Top mass measurements and MC definitions -- an inexpert precis

I was just recently notified that the world top mass combination uses "my" MCnet review paper on MC generators to justify stating that the definition of the top quark mass used in all (!) event generators is equivalent to the "pole" mass.

I've heard that statement very often, but not backed up by anything more concrete, so I was interested to read this section of the paper (Appendix C, starting on p184 of the PDF), which turns out to be rather good, interesting, and elegantly presented. Not to mention slightly embarrassing that I hadn't read it before, given that it has my name on the front! (In my defence, I did write some of this paper, just not that bit. I suspect most of the authors haven't read everything in it.)

Anyway, it definitely does not say that MC mass equals pole mass, so I thought it might be interesting to post my explanation of what it does say, at least as far as a dumb fence-sitting experimentalist/MC guy like myself can understand...

The argument is that the pole mass is in a scheme of asymptotically long-distance physics, i.e. an isolated particle with only self-interactions. However, that involves integrating terms with alpha_s at long distances, including the non-perturbative region where it diverges: this introduces the "renormalon ambiguity" of order LambdaQCD on any pole scheme quantity.

By comparison it can be shown that the renormalon ambiguity disappears (is cancelled by the same term in the inter- quark potential) in short-distance schemes like MSbar. This use of the inter-quark potential is why the statement is made that the ttbar cross-section is connected unambigously to the MSbar mass. I think once more exclusive properties of one top are looked at, this cancellation is no longer guaranteed and hence a discussion about the meaning of the MC top mass is needed... but that is rather an extrapolation on my part.

The final step is to argue that due to generator treatments of shower cutoffs, the top width, etc. the "MC scheme" is somewhere in-between the short-distance MSbar-type schemes and the long-distance pole scheme. This is roughly quantified by using the equation given (with unknown, assumed order-unity coefficients) for perturbatively relating short-distance schemes to the pole one (i.e. adding contributions including the renormalon term), and placing the "MC scheme" at a scale of about 1 GeV where the shower cutoff lives (i.e. not seeing much of the renormalon region). This gives the estimate that the true pole mass is of order 1 GeV higher than the mass which would be obtained by template matching to MC generator parameters -- the latter being what has so far been done experimentally. The dm = 1 GeV figure is an order of magnitude estimate, and would depend in detail on the way that the generator behaves -- including to some extent the shower, hadronization and other soft physics.

So any statement that this paper claims m_MC = m_pole is unjustified. The true claim is that the generator mass is neither a pole mass nor e.g. an MSbar mass, but something in-between whose exact relation to either is unknown. And as the first and last paragraphs say " this application warrants a deeper investigation of precisely how the top quark mass is de fined... Since the current experimental uncertainty is 1:1 GeV, clarifying this relation clearly demands more attention." Indeed.


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