arXiv subjects

Yanbing Cai

Publications and source records attributed to Yanbing Cai.

At least 19 recordsLinked to original sources

arXiv2026

Analytical Solution of the Sudakov--BFKL Interpolation Equation for Small-$x$ Gluon TMDs

We analytically solve the evolution equation for small-$x$ gluon transverse-momentum-dependent distributions, which describes the interpolation between the Sudakov and BFKL regimes. We first derive its two limiting forms: the BFKL equation for $\xi = \alpha\sigma s{\bm z}^2/4 \ll 1$ and the Sudakov equation for $\xi \gg 1$. The analytical solutions in these limits are obtained through Mellin-space diagonalization of the BFKL kernel and direct integration of the Sudakov evolution equation, respectively. We then solve the full interpolation equation using a Mellin-space diagonalization ansatz, in which the evolution factor $F(Y,\xi)$ describes the nontrivial $\xi$-dependent modification of a Mellin eigenfunction of the BFKL kernel. This procedure reduces the original two-dimensional integral to a one-dimensional form and permits an analytical evaluation of the resulting evolution kernel. The obtained solution interpolates consistently between the BFKL and Sudakov regimes through an exponential factor $\exp[H(\xi,\gamma)]$. An analysis of the structure of $H(\xi,\gamma)$ allows a quantitative estimation of the transition region between the two dynamical regimes. Our calculation implies a potential matching point in the range of $\xi^{*}\simeq 0.04-0.15$, which is substantially smaller than the naive evaluation value.

hep-ph↗

arXiv2026

Pion and Kaon PDFs via Infrared-Safe Evolution augmented by $J/\psi$ Data Constraints

Probing the partonic structure of the pion and the kaon provides essential insights into the non-perturbative dynamics of QCD, yet their parton distribution functions (PDFs) remain poorly constrained due to the scarcity of high-precision experimental data, especially for the gluon distributions. We present an improved determination of pion and kaon PDFs within the dynamical parton model combined with the maximum entropy method (MEM) framework. Our analysis features two key advancements: firstly, we employ an infrared-safe QCD evolution scheme, allowing the evolution to be reliably extended down to very low $Q^2$, approaching the hadronic scale; secondly, we incorporate pion- and kaon-induced $J/\psi$ hadroproduction data as crucial constraints in the global fit. We find that our approach yields a good description of the available Drell-Yan data, deep-inelastic scattering structure functions ($F_2$), and $J/\psi$ production across various energies and targets. The results provide significantly improved constraints on the gluon distributions at moderate and large $x$ in both the pion and the kaon, offering a more complete picture of their internal structure.

hep-ph↗

arXiv2026

Physics-guided residual correction of $\alpha$-decay half-lives based on the effective liquid drop model

To improve the prediction accuracy of $\alpha$-decay half-lives in heavy and superheavy nuclei, a physics-guided residual-correction framework combining the effective liquid drop model (ELDM) with machine-learning methods is proposed. The ELDM is first used as the macroscopic baseline for describing the barrier-penetration process, and XGBoost and TabPFN models are then employed to learn the residual deviations between ELDM predictions and experimental data. To incorporate microscopic nuclear-structure information, several physically motivated descriptors are constructed, including deformation-related quantities, Geiger--Nuttall-related features, and minimum orbital angular momentum. The results show that machine-learning residual correction significantly improves the predictive performance of the ELDM baseline. Among all models, TabPFN-term3 achieves the best accuracy, reducing the RMSE and MAE to 0.348 and 0.248, corresponding to improvements of 38.60\% and 40.46\%, respectively. Residual-distribution and feature-ablation analyses further indicate that the corrected predictions are closer to experimental values and that physically motivated descriptors play an important role in learning nonlinear residual structures. Overall, the proposed ELDM-based residual-correction framework can effectively compensate for missing microscopic nuclear-structure effects while preserving physical interpretability, providing a feasible strategy for high-precision $\alpha$-decay half-life prediction.

