# Reduction of loop integrals in FeynCalc

I'd like to use the PaVeReduce function within FeynCalc in Mathematica to reduce a triangle integral down to bubbles and tadpoles. I found the wolfram help page about this function but I did not find what all the options meant with the result that I was unable to produce the reduction I wanted. Has anyone used this function in FeynCalc before?

I have used other software for this reduction and I know what the answer is so I'm just playing about with FeynCalc at the moment. I tried

 PaVeReduce[C0[0, m^2, m^2/y, 0, 0, m^2]] // TraditionalForm


but this didn't do the required reduction. I played about with the options too in

 SetOptions[PaVeReduce, A0ToB0 -> True, BReduce -> True, Collecting -> True, Dimension -> True, FCVerbose -> False, Factoring -> Factor2, IsolateNames -> False, Mandelstam -> {}, PaVeAutoReduce -> True, PaVeOrderList -> {}, WriteOutPaVe -> True]


but couldn't get the reduction to go ahead.

Thanks for any comments! There is also the possibility that I am using the wrong function because I know that Pass-Velt prescription is usually done for the reduction of tensor to scalar integrals and I'm trying to do a scalar to sum of simpler scalar integrals reduction.

• Best to ask here: feyncalc.github.io/forum Commented Sep 23, 2017 at 1:59
• If you use Package-X, and use the expansion pack PVReduce, you can get some result with PVReduce[PVC[0, 0, 0, 0, m^2, m^2/y, 0, 0, m], "IRDivCToB" -> True]. Commented Sep 23, 2017 at 3:27
• @QuantumDot Thanks! I see that to use PVReduce I need to request the download from the website, did I understand that correctly? Actually Package-X in itself might be good enough for what I want, does this package allow one to input a given scalar loop integral evaluated in dim reg say and get an analytic expression for it to all orders in epsilon?
– CAF
Commented Sep 23, 2017 at 11:49
• I've been looking for software that will provide me with the analytic expression for a scalar integral, not some numerical evaluation but rather the analytic expression to all orders in epsilon.
– CAF
Commented Sep 23, 2017 at 11:50
• Package-X does give analytic expressions, but not all orders in epsilon. So maybe you need PVReduce; then you can insert the all orders expression yourself after reducing. Commented Sep 23, 2017 at 14:01

## 1 Answer

As mentioned in the comments, you can use the Package-X expansion pack PVReduce to reduce Passarino-Veltman functions.

<<X
<<PVReduce

PVReduce[PVC[0, 0, 0, 0, m^2, m^2/y, 0, 0, m], "IRDivCToB" -> True]


PVReduce gives results that are correct to all orders in ϵ. But be careful of the fact that the factors of -4+d in the denominator lead to 1/ϵ poles multiplying the Passarino-Veltman functions.