VedLR"]) - ((16)/(3))*CF*e**2*qe*qd*my_einsum("ws,wt,pr",C["dG"].conj(),C["dG"],C["delta"]) + 8*CF*e*g*qe*(my_einsum("ws,wt,pr",C["dG"].conj(),C["dgamma"],C["delta"]) + my_einsum("ws,wt,pr",C["dgamma"].conj(),C["dG"],C["delta"])) + e**2*(((32)/(3))*qe*qd - 24*qd**2)*my_einsum("pw,rw,st",C["egamma"],C["egamma"].conj(),C["delta"]) + e**2*(((32)/(3))*qe*qd - 24*qe**2)*my_einsum("ws,wt,pr",C["dgamma"].conj(),C["dgamma"],C["delta"]) + 2*e**2*qd*qe*zetae*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["VueLR"] = ((4)/(3))*e**2*qu*(Nc*qd*my_einsum("pr,wwst",C["delta"],C["VdeLR"]) + Nc*qd*my_einsum("pr,stww",C["delta"],C["VedRR"]) + Nc*qu*my_einsum("pr,wwst",C["delta"],C["VueLR"]) + Nc*qu*my_einsum("pr,stww",C["delta"],C["VeuRR"]) + qe*(my_einsum("pr,wwst",C["delta"],C["VeeLR"]) + 4*my_einsum("pr,stww",C["delta"],C["VeeRR"]))) + ((4)/(3))*e**2*qe*(Nc*qd*my_einsum("st,prww",C["delta"],C["V1udLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["V1udLR"]) + Nc*qu*(2*my_einsum("st,prww",C["delta"],C["VuuLL"]) + my_einsum("st,prww",C["delta"],C["V1uuLR"])) + qe*my_einsum("st,wwpr",C["delta"],C["VeuLL"]) + qe*my_einsum("st,prww",C["delta"],C["VueLR"]) + 2*qu*my_einsum("st,pwwr",C["delta"],C["VuuLL"])) - 12*e**2*qe*qu*my_einsum("prst",C["VueLR"]) - ((16)/(3))*CF*e**2*qe*qu*my_einsum("pw,rw,st",C["uG"],C["uG"].conj(),C["delta"]) + 8*CF*e*g*qe*(my_einsum("pw,rw,st",C["uG"],C["ugamma"].conj(),C["delta"]) + my_einsum("pw,rw,st",C["ugamma"],C["uG"].conj(),C["delta"])) + e**2*(((32)/(3))*qe*qu - 24*qe**2)*my_einsum("pw,rw,st",C["ugamma"],C["ugamma"].conj(),C["delta"]) + e**2*(((32)/(3))*qe*qu - 24*qu**2)*my_einsum("ws,wt,pr",C["egamma"].conj(),C["egamma"],C["delta"]) + 2*e**2*qu*qe*zetae*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["VdeLR"] = ((4)/(3))*e**2*qd*(Nc*qd*my_einsum("pr,wwst",C["delta"],C["VdeLR"]) + Nc*qd*my_einsum("pr,stww",C["delta"],C["VedRR"]) + Nc*qu*my_einsum("pr,wwst",C["delta"],C["VueLR"]) + Nc*qu*my_einsum("pr,stww",C["delta"],C["VeuRR"]) + qe*(my_einsum("pr,wwst",C["delta"],C["VeeLR"]) + 4*my_einsum("pr,stww",C["delta"],C["VeeRR"]))) + ((4)/(3))*e**2*qe*(Nc*qd*2*my_einsum("st,prww",C["delta"],C["VddLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["V1ddLR"]) + Nc*qu*(my_einsum("st,wwpr",C["delta"],C["V1udLL"]) + my_einsum("st,prww",C["delta"],C["V1duLR"])) + qe*my_einsum("st,wwpr",C["delta"],C["VedLL"]) + qe*my_einsum("st,prww",C["delta"],C["VdeLR"]) + 2*qd*my_einsum("st,pwwr",C["delta"],C["VddLL"])) - 12*e**2*qd*qe*my_einsum("prst",C["VdeLR"]) - ((16)/(3))*CF*e**2*qe*qd*my_einsum("pw,rw,st",C["dG"],C["dG"].conj(),C["delta"]) + 8*CF*e*g*qe*(my_einsum("pw,rw,st",C["dG"],C["dgamma"].conj(),C["delta"]) + my_einsum("pw,rw,st",C["dgamma"],C["dG"].conj(),C["delta"])) + e**2*(((32)/(3))*qe*qd - 24*qe**2)*my_einsum("pw,rw,st",C["dgamma"],C["dgamma"].conj(),C["delta"]) + e**2*(((32)/(3))*qe*qd - 24*qd**2)*my_einsum("ws,wt,pr",C["egamma"].conj(),C["egamma"],C["delta"]) + 2*e**2*qd*qe*zetae*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["VnueduLR"] = - 6*e**2*qe*qd*my_einsum("prst",C["VnueduLR"]) + + Beta["V1uuLR"] = ((4)/(3))*e**2*qu*(Nc*qd*my_einsum("pr,wwst",C["delta"],C["V1duLR"]) + Nc*qd*my_einsum("pr,stww",C["delta"],C["V1udRR"]) + Nc*qu*(my_einsum("pr,wwst",C["delta"],C["V1uuLR"]) + 2*my_einsum("pr,stww",C["delta"],C["VuuRR"])) + qe*my_einsum("pr,wwst",C["delta"],C["VeuLR"]) + qe*my_einsum("pr,wwst",C["delta"],C["VeuRR"]) + 2*qu*my_einsum("pr,swwt",C["delta"],C["VuuRR"])) + ((4)/(3))*e**2*qu*(Nc*qd*my_einsum("st,prww",C["delta"],C["V1udLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["V1udLR"]) + Nc*qu*(2*my_einsum("st,prww",C["delta"],C["VuuLL"]) + my_einsum("st,prww",C["delta"],C["V1uuLR"])) + qe*my_einsum("st,wwpr",C["delta"],C["VeuLL"]) + qe*my_einsum("st,prww",C["delta"],C["VueLR"]) + 2*qu*my_einsum("st,pwwr",C["delta"],C["VuuLL"])) - 12*e**2*qu**2*my_einsum("prst",C["V1uuLR"]) - 6*g**2*((CF)/(Nc))*my_einsum("prst",C["V8uuLR"]) + (96*g**2*C1*((1)/(Nc)) + 24*g**2*Cd*((Nc**2 - 1)/(2*Nc**2)) + 48*e**2*qu**2*((Nc**2 - 1)/(2*Nc**2)))*my_einsum("pt,rs",C["uG"],C["uG"].conj()) - (((16)/(3))*CF*e**2*qu**2 + 24*g**2*C1)*(my_einsum("pw,rw,st",C["uG"],C["uG"].conj(),C["delta"]) + my_einsum("ws,wt,pr",C["uG"].conj(),C["uG"],C["delta"])) + 48*e*g*qu*((Nc**2 - 1)/(2*Nc**2))*(my_einsum("pt,rs",C["ugamma"],C["uG"].conj()) + my_einsum("pt,rs",C["uG"],C["ugamma"].conj())) + 8*CF*e*g*qu*(my_einsum("pw,rw,st",C["uG"],C["ugamma"].conj(),C["delta"]) + my_einsum("pw,rw,st",C["ugamma"],C["uG"].conj(),C["delta"])) + 8*CF*e*g*qu*(my_einsum("ws,wt,pr",C["uG"].conj(),C["ugamma"],C["delta"]) + my_einsum("ws,wt,pr",C["ugamma"].conj(),C["uG"],C["delta"])) + (96*e**2*qu**2*((1)/(Nc)) + 48*g**2*((Nc**2 - 1)/(2*Nc**2)))*my_einsum("pt,rs",C["ugamma"],C["ugamma"].conj()) - ((40)/(3))*e**2*qu**2*(my_einsum("pw,rw,st",C["ugamma"],C["ugamma"].conj(),C["delta"]) + my_einsum("ws,wt,pr",C["ugamma"].conj(),C["ugamma"],C["delta"])) + 2*e**2*qu**2*zetae*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["V8uuLR"] = ((2)/(3))*g**2*(my_einsum("pr,wwst",C["delta"],C["V8duLR"]) + my_einsum("pr,stww",C["delta"],C["V8udRR"]) + my_einsum("pr,wwst",C["delta"],C["V8uuLR"]) + 4*my_einsum("pr,swwt",C["delta"],C["VuuRR"])) + ((2)/(3))*g**2*(my_einsum("st,prww",C["delta"],C["V8udLL"]) + my_einsum("st,prww",C["delta"],C["V8udLR"]) + 4*my_einsum("st,pwwr",C["delta"],C["VuuLL"]) + my_einsum("st,prww",C["delta"],C["V8uuLR"])) - 12*g**2*my_einsum("prst",C["V1uuLR"]) - (12*e**2*qu**2 + 6*g**2*Nc - ((12*g**2)/(Nc)))*my_einsum("prst",C["V8uuLR"]) + (192*g**2*C1 - 24*g**2*Cd*((1)/(Nc)) - 48*e**2*qu**2*((1)/(Nc)))*my_einsum("pt,rs",C["uG"],C["uG"].conj()) + (((32)/(3))*CF - 6*Cd - 10*CA)*g**2*(my_einsum("pw,rw,st",C["uG"],C["uG"].conj(),C["delta"]) + my_einsum("ws,wt,pr",C["uG"].conj(),C["uG"],C["delta"])) - 48*e*g*qu*((1)/(Nc))*(my_einsum("pt,rs",C["ugamma"],C["uG"].conj()) + my_einsum("pt,rs",C["uG"],C["ugamma"].conj())) - 16*e*g*qu*(my_einsum("pw,rw,st",C["ugamma"],C["uG"].conj(),C["delta"]) + my_einsum("pw,rw,st",C["uG"],C["ugamma"].conj(),C["delta"])) - 16*e*g*qu*(my_einsum("ws,wt,pr",C["ugamma"].conj(),C["uG"],C["delta"]) + my_einsum("ws,wt,pr",C["uG"].conj(),C["ugamma"],C["delta"])) + (192*e**2*qu**2 - 48*g**2*((1)/(Nc)))*my_einsum("pt,rs",C["ugamma"],C["ugamma"].conj()) - ((16)/(3))*g**2*(my_einsum("pw,rw,st",C["ugamma"],C["ugamma"].conj(),C["delta"]) + my_einsum("ws,wt,pr",C["ugamma"].conj(),C["ugamma"],C["delta"])) + 2*g**2*zetag*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["V1udLR"] = ((4)/(3))*e**2*qu*(Nc*qd*my_einsum("pr,wwst",C["delta"],C["V1ddLR"]) + 2*Nc*qd*my_einsum("pr,stww",C["delta"],C["VddRR"]) + Nc*qu*(my_einsum("pr,wwst",C["delta"],C["V1udLR"]) + my_einsum("pr,wwst",C["delta"],C["V1udRR"])) + qe*my_einsum("pr,wwst",C["delta"],C["VedLR"]) + qe*my_einsum("pr,wwst",C["delta"],C["VedRR"]) + 2*qd*my_einsum("pr,swwt",C["delta"],C["VddRR"])) + ((4)/(3))*e**2*qd*(Nc*qd*my_einsum("st,prww",C["delta"],C["V1udLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["V1udLR"]) + Nc*qu*(2*my_einsum("st,prww",C["delta"],C["VuuLL"]) + my_einsum("st,prww",C["delta"],C["V1uuLR"])) + qe*my_einsum("st,wwpr",C["delta"],C["VeuLL"]) + qe*my_einsum("st,prww",C["delta"],C["VueLR"]) + 2*qu*my_einsum("st,pwwr",C["delta"],C["VuuLL"])) - 12*e**2*qd*qu*my_einsum("prst",C["V1udLR"]) - 6*g**2*((CF)/(Nc))*my_einsum("prst",C["V8udLR"]) - (((16)/(3))*CF*e**2*qu*qd + 24*g**2*C1)*(my_einsum("pw,rw,st",C["uG"],C["uG"].conj(),C["delta"]) + my_einsum("ws,wt,pr",C["dG"].conj(),C["dG"],C["delta"])) + 8*CF*e*g*qd*(my_einsum("pw,rw,st",C["uG"],C["ugamma"].conj(),C["delta"]) + my_einsum("pw,rw,st",C["ugamma"],C["uG"].conj(),C["delta"])) + 8*CF*e*g*qu*(my_einsum("ws,wt,pr",C["dG"].conj(),C["dgamma"],C["delta"]) + my_einsum("ws,wt,pr",C["dgamma"].conj(),C["dG"],C["delta"])) + e**2*(((32)/(3))*qu*qd - 24*qd**2)*my_einsum("pw,rw,st",C["ugamma"],C["ugamma"].conj(),C["delta"]) + e**2*(((32)/(3))*qu*qd - 24*qu**2)*my_einsum("ws,wt,pr",C["dgamma"].conj(),C["dgamma"],C["delta"]) + 2*e**2*qu*qd*zetae*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["V8udLR"] = ((2)/(3))*g**2*(my_einsum("pr,wwst",C["delta"],C["V8udLR"]) + my_einsum("pr,wwst",C["delta"],C["V8ddLR"]) + 4*my_einsum("pr,swwt",C["delta"],C["VddRR"]) + my_einsum("pr,wwst",C["delta"],C["V8udRR"])) + ((2)/(3))*g**2*(my_einsum("st,prww",C["delta"],C["V8udLL"]) + my_einsum("st,prww",C["delta"],C["V8udLR"]) + 4*my_einsum("st,pwwr",C["delta"],C["VuuLL"]) + my_einsum("st,prww",C["delta"],C["V8uuLR"])) - 12*g**2*my_einsum("prst",C["V1udLR"]) - (12*e**2*qd*qu + 6*g**2*Nc - ((12*g**2)/(Nc)))*my_einsum("prst",C["V8udLR"]) + (((32)/(3))*CF - 6*Cd - 10*CA)*g**2*(my_einsum("pw,rw,st",C["uG"],C["uG"].conj(),C["delta"]) + my_einsum("ws,wt,pr",C["dG"].conj(),C["dG"],C["delta"])) - 16*e*g*qd*(my_einsum("pw,rw,st",C["ugamma"],C["uG"].conj(),C["delta"]) + my_einsum("pw,rw,st",C["uG"],C["ugamma"].conj(),C["delta"])) - 16*e*g*qu*(my_einsum("ws,wt,pr",C["dgamma"].conj(),C["dG"],C["delta"]) + my_einsum("ws,wt,pr",C["dG"].conj(),C["dgamma"],C["delta"])) - ((16)/(3))*g**2*(my_einsum("pw,rw,st",C["ugamma"],C["ugamma"].conj(),C["delta"]) + my_einsum("ws,wt,pr",C["dgamma"].conj(),C["dgamma"],C["delta"])) + 2*g**2*zetag*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["V1duLR"] = ((4)/(3))*e**2*qd*(Nc*qd*my_einsum("pr,wwst",C["delta"],C["V1duLR"]) + Nc*qd*my_einsum("pr,stww",C["delta"],C["V1udRR"]) + Nc*qu*(my_einsum("pr,wwst",C["delta"],C["V1uuLR"]) + 2*my_einsum("pr,stww",C["delta"],C["VuuRR"])) + qe*my_einsum("pr,wwst",C["delta"],C["VeuLR"]) + qe*my_einsum("pr,wwst",C["delta"],C["VeuRR"]) + 2*qu*my_einsum("pr,swwt",C["delta"],C["VuuRR"])) + ((4)/(3))*e**2*qu*(Nc*qd*2*my_einsum("st,prww",C["delta"],C["VddLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["V1ddLR"]) + Nc*qu*(my_einsum("st,wwpr",C["delta"],C["V1udLL"]) + my_einsum("st,prww",C["delta"],C["V1duLR"])) + qe*my_einsum("st,wwpr",C["delta"],C["VedLL"]) + qe*my_einsum("st,prww",C["delta"],C["VdeLR"]) + 2*qd*my_einsum("st,pwwr",C["delta"],C["VddLL"])) - 12*e**2*qd*qu*my_einsum("prst",C["V1duLR"]) - 6*g**2*((CF)/(Nc))*my_einsum("prst",C["V8duLR"]) - (((16)/(3))*CF*e**2*qu*qd + 24*g**2*C1)*(my_einsum("pw,rw,st",C["dG"],C["dG"].conj(),C["delta"]) + my_einsum("ws,wt,pr",C["uG"].conj(),C["uG"],C["delta"])) + 8*CF*e*g*qu*(my_einsum("pw,rw,st",C["dG"],C["dgamma"].conj(),C["delta"]) + my_einsum("pw,rw,st",C["dgamma"],C["dG"].conj(),C["delta"])) + 8*CF*e*g*qd*(my_einsum("ws,wt,pr",C["uG"].conj(),C["ugamma"],C["delta"]) + my_einsum("ws,wt,pr",C["ugamma"].conj(),C["uG"],C["delta"])) + e**2*(((32)/(3))*qu*qd - 24*qu**2)*my_einsum("pw,rw,st",C["dgamma"],C["dgamma"].conj(),C["delta"]) + e**2*(((32)/(3))*qu*qd - 24*qd**2)*my_einsum("ws,wt,pr",C["ugamma"].conj(),C["ugamma"],C["delta"]) + 2*e**2*qu*qd*zetae*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["V8duLR"] = ((2)/(3))*g**2*(my_einsum("pr,wwst",C["delta"],C["V8duLR"]) + my_einsum("pr,stww",C["delta"],C["V8udRR"]) + my_einsum("pr,wwst",C["delta"],C["V8uuLR"]) + 