Anatomy of the $\ddot{I}$ resonance from lattice QCD at the physical point

Abstract

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

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