Spectral parameters of the $\rho$ resonance from lattice QCD

TL;DR

This paper uses lattice QCD with multiple ensembles to accurately determine the mass and width of the $ ho$ resonance, employing phase shift analysis and effective field theory, achieving the most precise results to date.

Contribution

It introduces a comprehensive lattice QCD approach combining finite volume energy levels and effective field theory to precisely extract the $ ho$ resonance parameters.

Findings

Mass of $ ho$ resonance: 781.6 MeV

Width of $ ho$ resonance: 146.5 MeV

Results agree with experimental values

Abstract

We present a lattice QCD investigation of the $\rho$ resonance using nine $N_f = 2 + 1$ Wilson-Clover ensembles with three lattice spacings and various pion masses ranging from $135$ to $320$ MeV. For each ensemble, a large number of finite volume energy levels are determined and the energy dependence of the phase shift obtained from L\"uscher's finite volume method. The mass and width of the $\rho$ resonance are then extracted by assuming the Breit-Wigner form. The mass and width are extrapolated to the physical pion mass and continuum limit ($\mathcal{O}(a^2)$) using a linear function of $a^2$ and $m^2_\pi$. The extrapolated values for the mass and width in the Breit-Wigner form are $(m_\rho,\,\Gamma_\rho) = (781.6\pm10.0,\, 146.5\pm 9.9)$ MeV, which are in good agreement with experiment. An alternative method of analysis, based on Hamiltonian effective field theory, involves directly fitting the lattice energy levels and accounting for the quark mass dependence of the hadronic loop diagrams which yield the leading and next-to-leading non-analytic behaviour. This approach also yields consistent $\rho$ parameters at the physical point. This represents the most precise determination to date of the mass and width of a hadron which is unstable under strong decay, achieved through comprehensive lattice QCD calculations and methods of analysis.