arXiv subjects

Adrian Dumitru

Publications and source records attributed to Adrian Dumitru.

At least 19 recordsLinked to original sources

arXiv2026

The eikonal spin-dependent Odderon and gluon Sivers function of a proton, and its small-$x$ evolution

The matrix element in the proton of the eikonal Odderon operator, with a helicity flip, has been shown to correspond to the dipole gluon Sivers function. We employ a three quark light-front model of the proton to determine the Sivers function at moderately small $x_0 \sim 0.1$ and transverse momentum $k_\perp \lesssim 1$~GeV. The model light-cone (LC) wave function predicts the properties of $x f_{1T}^{\perp g}(x,k_\perp)$ such as its overall magnitude, the position of its peak in $k_\perp$, and its behavior at small $k_\perp$. We then compute numerically the BFKL anomalous dimension characterizing the power-law tail at $k_\perp \gtrsim 1.5$~GeV of the gluon Sivers function at small (but pre-asymptotic) LC momentum fractions, $\alpha_s \log x_0/x = 1$: $x f_{1T}^{\perp g}(x,k_\perp) \sim k_\perp^{-3.3}$.

hep-ph↗

arXiv2025

Off forward non-SCHC contributions to exclusive vector quarkonium production from the "spin dependent BFKL Pomeron"

A novel contribution to off-forward, exclusive vector quarkonium production, $\gamma^{(*)}+p \to V+p$, at high energy is derived which corresponds to a $t$-channel exchange of a BFKL hard Pomeron, with a helicity flip of the proton. This ``spin-dependent BFKL Pomeron" is required in a consistent expansion in powers of the momentum transfer $ t \approx -\Delta_\perp^2$ beyond first order. The spin-dependent Pomeron violates $s$-channel helicity conservation (SCHC) at ${\cal O}(\Delta_\perp^2)$, and beyond. Expanding to leading twist only, it corresponds to GPD $E_g(x,t)$ for vanishing skewness. We derive explicit expressions for the eikonal BFKL amplitudes, to all orders in dipole size times momentum transfer, for all helicity configurations of the particles in the initial and final states. We also provide numerical estimates of the helicity flip two gluon exchange amplitude at moderate $x$ from a light-cone quark model of the proton. The spin dependent BFKL Pomeron could, in principle, be discovered via double spin asymmetries in $e+p \to e+p+J/\psi$ with transversely polarized proton and longitudinally polarized electron in the initial state.

hep-ph↗

arXiv2025

Violation of energy conditions and the gravitational radius of the proton

The energy-momentum tensor (EMT) of the proton encodes fundamental information about its mass, pressure, and shear distributions. Using recent lattice QCD data for the gravitational form factors, we show that the Breit-frame Wigner EMT may be of Hawking-Ellis type IV in the proton's core. Such EMT violates all pointwise energy conditions and lacks a causal rest frame so that the usual mechanical picture fails at short distances. We define the gravitational radius -- a new hadronic observable marking the scale where the EMT becomes ordinary (type I) and the classical interpretation is restored. We also derive from the Averaged Null Energy Condition (ANEC) non-perturbative, model-independent QFT constraints on gravitational form factors.

hep-ph↗

arXiv2025

Gluon Sivers function from forward exclusive $χ_{c1}$ photoproduction on unpolarized protons

Exclusive production of a $χ_{c1}$ axial vector quarkonia in photon-proton scattering at high energies requires a $C$-odd $t$-channel exchange. In the limit of vanishing momentum transfer this occurs either via the exchange of a photon, the Primakoff process, where the spin of the proton does not change. For axial-vector meson production, as a consequence of the Landau-Yang theorem, the Primakoff cross section is finite as $t \to 0$. Alternatively, a $C$-odd spin dependent Odderon can be exchanged, which involves a spin flip of the proton. The resulting cross section is related to the square of the collinear trigluon correlator or the $k_\perp$-moment of the gluon Sivers function. Using two models for the gluon Sivers function from the literature we compute the ratio of Sivers to Primakoff cross sections and the angular coefficient $λ_θ$ governing the angular distribution of the $χ_{c1} \to J/ψ+ γ$ decay as functions of $x$. We point out that these observables constrain the magnitude of the gluon Sivers function at small $x$ which could be accessed in electron-proton scattering and ultraperipheral proton-proton and nucleus-proton collisions.

