Monday, February 16, 2015

Perspectives and Challenges in Lattice Gauge Theory, Day One

Hello from Mumbai, where I'm attending the workshop "Perspectives and Challenges in Lattice Gauge Theory" at the Tata Institute for Fundamental Research. I arrived on Sunday at an early hour, and had some opportunity to see some of the sights of Mumbai while trying to get acclimatized and jetlag-free.

Today was the first day of the workshop, which started with a talk by Gergely Endrődi on the magnetic response of isospin-asymmetric QCD matter. This is relevant both for heavy-ion collisions and for the astrophysics of neutron stars, where in both cases strong magnetic fields interact with nuclear matter that has more neutrons than protons. From analytical calculations it is known that free quarks would form a paramagnetic state of matter, whereas pions would yield diamagnetism. As QCD matter at low energies should be mostly a hadron gas, and at high temperatures a quark-gluon plasma, the expectation would be that the behaviour of QCD at zero chemical potential changes from diamagnetic to paramagnetic as the temperature increases. On the other hand, at zero temperature and non-zero isospin chemical potential, at small isospin chemical potential the magnetic susceptibility vanishes (by the "Silver Blaze" effect), before suddenly going negative from pion condensation when the chemical potential exceeds half the pion mass, and again going positive as the chemical potential is increased further. Lattice simulations confirm this overall picture, although the susceptibility remains finite at μI=1/2 mπ since the pions already start to melt rather than to condense into a superconductor).

After the coffee break, it was my turn to talk about recent work we have done at Mainz regarding the importance of excited-state effects on nucleon form factors. Briefly summarised, the splitting to the first excited state (nucleon+pion P-wave, or nucleon+2 pions S-wave) gets very small in the chiral regime, but the errors on the nucleon two- and three-point functions grow exponentially as the source-sink separation is increased, making it very hard to find a Euclidean time region of both clean ground-state signal and reasonable statistical precision. Treating the excited states using different methods (summation method and explicit two-state fits) yields indications hinting that the current discrepancy between the nucleon charge radius obtained from lattice simulations and experiment may be due mostly to excited-state effects.

This was followed by Andreas Schäfer speaking about much more ambitious hadron structure observables, namely Transverse Momentum Distributions (TMDs), Parton Distribution Functions (PDFs) and Generalised Parton Distributions (GPDs). Knowledge of these is important to clarify systematics for some of the LHC measurements, so lattice results could certainly have a huge impact here, but the necessary calculations appear quite involved.

After the lunch break, Stefan Dürr reviewed some of the newer inhabitants of the fermion zoo, namely firstly the Brillouin fermions obtained by replacing the standard discretisation of the Laplacian in the Wilson action with its Brillouin discretisation, and the symmetric derivative with its isotropic alternative, and secondly the staggered Wilson fermions of Adams (Adams fermions). In particular for heavier quark masses, the Brillouin fermions seem to do much better than standard Wilson fermions, including by giving a much more continuum-like dispersion relation.

After a more technical talk on simulating the Gross-Neveu model with Boriçi-Creutz fermions by Jinshu Goswami, Kalman Szabo gave a colloquium for a more general audience explaining the origin of mass from QCD, electromagnetism and the Higgs effect (which is roughly the order of importance for ordinary matter), and how to determine the proton-neutron mass difference (which is after all of great anthropic significance, since an even slightly smaller value would leave hydrogen atoms unstable under inverse β-decay, whereas a somewhat larger value would create too much of a bottleneck in the creation of heavier elements) on the lattice. The lattice results are certainly impressive both in terms of the theoretical and computational effort needed to obtain them and in the accuracy with which they reproduce the experimentally-known situation.

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