FCRerouteMomenta
FCRerouteMomenta[exp, {p1, p2, ...}, {k1, k2, ...}]
changes the routing of the momenta by exploiting the 4-momentum conservation law p1+p2+…=k1+k2+….
The main aim of this function is to simplify the input expression by replacing simple linear combinations of the external momenta with shorter expressions.
For example, in a process a(p1)+b(p2)−>c(k1)+d(k2)+e(k3), the combination k1+k2−p2 can be replaced with the shorter expression p1−k3.
The replacements are applied using the FeynCalcExternal
form of the expression. Ideally, this function should be used directly on the output of a diagram generator such as FeynArts or QGRAF.
See also
Overview.
Examples
Reroute momenta according to the momentum conservation relation l1+l2=p1+p2+kp.
exp = (-I)*Spinor[-Momentum[l2], ME, 1] . GA[\[Mu]] . Spinor[Momentum[l1], ME,
1]*Spinor[Momentum[p1], SMP["m_Q"], 1] . GS[Polarization[kp, -I,
Transversality -> True]] . (GS[kp + p1] + SMP["m_Q"]) . GA[\[Mu]] . Spinor[-Momentum[p2],
SMP["m_Q"], 1]*FAD[kp + p1 + p2, Dimension -> 4]*FAD[{-l1 - l2 - p2, SMP["m_Q"]},
Dimension -> 4]*SDF[cq, cqbar]*SMP["e"]^3*SMP["Q_u"]^2
−(kp+p1+p2)2((−l1−l2−p2)2−mQ2)ie3Qu2δcqcqbar(φ(−l2,ME)).γˉμ.(φ(l1,ME))(φ(p1,mQ)).(γˉ⋅εˉ∗(kp)).(γˉ⋅(kp+p1)+mQ).γˉμ.(φ(−p2,mQ))
FCRerouteMomenta[exp, {l1, l2}, {p1, p2, kp}]
−(l1+l2)2((−l1−l2−p2)2−mQ2)ie3Qu2δcqcqbar(φ(−l2,ME)).γˉμ.(φ(l1,ME))(φ(p1,mQ)).(γˉ⋅εˉ∗(kp)).(γˉ⋅(kp+p1)+mQ).γˉμ.(φ(−p2,mQ))