Hard constituent quarks and electroweak properties of pseudoscalar mesons

The high momentum components generated in the wave function of pseudoscalar mesons by the one-gluon-exchange interaction are investigated within a relativistic constituent quark model. Adopting the light-cone formalism, the sensitivity of the weak decay constant and the charge form factor to hard constituent quarks is illustrated. Phys. Lett. B, in press. The investigation of the electroweak properties of mesons and baryons can shed light on the effective constituents of hadrons and their dynamics. In particular, the understanding of hadron electroweak properties has recently received much theoretical attention within the context of constituent quark models both in the framework of light-cone dynamics [1, 2, 3, 4] and in a diagrammatic approach [5]. It has also been argued that existing experimental data on the weak decay constant and the charge form factor of mesons can be accounted for within a constituent qq̄ picture [4]. However, such a conclusion has been obtained by adopting a simplified description of the dynamics of the constituent quarks inside the meson, namely, by using gaussian-like wave functions which are expected to describe the effects of the confinement scale only. In this letter the wave functions of pseudoscalar (S-wave) mesons are analyzed within the relativized constituent quark model of ref. [6], which properly describes meson (as well as baryon [7]) mass spectra in terms of an effective (QCD motivated) qq̄ interaction composed by a one-gluon-exchange term and a linear confining potential. It is shown that high momentum components, generated in the meson wave function by the onegluon-exchange term, sharply affect the weak decay constant and the charge form factor. The agreement with existing experimental data can be obtained by introducing an axial-vector coupling constant and a charge form factor of the constituent quark. As in refs. [1, 2, 3, 4], meson electroweak properties will be evaluated adopting the light-cone formalism [8], which represents the natural framework for constructing a relativistic quark model featuring the dominance of the qq̄ component of mesons [9]. 1. Light-cone meson wave functions. As is known, light-cone wave functions are eigenfunctions of the mass operator, e.g. M = M0 + V (1) and of the usual angular momentum operators j and jn, where the vector n̂ = (0, 0, 1) defines the spin quantization axis. In eq. (1) V is a Poincaré invariant interaction term and M0 is the free mass operator, which reads as M 0 = k ⊥ +mq 2 ξ + k ⊥ +mq̄ 2 1− ξ (2) where mq(mq̄) is the constituent quark (antiquark) mass and the intrinsic light-cone variables ~k⊥ and ξ are ξ = pq /P + = 1− pq̄ /P (3) ~k⊥ = ~pq⊥ − ξ ~ P⊥ = −~ pq̄⊥ + (1− ξ)~ P⊥ (4) The subscript ⊥ indicates the projection perpendicular to the spin quantization axis and the plus component of a 4-vector p ≡ (p,p) is given by p = p + n̂ · p; in eqs. (34) ~ P ≡ (P, ~ P⊥) = ~ pq + ~ pq̄ is the total momentum of the meson, and ~ pq(~ pq̄) is the quark (antiquark) momentum. The structure of M0 is more transparent if the fraction ξ is replaced by the longitudinal momentum kn defined as kn = (ξ − 1 2 )M0 + mq̄ −mq 2M0 (5)