nucl-th↗

arXiv2025

Valence Quark Distributions in Pions: Insights from Tsallis Entropy

We investigate the valence quark distributions of pions at a low initial scale ($Q^2_0$) by employing Tsallis entropy, a non-extensive measure that effectively captures long-range correlations among internal constituents. Utilizing the maximum entropy approach, we adopt two distinct functional forms and fit experimental data through the elegant GLR-MQ-ZRS evolution equation to derive the model parameters. Our findings indicate that the resulting valence quark distributions provide an optimal fit to experimental data, with the values of the $q$ parameter deviating from unity. This deviation indicates the significant role that correlations among valence quarks play in shaping our understanding of pion internal structure. Additionally, our computations of the first three moments of pion quark distributions at $ Q^2 = 4 \, \mathrm{GeV}^2$ display consistency with other theoretical models, thereby reinforcing the importance of incorporating valence quark correlations within this analytical framework.

hep-ph↗

arXiv2024

An analysis of the longitudinal structure function at next-to-leading order approximation at small-$x$

The longitudinal structure function is considered at the next-to-leading order approximation using the expansion method, as defined by M.B.Gay Ducati and P.B.Goncalves [Phys.Lett.B {\bf390}, 401 (1997)] and further developed by Jingxuan Chen et al., [Chin.Phys.C {\bf48}, 063104 (2024)]. This method provides results for a wide range of $x$ and $Q^2$ values. It is observed that the behavior of the longitudinal structure function depends on the fractional momentum carried by gluons at low $x$. The extracted longitudinal structure functions $F_{L}(x,Q^2)$ are in line with data from the H1 Collaboration [V. Andreev et al. (H1 Collaboration), Eur. Phys. J. C 74, 2814 (2014)] and the CT18 parametrization method [T.-J. Hou et al., Phys. Rev. D 103, 014013 (2021)].

hep-ph↗

arXiv2024

Exploring the Impact of anti-shadowing effect on Unintegrated Gluon Distributions in the MD-BFKL Equation

This paper presents a comprehensive analysis of the MD-BFKL equation, considering both shadowing and anti-shadowing effects in gluon recombination processes. By deriving analytical expressions for unintegrated gluon distributions through the solution of the MD-BFKL equation, with and without the incorporation of anti-shadowing effect, we offer new insights into the influence of these effects on the behavior of unintegrated gluon distributions. Our results, when compared to the CT18NLO gluon distribution function, demonstrate that the anti-shadowing effect has a notably stronger impact on the characteristics of unintegrated gluon distributions, particularly in regions of high rapidity and momentum. This work significantly contributes to the understanding of gluon recombination mechanisms and their implications in high energy physics.

hep-ph↗

arXiv2024

Accessing the stringy structure of proton in the framework of Color Glass Condensate

To investigate the possible geometric structure of the proton, an improved stringy proton model is constructed beyond the smallest distance approximation, where the constituent quarks are connected by gluon tubes which merge at the Fermat point of the quark triangle. The exclusive diffractive vector meson production process in electron-proton deep inelastic scattering is used to test the stringy structure of the proton. We calculate the coherent and incoherent differential cross sections of the exclusive diffractive $J/Ψ$ photoproduction in the framework of Color Glass Condensate. The results show that our calculations are in good agreement with HERA data. Especially, our results give a better description of the HERA data at small $t$ as compared to the ones from the hot spot model where the constituent quarks are uncorrelated distributed in the proton. Meanwhile, the radius of the proton resulting from the improved stringy proton model is coincident with the one from fitting to the data from GlueX Collaboration at Jefferson Lab, which indicates that the predictive power of the stringy proton model is significantly improved once it goes beyond the smallest distance approximation. Moreover, we assume that the transverse shape of gluon tube satisfies Gaussian distribution, and explore the distribution width of the individual gluon tubes. We find an interesting result that the up quark induced gluon tube seems to have larger distribution width than the down quark induced gluon tube, which is favored by the HERA data.

hep-ph↗

arXiv2024

New exact analytical solution of the nonlinear Gribov-Levin-Ryskin-Mueller-Qiu equation

