Universality of theρMeson Coupling in Effective Field Theory

Abstract

It is shown that both the universal coupling of the ρ meson and the Kawarabayashi-SuzukiRiadzuddin-Fayyazuddin expression for the magnitude of its coupling constant follow from the requirement that chiral perturbation theory of pions, nucleons, and ρ mesons is a consistent effective field theory. The prerequisite of the derivation is that all ultraviolet divergences can be absorbed in the redefinition of fields and the available parameters of the most general effective Lagrangian.PACS numbers: 11.10. Gh, 12.39.Fe. Already in the 1960s, vector mesons were discussed in the framework of phenomenological low-energy chiral Lagrangians [1,2,3]. For the details of the construction of chirally invariant effective Lagrangians describing the interaction of vector mesons with pseudoscalars and baryons see, e.g., Refs. [4,5,6,7,8,9,10,11,12]. In Ref. [12], different formulations of vector-meson effective theories were shown to be equivalent. In the massive Yang-Mills approach (for a review see, e.g., Ref.[4]) vector mesons are treated as gauge bosons of local chiral symmetry (with symmetry breaking mass terms added by hand). This scenario implies that the ρ meson couples universally, i.e. with the same strength, to fermions and pseudoscalars. In the so-called hidden chiral symmetry approach (see, e.g., Refs. [4, 5, 6]) ρ-coupling universality is obtained only with a specific choice of a free parameter of the Lagrangian. Although the hypotheses of dynamical bosons of both approximate and hidden local chiral symmetry are attractive, there is, as was emphasized in Ref. [8], no proof for the existence of such gauge bosons of local chiral symmetry in QCD.Besides the construction of the effective Lagrangian, a consistent effective field theory (EFT) program requires a systematic power counting which allows one to organize the perturbation series. For example, within the extended on-mass-shell renormalization scheme of Ref. [13] it is possible to consistently include virtual (axial-) vector mesons in a manifestly Lorentz-invariant formulation of the EFT [14], provided they appear only as internal lines in Feynman diagrams involving soft external pions and nucleons with small three-momenta. Moreover, a consistent power counting also exists within the reformulated version [15] of the infrared renormalization of Becher and Leutwyler [16].In this letter we consider the effective Lagrangian of Ref.[3] describing the interaction among ρ mesons, pions, and nucleons. In principle, the Lagrangian contains all interaction terms which respect Lorentz invariance, the discrete symmetries, and chiral symmetry. As was stressed in Ref. [3], the equality of the ρππ and the ρN N coupling constants does not follow as a consequence of the symmetries of the Lagrangian. Below we perform a one-loop order analysis of the nucleon and ρ-meson self-energies as well as the ρρρ and ρN N vertex functions. In accordance with the general principles of effective field theory [17], we require that all ultra-violet (UV) divergences can be absorbed into the redef...

Interaction of the vector-meson octet with the baryon octet in effective field theory

“…Before addressing the universality principle in SU(3), we first want to reproduce the case of SU(2) [22]. To that end, we consider the diagrams of Fig.…”

“…Consequently, from the EFT perspective, the universal coupling g V N N = g is a result of the consistency conditions imposed by the requirement of perturbative renormalizability (see also Ref. [22]). …”

Quantum Electrodynamics for Vector Mesons

“…[4] we have shown how the universal coupling of the ρ meson and the Kawarabayashi-Suzuki-RiadzuddinFayyazuddin (KSRF) relation [5,6] follow from the requirement that chiral perturbation theory of pions, nucleons, and ρ mesons is a consistent EFT. Although EFTs are non-renormalizable in the traditional sense, the general principles of EFT [7] require that all ultraviolet divergences can be absorbed into the redefinition of fields and parameters of the most general Lagrangian [8].…”

Properties of the vector meson nonet at largeNcbeyond the chiral limit

“…[29,32,33], see also comment in [7]). We note in passing that the relations (19) have also been obtained recently in a more general framework by demanding perturbative renormalizability in the sense of effective field theories of a Lagrangian involving pions, ρ-mesons, nucleons and photons [34,35].…”