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