**Next message:**Xiu-Lei Ren: "Re:Re:Re: Question about TID in FC9.2.0"**Previous message:**Vladyslav Shtabovenko: "Re: Question about TID in FC9.2.0"**In reply to:**Vladyslav Shtabovenko: "Re: Question about TID in FC9.2.0"**Next in thread:**Vladyslav Shtabovenko: "Re: Question about Subscript[E, 0](0,0,Overscript[p, _]^2,0,Overscript[p, _]^2,0,Overscript[p, _]^2,Overscript[p, _]^2,Overscript[p, _]^2,Overscript[p, _]^2,0,0,0,0,0)"**Reply:**Vladyslav Shtabovenko: "Re: Question about Subscript[E, 0](0,0,Overscript[p, _]^2,0,Overscript[p, _]^2,0,Overscript[p, _]^2,Overscript[p, _]^2,Overscript[p, _]^2,Overscript[p, _]^2,0,0,0,0,0)"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

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 Yangâ€“Mills Gravity (https://sites.google.com/site/yangmillsgravity123/)

----- Original Message -----

From: "Vladyslav Shtabovenko" <noreply@feyncalc.org>

To: feyncalc@feyncalc.org

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 -> {{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
*

*>>
*

*>
*

**Next message:**Xiu-Lei Ren: "Re:Re:Re: Question about TID in FC9.2.0"**Previous message:**Vladyslav Shtabovenko: "Re: Question about TID in FC9.2.0"**In reply to:**Vladyslav Shtabovenko: "Re: Question about TID in FC9.2.0"**Next in thread:**Vladyslav Shtabovenko: "Re: Question about Subscript[E, 0](0,0,Overscript[p, _]^2,0,Overscript[p, _]^2,0,Overscript[p, _]^2,Overscript[p, _]^2,Overscript[p, _]^2,Overscript[p, _]^2,0,0,0,0,0)"**Reply:**Vladyslav Shtabovenko: "Re: Question about Subscript[E, 0](0,0,Overscript[p, _]^2,0,Overscript[p, _]^2,0,Overscript[p, _]^2,Overscript[p, _]^2,Overscript[p, _]^2,Overscript[p, _]^2,0,0,0,0,0)"**Messages sorted by:**[ date ] [ thread ] [ subject ] [ author ]**Mail actions:**[ respond to this message ] [ mail a new topic ]

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