$\rho$ and $K^{\ast }$ resonances on the lattice at nearly physical quark masses and $N_f=2$

Abstract

Working with a pion mass $m_{\pi }\approx 150$ MeV, we study $\pi \pi$ and $K\pi$ scattering using two flavours of non-perturbatively improved Wilson fermions at a lattice spacing $a\approx 0.071$ fm. Employing two lattice volumes with linear spatial extents of $N_s=48$ and $N_s=64$ points and moving frames, we extract the phase shifts for p-wave $\pi \pi$ and $K\pi$ scattering near the $\rho$ and $K^{\ast }$ resonances.Comparing our results to those of previous lattice studies, that used pion masses ranging from about 200 MeV up to 470 MeV, we find that the coupling $g_{\rho \pi \pi }$ appears to be remarkably constant as a function of $m_{\pi }$.

Comments: 16 pages, 8 figures, v2: "and $N_f=2$" added to the title, references updated, some figures replaced, including improved summary plots, alternative parametrizations are considered and analytical continations are performed to determine pole positions on the second Riemann sheet