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 non-perturbative 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 Q2 larger than ∼2 GeV2 and that quarks in the pion have a momentum fraction smaller than in the proton case.
Highlights
Deep-inelastic scattering (DIS) experiments provide us with a wealth of information about the structure of hadrons, usually cast in the form of structure functions
The structure functions can be related to the quark distributions: F1
The imaginary part of the forward elastic scattering does not show any divergence. This quantity cannot provide the quark distributions readily since the numerical importance of the so-called crossed diagrams precludes the existence of such a relationship
Summary
Deep-inelastic scattering (DIS) experiments provide us with a wealth of information about the structure of hadrons, usually cast in the form of structure functions. There have been several theoretical investigations along these lines in recent years [6,7,8,9] They rely on the assumption that distributions evaluated in leading-twist approximation at small Q2, where these models apply, can serve as input in the DGLAP evolution equations [10] to generate parton distributions that are directly comparable with experimental data at large Q2 [11,12,13,14,15]. It is possible to cope with this requirement by imposing a finite momentum cut-off, which mimics the effect of a pion wave function Such a step leads to the appearance of a straightforward relation between the γ⋆ − π cross sections and the quark distributions at high enough Q2, as we shall show
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