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Jean-Philippe Lansberg

University of Liege, Belgium
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Forward and Off-forward parton distributions of the pion

We show how, from a simple model, one can obtain the forward and
off-forward parton distributions of the pion. In this model, the pion
and the constituent quarks are coupled through the simplest pseudoscalar
coupling and the forward (resp. off-forward) structure functions are
obtained through a calculation of the imaginary part of the forward
(resp. off-forward) γ^{*} π → γ^{*} π scattering amplitude at
lowest order.
In the off-forward case, this amplitude is decomposed into five
structure functions, F_{1},...,F_{5} and relations between these functions
are obtained in the high-Q^{2} limit. Non-perturbative effects, mimicking
the finite size function of the pion, are introduced through a cut-off,
in a gauge-independent way. In this very simple model, one can see that
the momentum sum rule is very likely to be wrong in the pion case.
Moreover, we show that this calculation of the imaginary part of
γ^{*}π → γ^{*} π is sufficient to determine the twist-two and
twist-three GPD's H,H3, Ht3. Relations between the latter are also
obtained and are compared with similar relations obtained with the
Wandzura-Wilczek approximation.

References:

1) A MODEL FOR THE OFF FORWARD STRUCTURE FUNCTIONS OF THE PION.
By F. Bissey (Liege U. & Massey U.), J.R. Cudell, J. Cugnon, J.P.
Lansberg, P. Stassart (Liege U.),. Oct 2003. 8pp.
Published in Phys.Lett.B587:189-200,2004
e-Print Archive: hep-ph/0310184

2) A MODEL FOR THE PION STRUCTURE FUNCTION.
By F. Bissey, J.R. Cudell, J. Cugnon, M. Jaminon, J.P. Lansberg, P.
Stassart (Liege U.),. Jul 2002. 14pp.
Published in Phys.Lett.B547:210-218,2002
e-Print Archive: hep-ph/0207107

3) PION STRUCTURE FUNCTION AND VIOLATION OF THE MOMENTUM SUM RULE.
By J.P. Lansberg, F. Bissey, J.R. Cudell, J. Cugnon, M. Jaminon, P.
Stassart (Liege U.),. Nov 2002. 14pp.
Published in AIP Conf.Proc.660:339-352,2003
e-Print Archive: hep-ph/0211450

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