Name: X.-L.Ren (email_not_shown)
Date: 09/12/17-02:04:40 AM Z

I am doing the non-relativistic expansion (1/mN, mN is nucleon mass) of one-loop integral with the help of FeynCalc 9.2 and FeynHelpers (on Mathematica 10.4).

I found that the expanded result from PaXSeries is not the same as the result from Series, which is right for sure. I did something wrong when using PaXSeries or a possible bug?

In order to see the details, the code is given below,

(* Diagrams * )
ltdia = FCI[
SpinorUBarD[p, mN,
1].(GSD[k].(GSD[p] - GSD[k] - mN).GSD[k]).SpinorUD[p, mN,
1] FAD[{k, m\[Pi]}, {p - k, mN}]]

(* Do Integration *)
ltintOS =
1/(2 mN) Collect2[
TID[ltdia, k, UsePaVeBasis -> True, ToPaVe -> True,
PaVeAutoReduce -> True], Spinor] // DiracSimplify;

(* 1: Using the PaXSeires[mN, infinity, 0] in PaXEvaluate *)

IntHBPCB = (PaXEvaluate[
ltintOS /. {Pair[Momentum[p, D], Momentum[p, D]] -> mN^2},
PaXImplicitPrefactor -> 1/(2 \[Pi])^D, PaXAnalytic -> True,
PaXSeries -> {{mN, \[Infinity], 0}}] // Normal //
FCHideEpsilon) /. {SMP["Delta"] -> 0} // Simplify //
FullSimplify

(* 2: Using the Seires[mN, infinity, 0] after PaXEvaluate *)

IntHBPCB2 = (Series[
PaXEvaluate[
ltintOS /. {Pair[Momentum[p, D], Momentum[p, D]] -> mN^2},
PaXImplicitPrefactor -> 1/(2 \[Pi])^D, PaXAnalytic -> True] //
FCHideEpsilon, {mN, \[Infinity], 0}] //
Normal) /. {SMP["Delta"] -> 0} // Simplify

(* They are different. While, IntHBPCB2 is right.*)

IntHBPCB2 - IntHBPCB // Expand // FullSimplify