Modeling the pion Generalized Parton Distribution

We compute the pion Generalized Parton Distribution (GPD) in a valence dressed quarks approach. We model the Mellin moments of the GPD using Ans\"atze for Green functions inspired by the numerical solutions of the Dyson-Schwinger Equations (DSE) and the Bethe-Salpeter Equation (BSE). Then, the GPD is reconstructed from its Mellin moment using the Double Distribution (DD) formalism. The agreement with available experimental data is very good.Comment: 8 pages, 4 figures, proceeding of the 21st International Symposium on Spin Physics, October 20-24 2014, Beijing, Chin

Little G. T. for lp-lattice summing operators

2000 Mathematics Subject Classification: 46B28, 47D15.In this paper we introduce and study the lp-lattice summing operators in the category of operator spaces which are the analogous of p-lattice summing operators in the commutative case. We study some interesting characterizations of this type of operators which generalize the results of Nielsen and Szulga and we show that Λ l∞( B(H) ,OH) ≠ Λ l2( B( H) ,OH), in opposition to the commutative case

Weak Grothendieck's theorem

Let En⊂L12n be the n-dimensional subspace which appeared in Kašin's theorem such that L12n=En⊕En⊥ and the L12n and L22n norms are universally equivalent on both En and En⊥. In this paper, we introduce and study some properties concerning extension and weak Grothendieck's theorem (WGT). We show that the Schatten space Sp for all 0<p≤∞ does not verify the theorem of extension. We prove also that Sp fails GT for all 1≤p≤∞ and consequently by one result of Maurey does not satisfy WGT for 1≤p≤2. We conclude by giving a characterization for spaces verifying WGT

Étude des distributions de partons généralisées, approches phénoménologiques et équations de Dyson-Schwinger

This study is devoted to generalised parton distributions (GPDs). First, the main properties of GPDs are given to the reader. One can stress the so-called support properties and the polynomiality property. The latter is automatically fulfiled when modeling GPDs from double distributions (DDs), GPDs being considered as the Radon transform of DDs. In the scalar case, two DDs denoted by F and G are required to describe the GPD H. Due to the integral relation existing between H on one hand, and F and G on the other hand, F and G are not defnied unambiguously. This ambiguity is exploited in the present work in order to develop a new phenomenological parametrisation. Using the Radyushkin Ansatz, it is then possible get a realistic model of GPDs, and to compare it with available experimental data. In the present case, two types of models, one neglecting the GPD E, the other taking it into account are compared with the Jlab Hall A DVCS data. In the former cae, one can notice a better flexibility allowing to better reproduced the beam-helicity independent cross sections. In the latter one, only the GPD E is deeply modified, and thus the comparison with available data does not change significantly with respect to previous parametrisations. Only data more sensitive to E will allow one to selet the most relevant parametrisation.In order to go beyond phenomenological parametrisations, a first step has been done toward a dynamical description of hadron structure. Using the Dyson-Schwinger equations, it has been possible to compute analytically the pion GPD within the triangle diagram approximation. The comparison with available data (Form factor and PDF) appears to be very good. Nevertheless, this first model does not fulfil all the required properties. Especially the soft pion theorem, which corresponds to a specific kinematical limit. It has been shown in this work that this is due to the violation of the Axial-Vector Ward-Takahashi identity, and that the triangle approximation is sufficient to ensure the sof pion theorem. Still it violates the exchange symmetry x, 1-x, and thus additional terms, previously neglected, are taken into account. It is then possible to compute the probability density to find a quark at a given position in the transverse plan carrying a given momentum fraction. Finally, perspective on lightcone computations are given in the last chapter.Cette étude est consacrée aux distributions de partons généralisées (GPDs, de l'anglais Generalised Parton Distributions). Dans un premier temps, les principales propriétés des GPDs sont rappelées. On insiste notamment sur les propriétés dites de support et sur la polynomialité. Cette dernière est automatiquement respectée lorsque l'on modélise les GPDs au travers des doubles distributions (DDs), les GPDs s'écrivant comme la transformée de Radon des DDs.Dans le cas scalaire, deux DDs, notées F et G, sont nécessaires pour décrire la GPD H. Du fait de la relation intégrale existant entre H d'un côté, et F et G de l'autre, F et G sont définies de manière ambiguë. Cette ambiguïté est exploitée dans le présent travail afin de développer une nouvelle paramétrisation phénoménologique. Utilisant l'Ansatz de Radyushkin, il est possible d'obtenir un modèle réaliste de GPD, et de le comparer aux données expérimentales disponibles. Dans le cas présent, deux types de modèles, l'un négligeant la GPD E, l'autre en tenant compte, sont comparés aux données de diffusion Compton profondément virtuelle (DVCS) de la collaboration Hall A au Jeffeson Laboratory (JLab). Dans le premier cas, on observe une plus grande flexibilité de la paramétrisation par rapport aux précédentes, ce qui permet une meilleure comparaison aux données sur les sections efficaces indépendantes de l'hélicité du faisceau. Dans le second cas, seule la GPD E est profondément modifiée. De ce fait la comparaison aux données change peu par rapport aux modèles précédents. Seules des données plus sensibles à E permettront de trancher entre les paramétrisations.Afin de dépasser les paramétrisations phénoménologiques, un premier pas a été fait vers la description dynamique des hadrons. En utilisant les équations de Dyson-Schwinger, il a été possible de calculer analytiquement la GPD de pion dans le cadre de l'approximation du diagramme triangle. La comparaison aux données expérimentales disponibles (facteur de forme et PDF) s'est révélée très bonne. Il est également possible de montrer que l'approximation du diagramme triangle permet de retrouver le théorème de pion mou. Néanmoins, ce premier modèle ne respecte pas l'ensemble des propriétés des GPDs. Elle viole la symétrie d'échange x, 1-x, et par conséquent des termes supplémentaires, précédemment négligés, sont pris en compte. On peut ainsi obtenir la densité de probabilité de trouver un quark portant une fraction d'impulsion x dans le plan transverse. Des perspectives de calculs sur le cône de lumière sont présentés dans le dernier chapitre

