Name: Vladyslav Shtabovenko (email_not_shown)
Date: 12/25/16-08:33:00 PM Z


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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