4*my_einsum("pr,swwt",C["delta"],C["VuuRR"])) + ((2)/(3))*g**2*(4*my_einsum("st,pwwr",C["delta"],C["VddLL"]) + my_einsum("st,wwpr",C["delta"],C["V8udLL"]) + my_einsum("st,prww",C["delta"],C["V8duLR"]) + my_einsum("st,prww",C["delta"],C["V8ddLR"])) - 12*g**2*my_einsum("prst",C["V1duLR"]) - (12*e**2*qd*qu + 6*g**2*Nc - ((12*g**2)/(Nc)))*my_einsum("prst",C["V8duLR"]) + (((32)/(3))*CF - 6*Cd - 10*CA)*g**2*(my_einsum("pw,rw,st",C["dG"],C["dG"].conj(),C["delta"]) + my_einsum("ws,wt,pr",C["uG"].conj(),C["uG"],C["delta"])) - 16*e*g*qu*(my_einsum("pw,rw,st",C["dgamma"],C["dG"].conj(),C["delta"]) + my_einsum("pw,rw,st",C["dG"],C["dgamma"].conj(),C["delta"])) - 16*e*g*qd*(my_einsum("ws,wt,pr",C["ugamma"].conj(),C["uG"],C["delta"]) + my_einsum("ws,wt,pr",C["uG"].conj(),C["ugamma"],C["delta"])) - ((16)/(3))*g**2*(my_einsum("pw,rw,st",C["dgamma"],C["dgamma"].conj(),C["delta"]) + my_einsum("ws,wt,pr",C["ugamma"].conj(),C["ugamma"],C["delta"])) + 2*g**2*zetag*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["V1ddLR"] = ((4)/(3))*e**2*qd*(Nc*qd*my_einsum("pr,wwst",C["delta"],C["V1ddLR"]) + 2*Nc*qd*my_einsum("pr,stww",C["delta"],C["VddRR"]) + Nc*qu*(my_einsum("pr,wwst",C["delta"],C["V1udLR"]) + my_einsum("pr,wwst",C["delta"],C["V1udRR"])) + qe*my_einsum("pr,wwst",C["delta"],C["VedLR"]) + qe*my_einsum("pr,wwst",C["delta"],C["VedRR"]) + 2*qd*my_einsum("pr,swwt",C["delta"],C["VddRR"])) + ((4)/(3))*e**2*qd*(Nc*qd*2*my_einsum("st,prww",C["delta"],C["VddLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["V1ddLR"]) + Nc*qu*(my_einsum("st,wwpr",C["delta"],C["V1udLL"]) + my_einsum("st,prww",C["delta"],C["V1duLR"])) + qe*my_einsum("st,wwpr",C["delta"],C["VedLL"]) + qe*my_einsum("st,prww",C["delta"],C["VdeLR"]) + 2*qd*my_einsum("st,pwwr",C["delta"],C["VddLL"])) - 12*e**2*qd**2*my_einsum("prst",C["V1ddLR"]) - 6*g**2*((CF)/(Nc))*my_einsum("prst",C["V8ddLR"]) + (96*g**2*C1*((1)/(Nc)) + 24*g**2*Cd*((Nc**2 - 1)/(2*Nc**2)) + 48*e**2*qd**2*((Nc**2 - 1)/(2*Nc**2)))*my_einsum("pt,rs",C["dG"],C["dG"].conj()) - (((16)/(3))*CF*e**2*qd**2 + 24*g**2*C1)*(my_einsum("pw,rw,st",C["dG"],C["dG"].conj(),C["delta"]) + my_einsum("ws,wt,pr",C["dG"].conj(),C["dG"],C["delta"])) + 48*e*g*qd*((Nc**2 - 1)/(2*Nc**2))*(my_einsum("pt,rs",C["dgamma"],C["dG"].conj()) + my_einsum("pt,rs",C["dG"],C["dgamma"].conj())) + 8*CF*e*g*qd*(my_einsum("pw,rw,st",C["dG"],C["dgamma"].conj(),C["delta"]) + my_einsum("pw,rw,st",C["dgamma"],C["dG"].conj(),C["delta"])) + 8*CF*e*g*qd*(my_einsum("ws,wt,pr",C["dG"].conj(),C["dgamma"],C["delta"]) + my_einsum("ws,wt,pr",C["dgamma"].conj(),C["dG"],C["delta"])) + (96*e**2*qd**2*((1)/(Nc)) + 48*g**2*((Nc**2 - 1)/(2*Nc**2)))*my_einsum("pt,rs",C["dgamma"],C["dgamma"].conj()) - ((40)/(3))*e**2*qd**2*(my_einsum("pw,rw,st",C["dgamma"],C["dgamma"].conj(),C["delta"]) + my_einsum("ws,wt,pr",C["dgamma"].conj(),C["dgamma"],C["delta"])) + 2*e**2*qd**2*zetae*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["V8ddLR"] = ((2)/(3))*g**2*(my_einsum("pr,wwst",C["delta"],C["V8udLR"]) + my_einsum("pr,wwst",C["delta"],C["V8ddLR"]) + 4*my_einsum("pr,swwt",C["delta"],C["VddRR"]) + my_einsum("pr,wwst",C["delta"],C["V8udRR"])) + ((2)/(3))*g**2*(4*my_einsum("st,pwwr",C["delta"],C["VddLL"]) + my_einsum("st,wwpr",C["delta"],C["V8udLL"]) + my_einsum("st,prww",C["delta"],C["V8duLR"]) + my_einsum("st,prww",C["delta"],C["V8ddLR"])) - 12*g**2*my_einsum("prst",C["V1ddLR"]) - (12*e**2*qd**2 + 6*g**2*Nc - ((12*g**2)/(Nc)))*my_einsum("prst",C["V8ddLR"]) + (192*g**2*C1 - 24*g**2*Cd*((1)/(Nc)) - 48*e**2*qd**2*((1)/(Nc)))*my_einsum("pt,rs",C["dG"],C["dG"].conj()) + (((32)/(3))*CF - 6*Cd - 10*CA)*g**2*(my_einsum("pw,rw,st",C["dG"],C["dG"].conj(),C["delta"]) + my_einsum("ws,wt,pr",C["dG"].conj(),C["dG"],C["delta"])) - 48*e*g*qd*((1)/(Nc))*(my_einsum("pt,rs",C["dgamma"],C["dG"].conj()) + my_einsum("pt,rs",C["dG"],C["dgamma"].conj())) - 16*e*g*qd*(my_einsum("pw,rw,st",C["dgamma"],C["dG"].conj(),C["delta"]) + my_einsum("pw,rw,st",C["dG"],C["dgamma"].conj(),C["delta"])) - 16*e*g*qd*(my_einsum("ws,wt,pr",C["dgamma"].conj(),C["dG"],C["delta"]) + my_einsum("ws,wt,pr",C["dG"].conj(),C["dgamma"],C["delta"])) + (192*e**2*qd**2 - 48*g**2*((1)/(Nc)))*my_einsum("pt,rs",C["dgamma"],C["dgamma"].conj()) - ((16)/(3))*g**2*(my_einsum("pw,rw,st",C["dgamma"],C["dgamma"].conj(),C["delta"]) + my_einsum("ws,wt,pr",C["dgamma"].conj(),C["dgamma"],C["delta"])) + 2*g**2*zetag*my_einsum("pr,st",C["delta"],C["delta"]) + + Beta["V1udduLR"] = - 6*e**2*(qd**2 + qu**2)*my_einsum("prst",C["V1udduLR"]) - 6*g**2*((CF)/(Nc))*my_einsum("prst",C["V8udduLR"]) + (96*g**2*C1*((1)/(Nc)) + 24*g**2*Cd*((Nc**2 - 1)/(2*Nc**2)) + 48*e**2*qu*qd*((Nc**2 - 1)/(2*Nc**2)))*my_einsum("pt,rs",C["uG"],C["dG"].conj()) + 48*e*g*qd*((Nc**2 - 1)/(2*Nc**2))*my_einsum("pt,rs",C["ugamma"],C["dG"].conj()) + 48*e*g*qu*((Nc**2 - 1)/(2*Nc**2))*my_einsum("pt,rs",C["uG"],C["dgamma"].conj()) + (96*e**2*qu*qd*((1)/(Nc)) + 48*g**2*((Nc**2 - 1)/(2*Nc**2)))*my_einsum("pt,rs",C["ugamma"],C["dgamma"].conj()) + + Beta["V8udduLR"] = - 12*g**2*my_einsum("prst",C["V1udduLR"]) - (6*e**2*(qu**2 + qd**2) + 6*g**2*Nc - ((12*g**2)/(Nc)))*my_einsum("prst",C["V8udduLR"]) + (192*g**2*C1 - 24*g**2*Cd*((1)/(Nc)) - 48*e**2*qu*qd*((1)/(Nc)))*my_einsum("pt,rs",C["uG"],C["dG"].conj()) - 48*e*g*qd*((1)/(Nc))*my_einsum("pt,rs",C["ugamma"],C["dG"].conj()) - 48*e*g*qu*((1)/(Nc))*my_einsum("pt,rs",C["uG"],C["dgamma"].conj()) + (192*e**2*qu*qd - 