Extracting excited states from lattice QCD: the Roper resonance

TL;DR

This paper introduces a novel lattice QCD method to extract excited states, specifically applied to identify the Roper resonance, by combining correlation functions at different times to isolate excited state signals.

Contribution

A new method for extracting excited states from lattice QCD correlation functions by subtracting the ground state contribution, demonstrated on nucleon excited states.

Findings

Consistent identification of the Roper resonance N'(1440).

No observed level switching at simulated quark masses.

Tentative expectation of level crossing near the physical point.

Abstract

We present a new method for extracting excited states from a single two-point correlation function calculated on the lattice. Our method simply combines the correlation function evaluated at different time slices so as to ``subtract'' the leading exponential decay (ground state) and to give access to the first excited state. The method is applied to a quenched lattice study (volume = 24^3 x 64, beta = 6.2, 1/a = 2.55 GeV) of the first excited state of the nucleon using the local interpolating operator O = [uT C gamma5 d] u. The results are consistent with the identification of our extracted excited state with the Roper resonance N'(1440). The switching of the level ordering with respect to the negative-parity partner of the nucleon, N*(1535), is not seen at the simulated quark masses and, basing on crude extrapolations, is tentatively expected to occur close to the physical point.