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

We propose a strategy to access the qq component of the resonance in lattice QCD. Through a mixed action formalism (overlap valence on domain wall sea), the energy of the qq component is derived at dierent valence quark masses, and shows a linear dependence on m²_π. The slope is determined to be c1=0:505(3)GeV^-1, from which the valence πρ sigma term is extracted to be δ(val) πρ = 9:82(6) MeV using the Feynman-Hellman theorem. At the physical pion mass, the mass of the qq component is interpolated to be mρ=775:9±6:0±1:8 MeV, which is close to the ρ resonance mass. We also obtain the leptonic decay constant of the qq component to be fρ- =208:5±5:5±0:9 MeV, which can be compared with the experimental value f exp ρ ≈221 MeV through the relation fexp ρ = p Zρfρ ±, with Zρ≈1:13 being the on-shell wavefunction renormalization ofρ owing to the ρ-π interaction. We emphasize that mρ and fρ of the qq component, which are obtained for the first time from QCD, can be taken as the input parameters of ρ in eective field theory studies where ρ acts as a fundamental degree of freedom.