Coupled channel analysis of theρmeson decay in lattice QCD

Abstract

We employ a variational basis with a number of " qq and lattice interpolating fields with quantum numbers of the resonance to extract the discrete energy spectrum in a finite volume. In the elastic region, this spectrum is related to the phase shift of the continuum scattering amplitude by Lüscher's formula, and the relation allows the extraction of resonance parameters from the spectrum calculation. The simulations are performed at three different total momenta of the coupled "qq À system, which allows us to extract the p-wave scattering phase at five values of pion relative momenta near the resonance region. The effective range formula describes the phase-shift dependence nicely, and we extract the resonance mass m ¼ 792ð7Þð8Þ MeV and the coupling g ¼ 5:13ð20Þ at our m ' 266 MeV. The coupling g is directly related to the width of the meson, and our value is close to the value derived from the experimental width. The simulations are performed using dynamical gauge configurations with two massdegenerate flavors of tree-level improved clover-Wilson fermions. Correlation functions are calculated using the recently proposed distillation method with Laplacian-Heaviside smearing of quarks, which enables flexible calculations, in many cases with unprecedented accuracy.

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

“…This might lead to shifts of 1 ++ energy levels (compared to the uncoupled ρ − ππ situation) if ππ and ρ levels are close in energy, i.e., within ≃ Γ ρ . We know from earlier work [3] that for our lattice parameters the ground state at rest ρ(0) has negligible overlap with the π(1)π(−1) operator. 1 This is because this lowest two-pion interpolator allowed by the conservation of momentum and angular momentum has energy 2(…”

“…The dynamical and valence u/d quarks have the same mass corresponding to m π = 266(4) MeV. The parameters of the ensemble are shown in table 1, while more details are given in [3]. Due to the limited data for just a single ensemble, our determination of the lattice spacing a reported in [3] results from taking a typical value of the Sommer parameter r 0 .…”

“…The parameters of the ensemble are shown in table 1, while more details are given in [3]. Due to the limited data for just a single ensemble, our determination of the lattice spacing a reported in [3] results from taking a typical value of the Sommer parameter r 0 . The uncertainty associated with this choice might lead to a small shift of all dimensionful quantities.…”

“…The sea and valence quarks obey periodic boundary conditions in space. Valence quark propagators periodic and anti-periodic in time are combined into so-called "P + A" propagators, which effectively extends the time direction to 2N T = 64 [3]. We use translation invariance in t to sum over correlators from sources in every time slice.…”

“…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.…”