6533b82cfe1ef96bd128ea7a

RESEARCH PRODUCT

I=1/2 S -wave and P -wave Kπ scattering and the κ and K* resonances from lattice QCD

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description

We present a lattice-QCD determination of the elastic isospin-$1/2$ $S$-wave and $P$-wave $K\ensuremath{\pi}$ scattering amplitudes as a function of the center-of-mass energy using L\"uscher's method. We perform global fits of $K$-matrix parametrizations to the finite-volume energy spectra for all irreducible representations with total momenta up to $\sqrt{3}\frac{2\ensuremath{\pi}}{L}$; this includes irreducible representations (irreps) that mix the $S$- and $P$-waves. Several different parametrizations for the energy dependence of the $K$-matrix are considered. We also determine the positions of the nearest poles in the scattering amplitudes, which correspond to the broad $\ensuremath{\kappa}$ resonance in the $S$-wave and the narrow ${K}^{*}(892)$ resonance in the $P$-wave. Our calculations are performed with $2+1$ dynamical clover fermions for two different pion masses of 317.2(2.2) and 175.9(1.8) MeV. Our preferred $S$-wave parametrization is based on a conformal map and includes an Adler zero; for the $P$-wave, we use a standard pole parametrization including Blatt-Weisskopf barrier factors. The $S$-wave $\ensuremath{\kappa}$-resonance pole positions are found to be $[0.86(12)\ensuremath{-}0.309(50)i]\text{ }\text{ }\mathrm{GeV}$ at the heavier pion mass and $[0.499(55)\ensuremath{-}0.379(66)i]\text{ }\text{ }\mathrm{GeV}$ at the lighter pion mass. The $P$-wave ${K}^{*}$-resonance pole positions are found to be $[0.8951(64)\ensuremath{-}0.00250(21)i]\text{ }\text{ }\mathrm{GeV}$ at the heavier pion mass and $[0.8718(82)\ensuremath{-}0.0130(11)i]\text{ }\text{ }\mathrm{GeV}$ at the lighter pion mass, which corresponds to couplings of ${g}_{{K}^{*}K\ensuremath{\pi}}=5.02(26)$ and ${g}_{{K}^{*}K\ensuremath{\pi}}=4.99(22)$, respectively.