48*g**2*((1)/(Nc)))*my_einsum("pt,rs",C["ugamma"],C["dgamma"].conj()) + + # \psi^4: (\overline L R)*(\overline L R) + + Beta["SeeRR"] = 16*e**2*qe**2*my_einsum("ptsr",C["SeeRR"]) - 4*e**2*qe**2*my_einsum("prst",C["SeeRR"]) - 96*e**2*qe**2*my_einsum("pr,st",C["egamma"],C["egamma"]) + + Beta["SeuRR"] = - (6*e**2*(qe**2 + qu**2) + 6*g**2*CF)*my_einsum("prst",C["SeuRR"]) - 96*e**2*qe*qu*my_einsum("prst",C["TeuRR"]) - 192*e**2*qe*qu*my_einsum("pr,st",C["egamma"],C["ugamma"]) + + Beta["TeuRR"] = - 2*e**2*qe*qu*my_einsum("prst",C["SeuRR"]) + (2*e**2*(qe**2 + qu**2) + 2*g**2*CF)*my_einsum("prst",C["TeuRR"]) + + Beta["SedRR"] = - (6*e**2*(qe**2 + qd**2) + 6*g**2*CF)*my_einsum("prst",C["SedRR"]) - 96*e**2*qe*qd*my_einsum("prst",C["TedRR"]) - 192*e**2*qe*qd*my_einsum("pr,st",C["egamma"],C["dgamma"]) + + Beta["TedRR"] = - 2*e**2*qd*qe*my_einsum("prst",C["SedRR"]) + (2*e**2*(qe**2 + qd**2) + 2*g**2*CF)*my_einsum("prst",C["TedRR"]) + + Beta["SnueduRR"] = - (6*e**2*qu*qd + 6*g**2*CF)*my_einsum("prst",C["SnueduRR"]) + 24*e**2*(qu**2 - qd**2)*my_einsum("prst",C["TnueduRR"]) + + Beta["TnueduRR"] = ((1)/(2))*e**2*(qu**2 - qd**2)*my_einsum("prst",C["SnueduRR"]) - (2*e**2*(2*qe**2 - qe*qu - qu**2) - 2*g**2*CF)*my_einsum("prst",C["TnueduRR"]) + + Beta["S1uuRR"] = - (4*e**2*qu**2 + 12*g**2*CF)*my_einsum("prst",C["S1uuRR"]) + ((1)/(Nc))*(16*e**2*qu**2 + 16*g**2*CF)*my_einsum("ptsr",C["S1uuRR"]) + 4*g**2*((CF)/(Nc))*my_einsum("prst",C["S8uuRR"]) + ((1)/(Nc))*(16*e**2*qu**2*CF + 2*g**2*(((2)/(Nc**2)) + Nc**2 - 3))*my_einsum("ptsr",C["S8uuRR"]) - 96*g**2*C1*my_einsum("pr,st",C["uG"],C["uG"]) + 4*g**2*CA*((Nc**2 - 1)/(Nc**2))*my_einsum("pt,sr",C["uG"],C["uG"]) - 96*e**2*qu**2*my_einsum("pr,st",C["ugamma"],C["ugamma"]) + + Beta["S8uuRR"] = 8*g**2*my_einsum("prst",C["S1uuRR"]) + (32*e**2*qu**2 - ((16*g**2)/(Nc)))*my_einsum("ptsr",C["S1uuRR"]) - (4*e**2*qu**2 - 4*g**2*CF)*my_einsum("prst",C["S8uuRR"]) - ((1)/(Nc))*(16*e**2*qu**2 - 4*g**2*(((2)/(Nc)) + Nc))*my_einsum("ptsr",C["S8uuRR"]) + (g**2*( - 24*Cd + 4*CA) - 48*e**2*qu**2)*my_einsum("pr,st",C["uG"],C["uG"]) - 8*g**2*((CA)/(Nc))*my_einsum("pt,sr",C["uG"],C["uG"]) - 48*e*g*qu*(my_einsum("pr,st",C["uG"],C["ugamma"]) + my_einsum("pr,st",C["ugamma"],C["uG"])) - 48*g**2*my_einsum("pr,st",C["ugamma"],C["ugamma"]) + + Beta["S1udRR"] = - (2*e**2*(3*qu**2 - 4*qu*qd + 3*qd**2) + 12*g**2*CF)*my_einsum("prst",C["S1udRR"]) + ((1)/(Nc))*(4*e**2*(qu + qd)**2 + 16*g**2*CF)*my_einsum("ptsr",C["S1udduRR"]) + 4*g**2*((CF)/(Nc))*my_einsum("prst",C["S8udRR"]) + ((1)/(Nc))*(4*e**2*(qu + qd)**2*CF + 2*g**2*(((2)/(Nc**2)) + Nc**2 - 3))*my_einsum("ptsr",C["S8udduRR"]) - 192*g**2*C1*my_einsum("pr,st",C["uG"],C["dG"]) - 192*e**2*qu*qd*my_einsum("pr,st",C["ugamma"],C["dgamma"]) + + Beta["S8udRR"] = 8*g**2*my_einsum("prst",C["S1udRR"]) + (8*e**2*(qu + qd)**2 - ((16*g**2)/(Nc)))*my_einsum("ptsr",C["S1udduRR"]) - (2*e**2*(3*qu**2 - 4*qu*qd + 3*qd**2) - 4*g**2*CF)*my_einsum("prst",C["S8udRR"]) - ((1)/(Nc))*(4*e**2*(qu + qd)**2 - 4*g**2*(((2)/(Nc)) + Nc))*my_einsum("ptsr",C["S8udduRR"]) + (g**2*( - 48*Cd + 8*CA) - 96*e**2*qu*qd)*my_einsum("pr,st",C["uG"],C["dG"]) - 96*e*g*qu*my_einsum("pr,st",C["uG"],C["dgamma"]) - 96*e*g*qd*my_einsum("pr,st",C["ugamma"],C["dG"]) - 96*g**2*my_einsum("pr,st",C["ugamma"],C["dgamma"]) + + Beta["S1ddRR"] = - (4*e**2*qd**2 + 12*g**2*CF)*my_einsum("prst",C["S1ddRR"]) + ((1)/(Nc))*(16*e**2*qd**2 + 16*g**2*CF)*my_einsum("ptsr",C["S1ddRR"]) + 4*g**2*((CF)/(Nc))*my_einsum("prst",C["S8ddRR"]) + ((1)/(Nc))*(16*e**2*qd**2*CF + 2*g**2*(((2)/(Nc**2)) + Nc**2 - 3))*my_einsum("ptsr",C["S8ddRR"]) - 96*g**2*C1*my_einsum("pr,st",C["dG"],C["dG"]) + 4*g**2*CA*((Nc**2 - 1)/(Nc**2))*my_einsum("pt,sr",C["dG"],C["dG"]) - 96*e**2*qd**2*my_einsum("pr,st",C["dgamma"],C["dgamma"]) + + Beta["S8ddRR"] = 8*g**2*my_einsum("prst",C["S1ddRR"]) + (32*e**2*qd**2 - ((16*g**2)/(Nc)))*my_einsum("ptsr",C["S1ddRR"]) - (4*e**2*qd**2 - 4*g**2*CF)*my_einsum("prst",C["S8ddRR"]) - ((1)/(Nc))*(16*e**2*qd**2 - 4*g**2*(((2)/(Nc)) + Nc))*my_einsum("ptsr",C["S8ddRR"]) + (g**2*( - 24*Cd + 4*CA) - 48*e**2*qd**2)*my_einsum("pr,st",C["dG"],C["dG"]) - 8*g**2*((CA)/(Nc))*my_einsum("pt,sr",C["dG"],C["dG"]) - 48*e*g*qd*(my_einsum("pr,st",C["dG"],C["dgamma"]) + my_einsum("pr,st",C["dgamma"],C["dG"])) - 48*g**2*my_einsum("pr,st",C["dgamma"],C["dgamma"]) + + Beta["S1udduRR"] = (2*e**2*(qu**2 - 4*qu*qd + qd**2) - 12*g**2*CF)*my_einsum("prst",C["S1udduRR"]) + ((1)/(Nc))*(16*e**2*qu*qd + 16*g**2*CF)*my_einsum("ptsr",C["S1udRR"]) + 4*g**2*((CF)/(Nc))*my_einsum("prst",C["S8udduRR"]) + ((1)/(Nc))*(16*e**2*qu*qd*CF + 2*g**2*(((2)/(Nc**2)) + Nc**2 - 3))*my_einsum("ptsr",C["S8udRR"]) + 8*g**2*CA*((Nc**2 - 1)/(Nc**2))*my_einsum("pt,sr",C["uG"],C["dG"]) + + Beta["S8udduRR"] = 8*g**2*my_einsum("prst",C["S1udduRR"]) + (2*e**2*(qu**2 - 4*qu*qd + qd**2) + 4*g**2*CF)*my_einsum("prst",C["S8udduRR"]) + (32*e**2*qd*qu - ((16*g**2)/(Nc)))*my_einsum("ptsr",C["S1udRR"]) - ((1)/(Nc))*(16*e**2*qd*qu - 4*g**2*(((2)/(Nc)) + Nc))*my_einsum("ptsr",C["S8udRR"]) - 16*g**2*((CA)/(Nc))*my_einsum("pt,sr",C["uG"],C["dG"]) + + # \psi^4: (\overline L R)*(\overline R L)\boldmath $\psi^4: (\overline # L R)*(overline R L) + + Beta["SeuRL"] = - (6*e**2*(qe**2 + qu**2) + 6*g**2*CF)*my_einsum("prst",C["SeuRL"]) - 192*e**2*qe*qu*my_einsum("pr,ts",C["egamma"],C["ugamma"].conj()) + + Beta["SedRL"] = - (6*e**2*(qe**2 + qd**2) + 6*g**2*CF)*my_einsum("prst",C["SedRL"]) - 192*e**2*qe*qd*my_einsum("pr,ts",C["egamma"],C["dgamma"].conj()) + + Beta["SnueduRL"] = - (6*e**2*qu*qd + 6*g**2*CF)*my_einsum("prst",C["SnueduRL"]) + + # \psi^4: \Delta L=4\boldmath $\psi^4: \Delta L=4$ + + Beta["SnunuLL"] = 0 + + # \psi^4: \Delta L=2\boldmath $\psi^4: \Delta L=2$ + + Beta["SnueLL"] = - 6*e**2*qe**2*my_einsum("prst",C["SnueLL"]) + + Beta["TnueLL"] = 2*e**2*qe**2*my_einsum("prst",C["TnueLL"]) + + Beta["SnueLR"] = - 6*e**2*qe**2*my_einsum("prst",C["SnueLR"]) + + Beta["SnuuLL"] = - 6*(e**2*qu**2 + g**2*CF)*my_einsum("prst",C["SnuuLL"]) + + Beta["TnuuLL"] = 2*(e**2*qu**2 + g**2*CF)*my_einsum("prst",C["TnuuLL"]) + + Beta["SnuuLR"] = - 6*(e**2*qu**2 + g**2*CF)*my_einsum("prst",C["SnuuLR"]) + + Beta["SnudLL"] = - 6*(e**2*qd**2 + g**2*CF)*my_einsum("prst",C["SnudLL"]) + + Beta["TnudLL"] = 2*(e**2*qd**2 + g**2*CF)*my_einsum("prst",C["TnudLL"]) + + Beta["SnudLR"] = - 6*(e**2*qd**2 + g**2*CF)*my_einsum("prst",C["SnudLR"]) + + Beta["SnueduLL"] = - 6*(e**2*qu*qd + g**2*CF)*my_einsum("prst",C["SnueduLL"]) + 24*e**2*(qu**2 - qd**2)*my_einsum("prst",C["TnueduLL"]) + + Beta["TnueduLL"] = (2*e**2*(qu**2 + qu*qe - 2*qe**2) + 2*g**2*CF)*my_einsum("prst",C["TnueduLL"]) + ((1)/(2))*e**2*(qu**2 - qd**2)*my_einsum("prst",C["SnueduLL"]) + + Beta["SnueduLR"] = - 6*(e**2*qu*qd + g**2*CF)*my_einsum("prst",C["SnueduLR"]) + + Beta["VnueduRL"] = - 6*e**2*qe*qd*my_einsum("prst",C["VnueduRL"]) + + Beta["VnueduRR"] = 6*e**2*qe*qu*my_einsum("prst",C["VnueduRR"]) + + # \psi^4: \Delta B=\Delta L=1\boldmath $\psi^4: \Delta B=\Delta L=1$ + + Beta["SuddLL"] = ( - 4*g**2 + e**2*(6*qu*qd - 2*(qu - qd)*qd))*my_einsum("prst",C["SuddLL"]) + 4*e**2*(qu - qd)*qd*my_einsum("psrt",C["SuddLL"]) + + Beta["SduuLL"] = ( - 4*g**2 + e**2*(6*(qd*qu + qu*qe) - 2*(qd - qu)*(qu - qe)))*my_einsum("prst",C["SduuLL"]) + 4*e**2*(qd - qu)*(qu - qe)*my_einsum("psrt",C["SduuLL"]) + + Beta["SuudLR"] = ( - 4*g**2 + 6*e**2*(qu**2 + qd*qe))*my_einsum("prst",C["SuudLR"]) + + Beta["SduuLR"] = ( - 4*g**2 + 6*e**2*(qd*qu + qu*qe))*my_einsum("prst",C["SduuLR"]) + + Beta["SuudRL"] = ( - 4*g**2 + 6*e**2*(qu**2 + qd*qe))*my_einsum("prst",C["SuudRL"]) + + Beta["SduuRL"] = ( - 4*g**2 + 6*e**2*(qd*qu + qu*qe))*my_einsum("prst",C["SduuRL"]) + + Beta["SdudRL"] = ( - 4*g**2 + 6*e**2*qd*qu )*my_einsum("prst",C["SdudRL"]) + + Beta["SdduRL"] = ( - 4*g**2 + 6*e**2*qd**2)*my_einsum("prst",C["SdduRL"]) + + Beta["SduuRR"] = ( - 4*g**2 + e**2*(6*(qd*qu + qu*qe) - 2*(qd - qu)*(qu - qe)))*my_einsum("prst",C["SduuRR"]) + 4*e**2*(qd - qu)*(qu - qe)*my_einsum("psrt",C["SduuRR"]) + + # \psi^4: \Delta B = - \Delta L=1\boldmath $\psi^4: \Delta B = - \Delta L=1$ + + Beta["SdddLL"] = ( - 4*g**2 + 6*e**2*(qd**2 - qe*qd))*my_einsum("prst",C["SdddLL"]) + + Beta["SuddLR"] = ( - 4*g**2 + 6*e**2*qu*qd)*my_einsum("prst",C["SuddLR"]) + + Beta["SdduLR"] = ( - 4*g**2 + 6*e**2*qd**2)*my_einsum("prst",C["SdduLR"]) + + Beta["SdddLR"] = ( - 4*g**2 + 6*e**2*(qd**2 - qe*qd))*my_einsum("prst",C["SdddLR"]) + + Beta["SdddRL"] = ( - 4*g**2 + 6*e**2*(qd**2 - qe*qd))*my_einsum("prst",C["SdddRL"]) + + Beta["SuddRR"] = ( - 4*g**2 + e**2*(6*qu*qd - 2*(qu - qd)*qd))*my_einsum("prst",C["SuddRR"]) + 4*e**2*(qu - qd)*qd*my_einsum("ptsr",C["SuddRR"]) + + Beta["SdddRR"] = ( - 4*g**2 + 6*e**2*(qd**2 - qe*qd))*my_einsum("prst",C["SdddRR"]) + + return Beta From 5af6a347a0ee684cb31f2ea27acc7b769de854f6 Mon Sep 17 00:00:00 2001 From: Peter Stangl Date: Fri, 11 Feb 2022 17:36:00 +0100 Subject: [PATCH 2/7] move WET beta functions to WET folder --- wilson/run/{smeft/betaleft.py => wet/beta.py} | 0 1 file changed, 0 insertions(+), 0 deletions(-) rename wilson/run/{smeft/betaleft.py => wet/beta.py} (100%) diff --git a/wilson/run/smeft/betaleft.py b/wilson/run/wet/beta.py similarity index 100% rename from wilson/run/smeft/betaleft.py rename to wilson/run/wet/beta.py From 86e8f4cddfc787b6d3eaa759f0dc4911bdb6da61 Mon Sep 17 00:00:00 2001 From: Peter Stangl Date: Fri, 11 Feb 2022 17:44:50 +0100 Subject: [PATCH 3/7] adjust notation and remove OrderedDict --- wilson/run/wet/beta.py | 11 +++++------ 1 file changed, 5 insertions(+), 6 deletions(-) diff --git a/wilson/run/wet/beta.py b/wilson/run/wet/beta.py index 0024691..c50f0de 100644 --- a/wilson/run/wet/beta.py +++ b/wilson/run/wet/beta.py @@ -1,6 +1,5 @@ from numpy import pi from wilson.run.smeft.beta import my_einsum -from collections import OrderedDict Nc = 3 @@ -11,8 +10,8 @@ Cd = (Nc**2-4)/Nc -qu = 0.6666666666666666 -qd = -0.3333333333333333 +qu = 2/3 +qd = -1/3 qe = -1 nu = 2 nd = 3 @@ -21,7 +20,7 @@ b0e = (-4*(Nc*nd*qd**2 + ne*qe**2 + Nc*nu*qu**2))/3. -def betaLEFT(C): +def beta(C): e = C["e"] g = C["gs"] @@ -31,7 +30,7 @@ def betaLEFT(C): zetag = (4/3)*(my_einsum("wv,wv",C["uG"],C["uG"].conj())+my_einsum("wv,wv",C["dG"],C["dG"].conj())) - Beta = OrderedDict() + Beta = {} # Dimension 3: Masses @@ -48,7 +47,7 @@ def betaLEFT(C): Beta["e"] = - b0e*e**3 - 8*e**2*qe*(my_einsum("rs,sr",C["egamma"],C["Me"]) + my_einsum("rs,rs",C["Me"].conj().T,C["egamma"].conj())) - 8*e**2*Nc*qu*(my_einsum("rs,sr",C["ugamma"],C["Mu"]) + my_einsum("rs,rs",C["Mu"].conj().T,C["ugamma"].conj())) - 8*e**2*Nc*qd*(my_einsum("rs,sr",C["dgamma"],C["Md"]) + my_einsum("rs,rs",C["Md"].conj().T,C["dgamma"].conj())) + 8*e*(2*my_einsum("ts,sr,rp,pt",C["Mnu"].conj().T,C["nugamma"],C["Mnu"].conj().T,C["nugamma"]) + 