On the effective light-cone QCD-Hamiltonian: Application to the pion and other mesons

Abstract

The effective interaction between a quark and an anti-quark as obtained previously with by the method of iterated resolvents is replaced by the ↑↓-model and applied to flavor off-diagonal mesons including the π + . The only free parameters are the canonical ones, the coupling constant and the masses of the quarks.The light-cone approach [1] to the bound-state problem in gauge theory [2] aims at solving H LC |Ψ = M 2 |Ψ . If one disregards possible zero modes [4] and works in the light-cone gauge, the (light-cone) Hamiltonian H LC is given as a Fock-space operator in [2], or in the compendium [3]. Its eigenvalues are the invariant mass-squares M 2 of physical particles associated with the eigenstates |Ψ . In general, they are superpositions of all possible Fock states with its many-particle configurations. For a meson, for example, holds [6], attacks this problem by DLCQ. Alternatively, one addresses to reduce the many-body problem behind a field theory to an effective one-body problem. The derivation of the effective interaction becomes then the key issue. By definition, an effective Hamiltonian acts only in the lowest sector of the theory (here: in the Fock space of one quark and one anti-quark) and has the same

Splitting of theπ−ρspectrum in a renormalized light-cone QCD-inspired model

“…The parameters of the present model are w, the ground state mass of the 3 S 1 meson and the renormalized strength of the Dirac-Delta interaction. We have here, the same number of parameters of the original model [1][2][3], which is the canonical number of 7 (α and 6 constituent quark masses) plus one, the strength of the renormalized Dirac-delta interaction. In the next, we show the numerical results for the splitting of the π − ρ and K − K * spectrum, due to the Dirac-delta interaction acting in the pseudo-scalar 1 S 0 channel.…”

Universal description ofS-wave meson spectra in a renormalized light-cone QCD-inspired model

“…[3] to include confinement. In the effective theory the bare mass operator equation for the lowest Light-Front Fock-state component of a bound system of a constituent quark and antiquark of masses m 1 and m 2 , is described as [1,2] …”

“…In the effective light-cone QCD theory [1,2] the lowest Fock component of the hadron wave function is an eigenfunction of an effective mass squared operator with constituent quark degrees of freedom and parameterized in terms of an interaction which contains a Coulomb-like potential and a Dirac-delta term. The Fock-state components of the hadron light-front wave function can be constructed recursively from the lowest Fock-state component.…”

Electromagnetic structure and weak decay of pseudoscalar mesons in a light-front QCD-inspired model

“…The hadronic structure viewed through effective light-front theories inspired by Quantum Chromodynamics [1,2,3,4,5,6] can shed light in the investigation of the interaction between the hadron constituents and in the study of the transition from effective to fundamental degrees of freedom that should be revealed at large momentum scales. The effective QCD-theory is expressed through a squared mass operator acting on the valence component of the hadron light-front wave function.…”

“…[3,4]. The squared mass operator includes a Coulomb-like and a Dirac-delta hyperfine interactions acting on the spin singlet state responsible for the mass separation between pseudoscalar and the vector meson states.…”