APS : Physical-mass calculation of $\rho(770)$ and $K^*(892)$ resonance parameters via $\pi \pi$ and $K \pi$ scattering amplitudes from lattice QCD

Boyle, Peter; Joswig, Fabian; Marshall, Michael; Gülpers, Vera; Hansen, Maxwell T.; Lachini, Nelson Pitanga; Erben, Felix; Portelli, Antonin

doi:10.1103/PhysRevD.111.054510

Article
Report number	arXiv:2406.19193 ; CERN-TH-2024-087
Title	*Physical-mass calculation of $\rho(770)$ and $K^(892)$ resonance parameters via $\pi \pi$ and $K \pi$ scattering amplitudes from lattice QCD**
Author(s)	Boyle, Peter (Brookhaven ; Edinburgh U.) ; Erben, Felix (Edinburgh U. ; CERN) ; Gülpers, Vera (Edinburgh U.) ; Hansen, Maxwell T. (Edinburgh U.) ; Joswig, Fabian (Edinburgh U.) ; Marshall, Michael (Edinburgh U.) ; Lachini, Nelson Pitanga (Edinburgh U. ; Cambridge U., DAMTP) ; Portelli, Antonin (Edinburgh U. ; CERN ; RIKEN AICS, Kobe)
Publication	2025-03-01
Imprint	2024-06-27
Number of pages	27
In:	Phys. Rev. D 111 (2025) 054510
DOI	10.1103/PhysRevD.111.054510 (publication)
Subject category	hep-ph ; Particle Physics - Phenomenology ; hep-lat ; Particle Physics - Lattice
Abstract	We present our study of the $\rho(770)$ and $K^(892)$ resonances from lattice quantum chromodynamics (QCD) employing domain-wall fermions at physical quark masses. We determine the finite-volume energy spectrum in various momentum frames and obtain phase-shift parameterizations via the Lüscher formalism, and as a final step the complex resonance poles of the $\pi \pi$ and $K \pi$ elastic scattering amplitudes via an analytical continuation of the models. By sampling a large number of representative sets of underlying energy-level fits, we also assign a systematic uncertainty to our final results. This is a significant extension to data-driven analysis methods that have been used in lattice QCD to date, due to the two-step nature of the formalism. Our final pole positions, $M+i\Gamma/2$, with all statistical and systematic errors exposed, are $M_{K^{}} = 893(2)(8)(54)(2) \mathrm{MeV}$ and $\Gamma_{K^{}} = 51(2)(11)(3)(0) \mathrm{MeV}$ for the $K^(892)$ resonance and $M_{\rho} = 796(5)(15)(48)(2) \mathrm{MeV}$ and $\Gamma_{\rho} = 192(10)(28)(12)(0) \mathrm{MeV}$ for the $\rho(770)$ resonance. The four differently grouped sources of uncertainties are, in the order of occurrence: statistical, data-driven systematic, an estimation of systematic effects beyond our computation (dominated by the fact that we employ a single lattice spacing), and the error from the scale-setting uncertainty on our ensemble.
Copyright/License	publication: © 2025 authors (License: CC BY 4.0), sponsored by SCOAP³ preprint: © 2024-2025 authors (License: arXiv nonexclusive-distrib 1.0)

$Non-interacting two-particle energies given by Eq.~\eqref{nonintCMformula} with the momenta assignments of the $K\pi$ (top) and $\pi\pi$ (bottom) two-bilinear operators that are included in the GEVP (full black lines labeled by $(\mathbf d_{K}^2) (\mathbf d_{\pi}^2)$ and $(\mathbf d_{\pi}^2) (\mathbf d_{\pi}^2)$, respectively). They are respectively distributed over $6$ and $10$ irreps on the $5$ momentum frames considered, where the odd-even wave mixing irreps were not considered in the $K \pi$ analysis. The horizontal axes show the variation of the free levels with the box size $L$ at constant lattice spacing $a$, where $a$ and $L/a=48$ correspond to the ensemble used in this work. The free energies corresponding to two-bilinear operators not included (where at least one meson has momentum $|\mathbf d|^2>4$) are also shown (dashed gray lines). The red dashed lines represent the free low-lying $K\pi\pi$ and $\pi\pi\pi\pi$ states in the corresponding irreps. We also show the model-averaged finite-volume energies extracted in this work (colored boxes), as described in Sec.~\ref{sec:spectrumdetermination}. The same energy levels overlaid to the lattice data can be seen in Appendix~\ref{apx:gevpeffspectra}. Any finite-volume energy above a grey or red dashed line does not enter the phase shift determination (Sec.~\ref{sec:phaseshiftdetermination}) and is also not shown in this figure. The relevant scattering thresholds are also shown for convenience (faint dots).$ $: $K\pi$ non-interacting energies and extracted finite-volume spectrum. We only consider the irreps that have a leading contribution from $P$-wave, which totals $6$ irreps in the $5$ momentum frames considered.$ $: $\pi\pi$ non-interacting energies and relevant thresholds. In addition to the irreps also present in the $K \pi$ analysis, the moving frame $A_1$ irreps have their leading contribution from $P$-wave, for a total of $10$ irreps in the $5$ momentum frames.$ Show more plots

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記錄創建於2024-06-29，最後更新在2025-05-10

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