Search for low-lying lattice QCD eigenstates in the Roper regime

Abstract

The positive-parity nucleon spectrum is explored in $2 + 1$-flavour lattice QCD in a search for new low-lying energy eigenstates near the energy regime of the Roper resonance. In addition to conventional three-quark operators, we consider novel, local five-quark meson-baryon type interpolating fields that hold the promise to reveal new eigenstates that may have been missed in previous analyses. Drawing on phenomenological insight, five-quark operators based on $\sigma{N}$, $\pi{N}$ and $a_0{N}$ channels are constructed. Spectra are produced in a high-statistics analysis on the PACS-CS dynamical gauge-field configurations with $m_{\pi} = 411\textrm{ MeV}$ via variational analyses of several operator combinations. Despite the introduction of qualitatively different interpolating fields, no new states are observed in the energy regime of the Roper resonance. This result provides further evidence that the low-lying finite-volume scattering states are not localised, and strengthens the interpretation of the Roper as a coupled-channel, dynamically-generated meson-baryon resonance.Comment: 7 Pages, 2 Figure

Roper state from overlap fermions

“…It is concluded that the Roper does not come down from the value calculated with the 3-quark interpolation field alone in this πN scattering calculation. A similar conclusion is reached with mixed 3-quark and 5-quark interpolation fields for the clover fermion at m π = 411 MeV [64]. To understand the results of these πN scattering calculations, we point out that there are other classes of diagrams that will lead to higher Fock space components.…”

Genuine quark state versus dynamically generated structure for the Roper resonance

“…This evolution is rather insensitive to the mass of the three-quark state which may be as large as 2000 MeV. In view of the difficulties in the quark model to explain the ordering of single-particle states in which the 2s state would lie lower than the 1p state, as well as the recent results of the lattice calculations [28,29] which have not found a sizable three-quark component below 1.65 and 2.0 GeV, respectively, the presented model appears to rule out the existence of a three-quark resonant state around or below 1500 MeV. It favors the picture in which the mass of the S-matrix pole is determined by the energy of the dynamically generated state while its width and modulus are strongly influenced by the three-quark resonant state.…”

“…The hunt for the Roper is also a perpetual challenge to lattice QCD which may ultimately resolve the dilemma about the origin of the resonance. Although the picture seems to be clearing slowly [27], the recent calculations of the GrazLjubljana group [28] including besides 3q interpolating fields also operators for πN in relative p wave and σ N in s wave, and a similar calculation by the Adelaide group [29] show, however, no evidence for a dominant 3q configuration below 1.65 and 2.0 GeV, respectively, that could be interpreted as a Roper state. The Graz-Ljubljana group has concluded that πN channel alone does not render a low-lying resonance and that coupling with ππN channels seems to be important, which supports the dynamical origin of the Roper.…”

Three-body unitarity versus finite-volume π+π+π+ spectrum from lattice QCD

“…[60]. Indeed, meson-baryon operators are often included in the operator basis [60][61][62][63]. Also, results on the Roper reso-nance at almost physical masses [60] suggest the need to map out finite-volume effects in two and three-body coupled channels, namely the πN, f 0 (500)N, π∆, ρN, .…”