Emergence of the $π(1300)$ Resonance from Lattice QCD

Abstract

The mass of the lightest hadron in nature, the pion, is one seventh of that of the nucleon, and one tenth of the mass of its first excited state, the $π(1300)$. This enormous energy difference opens an interesting window into the confinement of quarks and the structure of the lightest hadrons. In this work, we provide the first calculation of resonance parameters of the $π(1300)$ from lattice QCD. For this purpose, recently derived state-of-the-art tools are adapted and applied both in the construction of three-hadron operators and for mapping finite-volume spectra to infinite-volume amplitudes, subsequently analytically continuing these to complex energies. For our heavy pion mass ensembles, we find a clear signal of the resonance. Crucial input is provided through Chiral Perturbation Theory, allowing us to robustly extrapolate to the physical point. Applying model averaging, we extract a pole position of $M_{π(1300)}=(1169\pm46)-i\,(62_{-62}^{+168})\,\rm MeV$ supporting values from phenomenology.