Light dynamical fermions on the lattice: toward the chiral regime of QCD

Algorithmic and technical progress achieved over the last few years makes QCD simulations with light dynamical quarks much faster than before. As a result lattices with pions as light as 250--300 MeV can be simulated with the present generation of computers. I review recent conceptual and numerical progress in this field, with particular emphasis on results obtained and difficulties encountered in simulations with significantly smaller quark masses with respect to previous computations. I also attempt to compare physical results for pion masses and decay constants available to date in the two-flavour theory with expectations from chiral perturbation theory.Comment: Plenary talk given at XXIVth International Symposium on Lattice Field Theory Lattice2006(plenary), Tucson, Arizona, 23-28 July 2006. Submitted to PoS in October 200

Thermodynamics of strongly interacting plasma with high accuracy

The equation of state of $SU(3)$ Yang-Mills theory is investigated in the framework of a moving reference frame. Results for the entropy density, the pressure, the energy density, and the trace anomaly are presented for temperatures ranging from 0 to 230 $T_c$, with $T_c$ the deconfinement temperature. The entropy density is the primary observable that has been measured and form which the other thermodynamic quantities are obtained. At least 4 different values of the lattice spacing have been considered at each physical temperature in order to extrapolate to the continuum limit. The final accuracy is 0.5%, increasing to about 1% close to the phase transition. A detailed comparison with the results available in the literature is discussed.Comment: Proceedings of the 34th International Symposium on Lattice Field Theory - 24-30 July 2016 - Southampton, UK. PoS (LATTICE2016) 06

Atomic parity violation and the HERA anomaly

We show that the two scenarios able to explain the HERA anomaly --- a new leptoquark coupling or a new contact interaction --- predict new contributions to atomic parity violation. These corrections are sufficiently large and different that a feasible reduction in the dominant atomic theory uncertainty could give some hint in favour of one of the two scenarios.Comment: 4 pages. Reference added, PDG value of weak charge revise

Equation of state of the SU(33) Yang-Mills theory: a precise determination from a moving frame

The equation of state of the SU($3$) Yang-Mills theory is determined in the deconfined phase with a precision of about 0.5%. The calculation is carried out by numerical simulations of lattice gauge theory with shifted boundary conditions in the time direction. At each given temperature, up to $230\, T_c$ with $T_c$ being the critical temperature, the entropy density is computed at several lattice spacings so to be able to extrapolate the results to the continuum limit with confidence. Taken at face value, above a few $T_c$ the results exhibit a striking linear behaviour in $\ln(T/T_c)^{-1}$ over almost 2 orders of magnitude. Within errors, data point straight to the Stefan-Boltzmann value but with a slope grossly different from the leading-order perturbative prediction. The pressure is determined by integrating the entropy in the temperature, while the energy density is extracted from $T s=(\epsilon + p )$. The continuum values of the potentials are well represented by Pad\'e interpolating formulas, which also connect them well to the Stefan-Boltzmann values in the infinite temperature limit. The pressure, the energy and the entropy densities are compared with results in the literature. The discrepancy among previous computations near $T_c$ is analyzed and resolved thanks to the high precision achieved.Comment: 7 pages, 3 figures. A few sentences and one reference adde

Low-mode averaging for baryon correlation functions

The low-mode averaging technique is a powerful tool for reducing large fluctuations in correlation functions due to low-mode eigenvalues of the Dirac operator. In this work we propose a generalization to baryons and test our method on two-point correlation functions of left-handed nucleons, computed with quenched Neuberger fermions on a lattice with extension L=1.5 fm. We show that the statistical fluctuations can be reduced and the baryon signal significantly improved.Comment: 6 pages, talk presented at the XXIIIrd International Symposium on Lattice Field Theory, 25-30 July 2005, Trinity College, Dublin, Irelan