2*my_einsum("pr,sr,st,pt",C["Mnu"],C["nugamma"].conj(),C["Mnu"],C["nugamma"].conj()) + my_einsum("ts,sr,rp,pt",C["Me"],C["egamma"],C["Me"],C["egamma"]) + my_einsum("pr,sr,st,pt",C["Me"].conj().T,C["egamma"].conj(),C["Me"].conj().T,C["egamma"].conj()) + Nc*my_einsum("ts,sr,rp,pt",C["Mu"],C["ugamma"],C["Mu"],C["ugamma"]) + Nc*my_einsum("pr,sr,st,pt",C["Mu"].conj().T,C["ugamma"].conj(),C["Mu"].conj().T,C["ugamma"].conj()) + Nc*my_einsum("ts,sr,rp,pt",C["Md"],C["dgamma"],C["Md"],C["dgamma"]) + Nc*my_einsum("pr,sr,st,pt",C["Md"].conj().T,C["dgamma"].conj(),C["Md"].conj().T,C["dgamma"].conj())) - Beta["g"] = - b0g*g**3 - 4*g**2*(my_einsum("rs,sr",C["uG"],C["Mu"]) + my_einsum("rs,rs",C["Mu"].conj().T,C["uG"].conj())) - 4*g**2*(my_einsum("rs,sr",C["dG"],C["Md"]) + my_einsum("rs,rs",C["Md"].conj().T,C["dG"].conj())) + 4*g*(my_einsum("ts,sr,rp,pt",C["Mu"],C["uG"],C["Mu"],C["uG"]) + my_einsum("pr,sr,st,pt",C["Mu"].conj().T,C["uG"].conj(),C["Mu"].conj().T,C["uG"].conj()) + my_einsum("ts,sr,rp,pt",C["Md"],C["dG"],C["Md"],C["dG"]) + my_einsum("pr,sr,st,pt",C["Md"].conj().T,C["dG"].conj(),C["Md"].conj().T,C["dG"].conj())) + Beta["gs"] = - b0g*g**3 - 4*g**2*(my_einsum("rs,sr",C["uG"],C["Mu"]) + my_einsum("rs,rs",C["Mu"].conj().T,C["uG"].conj())) - 4*g**2*(my_einsum("rs,sr",C["dG"],C["Md"]) + my_einsum("rs,rs",C["Md"].conj().T,C["dG"].conj())) + 4*g*(my_einsum("ts,sr,rp,pt",C["Mu"],C["uG"],C["Mu"],C["uG"]) + my_einsum("pr,sr,st,pt",C["Mu"].conj().T,C["uG"].conj(),C["Mu"].conj().T,C["uG"].conj()) + my_einsum("ts,sr,rp,pt",C["Md"],C["dG"],C["Md"],C["dG"]) + my_einsum("pr,sr,st,pt",C["Md"].conj().T,C["dG"].conj(),C["Md"].conj().T,C["dG"].conj())) Beta["thetaQCD"] = ((64*pi**2)/(g))*(1j*my_einsum("rs,sr",C["uG"],C["Mu"]) - 1j*my_einsum("rs,rs",C["Mu"].conj().T,C["uG"].conj())) + ((64*pi**2)/(g))*(1j*my_einsum("rs,sr",C["dG"],C["Md"]) - 1j*my_einsum("rs,rs",C["Md"].conj().T,C["dG"].conj())) + ((32*pi**2)/(g**2))*2j*( - my_einsum("ts,sr,rp,pt",C["Mu"],C["uG"],C["Mu"],C["uG"]) + my_einsum("ts,sr,rp,pt",C["Mu"].conj(),C["uG"].conj(),C["Mu"].conj(),C["uG"].conj()) - my_einsum("ts,sr,rp,pt",C["Md"],C["dG"],C["Md"],C["dG"]) + my_einsum("ts,sr,rp,pt",C["Md"].conj(),C["dG"].conj(),C["Md"].conj(),C["dG"].conj())) From a2b54e960ac9ab5aaa69846a66491c08a0c7dc81 Mon Sep 17 00:00:00 2001 From: Peter Stangl Date: Fri, 11 Feb 2022 17:56:51 +0100 Subject: [PATCH 4/7] comment out beta functions of undefined operators --- wilson/run/wet/beta.py | 48 +++++++++++++++++++++--------------------- 1 file changed, 24 insertions(+), 24 deletions(-) diff --git a/wilson/run/wet/beta.py b/wilson/run/wet/beta.py index c50f0de..36ddd9b 100644 --- a/wilson/run/wet/beta.py +++ b/wilson/run/wet/beta.py @@ -49,9 +49,9 @@ def beta(C): Beta["gs"] = - b0g*g**3 - 4*g**2*(my_einsum("rs,sr",C["uG"],C["Mu"]) + my_einsum("rs,rs",C["Mu"].conj().T,C["uG"].conj())) - 4*g**2*(my_einsum("rs,sr",C["dG"],C["Md"]) + my_einsum("rs,rs",C["Md"].conj().T,C["dG"].conj())) + 4*g*(my_einsum("ts,sr,rp,pt",C["Mu"],C["uG"],C["Mu"],C["uG"]) + my_einsum("pr,sr,st,pt",C["Mu"].conj().T,C["uG"].conj(),C["Mu"].conj().T,C["uG"].conj()) + my_einsum("ts,sr,rp,pt",C["Md"],C["dG"],C["Md"],C["dG"]) + my_einsum("pr,sr,st,pt",C["Md"].conj().T,C["dG"].conj(),C["Md"].conj().T,C["dG"].conj())) - Beta["thetaQCD"] = ((64*pi**2)/(g))*(1j*my_einsum("rs,sr",C["uG"],C["Mu"]) - 1j*my_einsum("rs,rs",C["Mu"].conj().T,C["uG"].conj())) + ((64*pi**2)/(g))*(1j*my_einsum("rs,sr",C["dG"],C["Md"]) - 1j*my_einsum("rs,rs",C["Md"].conj().T,C["dG"].conj())) + ((32*pi**2)/(g**2))*2j*( - my_einsum("ts,sr,rp,pt",C["Mu"],C["uG"],C["Mu"],C["uG"]) + my_einsum("ts,sr,rp,pt",C["Mu"].conj(),C["uG"].conj(),C["Mu"].conj(),C["uG"].conj()) - my_einsum("ts,sr,rp,pt",C["Md"],C["dG"],C["Md"],C["dG"]) + my_einsum("ts,sr,rp,pt",C["Md"].conj(),C["dG"].conj(),C["Md"].conj(),C["dG"].conj())) + #Beta["thetaQCD"] = ((64*pi**2)/(g))*(1j*my_einsum("rs,sr",C["uG"],C["Mu"]) - 1j*my_einsum("rs,rs",C["Mu"].conj().T,C["uG"].conj())) + ((64*pi**2)/(g))*(1j*my_einsum("rs,sr",C["dG"],C["Md"]) - 1j*my_einsum("rs,rs",C["Md"].conj().T,C["dG"].conj())) + ((32*pi**2)/(g**2))*2j*( - my_einsum("ts,sr,rp,pt",C["Mu"],C["uG"],C["Mu"],C["uG"]) + my_einsum("ts,sr,rp,pt",C["Mu"].conj(),C["uG"].conj(),C["Mu"].conj(),C["uG"].conj()) - my_einsum("ts,sr,rp,pt",C["Md"],C["dG"],C["Md"],C["dG"]) + my_einsum("ts,sr,rp,pt",C["Md"].conj(),C["dG"].conj(),C["Md"].conj(),C["dG"].conj())) - Beta["thetaQED"] = ((128*pi**2*qe)/(e))*(1j*my_einsum("rs,sr",C["egamma"],C["Me"]) - 1j*my_einsum("rs,rs",C["Me"].conj().T,C["egamma"].conj())) + ((128*Nc*pi**2*qu)/(e))*(1j*my_einsum("rs,sr",C["ugamma"],C["Mu"]) - 1j*my_einsum("rs,rs",C["Mu"].conj().T,C["ugamma"].conj())) + ((128*Nc*pi**2*qd)/(e))*(1j*my_einsum("rs,sr",C["dgamma"],C["Md"]) - 1j*my_einsum("rs,rs",C["Md"].conj().T,C["dgamma"].conj())) + ((32*pi**2)/(e**2))*4j*(2*my_einsum("ts,sr,rp,pt",C["Mnu"].conj().T,C["nugamma"],C["Mnu"].conj().T,C["nugamma"]) - 2*my_einsum("pr,sr,st,pt",C["Mnu"],C["nugamma"].conj(),C["Mnu"],C["nugamma"].conj()) - my_einsum("ts,sr,rp,pt",C["Me"],C["egamma"],C["Me"],C["egamma"]) + my_einsum("pr,sr,st,pt",C["Me"].conj().T,C["egamma"].conj(),C["Me"].conj().T,C["egamma"].conj()) - Nc*my_einsum("ts,sr,rp,pt",C["Mu"],C["ugamma"],C["Mu"],C["ugamma"]) + Nc*my_einsum("pr,sr,st,pt",C["Mu"].conj().T,C["ugamma"].conj(),C["Mu"].conj().T,C["ugamma"].conj()) - Nc*my_einsum("ts,sr,rp,pt",C["Md"],C["dgamma"],C["Md"],C["dgamma"]) + Nc*my_einsum("pr,sr,st,pt",C["Md"].conj().T,C["dgamma"].conj(),C["Md"].conj().T,C["dgamma"].conj())) + #Beta["thetaQED"] = ((128*pi**2*qe)/(e))*(1j*my_einsum("rs,sr",C["egamma"],C["Me"]) - 1j*my_einsum("rs,rs",C["Me"].conj().T,C["egamma"].conj())) + ((128*Nc*pi**2*qu)/(e))*(1j*my_einsum("rs,sr",C["ugamma"],C["Mu"]) - 