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

We propose a strategy to access the qq component of the p resonance in lattice QCD. Through a mixed action formalism(overlap valence on domain wall sea), the energy of the qq 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 πρ sigma term is extracted to be σ_(πρ)~(val)= 9.82(6) MeV using the Feynman-Hellman theorem. At the physical pion mass, the mass of the qq component is interpolated to be m_ρ = 775.9±6.0±1.8 MeV, which is close to the p resonance mass. We also obtain the leptonic decay constant of the qq 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)=(1/2)Zf_ρ±, with Z_ρ≈1.13 being the on-shell wavefunction renormalization of p owing to the ρ-π interaction. We emphasize that m_ρand f_ρ of the qq component, which are obtained for the first time from QCD, can be taken as the input parameters of p in effective field theory studies where p acts as a fundamental degree of freedom.