Light-Meson Distribution Amplitude: Simple Relativistic Model

Abstract

With the basic concepts of the constituent-quark model formulated in the light-cone Fock approach we present a relativistic model of the pion and p-meson valence-quark structure. We point out that a nonstatic relativistic spin wave function and small transverse size of the valence configuration are essential to reproduce the basic features of the Chernyak-Zhitnitsky amplitudes for the n and p as they are obtained from QCD sum-rule techniques.PACS numbers: 12.38.Lg A basic part of perturbative-quantum-chromodynamics (QCD) predictions are the hadronic wave functions which determine distribution amplitudes and structure functions of hadrons which enter any highmomentum-transfer reaction. In the case of exclusive processes via the factorization theorem,' any hadronic amplitude can be written as a convolution of a hardscattering amplitude TM with the hadronic distribution amplitude (p(x,Q). Recently interesting information on the meson distribution amplitude has been obtained with the use of powerful nonperturbative methods.Through QCD sum rules, Chernyak and Zhitnitsky^'-^ derived the lowest two moments of the distribution amplitude. This information allowed them to formulate a model for the pion and the p meson. The following surprising picture of the momentum-space valence structure of the mesons emerged. First, there is quite substantial spin dependence. The K distribution has highly structured double-humped form, very different from the p amplitude. Furthermore, the shape of the p function depends on its helicity A. Second, there is a large asymmetry between quarks, i.e., for the pion, a large part of the momentum is carried by one quark. Finally, the quarks are highly relativistic. All distributions are broad and very different from the nonrelativistic ^-function form.Quite recently Gottlieb and Kronfeld'* with the use of lattice gauge theory calculated the first two moments of the 71 and p distribution amplitudes. The results for the second moments are larger than those of Ref. 2. Hence, their pion and p distribution are even more structured and oscillating then the Chernyak-Zhitnitsky ones.Both approaches suggest that the remarkable features of the meson wave function (WF) are a consequence of nonperturbative QCD. However, it is difficult to assess which of the fundamentals of QCD dynamics used in the calculations of Ref. 2 and Ref. 4 are decisive for the determination of the meson WF. This fact prompted us to derive the light-meson amplitudes in a more direct way, with use of more transparent assumptions.In an attempt to follow the suggestion we present a simple relativistic model of the meson WF. We use the basic concepts of the constituent-quark model formulated in the light-cone approach, i.e., (a) meson states are dominated by the valence qq configuration with typical constituent masses, (b) the quark-antiquark pair is a system with substantial relativistic motion, and (c) the K and p have standard quark-model spin and parity assignments.There is a natural covariant framework for describing the composite...

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