Emergence of the $\pi (1300)$ 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 $\pi (1300)$. This enormous energy difference opens an interesting window into the confinement of quarks and the structure of the lightest hadrons. In this Letter, we provide the first calculation of resonance parameters of the $\pi (1300)$ from lattice quantum chromodynamics (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. Making a simple assumption of vanishing pion mass dependence for the three-body force, but incorporating constraints from Chiral Perturbation Theory for all the two-body channels, enables a robust extrapolation to the physical point. Applying model averaging, we extract a pole position of $M_{π(1300)}=(1169\pm46)-i(62_{-62}^{+168})\,\MeV$ supporting values from phenomenology.

20 pages, 22 figures, 2 tables. v2: version published in PRL

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