Impact Parameter Dependence Research Articles

Measurement of the impact-parameter dependent azimuthal anisotropy in coherent ρ0 photoproduction in Pb–Pb collisions at [formula omitted] TeV

This Letter presents the first measurement of the impact-parameter dependent angular anisotropy in the decay of coherently photoproduced ρ0 mesons. The ρ0 mesons are reconstructed through their decay into pion pairs. The measured anisotropy corresponds to the amplitude of the cos⁡(2ϕ) modulation, where ϕ is the angle between the two vectors formed by the sum and the difference of the transverse momenta of the pions, respectively. The measurement was performed by the ALICE Collaboration at the LHC using data from ultraperipheral Pb–Pb collisions at a center-of-mass energy of sNN=5.02 TeV per nucleon pair. Different impact-parameter regions are selected by classifying the events in nuclear-breakup classes. The amplitude of the cos⁡(2ϕ) modulation is found to increase by about one order of magnitude from large to small impact parameters. Theoretical calculations describe the measured cos⁡(2ϕ) anisotropy and its impact-parameter dependence as the result of a quantum interference effect at the femtometer scale, arising from the ambiguity regarding which of the nuclei is the photon source in the interaction.

D meson production in p+Pb collisions with the analytical transverse momentum distribution from the color dipole models* *Supported by the National Natural Science Foundation of China Joint for Large Scientific Units (U1832120), the Hebei Province Outstanding Youth Fund (A2020210012), the S&T Program of Hebei (Grant No. 236Z4601G), and the Scientific Research Foundation for the Introducing Returned Overseas Chinese Scholars of

D meson production in proton–lead (p+Pb) collisions is globally investigated within the color dipole framework. To simplify the Fourier transform, the analytical transverse momentum distribution functions extracted from different color dipole models are used. With the Glauber–Gribov method, the impact parameter dependence is considered for the nuclear modification of the gluon density. We obtain from comparison with recent experimental data from the LHCb and ALICE Collaborations that the theoretical results from the Kovchegov, Lu and Rezaeian (KLR) model are in good agreement with the experimental data at small P T, and the results from the Golec–Biernat–Wüsthoff (GBW) and Bartels, Golec-Biernat and Kowalski (BGK) model are reasonable at all rapidity bins. Then, the influence of the initial-state energy loss effect on D meson production in p+Pb collisions is analyzed. A clear reduction of the nuclear modification factor is shown at backward rapidity. Finally, the predictive results for D0 and D+ production differential cross section versus rapidity (Y) in p+Pb collisions are given.

Forward dijet production at the LHC within an impact parameter dependent TMD approach

We investigate possible signatures of gluon saturation using forward p + A → j + j + X di-jet production processes at the Large Hadron Collider. In the forward rapidity region, this is a highly asymmetric process where partons with large longitudinal momentum fraction x in the dilute projectile are used as a probe to resolve the small x partonic content of the dense target. Such dilute-dense processes can be described in the factorization framework of Improved Transverse Momentum Distributions (ITMDs). We present a new model for ITMDs where we explicitly introduce the impact parameter (b) dependence in the ITMDs, to properly account for the nuclear enhancement of gluon saturation effects, and discuss the phenomenological consequences for p − Pb, p − Xe and p − O collisions at the LHC. While the case of p − p and e − p collisions is used to fix the model parameters, we find that, on average, the nuclear enhancement of the saturation scale is noticeably weaker than expected from naive scaling with a simple dependence on the atomic number. Since our model explicitly accounts for event-by-event fluctuations of the nuclear geometry, it can also be applied to study forward central correlations in p − A collisions.

Illuminating the impact-parameter dependence of UPC dijet photoproduction

We present new NLO pQCD predictions for photoproduction of dijets in ultraperipheral PbPb collisions at 5.02 TeV with a realistic photon flux and up-to-date nuclear PDFs. Our calculation of the impact parameter dependence of the photon flux includes the effects of the nuclear form factor in the photon-emitting nucleus and the spatial dependence of nuclear PDFs of the target nucleus, which are estimated using theWood-Saxon nuclear density profile. We show that a significant portion of the measured dijets at large zγ originate from events with impact parameters of the order of a few nuclear radii, and that the cross section predictions therefore become sensitive to the modelling of the nuclear geometry and photon flux close to the source nucleus.