Caractérisation Des Espaces 1-Matriciellement Normés

Let X be a closed subspace of B(H) for some Hilbert space H. In [9], Pisier introduced Sp [X] (1 ≤ p ≤ +∞) by setting Sp [X] = (S∞ [X] , S1 [X])θ , (where θ =1/p , S∞ [X] = S∞ ⊗min X and S1 [X] = S1 ⊗∧ X) and showed that there are p−matricially normed spaces. In this paper we prove that conversely, if X is a p−matricially normed space with p = 1, then there is an operator structure on X, such that M1,n (X) = S1 [X] where Sn,1 [X] is the finite dimentional version of S1 [X]. For p = 1, we have no answer

Process-independent effective coupling. From QCD Green's functions to phenomenology

This article reports on a very recent proposal for a new type of process-independent QCD effective charge [Phys.Rev.D96(2017)054026] defined, as an anologue of the Gell-Mann-Low effective charge in QCD, on the ground of nothing but the knowledge of the gauge-field two-point Green's function, albeit modified within a particular computational framework; namely, the combination of pinch technique and background field method which makes possible a systematic rearranging of classes of diagrams in order to redefine the Green's function and have them obey linear QED-like Slavnov-Taylor identities. We have here calculated that effective charge, shown how strikingly well it compares to a process-dependent effective charge based on the Bjorken sum rule; and, finally, employed it in an exploratory calculation of the proton electromagnetic form factor in the hard scattering regime.Comment: 13 pages, 3 figues; contribution to NStar 2017 (Columbia, USA

Pion's valence-quark GPD and its extension beyond DGLAP region

We briefly report on a recent computation, with the help of a fruitful algebraic model, sketching the pion valence dressed-quark generalized parton distribution and, very preliminary, discuss on a possible avenue to get reliable results in both Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) and Efremov-Radyushkin-Brodsky-Lepage (ERBL) kinematial regions.Comment: 6 pages, 4 figures, contribution to 21st International conference on Few-Body Problem