Name: Vladyslav Shtabovenko (email_not_shown)
Date: 12/19/16-08:45:00 AM Z


Hi,

Package-X by default does not want to evaluate the most general cases of
C0 and D0, as the expressions turn out to be quite large and
complicated, while usually the number of cases where people really need
an *analytic* result for that is quite small. Nevertheless, it is of
course still possible using X's options Explicit0, C0Expand and D0Expand
(for the boxes). With FeynHelpers you can just use

In[] PaXEvaluate[C0[0, 0, mH^2, ma^2, mb^2, ma^2], PaXC0Expand -> True]

Out[] (1/(2 mH^2))(Log[(
    ma^2 (3 mH^2 - Sqrt[-4 ma^2 mH^2 + mH^4]) + (mb^2 + mH^2) (-mH^2 +
        Sqrt[-4 ma^2 mH^2 + mH^4]))/(2 ma^2 mH^2)]^2 -
   Log[(ma^2 (mH^2 - Sqrt[-4 ma^2 mH^2 + mH^4]) +
     mb^2 (mH^2 + Sqrt[-4 ma^2 mH^2 + mH^4]))/(2 ma^2 mH^2)]^2 -
   2 PolyLog[2, ((ma - mb)^2 (ma + mb)^2)/(
     ma^4 - 2 ma^2 mb^2 + mb^4 + mb^2 mH^2)] +
   2 PolyLog[2, ((ma^2 - mb^2) (ma^2 - mb^2 - mH^2))/(
     ma^4 - 2 ma^2 mb^2 + mb^4 + mb^2 mH^2)] +
   2 PolyLog[
     2, ((ma^2 - mb^2 - mH^2) (-mH^2 + Sqrt[-4 ma^2 mH^2 + mH^4]))/(
     2 ma^2 mH^2)] +
   2 PolyLog[
     2, ((ma^2 - mb^2) (2 ma^2 - 2 mb^2 - mH^2 +
        Sqrt[-4 ma^2 mH^2 + mH^4]))/(
     2 (ma^4 - 2 ma^2 mb^2 + mb^4 + mb^2 mH^2))] -
   2 PolyLog[
     2, ((ma^2 - mb^2 - mH^2) (2 ma^2 - 2 mb^2 - mH^2 +
        Sqrt[-4 ma^2 mH^2 + mH^4]))/(
     2 (ma^4 - 2 ma^2 mb^2 + mb^4 + mb^2 mH^2))] -
   2 PolyLog[2, ((ma^2 - mb^2) (mH^2 + Sqrt[-4 ma^2 mH^2 + mH^4]))/(
     2 ma^2 mH^2)])

Cheers,
Vladyslav

Am 19.12.2016 um 05:48 schrieb Michael Park:
> Hi. I have been having a lot of trouble trying to compute the scalar C0 integral for general masses using the Package-X routines.
>
> Using the FeynCalc interface
>
> in: PaXEvaluate[C0[0,0,mH^2,ma^2,ma^2,ma^2]]
>
> out: log^2((-mH^2+Sqrt[mH^4-4 mH^2 MT3^2]+2 MT3^2)/(2 MT3^2))/(2 mH^2)
>
> ...however, when I try more general masses it seems to give up
>
> in: PaXEvaluate[C0[0,0,mH^2,ma^2,mb^2,ma^2]]
> out: C0[0,0,mH^2,ma^2,mb^2,ma^2]
>
> Similarly, if I use the straight Package-X routines it gives me a reasonable answer for massless final states and one flavor in the loop
>
> in: LoopIntegrate[Spur[\[DoubleStruckOne]],
> q, {q - k1, ma}, {q + k2, ma}, {q, ma}] /. {k1.k1 -> 0,
> k2.k2 -> 0, q.q -> mH^2, q -> k1 + k2,
> k1.k2 -> (mH^2 - 2 mW^2)/2} /. {LTensor[k1, \[Mu]] -> 0,
> LTensor[k2, \[Nu]] -> 0} // LoopRefine // Simplify
> out: (2 Log[(2 ma^2 - mH^2 + 2 mW^2 +
> Sqrt[(mH^2 - 2 mW^2) (-4 ma^2 + mH^2 - 2 mW^2)])/(
> 2 ma^2)]^2)/(mH^2 - 2 mW^2)
>
> ..however if I make the final state particles massive or if I enter more general loop masses, the computation seems to quit
>
> I was wondering if there was any way to handle these more complicated C0 integrals? Thanks very much!
>



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