Solutions to the Balitsky-Kovchegov equation including the dipole orientation

Solutions of the target-rapidity Balitsky-Kovchegov (BK) equation are studied considering, for the first time, the complete impact-parameter dependence, including the orientation of the dipole with respect to the impact-parameter vector. In our previous work [1] it has been demonstrated that the spurious Coulomb tails could be tamed using the collinearly-improved kernel and an appropriate initial condition in the projectile-rapidity BK equation. Introducing a different interpretation of the evolution variable, the target-rapidity formulation of the BK equation brings non-locality in rapidity and a kernel modification, removing the term that previously helped to suppress the Coulomb tails. To address this newly emerged non-locality, three different prescriptions are explored here to take into account the rapidities preceding the initial condition. Two of these approaches induce mild Coulomb tails, while the other is free from this effect within the studied rapidity range. The range is chosen to correspond to that of interest for existing and future experiments. To demonstrate that this set up can be used for phenomenological studies, the obtained solutions are used to compute the F2 structure function of the proton and the diffractive photo- and electro-production of J/ψ off protons. The predictions agree well with HERA data, confirming that the target-rapidity Balitsky-Kovchegov equation with the full impact-parameter dependence is a viable tool to study the small Bjorken-x limit of perturbative QCD at current facilities like RHIC and LHC as well as in future colliders like the EIC.

Dielectron production at midrapidity at low transverse momentum in peripheral and semi-peripheral Pb–Pb collisions at {sqrt{s}}_{textrm{NN}} = 5.02 TeV

The first measurement of the e+e− pair production at low lepton pair transverse momentum (pT,ee) and low invariant mass (mee) in non-central Pb–Pb collisions at {sqrt{s}}_{textrm{NN}} = 5.02 TeV at the LHC is presented. The dielectron production is studied with the ALICE detector at midrapidity (|ηe| < 0.8) as a function of invariant mass (0.4 ≤ mee< 2.7 GeV/c2) in the 50–70% and 70–90% centrality classes for pT,ee< 0.1 GeV/c, and as a function of pT,ee in three mee intervals in the most peripheral Pb–Pb collisions. Below a pT,ee of 0.1 GeV/c, a clear excess of e+e− pairs is found compared to the expectations from known hadronic sources and predictions of thermal radiation from the medium. The mee excess spectra are reproduced, within uncertainties, by different predictions of the photon–photon production of dielectrons, where the photons originate from the extremely strong electromagnetic fields generated by the highly Lorentz-contracted Pb nuclei. Lowest-order quantum electrodynamic (QED) calculations, as well as a model that takes into account the impact-parameter dependence of the average transverse momentum of the photons, also provide a good description of the pT,ee spectra. The measured sqrt{leftlangle {p}_{textrm{T},textrm{ee}}^2rightrangle } of the excess pT,ee spectrum in peripheral Pb–Pb collisions is found to be comparable to the values observed previously at RHIC in a similar phase-space region.

Collision-energy dependence of the Breit-Wheeler process in heavy-ion collisions and its application to nuclear charge radius measurements

The collision energy dependence of the cross section and the transverse momentum distribution of dielectrons from the Breit-Wheeler process in heavy-ion collisions are computed in the lowest-order QED and found to be sensitive to the nuclear charge distribution and the infrared divergence of the ultra-Lorentz-boosted Coulomb field. Within a given experimental kinematic acceptance, the cross section is found to increase while the pair transverse momentum ($\sqrt{\ensuremath{\langle}{p}_{T}^{2}\ensuremath{\rangle}}$) decreases with increasing beam energy. We demonstrate that the transverse-momentum component of Weizs\"acker-Williams photons is due to the finite extent of the charge source and electric field component in the longitudinal direction. We further clarify the connection between the nuclear charge distribution and the kinematics of produced ${e}^{+}{e}^{\ensuremath{-}}$ from the Breit-Wheeler process, and propose a criterion for the validity of the Breit-Wheeler process in relativistic heavy-ion collisions. Following this approach we demonstrate that the experimental measurements of the Breit-Wheeler process in ultrarelativistic heavy-ion collisions can be used to quantitatively constrain the nuclear charge radius. The extracted parameters show sensitivity to the impact parameter dependence, and can be used to study the initial-state and final-state effects in hadronic interactions.

Initial electromagnetic field dependence of photon-induced production in isobaric collisions at STAR

In these proceedings, we present the measurements of e+e− pair production at very low transverse momentum in 4496Ru + 4496Ru and 4096Zr + 4096Zr collisions at √SNN = 200 GeV by the STAR experiment. The electromagnetic field dependence of photon-induced production is studied for the first time, via comparisons between the measurements in isobaric collisions to the published results in Au+Au and U+U collisions. Taken the initial electromagnetic field dependence into account, the excess yield of e+e− pair production shows an impact parameter dependence. The results are also compared to model calculations based on EPA-QED, which describe the observed excess yields for different collision species.

