Thursday, November 24, 2005

Dirac eigenvalues

In a recent talk entitled "Fun with Dirac eigenvalues", Michael Creutz discusses some issues arising in the study of the Dirac spectrum. The discussion involves a number of deceptively simple arguments on a rather complicated matter, and you should read it (and think about it) for yourself. The chiral condensate and the Banks-Casher relation, in particular, are discussed in a way that is obviously intended to first confuse, then astonish and finally enlighten the reader. Other points which I never thought about before are how the number of flavours influences the density of low-lying eigenvalues via the effects of the high eigenvalues on the gauge fields, and why topologically non-trivial configurations' contributions to correlation functions can be a problem in numerical simulations.

The discussion is kept in the context of the overlap operator, which makes sense for an analytical discussion of chiral properties. For an investigation of many of these issues in the context of the more widely used staggered quarks, see this paper by members of the HPQCD and UKQCD collaborations, where they show that, with improvement, staggered quarks exhibit all the properties expected of the Dirac spectrum, including obeying the Atiyah-Singer index theorem.

Sunday, November 20, 2005

Comment spam

After removing all the comment spam that had accumulated on this blog (one post had received 83 spam comments!), I feel I need a little amusement. So let me for a moment entertain the thought that all this spam wasn't posted by mindless bots, but was manually produced by actual human individuals responding to the article in question.

First conclusion: the literacy crisis is far worse than anybody is willing to admit! I mean, if somebody replies to "This is just a test of my new gnome blogger app" with "great post, keep up the good work," they either have a very warped sense of humor, or their reading comprehension caps out at two-word sentences, to say nothing of the poor people who seem to read messages about cheap mortgages, anatomical "enhancements" or cracked software downloads into this blog, and whose problems might require the attention of not just an elementary school teacher, but also that of a clinical psychologist.

Second conclusion: some people seem to feel sexually excited by Lattice QCD! The number of self-professed "hot girls" offering themselves for dates and more in reply to posts about fermion discretization issues is truly staggering ... but Matthew is married, and I still have certain standards, which include requiring a basic command of orthography and punctuation (or at least the ability to use a spelling checker!) from any potential date. Sorry, girls!

Third conclusion: The world is even weirder than I thought. One comment advertised photography courses, and was kept entirely in Greek; numerous comments consisted of fairly random French words in alphabetical order; and one person repeatedly urged the world to visit his ##KEYWORD HERE## site (located at http://www.yoururlhere/). What is that supposed to tell us? (Other than that some people are too stupid even to spam - remember, we are pretending these comments were real!)

Hmm, this counterfactual leads us to a bad, half a good (who doesn't dream of a world in which top models chase after theoretical physicists? -- but where's the fun if they are too dumb to form a coherent sentence?) and an outright weird difference to the real world. I suppose that can be counted as empirical evidence that Leibniz was right when he postulated that the real world was the best of all possible worlds. Oh, well ...

Friday, November 18, 2005

Was Einstein right? -- Tests of General Relativity

This is not directly related to Lattice QCD, but it is interesting nevertheless.

There recently was a public lecture entitled "Was Einstein right?" here at Regina, given by Clifford Will. Unfortunately bad weather meant he couldn't be here in time to give the technical version of this to the physics department, but a printed version of what he probably would have said can be found in this review. It appears that General Relativity is beginning to approach the same kinds of precision in its tests that we know from QED.

A new determination of light quark masses

In a recent paper (hep-ph/0511160), members of the HPQCD collaboration have presented the most precise determination of the light (up, down and strange) quark masses to date.

This required both extensive unquenched simulations of QCD using some of the lightest (and hence hardest to work with) quark masses used so far, and a massive perturbative calculation at the two-loop order. The perturbative calculation is needed in order to connect the lattice-regularized bare quark masses to the masses as defined in the usually quoted MSbar scheme. The bare-quark masses required as input to the perturbative calculation come from simulations performed by the MILC collaboration, who use a highly-efficient formalism with so-called ``staggered'' quarks, with three flavors of light quarks in the Dirac sea.

Putting all these ingredients together, they find the MSbar masses at a scale of 2 GeV to be $$m_s = 87(0)(4)(4)(0)$$ MeV, $$m_u = 1.9(0)(1)(1)(2)$$ MeV and $$m_d = 4.4(0)(2)(2)(2)$$ MeV. The respective uncertainties are from statistics, simulation systematics, perturbation theory, and electromagnetic/isospin effects.

This means that the errors on the still rather contentious strange quark mass, for which a number of incompatible results exist, have been greatly reduced. This is a very major result, and a great success for Lattice QCD.

Thursday, November 17, 2005

New poster

Announcing a new lattice QCD blogger. Everybody please welcome Life on the Lattice's new co-blogger Georg von Hippel. Georg is a postdoc at the University of Regina, with similiar research interests to myself. This is now officially the worlds first group blog devoted to Lattice QCD.


Wednesday, November 09, 2005

A couple of brief things

It's been busier than usual the past few days. So this will be a cheap "links only" post. Hat tip to Georg for pointing out this nice writeup of a public lecture by Frank Wilczek. There's lots of good stuff in there, the highlight is when he refers to the calculation of the hadron spectrum from lattice QCD as "is one of the greatest scientific achievements of all time." Who am I to disagree with a nobel prize winner?

Also, for those interested in the computing behind lattice QCD, there's a short writeup in the latest Symmetry magazine, here. There's some details on both the efforts to create custom machines, and the use of off the shelf PC clusters.