Decay of rho and a1 mesons on the lattice using distillation

Abstract

We extract the P-wave ππ phase shift for five values of pion relative momenta, which gives information on the ρ resonance. The Breit-Wigner formula describes the ππ phase shift dependence nicely and we extract m ρ = 792(7)(8) MeV and the coupling g ρππ = 5.13(20) at our m π = 266 MeV. We extract the P-wave scattering length a ππ l=1 = 0.082(10)(3) fm 3 from the state with the lowest pion relative momenta. We also determine the S-wave ρπ phase shift for two values of relative momenta, which provides parameters of the lowest axial resonance a 1 (1260). Using the Breit-Wigner fit we extract m a1 = 1.44(4) GeV and the coupling g a 1 ρπ = 1.1(3) GeV. From the lowest state we also extract the ρπ scattering length a ρπ l=0 = 0.23( 12) fm for our m π . The simulation is performed using one N f = 2 ensemble of gauge configurations with cloverimproved Wilson quarks. The phase shifts are determined from the lowest two energy-levels, which are obtained by the variational analysis with a number of quark-antiquark and mesonmeson interpolators. The correlation functions are calculated using the distillation method with the Laplacian Heaviside (LapH) smearing of quarks.

Scattering phase shifts for two particles of different mass and nonzero total momentum in lattice QCD

“…The analytic studies of the phase shift relations with P = 0 that may reveal the nature of the scalars mesons in these channels were presented in [22]. The ρπ scattering and the related a 1 resonance ware simulated in [23], while the corresponding phase shift-relations for the scattering of unstable particles was analytically studied in [24]. The preliminary results for channels including charmed and charmonium states were presented in [25], while D * D 1 scattering relevant for Z + (4430) was simulated in [26].…”

Scattering of unstable particles in a finite volume: The case ofπρscattering and thea1(1260)resonance

“…In the present problem the threshold of KK * is above the mass of the a 1 (1260) resonance and, as found in [33], the πρ channel is more important than the KK * one. For this reason we shall perform the analysis with just the πρ channel, as also done for the lattice calculation of [31].…”

“…( 31), and the dashed lines are the same calculation but setting Π = 0 in Eq. (31), i.e., considering the case of stable ρ meson. There is an infinite number of levels and we have plotted the first six ones for illustration.…”

“…So far, problems which would require this treatment have been studied assuming stable particles. This is the case of the πρ scattering, from where the a 1 (1260) resonance is qualitatively obtained, assuming the ρ to be a stable particle, in an actual lattice QCD simulation using the first two levels for a fixed size of the box [31]. In the present paper we face directly this problem and provide the formalism to address it, also for the case of an unstable ρ resonance.…”

Hadronic Resonances in Lattice QCD

“…Over the past year we performed the first simulation of the Kπ [5], Dπ, D * π [4] and ρπ [9] scattering and the corresponding resonances. Since this involves scattering of two particles with different masses, we considered only P = 0 when the mixing of different l is absent or negligible [8].…”