A model for the pion structure function

Abstract

The pion structure function is investigated in a simple model, where pion and constituent quark fields are coupled through the simplest pseudoscalar coupling. The imaginary part of the forward γ ⋆ π → γ ⋆ π scattering amplitude is evaluated and related to the structure functions. It is shown that the introduction of nonperturbative effects, linked to the size of the pion and preserving gauge invariance, allows a connection with the quark distribution. It is predicted that higher-twist terms become negligible for Q 2 larger than ∼2 GeV 2 and that quarks in the pion have a momentum fraction smaller than in the proton case.

Generalized parton distributions of the pion

“…As explained in Ref. [2], owing to these conditions and for small t, the crossed diagrams are suppressed by a power Λ 2 /Q 2 , compared to the box diagrams. We keep the coupling constant g as in the diagonal case, where it was determined by imposing that there are only two constituent quarks in the pion, or equivalently that the following relation…”

“…They have been obtained with the same cut-off value as in Ref. [2], namely Λ= 0.75 GeV, a value consistent with the hard core radius of the pion in the chiral bag model [5].…”

“…We recall that, for the diagonal case (elastic scattering in the forward direction), we found in Ref. [2] that the momentum fraction carried by the quarks…”

A Model for the Generalized Parton Distribution of the Pion

“…Based on the model we built to calculate the diagonal structure functions of the pion in a gaugeinvariant, regularization-independent way [2], we have performed the calculations of off-forward structure functions and link them to generalized parton distributions.…”

A model for the off-forward structure functions of the pion

“…These models can be used to depict the behaviour of the structure functions and to understand the connection between data and non-perturbative aspects of hadrons. There has been extensive work on diagonal distributions along these lines (see Refs [1]- [2] for the pion case). These distributions can be used as the initial condition for a DGLAP evolution, which is necessary before a comparison with data [3].…”