1j*my_einsum("rs,rs",C["Mu"].conj().T,C["ugamma"].conj())) + ((128*Nc*pi**2*qd)/(e))*(1j*my_einsum("rs,sr",C["dgamma"],C["Md"]) - 1j*my_einsum("rs,rs",C["Md"].conj().T,C["dgamma"].conj())) + ((32*pi**2)/(e**2))*4j*(2*my_einsum("ts,sr,rp,pt",C["Mnu"].conj().T,C["nugamma"],C["Mnu"].conj().T,C["nugamma"]) - 2*my_einsum("pr,sr,st,pt",C["Mnu"],C["nugamma"].conj(),C["Mnu"],C["nugamma"].conj()) - my_einsum("ts,sr,rp,pt",C["Me"],C["egamma"],C["Me"],C["egamma"]) + my_einsum("pr,sr,st,pt",C["Me"].conj().T,C["egamma"].conj(),C["Me"].conj().T,C["egamma"].conj()) - Nc*my_einsum("ts,sr,rp,pt",C["Mu"],C["ugamma"],C["Mu"],C["ugamma"]) + Nc*my_einsum("pr,sr,st,pt",C["Mu"].conj().T,C["ugamma"].conj(),C["Mu"].conj().T,C["ugamma"].conj()) - Nc*my_einsum("ts,sr,rp,pt",C["Md"],C["dgamma"],C["Md"],C["dgamma"]) + Nc*my_einsum("pr,sr,st,pt",C["Md"].conj().T,C["dgamma"].conj(),C["Md"].conj().T,C["dgamma"].conj())) # Dimension 5: Dipole Operators @@ -197,37 +197,37 @@ def beta(C): # \psi^4: \Delta L=4\boldmath $\psi^4: \Delta L=4$ - Beta["SnunuLL"] = 0 + #Beta["SnunuLL"] = 0 # \psi^4: \Delta L=2\boldmath $\psi^4: \Delta L=2$ - Beta["SnueLL"] = - 6*e**2*qe**2*my_einsum("prst",C["SnueLL"]) + #Beta["SnueLL"] = - 6*e**2*qe**2*my_einsum("prst",C["SnueLL"]) - Beta["TnueLL"] = 2*e**2*qe**2*my_einsum("prst",C["TnueLL"]) + #Beta["TnueLL"] = 2*e**2*qe**2*my_einsum("prst",C["TnueLL"]) - Beta["SnueLR"] = - 6*e**2*qe**2*my_einsum("prst",C["SnueLR"]) + #Beta["SnueLR"] = - 6*e**2*qe**2*my_einsum("prst",C["SnueLR"]) - Beta["SnuuLL"] = - 6*(e**2*qu**2 + g**2*CF)*my_einsum("prst",C["SnuuLL"]) + #Beta["SnuuLL"] = - 6*(e**2*qu**2 + g**2*CF)*my_einsum("prst",C["SnuuLL"]) - Beta["TnuuLL"] = 2*(e**2*qu**2 + g**2*CF)*my_einsum("prst",C["TnuuLL"]) + #Beta["TnuuLL"] = 2*(e**2*qu**2 + g**2*CF)*my_einsum("prst",C["TnuuLL"]) - Beta["SnuuLR"] = - 6*(e**2*qu**2 + g**2*CF)*my_einsum("prst",C["SnuuLR"]) + #Beta["SnuuLR"] = - 6*(e**2*qu**2 + g**2*CF)*my_einsum("prst",C["SnuuLR"]) - Beta["SnudLL"] = - 6*(e**2*qd**2 + g**2*CF)*my_einsum("prst",C["SnudLL"]) + #Beta["SnudLL"] = - 6*(e**2*qd**2 + g**2*CF)*my_einsum("prst",C["SnudLL"]) - Beta["TnudLL"] = 2*(e**2*qd**2 + g**2*CF)*my_einsum("prst",C["TnudLL"]) + #Beta["TnudLL"] = 2*(e**2*qd**2 + g**2*CF)*my_einsum("prst",C["TnudLL"]) - Beta["SnudLR"] = - 6*(e**2*qd**2 + g**2*CF)*my_einsum("prst",C["SnudLR"]) + #Beta["SnudLR"] = - 6*(e**2*qd**2 + g**2*CF)*my_einsum("prst",C["SnudLR"]) - Beta["SnueduLL"] = - 6*(e**2*qu*qd + g**2*CF)*my_einsum("prst",C["SnueduLL"]) + 24*e**2*(qu**2 - qd**2)*my_einsum("prst",C["TnueduLL"]) + #Beta["SnueduLL"] = - 6*(e**2*qu*qd + g**2*CF)*my_einsum("prst",C["SnueduLL"]) + 24*e**2*(qu**2 - qd**2)*my_einsum("prst",C["TnueduLL"]) - Beta["TnueduLL"] = (2*e**2*(qu**2 + qu*qe - 2*qe**2) + 2*g**2*CF)*my_einsum("prst",C["TnueduLL"]) + ((1)/(2))*e**2*(qu**2 - qd**2)*my_einsum("prst",C["SnueduLL"]) + #Beta["TnueduLL"] = (2*e**2*(qu**2 + qu*qe - 2*qe**2) + 2*g**2*CF)*my_einsum("prst",C["TnueduLL"]) + ((1)/(2))*e**2*(qu**2 - qd**2)*my_einsum("prst",C["SnueduLL"]) - Beta["SnueduLR"] = - 6*(e**2*qu*qd + g**2*CF)*my_einsum("prst",C["SnueduLR"]) + #Beta["SnueduLR"] = - 6*(e**2*qu*qd + g**2*CF)*my_einsum("prst",C["SnueduLR"]) - Beta["VnueduRL"] = - 6*e**2*qe*qd*my_einsum("prst",C["VnueduRL"]) + #Beta["VnueduRL"] = - 6*e**2*qe*qd*my_einsum("prst",C["VnueduRL"]) - Beta["VnueduRR"] = 6*e**2*qe*qu*my_einsum("prst",C["VnueduRR"]) + #Beta["VnueduRR"] = 6*e**2*qe*qu*my_einsum("prst",C["VnueduRR"]) # \psi^4: \Delta B=\Delta L=1\boldmath $\psi^4: \Delta B=\Delta L=1$ @@ -251,18 +251,18 @@ def beta(C): # \psi^4: \Delta B = - \Delta L=1\boldmath $\psi^4: \Delta B = - \Delta L=1$ - Beta["SdddLL"] = ( - 4*g**2 + 6*e**2*(qd**2 - qe*qd))*my_einsum("prst",C["SdddLL"]) + #Beta["SdddLL"] = ( - 4*g**2 + 6*e**2*(qd**2 - qe*qd))*my_einsum("prst",C["SdddLL"]) - Beta["SuddLR"] = ( - 4*g**2 + 6*e**2*qu*qd)*my_einsum("prst",C["SuddLR"]) + #Beta["SuddLR"] = ( - 4*g**2 + 6*e**2*qu*qd)*my_einsum("prst",C["SuddLR"]) - Beta["SdduLR"] = ( - 4*g**2 + 6*e**2*qd**2)*my_einsum("prst",C["SdduLR"]) + #Beta["SdduLR"] = ( - 4*g**2 + 6*e**2*qd**2)*my_einsum("prst",C["SdduLR"]) - Beta["SdddLR"] = ( - 4*g**2 + 6*e**2*(qd**2 - qe*qd))*my_einsum("prst",C["SdddLR"]) + #Beta["SdddLR"] = ( - 4*g**2 + 6*e**2*(qd**2 - qe*qd))*my_einsum("prst",C["SdddLR"]) - Beta["SdddRL"] = ( - 4*g**2 + 6*e**2*(qd**2 - qe*qd))*my_einsum("prst",C["SdddRL"]) + #Beta["SdddRL"] = ( - 4*g**2 + 6*e**2*(qd**2 - qe*qd))*my_einsum("prst",C["SdddRL"]) - Beta["SuddRR"] = ( - 4*g**2 + e**2*(6*qu*qd - 2*(qu - qd)*qd))*my_einsum("prst",C["SuddRR"]) + 4*e**2*(qu - qd)*qd*my_einsum("ptsr",C["SuddRR"]) + #Beta["SuddRR"] = ( - 4*g**2 + e**2*(6*qu*qd - 2*(qu - qd)*qd))*my_einsum("prst",C["SuddRR"]) + 4*e**2*(qu - qd)*qd*my_einsum("ptsr",C["SuddRR"]) - Beta["SdddRR"] = ( - 4*g**2 + 6*e**2*(qd**2 - qe*qd))*my_einsum("prst",C["SdddRR"]) + #Beta["SdddRR"] = ( - 4*g**2 + 6*e**2*(qd**2 - qe*qd))*my_einsum("prst",C["SdddRR"]) return Beta From b399e2862dabd3ab91d4413997399190cde7cdd4 Mon Sep 17 00:00:00 2001 From: Peter Stangl Date: Fri, 11 Feb 2022 20:15:44 +0100 Subject: [PATCH 5/7] set undefined Wilson coefficients to zero --- wilson/run/wet/beta.py | 19 ++++++++++++++++++- 1 file changed, 18 insertions(+), 1 deletion(-) diff --git a/wilson/run/wet/beta.py b/wilson/run/wet/beta.py index 36ddd9b..9ad06d4 100644 --- a/wilson/run/wet/beta.py +++ b/wilson/run/wet/beta.py @@ -1,3 +1,4 @@ +import numpy as np