On light vector mesons and chiral SU(3) extrapolations

Abstract

A chiral extrapolation of the light vector meson masses in the up, down and strange quark masses of QCD is presented. We apply an effective chiral Lagrangian based on the hadrogenesis conjecture to QCD lattice ensembles of PACS-CS, QCDSF-UKQCD and HSC in the strict isospin limit. The leading orders low-energy constants are determined upon a global fit to the lattice data set. We use the pion and kaon masses as well as the size of the finite volume as lattice ensemble parameters only. The quark mass ratio on the various ensembles are then predicted in terms of our set of low-energy constants. An accurate reproduction of the vector meson masses and quark-mass ratios as provided by the lattice collaborations and the Particle Data Group (PDG) is achieved. Particular attention is paid to the ω − φ mixing phenomenon, which is demonstrated to show a strong quark mass dependence.

On pion and kaon decay constants and their chiral SU(3) extrapolations

“…Second, we consider a chiral Lagrangian with explicit vector meson degrees of freedom [20,21,19]. Its low-energy constants have been determined recently at the one-loop level in [22] from lattice data on meson masses from PACS-CS, QCDSF-UKQCD and HSC [23,24,25,26]. In particular a rather small value for f = (70.5±3.0) MeV was obtained compatible with the range suggested by the two-loop estimates of χPT in [15].…”

“…We assure that upon a further chiral expansion of f χ−PT P the traditional form is recovered identically. The contributions of the vector mesons are implied by a bubble loop contributions to the polarization function Π P (s = m 2 P ) as was derived in [19,22]. The latter involves the masses of the Goldstone bosons, m P , and the vector mesons, M V , in their isospin limit.…”

“…Our analysis on the pion and kaon decay constants is based on the chiral Lagrangian with dynamical vector meson degrees of freedom as further developed recently in [19,22]. For the specifics of the Lagrangian and explicit expressions valid at the one-loop level properly derived in a finite volume we refer to our previous works [19,22]. Note that as in [19] we do not yet consider the explicit effects of the η field [21].…”

“…In the determination of our low-energy constants [22] from QCD lattice data we considered finite-box energy levels from PACS-CS, QCDSF-UKQCD and HSC [23,24,25,26]. For any lattice ensemble of a given finite-box size we took the pion and kaon masses as input parameters.…”

Low-energy constants from charmed baryons on QCD lattices

“…Significant sets of low-energy parameters to be used in flavour SU(3) chiral Lagrangians were established from the available lattice data on such hadron masses. So far results are available for mesons and baryons composed of up, down and strange quarks [2,5,6]. In addition a complete set of relevant low-energy constants in the open-charm sector of QCD was established in [3].…”