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

Understand

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 $c_1=0.505(3)\,{\rm GeV}^{-1}$, from which the valence $\pi \rho$ sigma term is extracted to be $\sigma_{\pi \rho}^{(\rm val)}=9.82(6)$ 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.