"Returning the list of remaining integrals" with TARCER

[CarolinaPerdomo]

Hi, good evening,

I am computing one of the two-loop diagrams for the quark self-energy of QCD (in this case, the "QuarkBubble").

After generating the amplitude with FeynArts and converted it to FeynCalc (and doing some trace evaluation) I got:

Now, I want to calculate the amplitude with TARCER. So,I used ToTFI[...] and TarcerRecurse[exp]:

Nevertheless, when I use TarcerExpand[], I got always the same output: "Returning the list of remaining integrals"

After reading the arXiv about TARCER, I think there is still something I did not understand. Why TARCER couldn't reduce those integrals?

If someone can help me with this, I am grateful.
C.

[vsht]

Hi,

Why TARCER couldn't reduce those integrals?

because those are your master integrals, so they can't be reduced any further.
It all makes sense, the integrals are a bubble, a sunrise and a dotted sunrise.

ints = {FAD[{p1 - q, m}, {p1 - p2, m}, {p2, m}], 
  FAD[{p1 - q, m, 2}, {p1 - p2, m}, {p2, m}], FAD[p1, {p1 - q, m}]}

tints = TarcerRecurse@ToTFI[#, {p1, p2}, {q}] & /@ ints

TarcerToFC[#, {p1, p2}] & /@ tints

Nevertheless, when I use TarcerExpand[], I got always the same output: "Returning the list of remaining integrals"

TarcerExpand is not really helpful here, since it contains only analytic results for a handful of integrals (cf. $BasisIntegrals)
Your integrals are off-shell, so here one anyhow needs to get the results from elsewhere (literature, other packages, ...)

Cheers,
Vladyslav

[CarolinaPerdomo]

Hi Vladyslav! thank you so much for answering my question, I am calmer now. Cheers!

[huansouza]

Hey @CarolinaPerdomo,

You can find the integrals you need in 0501132 and 0307101. If you are interested, I and some collaborators have been working with TARCER to compute such diagrams, you can take a look at our work here: 2105.12577. The Mathematica notebook is available at https://github.com/lehum/einstein-qed

Best wishes,

Huan.