Cancellations in cross section with EW gauge bosons

Asked by Jan Heisig

Hi Olivier, Hi All,

I'm computing the XS for a 2 to 4 annihilation process for dark matter:

DM DM > w+ w+ w- w-

It's the simple singlet scalar Higgs-portal model. But probably the model does not matter too much.

The thing is that there are large cancellations of the contributions of different diagrams in the process. You can see this when you leave out some diagrams. Then the XS grows like m_DM^2 which is basically a growth like E^2 as I keep the velocity fixed while varying m_DM. I guess that's very similar to what happens in vector boson scattering when you leave out the Higgs-exchange diagram. There you have a similar growth like E^2 if I recall correctly.

Now, here comes the issue. Even if I take into account all diagrams at a given order (rendering the XS a meaningful, gauge-invariant quantity), at some point for large m_DM (around m_DM=10^5GeV) the mDM^2 growth of the XS kicks in. But only if I choose unitarity gauge whereas for Feynman gauge the XS proceeds behaving as expected, namely decreases further towards large m_DM.

I assume that in unitary gauge, cancellations are harder to be recognised by MG. (I guess unitary gauge is not a good choice for E>>M_W anyway.) So I reckon we end up with numerical remnants from imperfect cancellations that grow like m_DM^2 (and just become larger than the actual XS for masses above 10^5 GeV). In contrast, for Feynman gauge, the limit E>>m_W is probably less critical and cancellations are not an issue.

Do you think that line of reasoning is correct? Or should MG do a perfect job regarding the cancellations even in unitary gauge, so that the issue described above should make me worry about something else being a problem here?

Thanks and best wishes

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Olivier Mattelaer (olivier-mattelaer) said :

I know that calchep was(or is) using feynman gauge to help numerical precision.

So this is not impossible but this sounds quite weird for me. The point is that feynman/unitary gauge only change the gauge for the propagator and therefore you just split the unitary gauge propagator into two diagram (because of the goldstone) and typically this does not have huge impact.

A more critical issue, is typically the width of the particle within the diagram. Using a fix width scheme (our default) does break gauge invariance and therefore leads to term growing in energy.
Since 2.8.0, we have decide to remove the width for all T-channel propagator which is not fully consistent but was helping to remove some of the gauge breaking term in some cases. ( You can actually desactivate that trick to put back those width).

Obviously, a more consistent method is to set all width to zero (when possible) or to use the complex mass scheme which restore gauge invariance.



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