Resonance parameters of the rho-meson from asymmetrical lattices

Abstract

We present a lattice QCD calculation of the parameters of the ρ meson decay. The study is carried out on spatially asymmetric boxes using nHYP-smeared clover fermions with two mass-degenerate quark flavors. Our calculations are carried out at a pion mass mπ = 304(2) MeV on the set of lattices V = 24 2 × η24 × 48 with η = 1.0, 1.25, and 2.0 with lattice spacing a = 0.1255(7) fm. The resonance mass mρ = 827(3)(5) MeV and coupling constant gρππ = 6.67(42) are calculated using the P-wave scattering phase shifts. We construct a 2×2 correlation matrix to extract the energy of the scattering states and compute the phase shifts using the finite volume formula. By varying the degree of asymmetry, we are able to compute a set of phase shifts that are evenly distributed throughout the spectral region where the ρ decays.

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.…”

Axial resonances a 1(1260), b 1(1235) and their decays from the lattice

“…The ρ mass in table 2 was extracted as m ρ = E ρ (p = 0) in [3] and is indeed found close to m res ρ in all simulations [1][2][3][4][5][6]. The ω energy is calculated using quark-antiquark interpolators O s=n 1−5 given by eq.…”

“…This is the case also for all vector (J P = 1 − ) and axial-vector (J P = 1 + ) mesons. The vector resonance ρ is the only hadronic resonance that has been treated on the lattice by several collaborations [1][2][3][4][5][6], taking into account its unstable nature and extracting its resonance mass as well as the width. First steps in this direction were also made recently for the vector resonance K * (892) [7], where mass and width were extracted.…”

Resonance Extraction from the Finite Volume

“…If the resonance is sufficiently far away from thresholds and in the absence of background, a simple Breit-Wigner parameterization allows to describe the phase shift and to determine the width. The prime examples are given by the ρ(770) [8][9][10][11][12][13] and also the K * (892) [14,15]. A first πK − ηK coupled-channel analysis has been carried out recently [16], see also Ref.…”