Anatomy of the ρ resonance from lattice QCD at the physical point

We propose a strategy to access the q\bar{q} component of the ρ 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}_{{π }}². The slope is determined to be {c}₁=0.505(3) {{{GeV}}}^-1, from which the valence {{π }}{{ρ }} sigma term is extracted to be {σ }_{{π }{{ρ }}}^({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}_{{ρ }}=775.9+/- 6.0+/- 1.8 {{MeV}}, which is close to the ρ resonance mass. We also obtain the leptonic decay constant of the q\bar{q} component to be {f}_{{{ρ }}^-}=208.5+/- 5.5+/- 0.9 {{MeV}}, which can be compared with the experimental value {f}_{{ρ }}^{{\exp }}≈ 221 {{MeV}} through the relation {f}_{{ρ }}^{{\exp }}=\sqrt{{Z}_{{ρ }}}{f}_{{{ρ }}^+/- }, with {Z}_{{ρ }}≈ 1.13 being the on-shell wavefunction renormalization of ρ owing to the {{ρ }}-{{π }} interaction. We emphasize that {m}_{{ρ }} and {f}_{{ρ }} of the q\bar{q} component, which are obtained for the first time from QCD, can be taken as the input parameters of ρ in effective field theory studies where ρ acts as a fundamental degree of freedom.

Supported in part by the U.S. DOE Grant No. DE-SC0013065, the National Nature Science Foundation of China (NSFC) (11335001, 11575196, 11575197, 11621131001) (CRC110 by DFG and NSFC), A. A. is supported in part by the National Science Foundation CAREER (PHY-1151648) and by U.S. DOE (DE-FG02-95ER40907), Y. C. thanks the CAS Center for Excellence in Particle Physics (CCEPP) for their support, this research used the resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy (DE-AC05-00OR22725)