Quark-Mass Dependence of Elastic πK Scattering from QCD

Abstract

We present a determination of the isospin-1 2 elastic πK scattering amplitudes in S and P partial waves using lattice Quantum Chromodynamics. The amplitudes, constrained for a large number of real-valued energy points, are obtained as a function of light-quark mass, corresponding to four pion masses between 200 and 400 MeV. Below the first inelastic threshold, the P -wave scattering amplitude is dominated by a single pole singularity that evolves from being a stable bound-state at the highest quark mass into a narrow resonance that broadens as the pion and kaon masses are reduced. As in experiment, the S-wave amplitude does not exhibit an obviously resonant behavior, but instead shows a slow rise from threshold, which is not inconsistent with the presence of a κ/K 0 (700)-like resonance at the considered quark masses. As has been found in analyses of experimental scattering data, simple analytic continuations into the complex energy plane of precisely-determined lattice QCD amplitudes on the real energy axis are not sufficient to model-independently determine the existence and properties of this state. The spectra and amplitudes we present will serve as an input for increasingly elaborate amplitude analysis techniques that implement more of the analytic structure expected at complex energies.

Determination of the Lightest Strange Resonance K0*(700) or κ , from a Dispersive Data Analysis

“…For unphysical pion masses of ∼400 MeV, it appears as a "virtual" pole below threshold in the second Riemann sheet, consistently with expectations from unitarized NLO ChPT extrapolated to higher masses [52]. However, using pion masses between 200 and 400 MeV the pole extraction using simple models is again unstable [53]. This makes the approach followed in the present work even more relevant, since in the future lattice will provide data at physical masses and energies around the κ=K Ã 0 ð700Þ region that will require a constraining data technique for a modelindependent description and its complex plane continuation.…”

Contributions of $$ {K}_0^{\ast } $$(1430) and $$ {K}_0^{\ast } $$(1950) in the three-body decays B → Kπh

“…The kaon-pion scattering has been extensively studied in refs. [74][75][76][77][78][79][80] in recent years. While the primary source of the information on I = 1/2 S-wave Kπ system comes from the LASS experiment for the reaction K − p → K − π + n [81].…”

Hadron Spectroscopy

“…We expect that there is a left hand circular cut in S-wave scattering. This analytic behavior should be incorporated into scattering amplitudes [41].…”

“…Hadron Spectroscopy Robert G. Edwards Figure 7: Results from Ref. [41]. The quark mass dependence in the isospin= 1 2 (top) S-wave and (borrom) P-wave phase shifts.…”