Non local lagrangians(I): the pion

We define a family of non local and chirally symmetric low energy lagrangians motivated by theoretical studies on Quantum Chromodynamics. These models lead to quark propagators with non trivial momentum dependencies. We define the formalism for two body bound states and apply it to the pion. We study the coupling of the photon and W bosons with special attention to the implementation of local gauge invariance. We calculate the pion decay constant recovering the Goldberger-Treiman and the Gell-Mann-Oakes-Renner relations. We recover a form of the axial current consistent with PCAC. Finally we study the pion form factor and we construct the operators involved in its parton distribution.Comment: Latex, 25 pages with 15 figures; added references for introduction and section

On BLM scale fixing in exclusive processes

We discuss the BLM scale fixing procedure in exclusive electroproduction processes in the Bjorken regime. We show that in the case of vector meson production the usual way to aplly the BLM method fails due to singularities present in equations fixing the BLM scale. We argue that the BLM scale should be extracted from the squared amplitudes which are directly related to observables.Comment: accepted for the publication in Eur.Phys.J.

Dispersion relations and subtractions in hard exclusive processes

We study analytical properties of the hard exclusive processes amplitudes. We found that QCD factorization for deeply virtual Compton scattering and hard exclusive vector meson production results in the subtracted dispersion relation with the subtraction constant determined by the Polyakov-Weiss $D$-term. The relation of this constant to the fixed pole contribution found by Brodsky, Close and Gunion and defined by parton distributions is proved, while its manifestation is spoiled by the small $x$ divergence. The continuation to the real photons limit is considered and the numerical correspondence between lattice simulations of $D$-term and low energy Thomson amplitude is found.Comment: 4 pages, journal versio

Hard Electroproduction of Hybrid Mesons

We estimate the sizeable cross section for deep exclusive electroproduction of an exotic $J^{PC}=1^{-+}$ hybrid meson in the Bjorken regime. The production amplitude scales like the one for usual meson electroproduction, {\it i.e.} as $1/Q^2$. This is due to the non-vanishing leading twist distribution amplitude for the hybrid meson, which may be normalized thanks to its relation to the energy momentum tensor and to the QCD sum rules technique. The hard amplitude is considered up to next--to--leading order in $\alpha_{S}$ and we explore the consequences of fixing the renormalization scale ambiguity through the BLM procedure.Comment: e-version for "Advanced Studies Institute Conference on Symmetries and Spin (SPIN-Praha-2004)", Prague, Czech Republic, 5-10 Jul 200

Extraction of the Compton Form Factor H from DVCS measurements at Jefferson Lab

In the framework of Generalised Parton Distributions, we study the helicity-dependent and independent cross sections measured in Hall A and the beam spin asymmetries measured in Hall B at Jefferson Laboratory. We perform a global fit of these data and fits on each kinematical bin. We extract the real and imaginary parts of the Compton Form Factor $\mathcal{H}$ under the main hypothesis of dominance of the Generalised Parton Distribution $H$ and twist 2 accuracy. We discuss our results and compare to previous extractions as well as to the VGG model. We pay extra attention to the estimation of errors on the extraction of $\mathcal{H}$.Comment: 24 pages, 8 figure

Recent and future experimental evidences for exotic mesons in hard reactions

The QCD analysis of the recent experimental data (L3@LEP) of the hard exclusive $\rho\rho$ production in two photon collisions shows that these data can be understood as a signal for the existence of an exotic isotensor resonance with a mass around $1.5 {\rm GeV}$. We also argue that hard exclusive reactions are a powerful tool for an experimental study of exotic hybrid mesons with $J^{PC}=1^{-+}$.Comment: Talk given at XXXIII International Conference on High Energy Physics, July 26 - August 2, Moscow, Russi

Probing the partonic structure of exotic particles in hard electroproduction

We argue that the electroproduction of exotic particles is a useful tool for study of their partonic structure. In the case of hybrid mesons, the magnitude of their cross sections shows that they are accessible for measurements in existing electroproduction experiments.Comment: 10 pages Latex, 5 figs., talk at Three Days of Hadronic Physics (HLPR04): Joint Meeting Heidelberg-Liege-Paris-Rostock, Liege, Belgium, 16-18 Dec 200

Hard production of exotic hybrid mesons

Exotic hybrid mesons H, with quantum numbers J^{PC}= 1^{- +} may be copiously produced in the hard exclusive processes gamma^*(Q^2) gamma -> H and gamma^*(Q^2) P(p) -> H P(p') because they have a leading twist distribution amplitude with a sizable coupling constant f_H, which may be estimated through QCD sum rules. The reaction rates scale in the same way as the corresponding rates for usual mesons.Comment: 4 pages Latex, talk at XIth International Conference on Elastic and Diffractive Scattering Chateau de Blois, France, May 15 - 20, 200

On the description of exclusive processes beyond the leading twist approximation

We describe hard exclusive processes beyond the leading twist approximation in a framework based on the Taylor expansion of the amplitude around the dominant light-cone directions. This naturally introduces an appropriate set of non-perturbative correlators whose number is minimalized after taking into account QCD equations of motion and the invariance under rotation on the light-cone. We examplify this method at the twist 3 level and show that the coordinate and momentum space descriptions are fully equivalent.Comment: 6 pages, 2 figures, modified and slightly expanded version to be published in Phys.Lett.

QCD factorization of exclusive processes beyond leading twist: gamma*T -> rhoT impact factor with twist three accuracy

We describe a consistent approach to factorization of scattering amplitudes for exclusive processes beyond the leading twist approximation. The method involves the Taylor expansion of the scattering amplitude in the momentum space around the dominant light-cone direction and thus naturally introduces an appropriate set of non-perturbative correlators which encode effects not only of the lowest but also of the higher Fock states of the produced particle. The reduction of original set of correlators to a set of independent ones is achieved with the help of equations of motion and invariance of the scattering amplitude under rotation on the light-cone. We compare the proposed method with the covariant method formulated in the coordinate space, based on the operator product expansion. We prove the equivalence of two proposed parametrizations of the rhoT distribution amplitudes. As a concrete application, we compute the expressions of the impact factor for the transition of virtual photon to transversally polarised rho-meson up to the twist 3 accuracy within these two quite differents methods and show that they are identical.Comment: 53 pages, 16 figure