hep-ph↗

arXiv2025

Stronger $C$-odd color charge correlations in the proton at higher energy

The non-forward eikonal scattering matrix for dipole-proton scattering at high energy obtains an imaginary part due to a $C$-odd three gluon exchange. We present numerical estimates for the perturbative Odderon amplitude as a function of dipole size, impact parameter, their relative azimuthal angle, and light-cone momentum cutoff $x$. The proton is approximated as $ψ_\mathrm{qqq}|qqq\rangle + ψ_\mathrm{qqqg}|qqqg\rangle$, where $ψ_\mathrm{qqq}$ is a non-perturbative three quark model wave function while the gluon emission is computed in light-cone perturbation theory. We find that the Odderon amplitude increases as $x$ decreases from 0.1 to 0.01. At yet lower $x$, the reversal of this energy dependence would reflect the onset of universal small-$x$ renormalization group evolution.

hep-ph↗

arXiv2025

Quantum entanglement correlations in double quark PDFs

Methods from Quantum Information Theory are used to scrutinize quantum correlations encoded in the two-quark density matrix over light-cone momentum fractions $x_1$ and $x_2$. A non-perturbative three quark model light-cone wavefunction predicts significant non-classical correlations associated with the "entanglement negativity" measure for asymmetric and small quark momentum fractions. We perform one step of QCD scale evolution of the entire density matrix, not just its diagonal (dPDF), by computing collinearly divergent corrections due to the emission of a gluon. Finally, we present first qualitative numerical results for single-step scale evolution of quantum entanglement correlations in double quark PDFs. At a higher $Q^2$ scale, the non-classical correlations manifest in the dPDF for nearly symmetric momentum fractions.

hep-ph↗

arXiv2024

Photon-Odderon interference in exclusive $χ_{c}$ charmonium production at the Electron-Ion Collider

Exclusive $C=+1$ scalar, axial-vector, and tensor quarkonium production in high-energy electron-proton scattering requires a $C$-odd $t$-channel exchange of a photon or a three gluon ladder. We derive the expressions for the corresponding amplitudes. The relative phase of the photon vs. three gluon exchange amplitudes is determined by the sign of the light-front matrix element of the eikonal color current operator $d^{abc}J^{+a}J^{+b}J^{+c}$ at moderate $x$, and is not affected by small-$x$ QCD evolution. Model calculations predict constructive interference, which is particularly strong for momentum transfer $|t|\sim 1$~GeV$^2$ where the cross section for $χ_{cJ}$ production exceeds that for pure photon exchange by up to a factor of 4. We find that exclusive $χ_{cJ}$ electroproduction at the Electron-Ion Collider should occur with well measurable rates and measurements of these processes should allow to find an evidence of the perturbative Odderon exchange. We also compute the total electroproduction cross section as a function of energy and provide first estimates of the number of $χ_{cJ}$ events per month at the Electron-Ion Collider design luminosity.

hep-ph↗

arXiv2024

Polarized Dipole Scattering Amplitudes meet the Valence Quark Model

The recently revised small-$x$ helicity evolution, resumming the double-logarithmic factor, $α_s\ln^2(1/x)$, allows for the study of helicity distributions of quarks and gluons at small Bjorken $x$, corresponding to high center-of-mass energy. In this work, we calculate the moderate-$x$ initial conditions in the regime, $α_s \ln^2(1/x)\sim 1$, for the small-$x$ helicity evolution using a light-front valence quark model of the proton, which provides additional physical information about the target. The perturbative emission and absorption of a gluon by the valence quarks are also included. The results, given in Eqs. (35), provide a new set of initial conditions with a significantly reduced number of free parameters than conventional models. Consequently, the predictive power of small-$x$ helicity evolution is expected to improve once the initial conditions from this work are incorporated.

hep-ph↗

arXiv2024

Cubic color charge correlator in a proton made of three quarks and a gluon

The three point correlation function of color charge densities is evaluated explicitly in light cone gauge for a proton on the light cone. This includes both $C$-conjugation even and odd contributions. We account for perturbative corrections to the three-quark light cone wave function due to the emission of an internal gluon which is not required to be soft. We verify the Ward identity as well as the cancellation of UV divergences in the sum of all diagrams so that the correlator is independent of the renormalization scale. It does, however, exhibit the well known soft and collinear singularities. The expressions derived here provide the $C$-odd contribution to the initial conditions for high-energy evolution of the dipole scattering amplitude to small $x$. Finally, we also present a numerical model estimate of the impact parameter dependence of quantum color charge three-point correlations in the proton at moderately small $x$.

hep-ph↗

arXiv2023

Sub-femtometer scale color charge fluctuations in a proton made of three quarks and a gluon