Impact parameter dependence of photon-photon interactions in relativistic heavy-ion collisions

The Lorentz-boosted electromagnetic fields surrounding relativistic heavy ions with large charges can be treated as a flux of linearly polarized quasireal photons, which can interact via the photon-photon scattering to produce lepton antilepton pairs. Those photon-photon interactions can happen even in heavy-ion collisions with hadronic overlap, making an opportunity to probe the electromagnetic properties of the produced deconfined quark-gluon plasma. In this paper, we review the recent experimental progress of the impact parameter dependent photon-photon interactions in heavy-ion collisions, and discuss their essential role in probing the possible electromagnetic properties of quark-gluon plasma produced in hadronic heavy-ion collisions.

Theoretical multiple-ionization cross sections of Ne-like molecules by light-ion impact: H2O

We present a simple theoretical model to calculate multiple-ionization cross sections (MICS) of Ne and Ne-like molecules (molecules with ten electrons as ${\mathrm{H}}_{2}\mathrm{O}, \mathrm{C}{\mathrm{H}}_{4}, \mathrm{N}{\mathrm{H}}_{3}$, and HF) for proton and light-ion impact, taking into account both direct and postcollisional emissions. In this paper, we tackle the case of water molecules, relevant to investigate the radiobiological effects of ion impact on living matter. The theory is developed in the framework of the independent electron model (IEM). To keep the model as simple as possible, we describe the impact parameter dependence of the single-particle ionization probabilities required by the IEM through decreasing exponential functions for each target orbital. We obtain the parameters of the exponential functions from the total net-ionization cross sections for each orbital by applying either the continuum distorted wave-eikonal initial-state (CDW-EIS) approximation or Rudd's model. We then calculate the contribution of Auger postcollisional electron emission to MICS by using the Ne postcollisional emission probabilities. This postcollisional treatment offers a very simple alternative to the much more complex molecular evaluation of postcollisional relaxation and provides results in close agreement with experimental data for proton and other light ions. We also demonstrate the relevance of considering postcollisional emission for water molecules after the $2{a}_{1}$ ($2s$ Ne-like) orbital direct ionization.

Impact parameter dependence of color charge correlations in the proton

The impact parameter dependence of color charge correlators in the proton is obtained from the light front formalism in light cone gauge. We include NLO corrections due to the |qqqg\rangle|qqqg⟩ Fock state via light-cone perturbation theory. Near the center of the proton, the bb-dependence of the correlations is very different from a ``transverse profile function’’. The resulting tt-dependence of exclusive J/\PsiJ/Ψ photoproduction transitions from exponential to power law at |t| \approx 1|t|≈1~GeV^22. This prediction could be tested at upcoming DIS facilities or in nucleus-proton ultraperipheral collisions (UPCs).

State-resolved differential cross sections of single-electron capture in swift collisions ofC4+(1s2s3S) ions with gas targets

We report on double and single differential cross section measurements of the $1s2{s}^{2}\phantom{\rule{0.16em}{0ex}}^{2}S$, $1s2s2p\phantom{\rule{0.16em}{0ex}}^{2}P_{\ifmmode\pm\else\textpm\fi{}}$, and $1s2s2p\phantom{\rule{0.16em}{0ex}}^{4}P$ doubly excited states produced by single-electron capture in 6--15 MeV collisions of pre-excited ${\mathrm{C}}^{4+}(1s2s\phantom{\rule{0.16em}{0ex}}^{3}S)$ ions with ${\mathrm{H}}_{2}$, He, Ne, and Ar targets. Ab initio cross section calculations based on a three active electrons atomic orbital close-coupling approach are compared to the measurements for collisions with the lighter ${\mathrm{H}}_{2}$ and He targets, showing an overall good agreement. Theoretical details concerning Auger electron angular distributions, partial cross sections, impact parameter dependencies, and radiative cascade feeding effects are discussed. The populations of the $1s2s2p\phantom{\rule{0.16em}{0ex}}^{4}P$, $^{2}P_{\ensuremath{-}}$, $^{2}P_{+}$ multiplets concerning the spin symmetry are finally presented for the four collision systems and discussed following the comparisons between theory and experiment.

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 $x$.

Deeply virtual Compton scattering at the EIC and LHeC: a comparison among saturation approaches

The impact of nonlinear effects in the deeply virtual Compton scattering (DVCS) process that will be measured in future electron-hadron collisions is investigated. We present, for the first time, the predictions derived using the solution to the Balitsky–Kovchegov equation with the collinearly-improved kernel and including the impact-parameter dependence. We estimate the total cross section and t-distribution of the DVCS process in ep and eA collisions and demonstrate that dsigma /dt is strongly dependent on the assumption for the impact-parameter dependence of the dipole-hadron scattering amplitude. Our results indicate that a future experimental analysis of this process will be useful to discriminate among different models for the saturation physics and, consequently, will allow us to constrain the description of QCD dynamics in parton densities.

