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

Abstract

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 $\mathcal{O}(g)$ corrections due to the emission of a gluon, and $\mathcal{O}(g^2)$ 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 ${\alpha }_s\simeq 0.2$. However, without the option to tune the initial amplitude at $x_0$, the fit of the high precision data results in ${\chi }^2/N_{\text{dof}}=2.3$ 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.

arXiv comment11 pages, 10 figures. Obtained dipole-proton amplitudes at different x are included in the ancillary files, v2 matches published version

References in corpus (48)

• Computing Quark and Gluon Distribution Functions for Very Large Nuclei
• Operator expansion for high-energy scattering
• Small-x F_2 Structure Function of a Nucleus Including Multiple Pomeron Exchanges
• Saturation Effects in Deep Inelastic Scattering at low $Q^2$ and its Implications on Diffraction
• The Color Glass Condensate
• Combined Measurement and QCD Analysis of the Inclusive ep Scattering Cross Sections at HERA
• An Impact Parameter Dipole Saturation Model
• Exclusive diffractive processes at HERA within the dipole picture
• Single and Double BFKL Pomeron Exchange and a Dipole Picture of High Energy Hard Processes
• Geometric scaling for the total gamma^* p cross section in the low x region
• Universality of Unintegrated Gluon Distributions at small x
• NLO evolution of color dipoles
• Quark contribution to the small-$x$ evolution of color dipole
• Gluon production in current-nucleus and nucleon-nucleus collisions in a quasi-classical approximation
• Cronin Effect and High-p_T Suppression in pA Collisions
• Elastic J/Psi Production at HERA
• Geometric scaling as traveling waves
• AAMQS: A non-linear QCD analysis of new HERA data at small-x including heavy quarks
• Large-Momentum Effective Theory
• The Large Hadron-Electron Collider at the HL-LHC
• Non-linear QCD meets data: A global analysis of lepton-proton scattering with running coupling BK evolution
• Single inclusive particle production at high energy from HERA data to proton-nucleus collisions
• Traveling wave fronts and the transition to saturation
• Resumming double logarithms in the QCD evolution of color dipoles
• Collinearly-improved BK evolution meets the HERA data
• Next-to-leading order Balitsky-Kovchegov equation with resummation
• Relativistic Constituent Quark Model of Electroweak Properties of Baryons
• Non-linear evolution in QCD at high-energy beyond leading order
• Color Glass Condensate at next-to-leading order meets HERA data
• Wavefunction-Independent Relations between the Nucleon Axial-Coupling g_A and the Nucleon Magnetic Moments
• Confronting impact parameter dependent JIMWLK evolution with HERA data
• In depth analysis of the combined HERA data in the dipole models with and without saturation
• On the implementation of NLO high energy factorization in single inclusive forward hadron production
• Small x nonlinear evolution with impact parameter and the structure function data
• Computing Light-Front Wave Functions Without Light-Front Quantization: A Large-Momentum Effective Theory Approach
• Massive quarks in NLO dipole factorization for DIS: Transverse photon
• Sub-femtometer scale color charge fluctuations in a proton made of three quarks and a gluon
• Massive quarks at one loop in the dipole picture of Deep Inelastic Scattering
• Hard scattering factorization and light cone hamiltonian approach to diffractive processes
• Color transparency in deeply inelastic diffraction
• Color charge correlations in the proton at NLO: beyond geometry based intuition
• Extracting many-body color charge correlators in the proton from exclusive DIS at large Bjorken x
• Multi-quark matrix elements in the proton and three gluon exchange for exclusive ${\eta }_c$ production in photon-proton diffractive scattering
• Proton structure functions at NLO in the dipole picture with massive quarks
• Parton distribution function for quarks in an s-channel approach
• Cubic color charge correlator in a proton made of three quarks and a gluon
• Stronger $C$-odd color charge correlations in the proton at higher energy
• Power-like corrections and the determination of the gluon distribution

Cited by in corpus (8)

• Inferring the initial condition for the Balitsky-Kovchegov equation
• Entanglement entropy of the proton in coordinate space
• Gluon Saturation Effects in Exclusive Heavy Vector Meson Photoproduction
• Global Bayesian Analysis of $\mathrm{J}/\psi$ Photoproduction on Proton and Lead Targets
• Complete Next-to-Leading Order Calculation of Single Inclusive ${\pi }^0$ Production in Forward Proton-Nucleus Collisions
• Determination of the initial condition for the Balitsky-Kovchegov equation with transformers
• Directed flow from parton spin-orbit coupling in $pp$ and $pA$ collisions
• Proton spin from small-$x$ with constraints from the valence quark model