The light-front wave function of a proton composed of three quarks and a perturbative gluon is computed. This is then used to derive expressions for the color charge density correlator $\langleρ^a(\vec q_1)\, ρ^b(\vec q_2)\rangle$ at ${\cal O}(g^4)$ due to the emission of a gluon by one of the quarks in light-cone gauge. The correlator exhibits the soft and collinear singularities. Albeit, we employ exact gluon emission and absorption vertices, and hence the gluon is not required to carry very small light-cone momentum, or to be collinear to the emitting quark. We verify that the correlator satisfies the Ward identity and that it is independent of the renormalization scale, i.e. that ultraviolet divergences cancel. Our expressions provide x-dependent initial conditions for Balitsky-Kovchegov evolution of the C-even part of the dipole scattering matrix to higher energies. That is, we determine the first non-trivial moment of the color charge fluctuations which act as sources for soft color fields in the proton with wavelengths greater than approximately $1/x \sim 10 - 100$.

hep-ph↗

arXiv2023

Quark pair angular correlations in the proton: entropy versus entanglement negativity

Two-particle correlations in the proton on the light-front are described by a mixed density matrix obtained by tracing over all other, unobserved, degrees of freedom. We quantify genuinely quantum quark azimuthal correlations in terms of the entanglement negativity measure of Quantum Information Theory. While the two-quark state in color space is one of high entropy and weak quantum correlation, we find that a standard three-quark model wave function from the literature predicts an azimuthally correlated state of low entropy and high entanglement negativity. Low entropy is consistent with expectations for many colors (at fixed 't Hooft coupling $g^2 N_c$) but high negativity indicates substantial two-particle quantum correlations at $N_c=3$. Suppressing quantum correlations associated with entanglement negativity strongly modifies quark pair azimuthal moments $\langle ζ^n \rangle$, $ζ= \exp(i (ϕ_1-ϕ_2))$, intrinsic to the proton state. We also describe how to account for the leading ${\cal O}(g^2)$ correction to the density matrix from light-cone perturbation theory which is due to the presence (or exchange) of a gluon in the proton. This correction increases the entropy and reduces the negativity of the density matrix for quark pair azimuthal correlations. Hence, the entanglement negativity measure may provide novel insight into the structure of the proton state of QCD.

hep-ph↗

arXiv2023

High-energy dipole scattering amplitude from evolution of low-energy proton light-cone wave functions

The forward scattering amplitude of a small dipole at high energies is given in the mean field approximation by the Balitsky-Kovchegov (BK) evolution equation. It requires an initial condition $N(r; x_0)$ describing the scattering of a dipole with size $r$ off the target that is probed at momentum fraction $x_0$. Rather than using ad hoc parameterizations tuned to high-energy data at $x\ll x_0$, here we attempt to construct an initial scattering amplitude that is consistent with low-energy, large-$x$ properties of the proton. We start from a non-perturbative three quark light-cone model wave function from the literature. We add ${\cal O}(g)$ corrections due to the emission of a gluon, and ${\cal O}(g^2)$ virtual corrections due to the exchange of a gluon, computed in light-cone perturbation theory with exact kinematics. We provide numerical data as well as analytic parameterizations of the resulting $N(r; x_0)$ for $x_0=0.01 - 0.05$. Solving the BK equation in the leading logarithmic (LL) approximation towards lower $x$, we obtain a fair description of the charm cross section in deeply inelastic scattering measured at HERA by fitting one parameter, the coupling constant $α_s\simeq 0.2$. However, without the option to tune the initial amplitude at $x_0$, the fit of the high precision data results in $χ^2/N_\text{dof} = 2.3$ at $N_\text{dof} =38$, providing clear statistical evidence for the need of systematic improvement e.g. of the photon wave function, evolution equation, and initial condition.

hep-ph↗

arXiv2023

The case for an EIC Theory Alliance: Theoretical Challenges of the EIC

We outline the physics opportunities provided by the Electron Ion Collider (EIC). These include the study of the parton structure of the nucleon and nuclei, the onset of gluon saturation, the production of jets and heavy flavor, hadron spectroscopy and tests of fundamental symmetries. We review the present status and future challenges in EIC theory that have to be addressed in order to realize this ambitious and impactful physics program, including how to engage a diverse and inclusive workforce. In order to address these many-fold challenges, we propose a coordinated effort involving theory groups with differing expertise is needed. We discuss the scientific goals and scope of such an EIC Theory Alliance.

hep-ph↗

arXiv2023

Entanglement entropy of the proton in coordinate space

We calculate the entanglement entropy of a model proton wave function in coordinate space by integrating out degrees of freedom outside a small circular region $\bar A$ of radius $L$, where $L$ is much smaller than the size of the proton. The wave function provides a nonperturbative distribution of three valence quarks. In addition, we include the perturbative emission of a single gluon and calculate the entanglement entropy of gluons in $\bar A$. For both, quarks and gluons we obtain the same simple result: $S_E =-\int\frac{dx}{Δx}\, N_{L^2}(x)\log[N_{a^2}(x)]$, where $a$ is the UV cutoff in coordinate space and $Δx$ is the longitudinal resolution scale. Here $N_{S}(x)$ is the number of partons (of the appropriate species) with longitudinal momentum fraction $x$ inside an area $S$. It is related to the standard parton distribution function (PDF) by $N_S(x)=\frac{S}{A_p}\, Δx\, F(x)$, where $A_p$ denotes the transverse area of the proton.

