Jean-Philippe Lansberg

University of Liege, Belgium

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, F1,...,F5 and relations between these functions are obtained in the high-Q2 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.


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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