<!--
.. title: Top mass measurements and MC definitions -- an inexpert precis
.. slug: top-mass-measurements-and-mc-definitions----an-inexpert-precis
.. date: 2014-02-28 00:00:00
.. type: text
.. category: blog
-->

I was just recently notified that the world top mass combination uses "my" [MCnet review paper on MC
generators](http://arxiv.org/abs/1101.2599) 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...

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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.
