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 at O(g(4)) due to the emission of a gluon by one of the quarks in the 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 nontrivial moment of the color charge fluctuations which act as sources for soft color fields in the proton with wavelengths greater than approximately 1/x similar to 10-100.Peer reviewe

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 -one 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.Peer reviewe

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 $\alpha_s\simeq 0.2$. 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.Comment: 11 pages, 10 figures. Obtained dipole-proton amplitudes at different x are included in the ancillary file

Gluon radiation from a classical point particle. II. Dense gluon fields

The goal of this paper is to extend the results of [K. Kajantie, L. D. McLerran, and R. Paatelainen, Gluon radiation from a classical point particle, Phys. Rev. D 100, 054011 (2019)., where formulas were derived for gluonic radiation for a high energy nucleus colliding with a classical colored particle. In [K. Kajantie, L. D. McLerran, and R. Paatelainen, Gluon radiation from a classical point particle, Phys. Rev. D 100, 054011 (2019).], we computed the amplitudes for radiation in the fragmentation region of the particle for a dilute gluonic field. In this paper, we compute the radiation by solving the fluctuation equations of the dense background field in a specific gauge, which makes it simple to solve the asymptotic radiation from an initial condition immediately after the passage of the nucleus. We identify and compute two components of gluon radiation, a bulk component which extends to the central region and bremsstrahlung, which may give rise to an experimentally observable intensity peak in the target fragmentation region.The goal of this paper is to extend the results of [K. Kajantie, L. D. McLerran, and R. Paatelainen, Gluon radiation from a classical point particle, Phys. Rev. D 100, 054011 (2019)., where formulas were derived for gluonic radiation for a high energy nucleus colliding with a classical colored particle. In [K. Kajantie, L. D. McLerran, and R. Paatelainen, Gluon radiation from a classical point particle, Phys. Rev. D 100, 054011 (2019)] we computed the amplitudes for radiation in the fragmentation region of the particle for a dilute gluonic field. In this paper, we compute the radiation by solving the fluctuation equations of the dense background field in a specific gauge, which makes it simple to solve the asymptotic radiation from an initial condition immediately after the passage of the nucleus. We identify and compute two components of gluon radiation, a bulk component which extends to the central region and bremsstrahlung, which may give rise to an experimentally observable intensity peak in the target fragmentation region.Peer reviewe

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

The nonforward 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 yrqqqjqqqi thorn yrqqqgjqqqgi, where yrqqq is a nonperturbative 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 evolution.Peer reviewe

Soft gluon self-energy at finite temperature and density: hard NLO corrections in general covariant gauge

We compute the next-to-leading order (NLO) hard correction to the gluon self-energy tensor with arbitrary soft momenta in a hot and/or dense weakly coupled plasma in Quantum Chromodynamics. Our diagrammatic computations of the two-loop and power corrections are performed within the hard-thermal-loop (HTL) framework and in general covariant gauge, using the real-time formalism. We find that after renormalization our individual results are finite and gauge-dependent, and they reproduce previously computed results in Quantum Electrodynamics in the appropriate limit. Combining our results, we also recover a formerly known gauge-independent matching coefficient and associated screening mass in a specific kinematic limit. Our NLO results supersede leading-order HTL results from the 1980s and pave the way to an improved understanding of the bulk properties of deconfined matter, such as the equation of state.Comment: 36 pages, 3 figure

Equation of state of cold quark matter to O(αs3ln⁡αs)O(\alpha_s^3 \ln \alpha_s)

Accurately understanding the equation of state (EOS) of high-density, zero-temperature quark matter plays an essential role in constraining the behavior of dense strongly interacting matter inside the cores of neutron stars. In this Letter, we study the weak-coupling expansion of the EOS of cold quark matter and derive the complete, gauge-invariant contributions from the long-wavelength, dynamically screened gluonic sector at next-to-next-to-next-to-leading order (N3LO) in the strong coupling constant $\alpha_s$. This elevates the EOS result to the $O(\alpha_s^3 \ln \alpha_s)$ level, leaving only one unknown constant from the unscreened sector at N3LO, and places it on par with its high-temperature counterpart from 2003. This is achieved by generalizing next-to-leading order gluon self-energies within the hard-thermal-loop limit from high temperatures and densities to zero temperature. We find that including these screened gluonic contributions at N3LO yields a remarkably well-converged EOS, with essentially no renormalization-scale dependence. Finally, we perform a Bayesian estimation of the remaining unscreened contribution at N3LO and find that the full EOS of cold quark matter at this order may show markedly improved convergence over the lower-order results.Comment: 7 pages (main text), 5 pages (supplemental material), 2 figures, 2 table

Systematics of the charged-hadron P_T spectrum and the nuclear suppression factor in heavy-ion collisions from sqrt{s}=200 GeV to sqrt{s} =2.76 TeV

In this paper, our goal is to make a simultaneous analysis of the high- and low-P_T parts of the charged-hadron P_T spectrum measured by the ALICE collaboration in central Pb-Pb collisions at sqrt{s}=2.76 TeV at the Large Hadron Collider (LHC), based on models which have been successfully applied and constrained in Au-Au collisions at Relativistic Heavy Ion Collider (RHIC). For the hydrodynamical modeling with which we obtain the low-P_T spectrum, we have computed the initial conditions based on perturbative QCD (pQCD) minijet production and saturation. The sensitivity of the obtained charged-hadron P_T spectrum on the hydrodynamic model parameters is studied. For the high-P_T part, we apply a number of parton-medium interaction models, which are tuned to describe the nuclear suppression factor R_AA measured at the RHIC in central Au-Au collisions at sqrt{s}=200 GeV. We find that the higher kinematic reach of the LHC, manifest in the hardening of the pQCD parton spectral slope, is in principle very efficient in discriminating the various models. However, due to the uncertainties in the p-p baseline, none of the tested models can be firmly ruled out with the present ALICE data. Comparison with the LHC data in this approach also shows that the matching of the hydrodynamic and pQCD+jet quenching components leaves fairly little room for other hadron production mechanisms in the cross-over region P_T=4-5 GeV.Comment: 12 pages, 4 figures, submitted to PR