hep-ph↗

arXiv2022

rSHG: Re-scan Second Harmonic Generation Microscopy

Second Harmonic Generation Microscopy (SHG) is generally acknowledged as a powerful tool for the label-free 3D visualization of tissues and advanced materials, with one of its most popular applications being collagen imaging. Although the great need, progress in super-resolved SHG imaging lags behind the developments reported over the past years in fluorescence-based optical nanoscopy. In this work, we quantitatively show on collagenous tissues that by combining SHG imaging with re-scan microscopy resolutions that surpass the diffraction limit with ~1.4x become available. Besides Re-scan Second Harmonic Generation Microscopy (rSHG), we demonstrate as well super-resolved Re-scan Two-Photon Excited Fluorescence Microscopy (rTPEF). These two techniques are implemented by modifying a Re-scan Confocal Microscope (RCM), retaining its initial function, resulting thus in a multimodal rSHG/rTPEF/RCM system. Given the simplicity and flexibility of re-scan microscopy, we consider that the reported results are likely to augment the number and nature of applications relying on super-resolved non-linear optical imaging.

physics.optics↗

arXiv2022

Quark and gluon entanglement in the proton on the light cone at intermediate $x$

In QCD with $N_c$ colors the anti-symmetric valence quark color space singlet state $\sim ε_{i_1\cdots i_{N_c}} |i_1,\cdots, i_{N_c}\rangle$ of the proton corresponds to the reduced density matrix $ρ_{ij}=(1/N_c) δ_{ij}$ for a single color degree of freedom. Its degenerate spectrum of eigenvalues, $λ_i=1/N_c$, the purity $\mathrm{tr}~ρ^2 = 1/N_c$, and the von~Neumann entropy $S_\mathrm{vN}=\log(N_c)$ all indicate maximal entanglement of color. On the other hand, for $N_c\to\infty$ the spatial wave function of the proton factorizes into valence quark wave functions determined by a mean field (E. Witten, Nucl. Phys. B 160 (1979) p. 57) where there is no entanglement of spatial degrees of freedom. A model calculation at $N_c=3$ using a simple three quark model light-front wave function by Brodsky and Schlumpf, predicts percent level entanglement of spatial degrees of freedom. Using light-cone perturbation theory we also derive the density matrix associated with the four parton $|qqqg\rangle$ Fock state. Tracing out the quarks, we construct the reduced density matrix for the degrees of freedom of the gluon, which encodes its entanglement with the sources. Our expressions provide the dependence of the density matrix on the soft cutoff $x$ for the gluon light-cone momentum, and on the collinear and ultraviolet regulators. Numerical results obtained in a simple approximation indicate stronger entanglement for the gluon (with $x_g < \langle x_q\rangle$) than for quarks in the three quark Fock state.

hep-ph↗

arXiv2021

Color charge correlations in the proton at NLO: beyond geometry based intuition

Color charge correlators provide fundamental information about the proton structure. In this Letter, we evaluate numerically two-point color charge correlations in a proton on the light cone including the next-to-leading order corrections due to emission or exchange of a perturbative gluon. The non-perturbative valence quark structure of the proton is modelled in a way consistent with high-$x$ proton structure data. Our results show that the correlator exhibits startlingly non-trivial behavior at large momentum transfer or central impact parameters, and that the color charge correlation depends not only on the impact parameter but also on the relative transverse momentum of the two gluon probes and their relative angle. Furthermore, from the two-point color charge correlator, we compute the dipole scattering amplitude. Its azimuthal dependence differs significantly from a impact parameter dependent McLerran-Venugopalan model based on geometry. Our results also provide initial conditions for Balitsky-Kovchegov evolution of the dipole scattering amplitude. These initial conditions depend not only on the impact parameter and dipole size vectors, but also on their relative angle and on the light-cone momentum fraction $x$ in the target.

hep-ph↗

arXiv2021

Azimuthal correlations in diffractive scattering at the Electron-Ion Collider

We calculate azimuthal correlations between the exclusively produced vector meson and the scattered electron in Deep Inelastic Scattering processes at the future Electron-Ion Collider (EIC). We identify "kinematical" and "intrinsic" contributions to these correlations, and show that the correlations are sensitive to the non-trivial correlations in the gluon distribution of the target. Realistic predictions at the EIC kinematics are provided using two different approaches to describe the dipole-proton interaction at relatively small $x$.

hep-ph↗