Resonances in coupledπK,ηKscattering from lattice QCD

Abstract

Coupled-channel πK and ηK scattering amplitudes are determined by studying the finite-volume energy spectra obtained from dynamical lattice QCD calculations. Using a large basis of interpolating operators, including both those resembling a qq construction and those resembling a pair of mesons with relative momentum, a reliable excited-state spectrum can be obtained. Working at mπ = 391 MeV, we find a gradual increase in the J P = 0 + πK phase-shift which may be identified with a broad scalar resonance that couples strongly to πK and weakly to ηK. The low-energy behavior of this amplitude suggests a virtual bound-state that may be related to the κ resonance. A bound state with J P = 1 − is found very close to the πK threshold energy, whose coupling to the πK channel is compatible with that of the experimental K (892). Evidence is found for a narrow resonance in J P = 2 + . Isospin-3/2 πK scattering is also studied and non-resonant phase-shifts spanning the whole elastic scattering region are obtained.Understanding the spectrum and properties of excited hadron states directly from the underlying theory of quarks and gluons, Quantum Chromodynamics (QCD), remains an unsolved problem. One challenge lies in the fact that excited hadrons are not asymptotically observable states, but rather appear as resonant enhancements in the scattering of lighter stable hadrons. Another challenge is the difficulty of computation within QCD which, at the energy scales of relevance, is a non-perturbative, relativistic theory. One technique which has shown significant progress when applied to hadron spectroscopy is lattice QCD. Lattice QCD is a systematically improvable calculational scheme in which the quark and gluon fields are discretized on a finite cubic grid, rendering the theory amenable to numerical computation. Monte-Carlo sampling of possible field configurations leads to estimates for hadronic correlation functions whose spectral content can then be explored.The interactions of the lightest octet of pseudoscalar mesons are important since they are the stable particles to which excited hadrons decay. In this manuscript we will explore πK scattering using lattice QCD techniques. This channel, having net strangeness, cannot proceed through intermediate quarkless states, which simplifies the phenomenology with respect to isospin-0 channels in which glueball states may appear.The bulk of our knowledge of kaon scattering amplitudes comes from kaon beam experiments at SLAC in the 1970s and 80s. πK scattering amplitudes were extracted from reactions using a proton target by extrapolating to small momentum transfer, t, where nearly-on-shell pion exchange dominates. Phase-shift analysis of the flavor exotic isospin-3/2 amplitudes as extracted from * dudek@jlab.org

Coupled-channel Dπ, Dη and D s K ¯ $$ {D}_s\overline{K} $$ scattering from lattice QCD

“…These methods have been demonstrated in a number of applications, notably for the ρ-resonance seen in P -wave ππ scattering [20][21][22][23][24][25][26][27][28][29], and for the σ resonance seen in S-wave ππ scattering [30]. It has also recently been shown that, with sufficiently extensive and precise spectra, information on coupled-channel hadron-hadron scattering amplitudes can be obtained [26,[31][32][33] -this is crucial for understanding highly excited states that are typically kinematically permitted to decay into several channels.…”

“…In order to circumvent this difficulty, we follow ref. [32] and parametrise the energy-dependence of the t-matrix with a relatively small number of parameters. Using eq.…”

S-waveKK*interactions in a finite volume and thefGeng1, Ren2, Zhou3 et al. 2015Phys. Rev. D282330View full textAdd to dashboardCite

“…A thorough study of the coupled πK and ηK channels has recently been done in Refs. [23,24] and for the coupled ππ and KK channels in Ref. [25].…”

Baryons as relativistic three-quark bound states

“…[276][277][278] and references therein), the baryon sector still waits to be explored. One reason is the worse signal to noise ratio as compared to the baryon sector.…”