Tdec failing with "The solution to the system of linear equations is incorrect" while using FCMultiLoopTID

[HBelusca]

• Your Mathematica version

11.3.0 for Microsoft Windows (64-bit) (March 7, 2018)

• Your FeynCalc version

9.4.0 master (fb9fc9a5935a3f18694d26df1b6076fe67c63e56)

• Did you try to reinstall FeynCalc (stable version) using the automatic installer to make sure that you have the latest bugfixes?

Using git master repo checkout

---

As part of some 2-loop calculation in the BMHV scheme for a self-energy (and containing loop of chiral fermions), the following integrand is generated:

FVD[l1, mu1] FVD[l1, mu2] FVD[l2, nu1] FVD[l2, nu2] FVD[l2, nu3]
    FAD[l1, l2, l2, l1 - p, l1 - p, l1 + l2 - p]

The opened Lorentz indices in the momenta come from the uncontraction step, made in FCMultiLoopTID[], because these momenta were originally contracted with 4-dimensional metrics.

Due to the high number of indices this triggers the usage of Tdec, which unexpectedly fails:

<snip...>

Requesting integral of type(l1  \[Mu]1
l1  \[Mu]2
l2  \[Nu]1
l2  \[Nu]2
l2  \[Nu]3

){FeynCalc`Tdec`Private`extMom(p)}in TIDL

Unfortunately, this decomposition formula is not available in TIDL.

Tdec::slow: Tdec is computing a decomposition that is not available in TIDL. This might take quite some time. If this integral often appears in your computations, it is recommended to compute it once and then save the result to the TIDL directory.

< ... snip ...>

During evaluation of In[38]:= ReplaceAll::reps: {Dispatch[FerSolve({....})]} is neither a list of replacement rules nor a valid dispatch table, and so cannot be used for replacing.

During evaluation of In[38]:= Tdec::failmsg: Error! TID has encountered a fatal problem and must abort the computation. The problem reads: The solution to the system of linear equations is incorrect.

Out[38]= $Aborted

</snip>

[vsht]

But

FCMultiLoopTID[
 FVD[l1, mu1] FVD[l1, mu2] FVD[l2, nu1] FVD[l2, nu2] FVD[l2, nu3]
  FAD[l1, l2, l2, l1 - p, l1 - p, l1 + l2 - p], {l1, l2}]

works fine, right? And why does it use FerSolve in your case?

[HBelusca]

Heh no, it doesn't work, that's the problem! See the attached notebook (in the zip) where I have enabled full verbosity. I have no idea why FerSolve is used. FCMultiLoopTID_Tdec_error.zip

[vsht]

Sorry, should be now fixed.

Note to myself: Don't mix private stuff with stuff in the master branch. Create a private repo for that.

[HBelusca]

Confirmed fixed! Thanks for your help!

[vsht]

Since there seem to be no further issues related to the fix, I'm closing this bug.