# Computing the pole mass from a given MS mass?

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## Main Question or Discussion Point

Given a Yukawa coupling as a function of scale and a vev, how can I compute the corresponding pole mas?

Understandably most paper explain how from a measured pole mass one can compute the running mass, for example, Eq. 19 here. However I want to compute the pole mass from the running mass. In all formulas I can find the pole mass seems to depend on the scale, although it shouldn't, and thus I'm not sure which value I should use for the scale in the formula...

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Hepth
Gold Member
Sorry for the late reply. Did you ever figure out what to do here?

I had a think about it. I came up with the following:

1) It depends under what your yukawa coupling is running. Are you considering both yukawa and full gauge coupling dependence (g1,g2,gs) in the running y(mu)? Then I think the conversion depends on the choice of renormalisation scheme (all msbar, or part msbar part on-shell scheme).

For example, it could be that you choose to renormalise electroweak couplings/gauge boson masses in the on-shell scheme. Then, the vev should be mu-independent, then you can directly convert the yukawa into the msbar mass using an input value of vev (or eliminating in terms of GFermi or similar).

2) Then you can apply the MSbar -> Mpole conversion according to the equations hepth linked too. Then, the mu-dependence of your answer should be removed in this conversion (i.e. it doesn't matter which scale you do it at) and the answer for the pole mass should not depend on mu.

How far did you get with this? Let me know and I can help farther