arXiv subjects

Anh Dung Le

Publications and source records attributed to Anh Dung Le.

14 recordsLinked to original sources

arXiv2025

Exclusive $\mathrm{J}/ψ$ production off a dilute proton within a refined hotspot description

We revisit the calculation of exclusive $\mathrm{J}/ψ$ production in electron-proton scattering within the QCD dipole model, employing a refined description of the proton in terms of gluonic hot spots in the dilute regime. In contrast to earlier studies, we incorporate key missing elements: the event-by-event fluctuations in both the number of hot spots and their local saturation scales, as well as the first relativistic corrections to the $\mathrm{J}/ψ$ wave function. We perform a Bayesian analysis to constrain the model parameters using HERA data. These enhancements significantly improve the agreement with HERA data. Saturation scale fluctuations are found to be more important than fluctuations in the number of hot spots. Including the first relativistic correction is found to be important, especially in order to describe the observed power-law behavior in the incoherent cross section at large $t$.

hep-ph↗

arXiv2025

Scattering from an external field in quantum chromodynamics at high energies: from foundations to interdisciplinary connections

We review the factorization of the $S$-matrix elements in the context of particle scattering off an external field, which can serve as a model for the field of a large nucleus. The factorization takes the form of a convolution of light cone wave functions describing the physical incoming and outgoing states in terms of bare partons, and products of Wilson lines. The latter represent the interaction between the bare partons and the external field. Specializing to elastic scattering amplitudes of onia at very high energies, we introduce the color dipole model, which formulates the calculation of the modulus-squared of the wave functions in quantum chromodynamics with the help of a branching random walk, and the scattering amplitudes as observables on this classical stochastic process. Methods developed for general branching processes produce analytical formulas for the asymptotics of such observables, and thus enable one to derive exact large-rapidity expressions for onium-nucleus cross sections, from which electron-nucleus cross sections may be inferred.

hep-ph↗

arXiv2024

High-energy nuclear scattering of neutrinos

We study the energy dependence of the total and diffractive neutrino-nucleon and neutrino-nucleus cross sections at very high energies. The calculation employs the QCD dipole model and the small-$x$ nonlinear Balitsky-Kovchegov evolution. We show the sensitivity of the nuclear effect quantification on the nuclear setup, and predict up to $\sim 10\%$ nuclear suppression in the inclusive neutrino-oxygen scattering stemming from the nonlinear evolution. Diffractive contribution to the total scattering is small, which is only few percentage. The $\left|q\bar{q}g\right>$ componnent of the $W^{\pm}$ boson is found to contribute significantly to the diffractive process, which reaches up to $\sim 40\%$ of the diffractive cross section.

hep-ph↗

arXiv2024

Inclusive and diffractive neutrino-nucleus scattering at high energy

We calculate the energy dependence of inclusive and diffractive neutrino-nucleus deep-inelastic scattering cross sections within the dipole picture, focusing on the ultra-high-energy regime. We predict an up to $\sim 10\%$ nuclear suppression in the inclusive neutrino-Oxygen scattering originating from the non-linear QCD dynamics in the small-$x$ Balitsky-Kovchegov evolution. Diffraction is found to be a small $1\dots 4\%$ contribution to the total cross section across a wide range of neutrino energies relevant for current and near-future experiments. The diffractive cross section is calculated separately for the coherent and incoherent channels that are found to be of equal importance. Additionally, we include the dominant contribution from the $|q\bar q g\rangle$ Fock state of the $W^\pm$ and $Z$ bosons in the high-$Q^2$ limit, along with the lowest-order $|q\bar q\rangle$ contribution. The $|q\bar{q}g\rangle$ contribution is found to be numerically significant, reaching up to 40\% of the diffractive cross section.

hep-ph↗

arXiv2023

Coherently diffractive dissociation in electron-hadron collisions: from HERA to the future EIC

We present numerical results on diffractive dissociation with large invariant mass diffractive final states in the scattering of an electron off a hadron. The diffractive large-mass resummation is performed using the nonlinear Kovchegov-Levin equation, taking into account running coupling corrections. For the scattering off the proton, a (modified) McLerran-Venugopalan amplitude is used as the initial condition for the nonlinear evolution, with free parameters being constrained by the HERA inclusive data. The results show a reasonable description of the HERA diffractive structure function data at moderately large diffractive mass when the impact parameter profile is constrained by the low-mass diffractive cross section data. The calculation is extended to nuclear scattering, where the initial condition is generalized from the proton case employing the optical Glauber model. The nonlinear large-mass resummation predicts a strong nuclear modification in diffractive scattering off a nuclear target in kinematics accessible at the future Electron-Ion collider.

