Mesons on a transverse lattice

Abstract

The meson eigenstates of the light-cone Hamiltonian in a coarse transverse lattice gauge theory are investigated. Building upon previous work in pure gauge theory, the Hamiltonian and its Fock space are expanded in powers of dynamical fields. In the leading approximation, the couplings appearing in the Hamiltonian are renormalised by demanding restoration of space-time symmetries broken by the cut-off. Additional requirements from chiral symmetry are discussed and difficulties in imposing them from first principles in the leading approximation are noted. A phenomenological calculation is then performed, in which chiral symmetry in spontaneously broken form is modelled by imposing the physical π-ρ mass splitting as a constraint. The light-cone wavefunctions of the resulting Hamiltonian are used to compute decay constants, form factors and quark momentum and spin distributions for the pion and rho mesons. Extensions beyond leading order, and the implications for first principles calculations, are briefly discussed.

Fermions on the light front transverse lattice

“…As an example, the usual chiral transformation on the four component fermion field is incompatible with the constraint equation for nonzero fermion mass [4]. There have been previous studies of fermions on the transverse lattice [5,6,7,8]. Our approach in this work is quite extensive and aims to understand the origin of the doublers.…”

The annihilation of virtual photons into pseudoscalar mesons

“…Between these extremes many studies, using e.g. light-cone QCD sum rules with non-local condensates [30], the transverse lattice [31], or the instanton model of QCD [32] obtain a distribution amplitude either slightly broader or slightly narrower than Φ AS .…”

Pion light-cone wave function and pion distribution amplitude in the Nambu–Jona-Lasinio model

“…The pion distribution amplitude has been evaluated with QCD sum rules [9,10,11,12,13,14], in standard [15] (only the second ξ-moment) and transverse lattice approaches [16,17,18], and in chiral quark models [19,20,21,22,23,24,25,26,27,28,29]. In chiral quark models the results are not always compatible to each other, and even their interpretation has not always been the same.…”