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


Dear Vladyslav,

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

I am looking forward to your reply.
Thank you in advance.

Best regards,
Xiu-Lei



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