Rho Meson Decay into pi+pi- on Asymmetrical Lattices

Abstract

The computation of the lowest-lying hadron masses was the earliest success of lattice QCD. Current spectroscopy is faced with the task of computing excited-states. This is particularly challenging when excited-states appear as scattering resonances. In this case, the resonance parameters have to be determined by studying the energies of the scattering states. Currently it is only computationally feasible to compute resonances of the simplest systems.

In our work, we carry out a calculation of the ρ(770) resonance seen in the isospin l = 1 two-pion system in the l = 1 channel. To determine the resonance parameters, we compute the scattering phase shifts from the two-pion spectrum using Luscher's formula. Unlike other studies which employ the moving frame formalism, we use lattices with one spatial direction elongated. To vary the momentum of the two-pion state, we adjust the length of the elongated direction. With this approach, the two-pion momentum can be tuned more finely, which allows one to map out the resonance more accurately.

In this work, we employed nHYP-smeared clover fermions with two mass-degenerate quarks. The lattice computations were carried out on large elongated lattices with spatial volumes ≥ 3³ fm³. We carried out an exploratory quenched study and found the two-pion spectrum to be compatible with the results obtained using dynamical fermions. Our results showed a disagreement with the physical decay at the level of 20% which is typical for quenched simulations. After completing the quenched study, we recomputed the resonance parameters on fully dynamical gauge configurations with a pion mass of 304(2) MeV. We found a value m_ρ = 827(3)(5) MeV and g_ρππ = 6.67(42) for the resonance mass and coupling constant. Our results are consistent with other lattice studies at similar pion masses and are in good agreement with the prediction from unitarized Chiral Perturbation Theory at NLO. The scattering phase shifts we computed are more evenly distributed throughout the resonance than other studies, and the uncertainty in our measurements is equal to or better than current lattice results at similar pion masses.