A Model for the Off-forward Structure Functions of the Pion

We extend our model for the pion, which we used previously to calculate its diagonal structure function, to the off-forward case. The imaginary part of the off-forward gamma* pi -> gamma* pi scattering amplitude is evaluated in the chiral limit (m_pi=0) and related to the twist-two and twist-three generalised parton distributions, H, H3, H3tilde. Non-perturbative effects, linked to the size of the pion and still preserving gauge invariance, are included. Remarkable new relations between H, H3 and H3tilde are obtained and discussed.Comment: 9 pages, 20 figures, LaTeX, uses ulg_ptf.cls (included); v2: Form factors dropped in favour of GPD's, comparison between Wandzura-Wilczek approximation and our relations adde

A Model for the Generalized Parton Distribution of the Pion

We calculate the off-forward structure function of the pion within a simple model where the size of the pion is accounted for using a momentum cut-off. Twist-two and twist-three generalized parton distributions are extracted. Relations between twist-three and twist-two contributions are obtained, the origin of which is not kinematical as they differ from those arising from the Wandzura-Wilczek approximation.Comment: Presented at 6th Conference on Quark Confinement and the Hadron Spectrum, Villasimius, Sardinia, Italy, 21-25 Sep 2004, 3 pages, 4 figures, LaTeX, uses aip-6s.clo, aipproc.cls and aipxfm.sty (included

The Valence Quark Distribution of the Pion

The pion structure function is investigated in a simple model, where the pion and its constituent quark fields are coupled through the simplest pseudoscalar coupling. The imaginary part of the forward gamma* pi -> gamma* pi 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, allows a connection with the quark distribution. It is predicted that higher-twist terms become negligible for Q^2 larger than ~2 GeV^2, that quarks in the pion have a momentum fraction smaller than in the proton case, and that the momentum sum rule is violated for the pion.Comment: Presented by J. P. Lansberg at the XXII Physics in Collision Conference (PIC02), Stanford, California, June 20-22, 2002, 3 pages, 4 figures, LaTeX, uses pic02.sty (included

A toy model for generalised parton distributions

We give the results of a simple model for the diagonal and off-diagonal valence quark distributions of a pion. We show that structure can be implemented in a gauge-invariant manner. This explicit model questions the validityof the momentum sum rule, and gives an explicit counter-example to the Wandzura-Wilczek ansatz for twist-3 GPD's.Comment: 11 pages, presented at HADRONIC PHYSICS (HLPR 2004): Joint Meeting-Heidelberg-Liege-Paris-Rostock, Spa, Belgium, 16-18 December 2004, 11 pages, 11 figures, LaTe

Pion Structure Function and Violation of the Momentum Sum Rule

We present a method to evaluate the pion structure functions from a box diagram calculation. Pion and constituent quark fields are coupled through the simplest pseudoscalar coupling. The gamma^* pi -> q \bar q cross-section is evaluated and related to the structure functions. We then show that the introduction of non-perturbative effects, related to the pion size and preserving gauge invariance, provides us with a straighforward relation with the quark distribution. It is predicted that higher-twist terms become negligible for Q^2 larger than about 2 GeV^2 and that quarks in the pion have a momentum fraction smaller than in the proton. We enlarge the discussion concerning this violation of the momentum sum rule, emphasizing that the sum rule is recovered in the chiral limit and also when the finite size condition is not imposed.Comment: Presented by J.P. Lansberg at the II International Workshop on Hadron Physics, 25-29 September, 2002, Coimbra, Portugal, 14 pages, 9 figures, LaTeX, uses aip-6s.clo, aipproc.cls and aipxfm.sty (included

Confinement and cut-off: a model for the pion quark distribution function

The pion structure function is investigated in a simple pseudo-scalar coupling model of pion and constituent quark fields. The imaginary part of the forward Compton scattering amplitude is evaluated. We show that the introduction of non-perturbative effects, linked through a cut-off to the size of the pion, allows the reproduction of important features of the pion quark distribution function.Comment: 3 pages, 1 figur

Comment on ``Parton distributions, d/u, and higher twist effects at high x''

In a recent paper Yang and Bodek extracted the free neutron structure function at large x by extrapolating the density dependence of the nuclear EMC ratios to the deuteron. We clarify why this approach is ill-defined for light nuclei, and introduces a large theoretical bias into the extraction of F_2n at large x.Comment: 3 pages, 1 figure, REVTeX, discussion expanded to clarify original criticisms of nuclear density extrapolation to the deutero