Hadron–Hadron interactions from $$N_\mathrm{{f}}=2+1+1$$ lattice QCD: the $$\rho \,$$-resonance

Abstract

We present an investigation of the ρ-meson from N f = 2 + 1 + 1 flavour lattice QCD.The calculation is performed based on gauge configuration ensembles produced by the ETM collaboration with three lattice spacing values and pion masses ranging from 230 MeV to 500 MeV. Applying the Lüscher method phase shift curves are determined for all ensembles separately. Assuming a Breit-Wigner form, the ρ-meson mass and width are determined by a fit to these phase shift curves. Mass and width combined are then extrapolated to the chiral limit, while lattice artefacts are not detectable within our statistical uncertainties. For the ρmeson mass extrapolated to the physical point we find good agreement with experiment. The corresponding decay width differs by about two standard deviations from the experimental value.

Numerical exploration of three relativistic particles in a finite volume including two-particle resonances and bound states

“…It is important to keep in mind in the following that, due to the possibility of switching the spectator particle, the contributions of s-and d-wave subchannels are coupled, even in infinite volume. 16 The first case we analyze is ma 0 = 0.1 and ma 2 = 3.0, leading to the spectrum shown in figure 12(a). For these parameters there is a d-wave dimer with M =2 d ≈ 1.886m but no s-wave dimer.…”

“…Currently, one of the major frontiers of numerical LQCD is the calculation of few-hadron observables. In particular, there has been substantial recent progress in the determination of scattering amplitudes, including cases for which multiple channels are open and couple to underlying resonances [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17]. 1 These studies rely on formalism that maps quantities obtained via LQCD, namely finite-volume observables, to infinite-volume amplitudes [19][20][21][22][23][24][25][26][27][28].…”

Light- and strange-quark mass dependence of the ρ(770) meson revisited

“…In summary, assuming that the pion decay JHEP11(2020)017 constant is the same in the two and three flavor simulations totally misses the effect of the strange quark and loops containing kaon and eta particles in pion observables. After our analysis was completed, several N f = 2 [61,62] and N f = 2 + 1 + 1 [70] new simulations have been performed using the pion decay constant to fix the scale. The comparison of these results with our N f = 2 + 1 analysis for the ρ-meson mass is depicted JHEP11(2020)017 in figure 41.…”

“…In recent simulations, lattice data on I = J = 1 ππ scattering have been extracted for several pion masses for two light flavors (N f = 2) [54][55][56][57][58][59][60][61][62] and including also the strange quark (N f = 2 + 1) [63][64][65][66][67][68][69]. See also [70,71] for recent N f = 2 + 1 + 1 simulations. Surprisingly, results for the ρ mass in N f = 2 simulations are at odds with experimental predictions.…”

Consistency checks for two-body finite-volume matrix elements. II. Perturbative systems

“…In the past decades, Lüscher's formalism has been extended to include nonzero momentum in the finite-volume frame as well as coupled two-particle channels and particles with spin [6][7][8][9][10][11][12][13][14]. Lattice QCD applications of the methodology have proven highly effective in the determination of two-hadron bound and resonant states [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33], including those at energies where multiple channels are kinematically open [34][35][36][37][38][39][40][41][42]. This success in the two-hadron sector has also motivated the extension to 2 → 3 and 3 → 3 scattering [43][44][45][46][47][48][49][50][51][52], with the first lattice QCD computat...…”