The GLR-MQ equation is a nonlinear evolution equation that takes into account the shadowing effect, which tames the growth of the gluon at small-$x$. In this study, we analytically solve for the first time the nonlinear GLR-MQ equation using the homogeneous balance method. The definite solution of the GLR-MQ equation is obtained by fitting the MSTW2008LO gluon distribution data. We find that the geometric scaling is an intrinsic property of our analytical solution and the gluon distribution functions from our solution are able to reproduce the MSTW2008LO data. These results indicate that our analytical solution from the homogeneous balance method is valid to describe the gluon behavior at small-$x$. Moreover, the saturation scale $Q_s$ has been extracted from our analytical solution, we find that the energy-dependent saturation scale obeys the exponential law $Q_s^2\,\propto\,Q_0^2 e^{λY}$.

hep-ph↗

arXiv2024

An analysis of the gluon distribution with next-to-leading order splitting function in small-$x$

An approximated solution for gluon distribution from DGLAP evolution equations with NLO splitting function in the small-$x$ limit is presented. We first obtain the simplified forms of LO and NLO splitting functions in the small-$x$ limit. With these approximated splitting functions, we obtain the analytical gluon distribution by using the Mellin transform. The free parameters in the boundary conditions are obtained by fitting the CJ15 gluon distribution data. We find that the asymptotic behavior of gluon distribution are consistent with the CJ15 data, however, the NLO results with the consideration of ``ladder'' structure of gluon emission are slightly better than those from LO. These results indicate that the corrections from NLO is significant and is necessary for a better description of the behavior of the gluon distribution in small-$x$ region. In addition, we investigate the DGLAP evolution of the proton structure function by using the analytical solution of the gluon distribution. The differential structure function shows that our results have a similar tendency with CJ15 at small-$x$.

hep-ph↗

arXiv2024

Deriving the QCD evolution equations under the Abelian decomposition scheme

The Abelian decomposition of QCD reveals two types of gluons: color-neutral ``neurons" and color-carrying ``chromons". This classification does not alter the overall properties of QCD, but the investigation of different types of gluon dynamics is necessary. By employing the Cho-Duan-Ge decomposition theorem, we have derived dynamic evolution equations for two types of gluons by using the time-ordered perturbation theory. We propose that the new equations are compatible with the DGLAP equations, requiring only the separate contributions of neurons and chromons to be summed. Surprisingly, with the evolution to high $Q^2$, the ratio of the number of chromons to neurons is approximately 3:1 in small-$x$ region regardless of the inputs at evolution starting point. The new gluon dynamic equations reevaluate the gluon distribution functions and allow for a elaborate inverstigation of the distinct contributions of gluons in high-energy collisions.

hep-ph↗

arXiv2023

Analytic solution of Balitsky-Kovchegov equation with running coupling constant using homogeneous balance method

In this study, we employ the homogeneous balance method to obtain an analytical solution to the Balitsky-Kovchegov equation with running coupling. We utilize two distinct prescriptions of the running coupling scale, namely the saturation scale dependent running coupling and the dipole momentum dependent running coupling. By fitting the proton structure function experimental data, we determine the free parameters in the analytical solution. The resulting $χ^{2}/d.o.f$ values are determined to be $1.07$ and $1.43$, respectively. With these definitive solutions, we are able to predict exclusive $J/ψ$ production, and demonstrate that analytical solutions with running coupling are in excellent agreement with $J/ψ$ differential and total cross section. Furthermore, our numerical results indicate that the analytical solution of the BK equation with running coupling can provide a reliable description for both the proton structure function and exclusive vector meson production.

hep-ph↗

arXiv2023

Imaging constituent quark shape of proton with exclusive vector meson production at HERA

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, $\mathrm{B_u} \geq \mathrm{B_d}$, $\mathrm{B_u} < \mathrm{B_d}$ 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. We find that only results calculated with $\mathrm{B_u} \geq \mathrm{B_d}$ 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 ($\mathrm{W_u}$ and $\mathrm{W_d}$) for the up and down quarks, respectively. It shows that the results calculated with $\mathrm{W_u}\geq\mathrm{W_d}$ 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.

hep-ph↗

arXiv2023

Production of exotic electromagnetic bound systems in ultra-peripheral heavy ion collisions with two-photon processes

