Exclusive meets inclusive at small Bjorken-xBx_B: how to relate exclusive measurements to PDFs based on evolution equations

Exclusive heavy-vector-meson photoproduction is a prominent signal in collider experiments with hadron beams. At the highest photon-hadron collision energies, this process is considered as a candidate to constrain gluon parton distribution functions (PDFs) at small longitudinal momentum fractions. However, in the framework of collinear factorisation, exclusive particle production is described in terms of generalised parton distributions (GPDs). In this contribution, we investigate at the leading order in $\alpha_s$ the connection between GPDs and PDFs. Our main result is a proposal to quantify the systematic uncertainty inherent to this connection. We put our approach into context with respect to the Shuavev transform. Our uncertainty estimate can be straightforwardly adapted to higher fixed orders and small-$x$ resummations. The question of extrapolating GPDs to vanishing skewness is paramount for the programme of the Electron Ion Collider (EIC), notably for the extraction of the radial distributions of partons.Comment: 17 pages, 7 figure

Phenomenology of generalised parton distributions from deeply virtual Compton scattering

Generalized parton distributions (GPDs) contain a wealth of information about the structure of hadrons. In particular, they describe three-dimensional distributions of quarks and gluons as well as the energy and pressure distributions in the hadronic medium. These properties motivate a major theoretical and experimental effort, which is reflected in the construction of new large-scale experimental facilities such as the electron-ion collider (EIC).GPDs are studied experimentally through exclusive processes, including in particular deeply virtual Compton scattering (DVCS) which is considered as one of the best theoretically established processes to access GPDs. The relationship between GPDs and experimental DVCS data is however complex, requiring in particular the solution of a deconvolution problem. In this paper we present the first systematic study of the characteristics of this problem at 1-loop in perturbation. We introduce the notion of shadow distributions as a quantitative tool to measure the difficulty of the deconvolution procedure, as well as an interesting modelling tool to perform GPD extractions while guaranteeing their theoretically correct properties. To achieve lesser model dependence, we will make use of neural networks modelling techniques. We investigate in detail the possibility of extracting mechanical properties in a less model-dependent way than current studies, and quantify the effect of the possible future facilities on both the experimental uncertainty of the DVCS and on the extraction of GPDs by the deconvolution procedure.Les distributions de partons généralisées (GPD) contiennent une riche information sur la structure des hadrons. Elles décrivent notamment des distributions de quarks et de gluons tri-dimensionnelles ainsi que les distributions en énergie et en pression dans le milieu hadronique. Ces propriétés motivent un effort théorique et expérimental important, qui se concrétise notamment par la construction de nouvelles installations expérimentales à grande échelle comme le collisionneur électron-ion (EIC).Les GPD sont étudiées expérimentalement aux travers de processus exclusifs, dont notamment la diffusion Compton profondément virtuelle (DVCS) qui est considérée comme l'un des processus les mieux établis théoriquement pour accéder aux GPD. La relation entre les GPD et les données expérimentales DVCS est cependant complexe, et nécessite notamment de résoudre un problème de déconvolution. Nous présentons dans ce document la première étude systématique des caractéristiques de ce problème à l'ordre sous-dominant en perturbation. Nous introduisons la notion de "shadow distributions" comme un outil quantitatif pour mesurer la difficulté de la procédure de déconvolution, ainsi qu'un outil de modélisation intéressant pour effectuer des extractions de GPD tout en garantissant leurs propriétés théoriques correctes. Afin de réduire la dépendence de modèle, nous utiliserons des techniques de modélisation par réseaux de neurones. Nous étudions en détail la possibilité d'extraire les propriétés mécaniques d'une manière moins dépendante de modèle que les études actuelles, et nous quantifions l'effet des futures installations envisagées à la fois sur l'incertitude expérimentale du DVCS et sur l'extraction des GPD par la procédure de déconvolution

Phenomenology of generalised parton distributions from deeply virtual Compton scattering

