Integral representations for nonperturbative generalized parton distributions in terms of perturbative diagrams

We propose new parameterizations for the border and skewness functions appearing in the description of 3D nucleon structure in the language of Generalized Parton Distributions (GPDs). These parameterizations are constructed in a way to fulfill the basic properties of GPDs, like their reduction to Parton Density Functions and Elastic Form Factors. They also rely on the power behavior of GPDs in the x → 1 limit and the propounded analyticity property of Mellin moments of GPDs. We evaluate Compton Form Factors (CFFs), the sub-amplitudes of the Deeply Virtual Compton Scattering (DVCS) process, at the leading order and leading twist accuracy. We constrain the restricted number of free parameters of these new parameterizations in a global CFF analysis of almost all existing proton DVCS measurements. The fit is performed within the PAR-TONS framework, being the modern tool for generic GPD studies. A distinctive feature of this CFF fit is the careful propagation of uncertainties based on the replica method. The fit results genuinely permit nucleon tomography and may give some insight into the distribution of forces acting on partons.

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“…(55) by using the Ansatz for H q val (x, 0, t) given in Eq. (54) and that for E q val (x, 0, t) given in Eq. (67).…”

Section: Analysis Of Dirac and Pauli Form Factorsmentioning

confidence: 99%

Border and skewness functions from a leading order fit to DVCS data

2018

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“…As pointed out in Ref. [26], one can construct further consistent models of GPDs by summing over these basic contributions evaluated at different constituent masses. This is the essence of the consistency of the spectral quark model GPDs computed in Ref.…”

Section: Introductionmentioning

confidence: 99%

Violation of positivity bounds in models of generalized parton distributions

Tiburzi

Verma

2017

Phys. Rev. D

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As with parton distributions, flexible phenomenological parameterizations of generalized parton distributions (GPDs) are essential for their extraction from data. The large number of constraints imposed on GPDs make simple Lorentz covariant models viable; but, such models are often incomplete in that they employ the impulse approximation. Using the GPD of the pion as a test case, we show that the impulse approximation can lead to violation of the positivity bound required of GPDs. We focus on a particular model of the pion bound-state vertex that was recently proposed and demonstrate that satisfying the bound is not guaranteed by Lorentz covariance. Violation of the positivity bound is tied to a problematic mismatch between the behavior of the quark distribution at the endpoint and the crossover value of the GPD.

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“…The polynomiality "entangles" the x and ξ dependencies. iii ) positivity constraints [41][42][43][44][45][46][47][48][49], which are inequalities ensuring positive norms in the Hilbert space of states. Because of the variety of these inequalities, we do not quote them all here.…”

Section: Theoretical Backgroundmentioning

confidence: 99%

“…Since h C (β, α) is normalized, see Eqs. (46) and (48), the neural network lacks the flexibility allowing for a significant contribution to the uncertainties in kinematic domains that are unconstrained by data.…”

Section: Fits To Datamentioning

confidence: 99%

Artificial neural network modelling of generalised parton distributions

Dutrieux,

Grocholski,

Moutarde

et al. 2021

Preprint

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We discuss the use of machine learning techniques in effectively nonparametric modelling of generalised parton distributions (GPDs) in view of their future extraction from experimental data. Current parameterisations of GPDs suffer from model dependency that lessens their impact on phenomenology and brings unknown systematics to the estimation of quantities like Mellin moments. The new strategy presented in this study allows to describe GPDs in a way fulfilling theory-driven constraints, keeping model dependency to a minimum. Getting a better grip on the control of systematic effects, our work will help the GPD phenomenology to achieve its maturity in the precision era commenced by the new generation of experiments. IntroductionGeneralised parton distributions (GPDs) [1][2][3][4][5] are widely recognised as one of the key objects to explore the structure of hadrons. They encompass information coming from one-dimensional parton distribution functions (PDFs) and elastic form factors (EFFs). GPDs allow for a hadron tomography [6][7][8], where densities of partons carrying a fraction of hadron momentum are studied in the plane perpendicular to the hadron's direction of motion. GPDs also provide access to the matrix elements of the energy-momentum tensor [2,3,9], making it possible to evaluate the total angular momentum and "mechanical" properties of hadrons, like pressure and shear stress at a given point of space [10][11][12][13].

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Integral representations for nonperturbative generalized parton distributions in terms of perturbative diagrams

Cited by 27 publications

References 34 publications

Border and skewness functions from a leading order fit to DVCS data

Border and skewness functions from a leading order fit to DVCS data

Violation of positivity bounds in models of generalized parton distributions

Artificial neural network modelling of generalised parton distributions

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