Rho resonance parameters from lattice QCD

Abstract

We perform a high-precision calculation of the phase shifts for π-π scattering in the I = 1, J = 1 channel in the elastic region using elongated lattices with two mass-degenerate quark flavors (N f = 2). We extract the ρ resonance parameters using a Breit-Wigner fit at two different quark masses, corresponding to mπ = 226 MeV and mπ = 315 MeV, and perform an extrapolation to the physical point. The extrapolation is based on a unitarized chiral perturbation theory model that describes well the phase-shifts around the resonance for both quark masses. We find that the extrapolated value, mρ = 720(1)(15) MeV, is significantly lower that the physical rho mass and we argue that this shift could be due to the absence of the strange quark in our calculation.

Coupled-channel Dπ, Dη and D s K ¯ $$ {D}_s\overline{K} $$ scattering from lattice QCD

“…In particular, the Lüscher method and its extensions for relating finite-volume spectra to scattering amplitudes are now well established for elastic [5][6][7][8][9][10][11][12][13][14] and coupled-channel [15][16][17][18][19] hadron-hadron scattering. These methods have been demonstrated in a number of applications, notably for the ρ-resonance seen in P -wave ππ scattering [20][21][22][23][24][25][26][27][28][29], and for the σ resonance seen in S-wave ππ scattering [30]. It has also recently been shown that, with sufficiently extensive and precise spectra, information on coupled-channel hadron-hadron scattering amplitudes can be obtained [26,[31][32][33] -this is crucial for understanding highly excited states that are typically kinematically permitted to decay into several channels.…”

Chiral extrapolations of the ρ(770) meson in Nf=2+1 lattice QCD simulations

“…A simulation close to the physical point was carried out by the RQCD Collaboration [18]. The GWU group extracted very precise phase shifts for two different pion masses (M π ≈ 226 MeV and ≈ 315 MeV) [19,20]. See also Refs.…”

“…In Refs. [20,24], the available N f = 2 lattice data were extrapolated to the physical point using unitarized Chiral Perturbation Theory based on the formulation of Ref. [25] with some modifications.…”

Recent results on the meson and baryon spectrum from lattice QCD

“…The large number of lattice data points results from using all lattice irreps for multiple center-of-mass momenta, and multiple lattice volumes. Figure 5 shows the current world data for g ρππ from the lattice determinations [10][11][12][13][14][15][16][17][18]. While there is in general a good agreement among the lattice data, the uncertainties in the plot are (in most cases) statistical only and there is no calculation demonstrating a full control of systematic uncertainties.…”

“…After a pioneering study by the CP-PACS collaboration [9], multiple groups provided proof of principle calculations demonstrating the feasibility of lattice resonance studies [10][11][12]. In the meantime a number of further studies exist [13][14][15][16][17][18]. Figure 4 shows an example of a state-of-the-art calculation by the Hadron Spectrum Collaboration [15].…”