Generalized parton distributions (GPDs) contain a wealth of information about the structure of hadrons. In particular, they describe three-dimensional distributions of quarks and gluons as well as the energy and pressure distributions in the hadronic medium. These properties motivate a major theoretical and experimental effort, which is reflected in the construction of new large-scale experimental facilities such as the electron-ion collider (EIC).GPDs are studied experimentally through exclusive processes, including in particular deeply virtual Compton scattering (DVCS) which is considered as one of the best theoretically established processes to access GPDs. The relationship between GPDs and experimental DVCS data is however complex, requiring in particular the solution of a deconvolution problem. In this paper we present the first systematic study of the characteristics of this problem at $1$-loop in perturbation. We introduce the notion of shadow distributions as a quantitative tool to measure the difficulty of the deconvolution procedure, as well as an interesting modelling tool to perform GPD extractions while guaranteeing their theoretically correct properties. To achieve lesser model dependence, we will make use of neural networks modelling techniques. We investigate in detail the possibility of extracting mechanical properties in a less model-dependent way than current studies, and quantify the effect of the possible future facilities on both the experimental uncertainty of the DVCS and on the extraction of GPDs by the deconvolution procedure.Les distributions de partons généralisées (GPD) contiennent une riche information sur la structure des hadrons. Elles décrivent notamment des distributions de quarks et de gluons tri-dimensionnelles ainsi que les distributions en énergie et en pression dans le milieu hadronique. Ces propriétés motivent un effort théorique et expérimental important, qui se concrétise notamment par la construction de nouvelles installations expérimentales à grande échelle comme le collisionneur électron-ion (EIC).Les GPD sont étudiées expérimentalement aux travers de processus exclusifs, dont notamment la diffusion Compton profondément virtuelle (DVCS) qui est considérée comme l'un des processus les mieux établis théoriquement pour accéder aux GPD. La relation entre les GPD et les données expérimentales DVCS est cependant complexe, et nécessite notamment de résoudre un problème de déconvolution. Nous présentons dans ce document la première étude systématique des caractéristiques de ce problème à l'ordre sous-dominant en perturbation. Nous introduisons la notion de "shadow distributions" comme un outil quantitatif pour mesurer la difficulté de la procédure de déconvolution, ainsi qu'un outil de modélisation intéressant pour effectuer des extractions de GPD tout en garantissant leurs propriétés théoriques correctes. Afin de réduire la dépendence de modèle, nous utiliserons des techniques de modélisation par réseaux de neurones. Nous étudions en détail la possibilité d'extraire les propriétés mécaniques d'une manière moins dépendante de modèle que les études actuelles, et nous quantifions l'effet des futures installations envisagées à la fois sur l'incertitude expérimentale du DVCS et sur l'extraction des GPD par la procédure de déconvolution

Phenomenology of generalised parton distributions from deeply virtual Compton scattering

Generalized parton distributions (GPDs) contain a wealth of information about the structure of hadrons. In particular, they describe three-dimensional distributions of quarks and gluons as well as the energy and pressure distributions in the hadronic medium. These properties motivate a major theoretical and experimental effort, which is reflected in the construction of new large-scale experimental facilities such as the electron-ion collider (EIC).GPDs are studied experimentally through exclusive processes, including in particular deeply virtual Compton scattering (DVCS) which is considered as one of the best theoretically established processes to access GPDs. The relationship between GPDs and experimental DVCS data is however complex, requiring in particular the solution of a deconvolution problem. In this paper we present the first systematic study of the characteristics of this problem at $1$-loop in perturbation. We introduce the notion of shadow distributions as a quantitative tool to measure the difficulty of the deconvolution procedure, as well as an interesting modelling tool to perform GPD extractions while guaranteeing their theoretically correct properties. To achieve lesser model dependence, we will make use of neural networks modelling techniques. We investigate in detail the possibility of extracting mechanical properties in a less model-dependent way than current studies, and quantify the effect of the possible future facilities on both the experimental uncertainty of the DVCS and on the extraction of GPDs by the deconvolution procedure.Les distributions de partons généralisées (GPD) contiennent une riche information sur la structure des hadrons. Elles décrivent notamment des distributions de quarks et de gluons tri-dimensionnelles ainsi que les distributions en énergie et en pression dans le milieu hadronique. Ces propriétés motivent un effort théorique et expérimental important, qui se concrétise notamment par la construction de nouvelles installations expérimentales à grande échelle comme le collisionneur électron-ion (EIC).Les GPD sont étudiées expérimentalement aux travers de processus exclusifs, dont notamment la diffusion Compton profondément virtuelle (DVCS) qui est considérée comme l'un des processus les mieux établis théoriquement pour accéder aux GPD. La relation entre les GPD et les données expérimentales DVCS est cependant complexe, et nécessite notamment de résoudre un problème de déconvolution. Nous présentons dans ce document la première étude systématique des caractéristiques de ce problème à l'ordre sous-dominant en perturbation. Nous introduisons la notion de "shadow distributions" comme un outil quantitatif pour mesurer la difficulté de la procédure de déconvolution, ainsi qu'un outil de modélisation intéressant pour effectuer des extractions de GPD tout en garantissant leurs propriétés théoriques correctes. Afin de réduire la dépendence de modèle, nous utiliserons des techniques de modélisation par réseaux de neurones. Nous étudions en détail la possibilité d'extraire les propriétés mécaniques d'une manière moins dépendante de modèle que les études actuelles, et nous quantifions l'effet des futures installations envisagées à la fois sur l'incertitude expérimentale du DVCS et sur l'extraction des GPD par la procédure de déconvolution

