ρ resonance from the I = 1 ππ potential in lattice QCD

We calculate the phase shift for the I = 1 ππ scattering in 2+1 flavor lattice QCD at mπ = 410 MeV, using all-to-all propagators with the LapH smearing. We first investigate the sink operator independence of the I = 2 ππ scattering phase shift to estimate the systematics in the LapH smearing scheme in the HAL QCD method at mπ = 870 MeV. The difference in the scattering phase shift in this channel between the conventional point sink scheme and the smeared sink scheme is reasonably small as long as the next-toleading analysis is employed in the smeared sink scheme with larger smearing levels. We then extract the I = 1 ππ potential with the smeared sink operator, whose scattering phase shift shows a resonant behavior (ρ resonance). We also examine the pole of the S-matrix corresponding to the ρ resonance in the complex energy plane.

LOCATION, CORRELATION, RADIATION: WHERE IS THE σ, WHAT IS ITS STRUCTURE, AND WHAT IS ITS COUPLING TO PHOTONS?

Scalar mesons are a key expression of the infrared regime of QCD. The lightest of these is the σ. Now that its pole in the complex energy plane has been precisely located, we can ask whether this state is transiently [Formula: see text] or [Formula: see text] or a multi-meson molecule or largely glue? The two-photon decay of the σ can, in principle, discriminate between these possibilities. We review here how the γγ → π+π-, π0π0 cross-sections can be accurately computed. The result not only agrees with experiment, but definitively fixes the radiative coupling of the σ. This equates to a two-photon width of (4.1 ± 0.3) keV, which accords with the simple nonrelativistic quark model expectation for a [Formula: see text], [Formula: see text] scalar. Nevertheless, robust predictions from relativistic strong coupling QCD are required for each of the possible compositions before we can be sure which one really delivers the determined γγ coupling.