hep-ph↗

arXiv2023

Rapidity gap distribution of diffractive small-$x_{I\hspace{-0.3em}P}$ events at HERA and at the EIC

We use the Kovchegov-Levin equation to resum contributions of large invariant mass diffractive final states to diffractive structure functions in the dipole picture of deep inelastic scattering. For protons we use a (modified) McLerran-Venugopalan model as the initial condition for the evolution, with free parameters obtained from fits to the HERA inclusive data. We obtain an adequate agreement to the HERA diffractive data in the moderately high-mass regimes when the proton density profile is fitted to the diffractive structure function data in the low-mass region. The HERA data is found to prefer a proton shape that is steeper than a Gaussian. The initial conditions are generalized to the nuclear case using the optical Glauber model. Strong nuclear modification effects are predicted in diffractive scattering off a nuclear target in kinematics accessible at the future Electron-Ion collider. In particular, the Kovchegov-Levin evolution has a strong effect on the Q 2 -dependence of the diffractive cross section.

hep-ph↗

arXiv2022

Probabilistic picture for particle number densities in stretched tips of the branching Brownian motion

In the framework of a stochastic picture for the one-dimensional branching Brownian motion, we compute the probability density of the number of particles near the rightmost one at a time $T$, that we take very large, when this extreme particle is conditioned to arrive at a predefined position $x_T$ chosen far ahead of its expected position $m_T$. We recover the previously-conjectured fact that the typical number density of particles a distance $Δ$ to the left of the lead particle, when both $Δ$ and $x_T-Δ-m_T$ are large, is smaller than the mean number density by a factor proportional to $e^{-ζΔ^{2/3}}$, where $ζ$ is a constant that was so far undetermined. Our picture leads to an expression for the probability density of the particle number, from which a value for $ζ$ may be inferred.

cond-mat.stat-mech↗

arXiv2022

Statistical properties of partonic configurations and diffractive dissociation in high-energy electron-nucleus scattering

In this thesis, we study the detailed partonic content of the quantum states of a quark-antiquark color dipole subject to high-energy evolution, which are represented by a set of dipoles generated by a stochastic binary branching process, in the scattering off a large nucleus, and produce predictions for diffractive dissociation in electron-ion collisions, based on the dipole picture of QCD. Our main results are as follows. First, the scattering events of a color dipole, when parameters are set in such a way that the total cross section is small, are triggered by rare partonic fluctuations, which look different as seen from different reference frames. It turns out that the freedom to select a frame allows to deduce an asymptotic expression for the rapidity distribution of the first branching of the slowest parent dipole of the set of those which scatter. In another aspect, such study implies the importance of the characterization of particle distribution in the frontier region in the states generated by the QCD dipole branching, and more generally, by any one-dimensional branching random walk model. To this aim, we develop a Monte Carlo algorithm to generate the frontier region of a branching random walk. Furthermore, we are able to calculate the diffractive cross section demanding a minimal rapidity gap $Y_0$ and the distribution of rapidity gaps $Y_{gap}$ in the diffractive dissociation of a small dipole off a large nucleus, in a well-defined parametric region. They are the asymptotic solutions to the so-called Kovchegov-Levin equation, which describes the diffractive dissociation at high energy. Finally, we present predictions for the rapidity gap distributionin realistic kinematics of future electron-ion machines, based on the numerical solutions of the original Kovchegov-Levin equation and of its next-to-leading extension taking into account the running of the strong coupling.

hep-ph↗

arXiv2021

Diffractive dissociation in future electron-ion colliders

We study diffractive scattering cross sections, focusing on the rapidity gap distribution in realistic kinematics at future electron-ion colliders. Our study consists in numerical solutions of the QCD evolution equations in both fixed and running coupling frameworks. The fixed and the running coupling equations are shown to lead to different shapes for the rapidity gap distribution. The obtained distribution when the coupling is fixed exhibits a shape characteristic of a recently developed model for diffractive dissociation, which indicates the relevance of the study of that diffractive observable for the partonic-level understanding of diffraction.