from numpy import pi from wilson.run.smeft.beta import my_einsum @@ -13,17 +14,33 @@ qu = 2/3 qd = -1/3 qe = -1 + nu = 2 nd = 3 ne = 3 + b0g = (11*Nc - 2*(nd + nu))/3. b0e = (-4*(Nc*nd*qd**2 + ne*qe**2 + Nc*nu*qu**2))/3. -def beta(C): +def beta(C, n_gen=3): e = C["e"] g = C["gs"] + # set undefined Wilson coefficients to zero + zeros_4F = np.zeros((n_gen,n_gen,n_gen,n_gen)) + zeros_2F = np.zeros((n_gen,n_gen)) + C['SnunuLL'] = zeros_4F + C['SnueLL'] = zeros_4F + C['SnueLR'] = zeros_4F + C['SnuuLL'] = zeros_4F + C['SnuuLR'] = zeros_4F + C['SnudLL'] = zeros_4F + C['SnudLR'] = zeros_4F + C['nugamma'] = zeros_2F + + # define Kronecker delta + C['delta'] = np.eye(n_gen) # Eq. (3.41) zetae = (8/3)*(2*my_einsum("wv,wv",C["nugamma"],C["nugamma"].conj())+my_einsum("wv,wv",C["egamma"],C["egamma"].conj())+Nc*my_einsum("wv,wv",C["ugamma"],C["ugamma"].conj())+Nc*my_einsum("wv,wv",C["dgamma"],C["dgamma"].conj())) From 24f6ab76d73ffd754313b9be62c7e4f1cce82a6c Mon Sep 17 00:00:00 2001 From: Peter Stangl Date: Sat, 12 Feb 2022 14:20:59 +0100 Subject: [PATCH 6/7] comment out beta function of undefined `nugamma` operator --- wilson/run/wet/beta.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/wilson/run/wet/beta.py b/wilson/run/wet/beta.py index 9ad06d4..3cfb197 100644 --- a/wilson/run/wet/beta.py +++ b/wilson/run/wet/beta.py @@ -72,7 +72,7 @@ def beta(C, n_gen=3): # Dimension 5: Dipole Operators - Beta["nugamma"] = - b0e*e**2*my_einsum("rs",C["nugamma"]) - 8*e*qe*(my_einsum("rs,vw,wv",C["nugamma"],C["egamma"],C["Me"]) + my_einsum("rs,vw,vw",C["nugamma"],C["Me"].conj().T,C["egamma"].conj())) - 8*e*Nc*qu*(my_einsum("rs,vw,wv",C["nugamma"],C["ugamma"],C["Mu"]) + my_einsum("rs,vw,vw",C["nugamma"],C["Mu"].conj().T,C["ugamma"].conj())) - 8*e*Nc*qd*(my_einsum("rs,vw,wv",C["nugamma"],C["dgamma"],C["Md"]) + my_einsum("rs,vw,vw",C["nugamma"],C["Md"].conj().T,C["dgamma"].conj())) + #Beta["nugamma"] = - b0e*e**2*my_einsum("rs",C["nugamma"]) - 8*e*qe*(my_einsum("rs,vw,wv",C["nugamma"],C["egamma"],C["Me"]) + my_einsum("rs,vw,vw",C["nugamma"],C["Me"].conj().T,C["egamma"].conj())) - 8*e*Nc*qu*(my_einsum("rs,vw,wv",C["nugamma"],C["ugamma"],C["Mu"]) + my_einsum("rs,vw,vw",C["nugamma"],C["Mu"].conj().T,C["ugamma"].conj())) - 8*e*Nc*qd*(my_einsum("rs,vw,wv",C["nugamma"],C["dgamma"],C["Md"]) + my_einsum("rs,vw,vw",C["nugamma"],C["Md"].conj().T,C["dgamma"].conj())) Beta["egamma"] = (10*qe**2 - b0e)*e**2*my_einsum("rs",C["egamma"]) - 8*e*Nc*qd*my_einsum("wv,rsvw",C["Md"],C["TedRR"]) - 8*e*Nc*qu*my_einsum("wv,rsvw",C["Mu"],C["TeuRR"]) + 2*e*qe*my_einsum("wv,rwvs",C["Me"],C["SeeRR"]) - 12*e*qe*my_einsum("rw,wv,vs",C["egamma"],C["Me"],C["egamma"]) - 8*e*qe*(my_einsum("vw,rw,vs",C["egamma"].conj(),C["egamma"],C["Me"].conj().T) + my_einsum("vw,vs,rw",C["egamma"].conj(),C["egamma"],C["Me"].conj().T)) - 8*e*qe*(my_einsum("rs,vw,wv",C["egamma"],C["egamma"],C["Me"]) + my_einsum("rs,vw,vw",C["egamma"],C["Me"].conj().T,C["egamma"].conj())) - 8*e*Nc*qu*(my_einsum("rs,vw,wv",C["egamma"],C["ugamma"],C["Mu"]) + my_einsum("rs,vw,vw",C["egamma"],C["Mu"].conj().T,C["ugamma"].conj())) - 8*e*Nc*qd*(my_einsum("rs,vw,wv",C["egamma"],C["dgamma"],C["Md"]) + my_einsum("rs,vw,vw",C["egamma"],C["Md"].conj().T,C["dgamma"].conj())) From 7972939cad5a8e68ecd4e20f2b87510ec8940d74 Mon Sep 17 00:00:00 2001 From: Peter Stangl Date: Fri, 10 Jun 2022 04:26:55 +0200 Subject: [PATCH 7/7] fix shape of Beta["VnunuLL"] --- wilson/run/wet/beta.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/wilson/run/wet/beta.py b/wilson/run/wet/beta.py index 3cfb197..749f100 100644 --- a/wilson/run/wet/beta.py +++ b/wilson/run/wet/beta.py @@ -92,7 +92,7 @@ def beta(C, n_gen=3): # \psi^4: (\overline L L)*(\overline L L) - Beta["VnunuLL"] = 0 + Beta["VnunuLL"] = 0 * C['VnunuLL'] Beta["VeeLL"] = 12*e**2*qe**2*my_einsum("prst",C["VeeLL"]) + ((1)/(3))*e**2*qe*(Nc*qd*my_einsum("pr,stww",C["delta"],C["VedLL"]) + Nc*qd*my_einsum("pr,stww",C["delta"],C["VedLR"]) + Nc*qu*my_einsum("pr,stww",C["delta"],C["VeuLL"]) + Nc*qu*my_einsum("pr,stww",C["delta"],C["VeuLR"]) + qe*(4*my_einsum("pr,stww",C["delta"],C["VeeLL"]) + my_einsum("pr,stww",C["delta"],C["VeeLR"]))) + ((1)/(3))*e**2*qe*(Nc*qd*my_einsum("st,prww",C["delta"],C["VedLL"]) + Nc*qd*my_einsum("st,prww",C["delta"],C["VedLR"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VeuLL"]) + Nc*qu*my_einsum("st,prww",C["delta"],C["VeuLR"]) + qe*(4*my_einsum("st,prww",C["delta"],C["VeeLL"]) + my_einsum("st,prww",C["delta"],C["VeeLR"]))) + ((1)/(3))*e**2*qe*(Nc*qd*my_einsum("pt,srww",C["delta"],C["VedLL"]) + Nc*qd*my_einsum("pt,srww",C["delta"],C["VedLR"]) + Nc*qu*my_einsum("pt,srww",C["delta"],C["VeuLL"]) + Nc*qu*my_einsum("pt,srww",C["delta"],C["VeuLR"]) + qe*(4*my_einsum("pt,srww",C["delta"],C["VeeLL"]) + my_einsum("pt,srww",C["delta"],C["VeeLR"]))) + ((1)/(3))*e**2*qe*(Nc*qd*my_einsum("sr,ptww",C["delta"],C["VedLL"]) + Nc*qd*my_einsum("sr,ptww",C["delta"],C["VedLR"]) + Nc*qu*my_einsum("sr,ptww",C["delta"],C["VeuLL"]) + Nc*qu*my_einsum("sr,ptww",C["delta"],C["VeuLR"]) + qe*(4*my_einsum("sr,ptww",C["delta"],C["VeeLL"]) + my_einsum("sr,ptww",C["delta"],C["VeeLR"]))) + ((26)/(3))*e**2*qe**2*(my_einsum("pw,rw,st",C["egamma"],C["egamma"].conj(),C["delta"]) + my_einsum("sw,tw,pr",C["egamma"],C["egamma"].conj(),C["delta"]) + my_einsum("pw,tw,sr",C["egamma"],C["egamma"].conj(),C["delta"]) + my_einsum("sw,rw,pt",C["egamma"],C["egamma"].conj(),C["delta"])) + e**2*qe**2*zetae*my_einsum("pr,st",C["delta"],C["delta"])