Anatomy of the $\rho$ resonance from lattice QCD at the physical point

Abstract

We propose a strategy to access the $q\bar{q}$ component of the $\rho$ resonance in lattice QCD. Through a mixed action formalism (overlap valence on domain wall sea), the energy of the $q\bar{q}$ component is derived at different valence quark masses, and shows a linear dependence on $m_{\pi }^2$. The slope is determined to be $c_1=0.505(3){\mathrm{GeV}}^{-1}$, from which the valence $\pi \rho$ sigma term is extracted to be ${\sigma }_{\pi \rho }^{(\mathrm{val})}=9.82(6)$ MeV using the Feynman-Hellman theorem. At the physical pion mass, the mass of the $q\bar{q}$ component is interpolated to be $m_{\rho }=775.9\pm 6.0\pm 1.8$ MeV, which is close to the $\rho$ resonance mass. We also obtain the leptonic decay constant of the $q\bar{q}$ component to be $f_{{\rho }^{-}}=208.5\pm 5.5\pm 0.9$ MeV, which can be compared with the experimental value $f_{\rho }^{\exp }\approx 221$ MeV through the relation $f_{\rho }^{\exp }=\sqrt{Z_{\rho }}{f}_{{\rho }^{\pm }}$ with $Z_{\rho }\approx 1.13$ being the on-shell wavefunction renormalization of $\rho$ owing to the $\rho -\pi$ interaction. We emphasize that $m_{\rho }$ and $f_{\rho }$ of the $q\bar{q}$ component, which are obtained for the first time from QCD, can be taken as the input parameters of $\rho$ in effective field theory studies where $\rho$ acts as a fundamental degree of freedom.

7 pages, 4 figures. Considerably modified, more discussions, matching to the published version

References in corpus (10)

• Domain wall QCD with physical quark masses
• $I=1$ and $I=2$ $\pi -\pi$ scattering phase shifts from $N_{\mathrm{f}}=2+1$ lattice QCD
• Rho resonance parameters from lattice QCD
• $\rho$ and $K^{\ast }$ resonances on the lattice at nearly physical quark masses and $N_f=2$
• Infrared regularization for spin-1 fields
• Studying the $\rho$ resonance parameters with staggered fermions
• Ordinary and Extraordinary Hadrons
• Variance Reduction and Cluster Decomposition
• eta' meson From Two Flavor Dynamical Domain Wall Fermions
• Non-perturbative renormalization of overlap quark bilinears on 2+1-flavor domain wall fermion configurations

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