hep-ph↗

arXiv2021

Nuclear scattering configurations of onia in different frames

In the scattering of a small onium off a large nucleus at high center-of-mass energies, when the parameters are set in such a way that the cross section at fixed impact parameter is small, events are triggered by rare partonic fluctuations of the onium, which are very deformed with respect to typical configurations. Using the color dipole picture of high-energy interactions in quantum chromodynamics, in which the quantum states of the onium are represented by sets of dipoles generated by a branching process, we describe the typical scattering configurations as seen from different reference frames, from the restframe of the nucleus to frames in which the rapidity is shared between the projectile onium and the nucleus. We show that taking advantage of the freedom to select a frame in the latter class makes possible to derive complete asymptotic expressions for some boost-invariant quantities, beyond the total cross section, from a procedure which leverages the limited available knowledge on the properties of the solutions to the Balitsky-Kovchegov equation that governs the rapidity-dependence of total cross sections. We obtain in this way an analytic expression for the rapidity-distribution of the first branching of the slowest parent dipole of the set of those which scatter. This distribution provides an estimator of the correlations of the interacting dipoles, and is also known to be related to the rapidity-gap distribution in diffractive dissociation, an observable measurable at a future electron-ion collider. Furthermore, our result may be formulated as a more general conjecture, that we expect to hold true for any one-dimensional branching random walk model, on the branching time of the most recent common ancestor of all the particles that end up to the right of a given position.

hep-ph↗

arXiv2021

Analytical asymptotics for hard diffraction

We show that the cross section for diffractive dissociation of a small onium off a large nucleus at total rapidity $Y$ and requiring a minimum rapidity gap $Y_{\text{gap}}$ can be identified, in a well-defined parametric limit, with a simple classical observable on the stochastic process representing the evolution of the state of the onium, as its rapidity increases, in the form of color dipole branchings: It formally coincides with twice the probability that an even number of these dipoles effectively participate in the scattering, when viewed in a frame in which the onium is evolved to the rapidity $Y-Y_{\text{gap}}$. Consequently, finding asymptotic solutions to the Kovchegov-Levin equation, which rules the $Y$-dependence of the diffractive cross section, boils down to solving a probabilistic problem. Such a formulation authorizes the derivation of a parameter-free analytical expression for the gap distribution. Interestingly enough, events in which many dipoles interact simultaneously play an important role, since the distribution of the number $k$ of dipoles participating in the interaction turns out to be proportional to $1/[k(k-1)]$.

hep-ph↗

arXiv2021

Rapidity gap distribution in diffractive dissociation: predictions for future electron-ion colliders

We present predictions for the distribution of rapidity gaps in realistic kinematics of future electron-ion colliders, based on numerical solutions of the original Kovchegov-Levin equation and of its next-to-leading extension taking into account the running of the strong coupling. We find that for the rapidities we have considered, the fixed and the running coupling equations lead to different distributions, rather insensitive to the chosen prescription in the running coupling case. The obtained distributions for the fixed coupling framework exhibit a shape characteristic of a recently proposed partonic picture of diffractive dissociation already at rapidities accessible at future electron-ion colliders. The modification of this shape in the running coupling case can also be understood qualitatively from that picture. Our results confirm the relevance of measurements of such observables for the microscopic understanding of diffractive dissociation in the framework of quantum chromodynamics.

hep-ph↗

arXiv2020

Monte Carlo study of the tip region of branching random walks evolved to large times

We implement a discretization of the one-dimensional branching Brownian motion in the form of a Monte Carlo event generator, designed to efficiently produce ensembles of realizations in which the rightmost lead particle at the final time $T$ is constrained to have a position $X$ larger than some predefined value $X_{\text{min}}$. The latter may be chosen arbitrarily far from the expectation value of $X$, and the evolution time after which observables on the particle density near the lead particle are measured may be as large as $T\sim 10^4$. We then calculate numerically the probability distribution $p_n(Δx)$ of the number $n$ of particles in the interval $[X-Δx,X]$ as a function of $Δx$. When $X_{\text{min}}$ is significantly smaller than the expectation value of the position of the rightmost lead particle, i.e. when $X$ is effectively unconstrained, we check that both the mean and the typical values of $n$ grow exponentially with $Δx$, up to a linear prefactor and to finite-$T$ corrections. When $X_{\text{min}}$ is picked far ahead of the latter but within a region extending over a size of order $\sqrt{T}$ to its right, the mean value of the particle number still grows exponentially with $Δx$, but its typical value is lower by a multiplicative factor consistent with $e^{-ζΔx^{2/3}}$, where $ζ$ is a number of order unity. These numerical results bring strong support to recent analytical calculations and conjectures in the infinite-time limit.

cond-mat.stat-mech↗

arXiv2020

How to generate the tip of branching random walks evolved to large times

In a branching process, the number of particles increases exponentially with time, which makes numerical simulations for large times difficult. In many applications, however, only the region close to the extremal particles is relevant (the "tip"). We present a simple algorithm which allows to simulate a branching random walk in one dimension, keeping only the particles that arrive within some distance of the rightmost particle at a predefined time $T$. The complexity of the algorithm grows linearly with $T$. We can furthermore choose to require that the realizations have their rightmost particle arbitrarily far on the right from its typical position. We illustrate our algorithm by evaluating an observable for which no other practical method is known.

cond-mat.stat-mech↗