Exclusive meets inclusive at small Bjorken-xBx_B: how to relate exclusive measurements to PDFs based on evolution equations

International audienceExclusive heavy-vector-meson photoproduction is a prominent signal in collider experiments with hadron beams. At the highest photon-hadron collision energies, this process is considered as a candidate to constrain gluon parton distribution functions (PDFs) at small longitudinal momentum fractions. However, in the framework of collinear factorisation, exclusive particle production is described in terms of generalised parton distributions (GPDs). In this contribution, we investigate at the leading order in $\alpha_s$ the connection between GPDs and PDFs. Our main result is a proposal to quantify the systematic uncertainty inherent to this connection. We put our approach into context with respect to the Shuavev transform. Our uncertainty estimate can be straightforwardly adapted to higher fixed orders and small-$x$ resummations. The question of extrapolating GPDs to vanishing skewness is paramount for the programme of the Electron Ion Collider (EIC), notably for the extraction of the radial distributions of partons

Revisiting evolution equations for generalised parton distributions

International audienceWe revisit the evolution of generalised parton distributions (GPDs) in momentum space. We formulate the evolution kernels at one-loop in perturbative QCD (pQCD) in a form suitable for numerical implementation and that allows for an accurate study of their properties. This leads to the first open-source implementation of GPD evolution equations able to cover the entire kinematic region and allowing for heavy-quark-threshold crossings. The numerical implementation of the GPD evolution equations is publicly accessible through the APFEL++ evolution library and is available within the PARTONS framework. Our formulation makes use of the operator definition of GPDs in light-cone gauge renormalised in the \overline{\mbox{MS}} scheme. For the sake of clarity, we recompute the evolution kernels at one-loop in pQCD, confirming previous calculations. We obtain general conditions on the evolution kernels deriving from the GPD sum rules and show that our formulation obeys these conditions. We analytically show that our calculation reproduces the DGLAP and the ERBL equations in the appropriate limits and that it guarantees the continuity of GPDs. We numerically check that the evolved GPDs fulfil DGLAP and ERBL limits, continuity, and polynomiality. We benchmark our numerical implementation against analytical evolution in conformal space. Finally, we perform a numerical comparison to an existing implementation of GPD evolution finding a general good agreement on the kinematic region accessible to the latter. This work provides a pedagogical description of GPD evolution equations which benefits from a renewed interest as future colliders, such as the electron-ion colliders in the US and in China, are being designed. It also paves the way to the extension of GPD evolution codes to higher accuracies in pQCD desirable for precision phenomenology at these facilities

Revisiting evolution equations for generalised parton distributions

We revisit the evolution of generalised parton distributions (GPDs) in momentum space. We formulate the evolution kernels at one-loop in perturbative QCD (pQCD) in a form suitable for numerical implementation and that allows for an accurate study of their properties. This leads to the first open-source implementation of GPD evolution equations able to cover the entire kinematic region and allowing for heavy-quark-threshold crossings. The numerical implementation of the GPD evolution equations is publicly accessible through the APFEL++ evolution library and is available within the PARTONS framework. Our formulation makes use of the operator definition of GPDs in light-cone gauge renormalised in the \overline{\mbox{MS}} scheme. For the sake of clarity, we recompute the evolution kernels at one-loop in pQCD, confirming previous calculations. We obtain general conditions on the evolution kernels deriving from the GPD sum rules and show that our formulation obeys these conditions. We analytically show that our calculation reproduces the DGLAP and the ERBL equations in the appropriate limits and that it guarantees the continuity of GPDs. We numerically check that the evolved GPDs fulfil DGLAP and ERBL limits, continuity, and polynomiality. We benchmark our numerical implementation against analytical evolution in conformal space. Finally, we perform a numerical comparison to an existing implementation of GPD evolution finding a general good agreement on the kinematic region accessible to the latter. This work provides a pedagogical description of GPD evolution equations which benefits from a renewed interest as future colliders, such as the electron-ion colliders in the US and in China, are being designed. It also paves the way to the extension of GPD evolution codes to higher accuracies in pQCD desirable for precision phenomenology at these facilities.Comment: 39 pages including 3 appendices and references, 12 figures with plots and diagram