**Next message:**V. Shtabovenko: "Fwd: Re: A possible bug: PaXSeries (FeynHelpers)"**Previous message:**X.-L.Ren: "A possible bug: PaXSeries (FeynHelpers)"**In reply to:**X.-L.Ren: "A possible bug: PaXSeries (FeynHelpers)"**Next in thread:**X.-L. Ren: "Re: A possible bug: PaXSeries (FeynHelpers)"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

Hi,

I think this is related to the way how Package-X expands B-functions

(using LoopRefineSeries), when the expansion parameter multiplies the

PaVe function. Consider the following code:

<< X`

diff = Table[

{(LoopRefineSeries[

mN^pow PVB[0, 0, mN^2, mN, mPi], {mN, Infinity, 0},

Analytic -> True] // Normal),

Series[

mN^pow (DiscExpand[LoopRefine[PVB[0, 0, mN^2, mN, mPi]]]), {mN,

Infinity, 0}] // Normal}, {pow, 0, 3}]

Simplify[PowerExpand[First[#] - Last[#]]] & /@ diff

% // TableForm

For mN^0 both expansions coincide exactly, but when the power is

different from 0, the difference between the two expansions is finite

and may also involve IR singularities. The case pow=2 is relevant for

your expansion.

In general, the expansion of an already computed integral (where you

implicitly assume mN to be finite) and the expansion on the level of the

Feynman parameters, where you are expanding the Feynman parameter

integral (possibly multiplied by an expansion parameter) first and the

compute it are not always the same.

This is because the expansion may generate new singularities that can be

properly regularized when evaluating Feynman parameter integrals but not

afterwards.

However, the current behavior of Package-X looks a bit strange to me,

so I'm not quite sure if this is intended or a bug.

I added Hiren Patel, the developer of Package-X to the CC of this mail,

so that he may explain us this behavior of his tool.

Cheers,

Vladyslav

Am 12.09.2017 um 08:04 schrieb X.-L.Ren:

*> 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
*

*>
*

**Next message:**V. Shtabovenko: "Fwd: Re: A possible bug: PaXSeries (FeynHelpers)"**Previous message:**X.-L.Ren: "A possible bug: PaXSeries (FeynHelpers)"**In reply to:**X.-L.Ren: "A possible bug: PaXSeries (FeynHelpers)"**Next in thread:**X.-L. Ren: "Re: A possible bug: PaXSeries (FeynHelpers)"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

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