High Energy Physics - Phenomenology · arXiv:2308.10136 v2 · submitted 20 Aug 2023
Imaging constituent quark shape of proton with exclusive vector meson production at HERA
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“These interesting findings seem to indicate that the up quark has more gluons around it than the down quark at high energy although the spatial distribution of gluons fluctuates event-by-event .”
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Abstract
We show within proton hot spot picture that the exclusive vector meson production in electron-proton deeply inelastic scattering is sensitive to the individual width of the constituent quarks of the proton. For comparison, we calculate the exclusive J/Ψ production cross-sections in three cases, Bu ≥ Bd, Bu < Bd and Bu ≠ B′u ≠ Bd, where the Bu, B′u and Bd denote the widths of two up quarks and down quark. We find that only results calculated with Bu ≥ Bd can give a reasonable description of the exclusive J/Ψ production cross-section data at HERA. To test that our results are independent of the details of the model, we retain the average width of the three constituent quarks unchanged and compute the exclusive J/Ψ production cross-sections with contribution weight by setting different proportional coefficients (Wu and Wd) for the up and down quarks, respectively. It shows that the results calculated with Wu ≥ Wd can well reproduce the exclusive J/Ψ production data at HERA, while the opposite case cannot describe the HERA data. These interesting findings seem to indicate that the up quark has more gluons around it than the down quark at high energy although the spatial distribution of gluons fluctuates event-by-event . To ensure the relevant results independent of the species of the vector meson, we also calculate the ρ production cross-sections with the same group of parameters used in the exclusive J/Ψ production and compare the predictions with the HERA data. It shows that all the results computed in the exclusive ρ productions are consistent with the findings obtained in the exclusive J/Ψ productions.
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abstract compiled · 2026-09-23 · no language-model review
How the main claim is stated: hedged possibility 0.99
What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.28 · human participants 0.01 · controlled comparison 0.36 · randomized assignment 0.01 · states quantitative result 0.16 · compares with prior results 0.46 · mentions code or data availability 0.02
The abstract, sentence by sentence
This table labels the abstract only (arXiv listing abstract v2). The number is the probability the classifier gave the label.
| Sentence | Role | The authors' own work | States the main conclusion | Strength |
|---|---|---|---|---|
| We show within proton hot spot picture that the exclusive vector meson production in electron-proton deeply inelastic scattering is sensitive to the individual width of the constituent quarks of the proton. | contribution 0.67 | 0.88 | 0.60 | asserted 1.00 |
| For comparison, we calculate the exclusive $J/\Psi$ production cross-sections in three cases, $\mathrm{B_u} \geq \mathrm{B_d}$, $\mathrm{B_u} < \mathrm{B_d}$ and $\mathrm{B_u}\neq\mathrm{B^{\prime}_u}\neq\mathrm{B_d}$, where the $\mathrm{B_u}$, $\mathrm{B^{\prime}_u}$ and $\mathrm{B_d}$ denote the widths of two up quarks and down quark. | method 0.92 | 0.92 | 0.04 | asserted 0.81 |
| We find that only results calculated with $\mathrm{B_u} \geq \mathrm{B_d}$ can give a reasonable description of the exclusive $J/\Psi$ production cross-section data at HERA. | result 1.00 | 0.96 | 0.46 | asserted 1.00 |
| To test that our results are independent of the details of the model, we retain the average width of the three constituent quarks unchanged and compute the exclusive $J/\Psi$ production cross-sections with contribution weight by setting different proportional coefficients ($\mathrm{W_u}$ and $\mathrm{W_d}$) for the up and down quarks, respectively. | method 0.94 | 0.96 | 0.03 | asserted 0.72 |
| It shows that the results calculated with $\mathrm{W_u}\geq\mathrm{W_d}$ can well reproduce the exclusive $J/\Psi$ production data at HERA, while the opposite case cannot describe the HERA data. | result 1.00 | 0.95 | 0.18 | asserted 1.00 |
| These interesting findings seem to indicate that the up quark has more gluons around it than the down quark at high energy although the spatial distribution of gluons fluctuates event-by-event . | interpretation 1.00 | 0.70 | 0.47 | hedged possibility 0.99 |
| To ensure the relevant results independent of the species of the vector meson, we also calculate the $\rho$ production cross-sections with the same group of parameters used in the exclusive $J/\Psi$ production and compare the predictions with the HERA data. | method 0.63 | 0.95 | 0.03 | asserted 0.76 |
| It shows that all the results computed in the exclusive $\rho$ productions are consistent with the findings obtained in the exclusive $J/\Psi$ productions. | result 1.00 | 0.93 | 0.09 | asserted 0.67 |
What kind of paper the classifier reports this is: theoretical result 0.57 · evidence from simulation or computation 0.86
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,806 input tokens.
Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON
How the literature uses it
1 arXiv paper cite this in 10 sentences
Papers citing it · 6 sentences without a confident label
Compares with it 1 paper
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This outcome is coincident with the results in Ref. [ref] where the up quark inspired hot spot width is larger or equal to the down quark inspired hot spot width.
