Friday, July 28, 2006

Lattice 2006 -- Day Four

Hello again from Tucson. Today started off somewhat unusual -- with rain, clouds and mist! So, no breakfast in the shade on the terrace; we didn't have to go hungry, though, as it was just relocated to the dining room instead.

The first plenary session of the morning was chaired by Anthony Williams. The first speaker was Kostas Orginos, who talked about recent lattice results on nucleon structure. Nucleons are tricky, because they have only light quarks, and it is known that the sea quarks actually play a bigger role than the valence quarks in determining the structure of the nucleons. However, with a lot of hard work and clever methods, people have made a lot of progress towards getting accurate results for the nucleon structure functions, momenta of generalised parton distributions, and various other structure-related quantities, and these results may one day soon help to lead to an understanding of e.g. the proton spin crisis.

The second speaker was Christian Schmidt, who spoke about lattice QCD at finite density. As mentioned yesterday, finite density QCD is hard on the lattice, because the action becomes complex and direct Monte Carlo simulations are no longer possible at non-zero chemical potential μ. The way to avoid this sign problem lies in one or another of a number of neat tricks such as reweighting configurations obtained at μ=0 to a finite value of μ, measuring Taylor expansions around μ=0 and resumming the series, simulations at imaginary μ (where the action remains real) with subsequent extrapolation to real μ, or some other method. A fair number of results exist now in this field, and while the quantitative precision still seems fairly low, there appears to be fair agreement on the qualitative features of the phase diagram. For large μ, however, new methods appear to be needed.

After the coffee break, the second plenary session, chaired by Sinya Aoki, had three speakers: First was Pilar Hernández, who reported on progress she and her collaborators had made towards understanding the ΔI=1/2 rule. This rule, which states that Kaon decays in which isospin changes by more than 1/2 are suppressed by a factor of approximately 20, is one of the longest-standing mysteries in QCD. Resolving it will require putting together a lot of work and know-how from both lattice QCD and chiral perturbation theory, and the people working on it seem to be far from a resolution in spite of a lot of recent progress.

Next was Michael Clark speaking about the Rational Hybric Monte Carlo (RHMC) algorithm. This algorithm is a variation on the well-known HMC algorithm and uses a rational approximation to maintain the exact nature of the HMC algorithm (which is needed in a many cases), while outperforming the Polynomial HMC (PHMC) algorithm through the better approximation properties of rational functions as opposed to polynomials. Apparently, with the proper implementation, this algorithm can push Wilson fermions into a speed range where they become competitive with staggered fermions.

Finally, Mikko Laine talked about warm dark matter (WDM) and hot QCD. One interesting candidate for a WDM particle are sterile right-handed neutrinos. These would have been created thermally in the early universe. As it turns out, for right-handed neutrino masses in the keV range, the production range peaks at temperatures of around the QCD scale, so that QCD contributions to the production rate, e.g. via u + d --> e- + νe, νe --> N1 might be dominant.

After lunch, there were parallel sessions again, featuring amongst others my talk (which went fine, thanks for asking) about our recent work on determining the QCD/NRQCD matching coefficients for leptonic widths of heavy quarkonia to O(αsv2) for realistic lattice NRQCD actions.

After the parallel sessions, we heard this year's keynote talk, delivered by Ann Nelson, who extended an invitation to all lattice theorists to work on beyond-the-Standard-Model physics, where models such as composite Higgs models could benefit from lattice simulations.

The day closed with dinner. There are going to be more plenary talks tomorrow, but you will have to wait for me to get back to Regina before I can report about them.