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Global Analyses of Generalized Parton Distributions with Diverse PDF Inputs

The MMGPDs Collaboration, Fatemeh Irani, Muhammad Goharipour, K. Azizi

Abstract

This paper investigates the crucial role of parton distribution functions (PDFs) in high-energy physics, particularly their impact on the extraction of generalized parton distributions (GPDs) at zero skewness. To this aim, we perform six global analyses of GPDs using different modern PDF sets (\texttt{NNPDF40}, \texttt{CT18}, and \texttt{MSHT20}) at three specific factorization scales ($ μ= 2 $, $ 1.3 $, and $ 1 $ GeV) and different perturbative orders. A wide range of elastic electron scattering data is included in the analysis to constrain GPDs in a broad interval in the momentum transfer squared $ t $. The analyses reveal that the best overall description of experimental data is achieved using \texttt{NNPDF40} PDFs at the next-to-leading order (NLO), with moderate sensitivity to the choice of PDF input, especially in the region of low $ t $. The dependence on the perturbative order is relatively mild, indicating stability in the extraction procedure. We also show that different GPD sets become more consistent at larger $ |t| $ values, with down-quark GPDs experiencing greater suppression than up-quark GPDs. The six extracted GPD sets, available at different scales and perturbative orders, provide valuable resources for future theoretical and phenomenological studies, offering flexibility for researchers in exploring the proton's internal structure.

Global Analyses of Generalized Parton Distributions with Diverse PDF Inputs

Abstract

This paper investigates the crucial role of parton distribution functions (PDFs) in high-energy physics, particularly their impact on the extraction of generalized parton distributions (GPDs) at zero skewness. To this aim, we perform six global analyses of GPDs using different modern PDF sets (\texttt{NNPDF40}, \texttt{CT18}, and \texttt{MSHT20}) at three specific factorization scales (, , and GeV) and different perturbative orders. A wide range of elastic electron scattering data is included in the analysis to constrain GPDs in a broad interval in the momentum transfer squared . The analyses reveal that the best overall description of experimental data is achieved using \texttt{NNPDF40} PDFs at the next-to-leading order (NLO), with moderate sensitivity to the choice of PDF input, especially in the region of low . The dependence on the perturbative order is relatively mild, indicating stability in the extraction procedure. We also show that different GPD sets become more consistent at larger values, with down-quark GPDs experiencing greater suppression than up-quark GPDs. The six extracted GPD sets, available at different scales and perturbative orders, provide valuable resources for future theoretical and phenomenological studies, offering flexibility for researchers in exploring the proton's internal structure.
Paper Structure (5 sections, 8 equations, 7 figures, 2 tables)

This paper contains 5 sections, 8 equations, 7 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Evolution of PDFs
  3. A Challenge in GPDs analysis
  4. Determination of GPDs at zero skewness
  5. Summary and conclusion

Figures (7)

  • Figure 1: The total $\chi^2$ divided by the number of degrees of freedom, $\chi^2/\mathrm{d.o.f.}$, as a function of $\mu$ in which the NNPDF40 PDFs set is chosen in the ansatz (\ref{['Eq4']}).
  • Figure 2: The quark number sum rule for the up valence PDF of the proton as a function of factorization $\mu$ for three PDF sets, namely NNPDF40NNPDF:2021njg, CT18Hou:2019efy, and MSHT20Bailey:2020ooq.
  • Figure 3: Same as Fig. \ref{['fig:uv']} but for the down valence PDF.
  • Figure 4: A comparison between our results for the GPD $xH_v^u(x)$ and those from the DK13 analysis Diehl:2013xca at four momentum transfer values: (a) $t = 0$, (b) $t = -1$, (c) $t = -3$, and (d) $t = -6~\mathrm{GeV}^2$. See the text for more details.
  • Figure 5: Same as Fig. \ref{['fig:Huv']} but for GPD $xH_v^d(x)$.
  • ...and 2 more figures