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Register a new userPions valence-quark GPD and its extension beyond DGLAP region
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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.
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We briefly report on a recent computation, with the help of a fruitful algebraic model, sketching the pion valence dressed-quark generalized parton distribution. Then, preliminary, we introduce on a sensible procedure to get reliable results in both Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) and Efremov-Radyushkin-Brodsky-Lepage (ERBL) kinematical regions, grounded on the GPD overlap representation and its parametrization of a Radon transform of the so-called double distribution (DD).
In-medium valence-quark distributions of $pi^+$ and $K^+$ mesons in symmetric nuclear matter are studied by combining the Nambu--Jona-Lasinio model and the quark-meson coupling model. The in-medium properties of the current quarks, which are used as inputs for studying the in-medium pion and kaon properties in the Nambu--Jona-Lasinio model, are calculated within the quark-meson coupling model. The light-quark condensates, light-quark dynamical masses, pion and kaon decay constants, and pion- and kaon-quark coupling constants are found to decrease as nuclear density increases. The obtained valence quark distributions in vacuum for both the $pi^+$ and $K^+$ could reasonably describe the available experimental data over a wide range of Bjorken-$x$. The in-medium valence $u$-quark distribution in the $pi^+$ at $Q^2=16~mbox{GeV}^2$ is found to be almost unchanged compared to the in-vacuum case. However, the in-medium to in-vacuum ratios of both the valence $u$-quark and valence $s$-quark distributions of the $K^+$ meson at $Q^2=16~mbox{GeV}^2$ increase with nuclear matter density, but show different $x$-dependence. Namely, the ratio for the valence $u$-quark distribution increases with $x$, while that for the valence $s$ quark decreases with $x$. These features are enhanced at higher density regions.
A systematic approach for the model building of Generalized Parton Distributions (GPDs), based on their overlap representation within the DGLAP kinematic region and a further covariant extension to the ERBL one, is applied to the valence-quark pions case, using light-front wave functions inspired by the Nakanishi representation of the pions Bethe-Salpeter amplitudes (BSA). This simple but fruitful pions GPD model illustrates the general model building technique and, in addition, allows for the ambiguities related to the covariant extension, grounded on the Double Distribution (DD) representation, to be constrained by requiring a soft-pion theorem to be properly observed.
We present a novel approach to compute Generalized Parton Distributions within the Lightfront Wave Function overlap framework. We show how to systematically extend Generalized Parton Distributions computed within the DGLAP region to the ERBL one, fulfilling at the same time both the polynomiality and positivity conditions. We exemplify our method using pion Lightfront Wave Functions inspired by recent results of non-perturbative continuum techniques and algebraic nucleon Lightfront Wave Functions. We also test the robustness of our algorithm on reggeized phenomenological parameterizations. This approach paves the way to a better understanding of the nucleon structure from non-perturbative techniques and to a unification of Generalized Parton Distributions and Transverse Momentum Dependent Parton Distribution Functions phenomenology through Lightfront Wave Functions.
Beginning with precise data on the ratio of structure functions in deep inelastic scattering (DIS) from $^3$He and $^3$H, collected on the domain $0.19 leq x_B leq 0.83$, where $x_B$ is the Bjorken scaling variable, we employ a robust method for extrapolating such data to arrive at a model-independent result for the $x_B=1$ value of the ratio of neutron and proton structure functions. Combining this with information obtained in analyses of DIS from nuclei, corrected for target-structure dependence, we arrive at a prediction for the protons valence-quark ratio: $left. d_v/u_v right|_{x_Bto 1} = 0.230 (57)$. Requiring consistency with this result presents a challenge to many descriptions of proton structure.
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