We calculate the production of exotic electromagnetic bound systems, which ia an consisting of a ($l^{+}l^{-}$) bound state system such as positronium, dimuonium, and ditauonium, by photon-photon interaction with the equivalent photon approximation in ultra-peripheral heavy ion collisions considering the nuclear form factor. The numerical results demonstrate that the experimental study of positronium, dimuonium, and ditauonium in ultra-peripheral collisions is feasible at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies.

hep-ph↗

arXiv2022

Production of $χ_{c}$ and $η_{c}$ production in ultra-peripheral collisions with two-photon processes

We calculate the production of $χ_{c}$ and $η_{c}$ by the semi-coherent and coherent two-photon interaction in ultra-peripheral heavy ion collisions at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies. The differential cross section of transverse momentum distribution and rapidity distribution for $AB\stackrel{γγ}{\longrightarrow}AHB$ (H=$χ_{c}$ and $η_{c}$), are estimated by using the equivalent photon approximation in ultra-peripheral nucleus-nucleus collisions. The numerical results demonstrate that the experimental study of $χ_{c}$ and $η_{c}$ in ultra-peripheral nucleus-nucleus collisions is feasible at RHIC and LHC energies.

hep-ph↗

arXiv2022

Compton scattering for photon and gluon in fixed-target collisions at AFTER@LHC

We calculate the Compton scattering for photon and gluon with the Klein-Nishina formula in fixed-target collisions by using the proton and lead beams at AFTER@LHC. In these collisions, we can investigate the particular case of Compton scattering at the partonic level, such as $γq\rightarrow qγ$, $γq\rightarrow qg$, $gq\rightarrow qγ$, and $gq\rightarrow qg$, that can help to check of the equivalent-photon approximation and understand the dynamics of hadron collisions at high energies, as well as probe the inner hadron structure.

hep-ph↗

arXiv2021

Coherent photoproduction of low-$p_{T}$ charmonium in peripheral heavy ion collisions within the color dipole model

We calculate the centrality dependence for coherent photoproduction of very low-$p_{T}$ $J/ψ$ at Relativistic Heavy Ion Collider (RHIC) and Large Hadron Collider (LHC) energies within the impact parameter dependent saturated color dipole model. By using the large equivalent photon fluxes, we present the differential cross section of very low-$p_{T}$ $J/ψ$ produced by coherent photonuclear in peripheral heavy-ion collisions. The numerical results demonstrate that our calculation are agree with $J/ψ$ data in peripheral heavy ion collisions at Relativistic Heavy Ion Collider (RHIC) energies.

hep-ph↗

arXiv2021

Extended collinearly-improved Balitsky-Kovchegov evolution equation in target rapidity

An extended collinearly-improved Balitsky-Kovchegov evolution equation in the target rapidity representation is derived by including the running coupling corrections during the expansion of the "real" $S$-matrix. We find that the running coupling brings important corrections to the evolution equation, as one can see that there are extra contributions to the evolution kernel once the running coupling is included. To identify the significance of the corrections, we numerically solve the evolution equation with and without the running coupling contributions during the $S$-matrix expansion. The numerical results show that the scattering amplitude is largely suppressed by the running coupling corrections, which indicate that one needs to consider the running coupling contributions during the derivation of the non-linear evolution equation in the target rapidity representation.

hep-ph↗

arXiv2020

Inclusive diffractive heavy quarkonium photoproduction including quark subprocesses

The inclusive $J/Ψ$, $Ψ(2S)$ and $Υ(1S)$ direct and resolved photoproduction are investigated by including the quark subprocesses in the framework of non-relativistic quantum chromodynamics (NRQCD). We find that the theoretical total cross section of heavy quarkonium productions are in good agreement with the data available at HERA, once the $γq$, $qg$ and $qq$ subprocesses in the heavy quark pair productions are taken into account. The inclusive diffractive rapidity and transverse momentum distributions of $J/Ψ$, $Ψ(2S)$ and $Υ(1S)$ in $pp$, $pPb$ and $PbPb$ collisions at LHC are also studied by our quark improved NRQCD model combined with the resolved pomeron model. We find that the contributions from the quark involved subprocesses can reach to $8\%$ in the rapidity distribution and $6\%$ in the transverse momentum distribution. The numerical results show that the contributions from quark involved subprocesses are significant in heavy quarkonium photoprodution.

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