Structure of Meson-Baryon Interaction Vertices

Abstract

We present a microscopic derivation of the form factors of strong-interaction πN N and πN ∆ vertices within a relativistic constituent quark model. The results are compared with form factors from phenomenological meson-baryon models and recent lattice QCD calculations. We give an analytical representation of the vertex form factors suitable for applications in further studies of hadron reactions. Understanding the meson-baryon strong-interaction vertices has been a hard and long-standing problem. Attempts to derive a microscopic explanation, desirably on the grounds of QCD, have not yet led to conclusive results. The problem is of considerable importance not only in particle but also in nuclear physics. Practically all realistic meson-exchange N N potentials, 3N forces, and πN dynamical models rely on certain inputs for strong form factors. Mostly they have been based on phenomenological arguments and one has usually employed monopole or dipole parametrizations with cut-off parameters fitted to experiment. Different parametrizations have big influences, e.g., on meson-baryon dynamical models (see Refs. [1,2,3,4,5,6]), on N N potentials often used in present-day nuclear calculations (e.g., the Nijmegen [7,8,9], Bonn [10,11,12], and Argonne [13, 14] potentials), and on 3N forces, see, e.g., refs. [15,16]. Consequently, a microscopic derivation of the meson-baryon interaction vertices constitutes an important problem and it has long and often been asked for (see, e.g., Refs. [17,18]).The uncertainty about the meson-baryon strong-interaction vertices has even been increased by the recent advent of lattice QCD calculations [19,20]. These works have led to results different among each other and partly distinct from earlier lattice QCD calculations by Liu et al. [21,22]. Lattice QCD results are furthermore at variance with form factors adopted so far in relativistic models of meson-baryon dynamics [4,5,6].Here, we perform a microscopic derivation of the strong meson-baryon form factors on the basis of a relativistic constituent quark model (RCQM). It is free of any phenomenological input (fit parameters), and the form-factor dependence on the relativistic four-momentum transfer Q 2 is directly predicted from the RCQM, which has already been successful in reproducing the invariant mass spectrum of baryons [23,24] and the electroweak structure of the nucleons and other baryon ground states [25,26,27,28,29]. The same RCQM has recently been employed in a covariant study of the mesonic decays of baryon resonances [30,31,32] leading to results for partial decay widths qualitatively rather different from previous nonrelativistic or relativized studies. The systematics found in the relativistic decay widths for all the π, η, and K decay modes has subsequently also led to a partly new classification of baryon resonances into flavor multiplets [33,34].In this paper we consider the πN N and πN ∆ form factors according to the process depicted in Fig. 1(a) and described by the matrix elements of the hadronic interaction Lagrangianw...

On the Microscopic Structure of $${\varvec{\pi }}$$ π NN, $${\varvec{\pi }}$$ π N $${\varvec{\Delta }}$$ Δ and $${\varvec{{\pi }\Delta \Delta }}$$ π Δ Δ Vertices

“…In the right plot of Fig. 1 our result for F π N 0 N 0 is compared with the outcome of another relativistic constituent-quark model [6] and with two parameterizations of this form factor that have been used in the hadronic models [7,8]. Up to Q 2 ≈ 1 GeV 2 our prediction is comparable with the form factor parameterization of Ref.…”

“…For the ratio of the coupling strengths we get f π N 0 0 : f π N 0 N 0 : f π 0 0 = 1.209:1:0.608. This Table 1 Our prediction for π N 0 N 0 , π N 0 0 and π 0 0 coupling constants in comparison with results from another relativistic constituent-quark model [6]. Shown are also values for these coupling constants used in two popular hadronic coupled-channel models [7,8].…”

“…The couplings given in Ref. [6] may be interpreted as "bare" couplings, since meson-cloud effects are not included explicitly, but physical N and masses are used for their extraction. The values for f π N and f π taken from Ref.…”

“…In the right plot the Q 2 behavior of F π N 0 N 0 (normalized to 1 at Q 2 = 0) is compared to the outcome of another relativistic constituent-quark model [6] and to phenomenological fits obtained within two purely hadronic dynamical coupled-channel models [7,8] (SL and PR) function is SU (6) symmetric. Rather than solving the confinement problem for a particular potential, we parameterize the momentum part of the 3q wave function of N 0 and 0 by means of a Gaussian Note that in our simple model the physical is still a stable particle, since the threshold of the only possible decay channel π N 0 is larger than the mass of the physical .…”

Baryons as relativistic three-quark bound states

“…Form factor calculations in the point form approach have been performed within the chiral quark model based on Goldstone-boson exchange [529][530][531][532], the hyperspherical constituent-quark model [533] and a recent quarkdiquark model [534]. The Goldstone-boson exchange model achieved remarkably good results for a range of baryon properties also beyond nucleon form factors [535][536][537][538] using pointlike constituent quarks only. The comparative calculation of Ref.…”