Name: Jongping Hsu Date: 12/26/16-03:35:23 AM Z

Hi,Vladyslav,
Happy Holidays!

I need some more relations to check the consistency of the OneLoop result:
What is the relation between B0(p^2,0,0) and F=E0(0,0,p^2,0,p^2,0,p^2,p^2,p^2,p^2,0,0,0,0,0) ?

When I used TID, e.g., “ ampssPT = (TID[#, q, ToPaVe -> True, UsePaVeBasis -> True] & /@
JPamp) “, I got almost 20 new and unfamiliar functions, E3, E4,…E444,..D002, D333, etc.
Is there a source or reference that one can get the relation between them and, say, B(p^2,0,0)?
Thanks. JP

HSU Jongping,
Chancellor Professor
Department of Physics
Univ. of Massachusetts Dartmouth,
North Dartmouth, MA 02747. FAX (508)999-9115
http://www.umassd.edu/engineering/phy/people/facultyandstaff/jong-pinghsu/
recent monograph: Space-Time Symmetry and Quantum Yang–Mills Gravity (https://sites.google.com/site/yangmillsgravity123/)

-—- Original Message —–

From: “Vladyslav Shtabovenko” <[noreply_at_HIDDEN-E-MAIL]>
To: [feyncalc_at_HIDDEN-E-MAIL]
Sent: Sunday, December 25, 2016 2:57:28 PM
Subject: Re: Question about TID in FC9.2.0

>> 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…

Sorry, ignore this part. Somehow I completely forgot that the 1-loop library of Package-X is loaded not immediately but during the first call of PaXEvaluate.

So if you have already done some calculations with PaXEvaluate on a running kernel, then

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

is sufficient. On a fresh kernel just call PaXEvaluate once (with any input) and then it will work as well:

$LoadAddOns = {“FeynHelpers”};
«FeynCalc`
PaXEvaluate[1]
exp = PaXDiLog[2.7, 1] /. PaXDiLog -> X`DiLog

Cheers,
Vladyslav

Am 25.12.2016 um 20:33 schrieb Vladyslav Shtabovenko:
> 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 -> , 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
>>
>