Lattice QCD and the two-photon decay of the neutral pion

Two-photon decays probe the structure of mesons and represent an important contribution to hadronic light-by-light scattering. For the neutral pion, the decay amplitude tests the effects of the chiral anomaly; for a heavy quarkonium state, it measures the magnitude of its wavefunction at the origin. We rederive the expression of the decay amplitude in terms of a Euclidean correlation function starting from the theory defined on the torus. The derivation shows that for timelike photons the approach to the infinite-volume decay amplitude is exponential in the periodic box size.Comment: 18 pages, no figure

Lattice QCD and the Timelike Pion Form Factor

We present a formula that allows one to calculate the pion form factor in the timelike region 2mpi <= sqrt{s} <= 4mpi in lattice QCD. The form factor quantifies the contribution of two-pion states to the vacuum polarization. It must be known very accurately in order to reduce the theoretical uncertainty on the anomalous magnetic moment of the muon. At the same time, the formula constitutes a rare example where, in a restricted kinematic regime, the spectral function of a conserved current can be determined from Euclidean observables without an explicit analytic continuation.Comment: 4 pages, 1 figure; corrects a factor 2 in Eq. (6) over the published versio

QCD at non-zero temperature from the lattice

I review the status of lattice QCD calculations at non-zero temperature. After summarizing what is known about the equilibrium properties of strongly interacting matter, I discuss in more detail recent results concerning the quark-mass dependence of the thermal phase transition and the status of calculations of non-equilibrium properties.Comment: 20 pages, 2 figures, proceedings of the Lattice 2015 conference in Kobe, Japa

The spectrum of SU(N) gauge theories in finite volume

We compute the spatial-volume dependence of the spectrum of 4D SU(3 <= N <= 6) gauge theories by lattice Monte-Carlo techniques. Setting the scale with the string tension, the spatial volume is L^3 with 0.78fm <= L <= 2.3fm. The Euclidean `time' direction is kept large enough to be considered infinite and the boundary conditions are periodic in all four dimensions. We study the mixing of torelon pairs with the scalar and tensor glueballs, using a 2x2 Hamiltonian based on large-N counting rules. Looking to the other symmetry channels, finite-volume effects on the glueball spectrum are already surprisingly small in SU(3), and they become rapidly smaller as N is increased: several low-lying SU(6) states have no finite-volume corrections at the 1-2% level, at least down to L=0.9fm. We discuss the relation of this work with analytic calculations in small and intermediate volume, and with Eguchi-Kawai reduction in the planar limit.Comment: 20 pages, 5 figures; major rewriting of section 2, and other minor improvements: version accepted in JHE