**Next message:**Vladyslav Shtabovenko: "Re: Question about TID in FC9.2.0"**Previous message:**Vladyslav Shtabovenko: "Re: Maybe a error at OneLoop"**In reply to:**Xiu-Lei Ren: "Re: Re: Question about TID in FC9.2.0"**Next in thread:**Vladyslav Shtabovenko: "Re: Question about TID in FC9.2.0"**Reply:**Vladyslav Shtabovenko: "Re: Question about TID in FC9.2.0"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

Dear Xiu-Lei,

actually, when doing the expansion by the means of Package-X, the LO

coefficient of the 1/mN expansion turns out to be zero (provided that I

got your example right):

SPD[p4, p4] = mN^2;

XC0 = C0[SPD[p4], SPD[q], SPD[p4 + q], mN^2, mpi^2, mpi^2] //

ExpandScalarProduct;

XC0Re = PaXEvaluate[XC0, PaXC0Expand -> True,

PaXSeries -> {{mN, Infinity, 0}}, PaXAnalytic -> True] // Normal

Doing the expansion with Series afterwards

SPD[p4, p4] = mN^2;

XC0 = C0[SPD[p4], SPD[q], SPD[p4 + q], mN^2, mpi^2, mpi^2] //

ExpandScalarProduct;

XC0Re = PaXEvaluate[XC0, PaXC0Expand -> True] // Normal;

Series[XC0Re, {mN, Infinity, 0}] // Normal // Simplify

produces several suspicious terms, like Sqrt[-SPD[q,q]]. As you probably

know, Mathematica is not always careful when choosing the branch cuts of

logs and square roots and does not really provide options to control

that consistently, so I would rather trust the output of Package-X

(which takes care of those things in a special way internally) than the

output of Series.

By the way, the author of Package-X has released several fixes

in the meantime (ver 2.0.3 being the most current). One can update

Package-X manually, by downloading the tarball from

packagex.hepforge.org or via FeynHelpers' installer

Import["https://raw.githubusercontent.com/FeynCalc/feynhelpers/master/\

install.m"]

InstallPackageX[]

As to the second part of your question:

PaXDiLog is just a placeholder that for the DiLog of Package-X. Its

relation to PolyLog is described in 1503.01469, Sec VI.

Unfortunately, at the moment one cannot evaluate it numerically directly

from FeynHelpers (while developing the add-on my main focus were

symbolic evaluations). However, you can easily do something like

exp = PaXDiLog[2.7, 1] /. PaXDiLog -> X`DiLog

Export["exp.m", exp]

Quit[]

<< X`

Import["exp.m"]

to obtain the numerical value from Package-X. I'll contact the developer

of Package-X to see if we can find a better solution...

I agree that PaXDiLog[Complex[-1,-6],-0.2] does not look correct at all.

Could you provide a minimal working code example that generates this

weird expression?

I also wish you happy holidays.

Cheers,

Vladyslav

Am 25.12.2016 um 10:51 schrieb Xiu-Lei Ren:

*> Dear Vladyslav,
*

*>
*

*> Thank you very much for your quick reply. It helps a lot.
*

*>
*

*> However, when i try to obtain the analytic expressions of triangle diagram mentioned in the previous email, I also encountered two questions about PaXDiLog.
*

*>
*

*> In order to avoid unexpected results when performing Dimension -> 4, I use the recommended FeynHelper--Package-X.
*

*>
*

*> When I do this, the treatment of pave coefficient C0 is necessary.
*

*> In my case, (I am handling the two-nucleon scattering with two-pion exchange.
*

*> mN, mpi deonte as nucleon and pion masses, p4 is the momentum of outgoing nucleon, q is the transfer momentum between two nucleons.)
*

*>
*

*> XC0 = C0[p4^2, q^2, (p4+q)^2, mN^2, mpi^2, mpi^2]
*

*>
*

*> should be replaced by using
*

*>
*

*> XC0Re = PaXEvaluate[XC0, PaXC0Expand -> True]//Normal
*

*>
*

*> Apparently, the output is lengthy with conditions.
*

*>
*

*> Then, perform the 1/mN expansion,
*

*>
*

*> Series[XC0Re, {mN, infty, 0}]//Normal
*

*>
*

*> The result always contains Li2 functions (PaXDiLog).
*

*>
*

*> 1) How one can transfer PaXDiLog to PolyLog?
*

*>
*

*> Furthermore, when I do the numerical evaluation for checking,
*

*> I also find another problem about PaXDiLog.
*

*>
*

*> 2) e.g. PaXDiLog[Complex[-1,-6],-0.2], it cannot give a numerical value.
*

*>
*

*> Could you kindly let me know how to handle these problem?
*

*>
*

*> Merry Christmas and happy new year.
*

*>
*

*> Cheers,
*

*> Xiu-Lei
*

*>
*

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