Dressed-quarks and the Roper resonance

Abstract

Abstract. A Dyson-Schwinger equation calculation of the light hadron spectrum, which correlates the masses of meson and baryon ground-and excited-states within a single framework, produces a description of the Roper resonance that corresponds closely with conclusions drawn recently by EBAC. Namely, the Roper is a particular type of radial excitation of the nucleon's dressed-quark core augmented by a material meson cloud component. There are, in addition, some surprises. . DCSB is an essentially quantum field theoretical effect. In quantum field theory a meson appears as a pole in the four-point quark-antiquark Green function. From this observation one can derive the Bethe-Salpeter equation. It is therefore unsurprising that a baryon appears as a pole in a six-point quark Green function; and one can derive a Poincaré covariant Faddeev equation to describe the associated bound state [4]. The Faddeev equation sums all possible exchanges and interactions that can take place between three dressedquarks. These dressed-quarks are one of the basic consequences of DCSB in QCD. A tractable Faddeev equation, Fig. 1, follows from the observation that an interaction which describes color-singlet mesons also generates quark-quark (diquark) correlations in the color-antitriplet channel [5].It should be emphasized that the diquark correlations within baryons are nonpointlike. They have a nonzero extent, which can be characterized by a charge radius. One finds, e.g., that isoscalar-scalar diquark correlations have a charge radius commensurate with that of the pion and the analogous axial-vector diquarks have radii similar to those of the ρ-meson [7]. Quantum mechanical models that employ pointlike diquark degrees of freedom have no relation to the Faddeev equation description of baryons in quantum field theory.

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

“…The results presented herein utilise the PACS-CS 2 + 1 flavour dynamical-fermion configurations [27] with an Iwasaki gauge action [28] which are made available through the ILDG [29]. The lattice size is 32 3 × 64 with a lattice spacing of 0.0907 fm which provides a physical volume of ≈ (2.90 fm) 3 . The light quark mass is set by the hopping parameter κ ud = 0.13754 which gives a pion mass of m π = 411 MeV, while the strange quark mass is set by κ s = 0.13640.…”

“…Since the inception of lattice QCD, significant effort has been invested in exploring hadronic spectra, both to shed light upon the nature and properties of various states, and to test the validity of the methodology itself. In particular, the community has shown notable interest in the positive-parity nucleon channel [1][2][3][4][5][6], where the first positive-parity J P = 1 2 + excitation of the nucleon, known as the Roper resonance N * (1440), remains a puzzle.…”

“…The CSSM lattice collaboration was the first to demonstrate that the inclusion of Gaussian-smeared fermion sources of wide widths are critical in enabling the extraction of the lowest-lying positive-parity excitation in the nucleon channel [1,12]. It was later shown that the * adrian.kiratidis@adelaide.edu.au quark probability distribution for this state is consistent with an N = 2 radial excitation [3,13].…”

Light baryons and their excitations

“…In the framework of Dyson-Schwinger, Bethe-Salpeter and Faddeev equations (see [23][24][25][26][27] for reviews) the properties of the Roper resonance have been analysed so far on two levels of sophistication [28][29][30][31]. Both of these approaches convert the three-body system into a two-body quark-diquark picture assuming strong quark-quark correlations inside baryons.…”

Looking into the Matter of Light-Quark Hadrons

“…Additional analysis [60] suggests a fascinating new feature of the Roper. The nucleon ground state is dominated by the scalar diquark, with a significantly smaller but nevertheless important axial-vector diquark component.…”