Accessing the stringy structure of proton in the framework of Color Glass Condensate · Dipole-proton cross section · 0.92
Cites it as background 1 paper
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Since then, several other models based on the hot spot model were introduced to study the detailed property of the proton [ref] , see a review [ref] and references therein.
Accessing the stringy structure of proton in the framework of Color Glass Condensate · Introduction · 0.87
What it cites · 51 sentences without a confident label
Builds on 2 papers
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So, the width $B_u$ and $B_d$ can take different values instead of the average value of the width of the three constituent quarks as done in Ref. [ref] .
Revealing proton shape fluctuations with incoherent diffraction at high energy · Hot spot model · 0.80
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So, the width $B_u$ and $B_d$ can take different values instead of the average value of the width of the three constituent quarks as done in Ref. [ref] .
Evidence of strong proton shape fluctuations from incoherent diffraction · Hot spot model · 0.80
Uses the method or tool of 3 papers
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In this work, we will use the Boosted Gaussian wave function from Ref. [ref] , since it successfully describes the vector meson production data at HERA.
Exclusive diffractive processes at HERA within the dipole picture · Exclusive vector meson production in dipole picture · 0.96
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We shall include the saturation scale fluctuations by following Ref. [ref] , in which the saturation scale fluctuates in terms of P(lnQ_s^2/⟨Q_s^2⟩)=1/√(2π)σexp[-ln^2Q_s^2/⟨Q_s^2⟩/2σ^2].
Revealing proton shape fluctuations with incoherent diffraction at high energy · Hot spot model · 0.89
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Moreover, our calculations can be improved by performing the QCD evolution (dipole scattering amplitude) via the collinearly-improved Balitsky-Kovchegove equation whose Coulomb tails are strongly suppressed by the resumed kernel and can give the numerical version of the impact parameter dependent dipole scattering amplitude [ref] , which is our next step work.
Collinearly improved kernel suppresses Coulomb tails in the impact-parameter dependent Balitsky-Kovchegov evolution · conclusions and discussions · 0.83
Uses data or values from 3 papers
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The average width is extracted from the exclusive $J/Ψ$ production data in Ref. [ref] .
Revealing proton shape fluctuations with incoherent diffraction at high energy · Introduction · 1.00
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By inspecting the measurements in Ref. [ref] , it shows that there are only two sets of data ($Q^2=3.3 GeV^2$ and $Q^2=6.6 GeV^2$) simultaneously measured for the coherent and incoherent exclusive $ρ$ productions.
Diffractive Electroproduction of rho and phi Mesons at HERA · $ρ$ production · 0.95
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Here, the $μ$ is related to the transverse dipole size as μ^2 = 4/r^2 + μ_0^2, and the initial $xg(x,μ^2)$ at $μ_0^2$ is xg(x,μ_0^2) = A_g x^-λ_g(1-x)^5.6, where the $μ_0$, $A_g$, and $λ_g$ are model parameters which were determined by fitting to the HERA DIS data in Ref. [ref] .
Analysis of combined HERA data in the Impact-Parameter dependent Saturation model · Dipole cross-section · 0.83
Compares with 1 paper
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We use the red curves to be as the reference to evaluate the compatibility of the parameters of our refined hot spot model, since the red curves give rather good descriptions of the HERA data [ref] .
Revealing proton shape fluctuations with incoherent diffraction at high energy · $J/Ψ$ production · 0.81
Cites as support 2 papers
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However, we will not use the BK evolution equation in this work, since the impact parameter dependence of the dipole scattering amplitude $N$ is a key aspect to calculate the diffractive scattering amplitude in Eq.([ref]), the numerical studies of the JIMWLK and BK equations showed that their numerical solutions develop unphysical Coulomb tails once the impact parameter dependence is included [ref] .
Small x nonlinear evolution with impact parameter and the structure function data · Dipole cross-section · 0.98
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However, we will not use the BK evolution equation in this work, since the impact parameter dependence of the dipole scattering amplitude $N$ is a key aspect to calculate the diffractive scattering amplitude in Eq.([ref]), the numerical studies of the JIMWLK and BK equations showed that their numerical solutions develop unphysical Coulomb tails once the impact parameter dependence is included [ref] .
On solutions of the Balitsky-Kovchegov equation with impact parameter · Dipole cross-section · 0.98
Cites as background 34 papers
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In recent years, a lot of efforts were put into studying proton shape based on the exclusive diffractive process [ref] .
The shape of the proton at high energies · Introduction · 0.93
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In recent years, a lot of efforts were put into studying proton shape based on the exclusive diffractive process [ref] .
Evidence of strong proton shape fluctuations from incoherent diffraction · Introduction · 0.93
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Several hot spot models were proposed to investigate the event-by-event fluctuation of the spatial distribution of gluons within the proton [ref] .
Revealing proton shape fluctuations with incoherent diffraction at high energy · Introduction · 0.85
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