Nonlinear evolution in the re-summed next-to-leading order of perturbative QCD: Confronting the experimental data

In this paper we compare the experimental HERA data with the next-to-leading order approach (NLO) of Ref.[C.~Contreras, E.~Levin, R.~Meneses and M.~Sanhueza,Eur. Phys. J. C 80 (2020) no.11, 1029). This approach includes the re-summed NLO corrections to the kernel of the evolution equation, the correct asymptotic behaviour in the NLO at $\tau = r^2 Q^2_s \,\gg\,1$; the impact parameter dependence of the saturation scale in accord with the Froissarrt theorem as well as the non-linear corrections. In this paper, we successfully describe the experimental data with the quality, which is not worse, than in the leading order fits with larger number of the phenomenological parameters. It is demonstrated, that the data could be described, taking into account both the diffusion on $\ln(k_T)$, which stems from perturbative QCD, and the Gribov's diffusion in impact parameters. It is shown an ability to describe the data at rather large values of $\alpha_S$.

On the Impact Parameter Dependence of the Ionization Energy Loss of Fast Negatively Charged Particles in an Oriented Crystal

When a fast charged particle passes through matter, it loses some of its energy to the excitation and ionization of atoms. This energy loss is called ionization energy loss. In rather thin layers of matter, the value of such energy loss is stochastic. It is distributed in accordance with the law, which was first received by L.D. Landau. In amorphous substances, such a distribution (or spectrum), known as the Landau distribution, has a single maximum that corresponds to the most probable value of particle energy loss. When a particle moves in crystal in a planar channeling mode, the probability of close collisions of the particle with atoms decreases (for a positive particle charge) or increases (for a negative charge), which leads to a change in the most probable energy loss compared to an amorphous target. It has recently been shown that during planar channeling of negatively charged particles in a crystal, the distribution of ionization energy loss of the particles is much wider than in the amorphous target. In this case, this distribution can be two-humped, if we neglect the incoherent scattering of charged particles on the thermal oscillations of the crystal atoms and the electronic subsystem of the crystal. This paper explains the reason for this distribution of ionization energy loss of particles. The ionization energy loss distribution of high-energy negatively charged particles which move in the planar channeling mode in a silicon crystal are studied with the use of numerical simulation. The dependence of this distribution on the impact parameter of the particles with respect to atomic planes is considered. The dependence of the most probable ionization energy loss of particles on the impact parameter is found. It is shown that, for a large group of particles, the most probable ionization energy loss during planar channeling in a crystal is lower than in an amorphous target.

GTMD model predictions for diffractive dijet production at EIC

In this paper we consider a small-$x$ model for gluon GTMDs that we fit to data on diffractive dijet production in electron-proton collisions obtained by HERA's H1 Collaboration. Assuming a small number of free parameters, each with a physical motivation, we are able to describe those data fairly well and with this model we obtain predictions for the EIC for both electroproduction and photoproduction which may allow to further test the underlying GTMD description. In the general discussion of the impact parameter dependence we recall some subtle issues related to localization of states, choice of frames, and discuss what these aspects imply for the range of applicability of the model.

Observation of Forward Neutron Multiplicity Dependence of Dimuon Acoplanarity in Ultraperipheral Pb-Pb Collisions at sqrt[s_{NN}]=5.02 TeV.

The first measurement of the dependence of γγ→μ^{+}μ^{-} production on the multiplicity of neutrons emitted very close to the beam direction in ultraperipheral heavy ion collisions is reported. Data for lead-lead interactions at sqrt[s_{NN}]=5.02 TeV, with an integrated luminosity of approximately 1.5 nb^{-1}, are collected using the CMS detector at the LHC. The azimuthal correlations between the two muons in the invariant mass region 8<m_{μμ}<60 GeV are extracted for events including 0, 1, or at least 2 neutrons detected in the forward pseudorapidity range |η|>8.3. The back-to-back correlation structure from leading-order photon-photon scattering is found to be significantly broader for events with a larger number of emitted neutrons from each nucleus, corresponding to interactions with a smaller impact parameter. This observation provides a data-driven demonstration that the average transverse momentum of photons emitted from relativistic heavy ions has an impact parameter dependence. These results provide new constraints on models of photon-induced interactions in ultraperipheral collisions. They also provide a baseline to search for possible final-state effects on lepton pairs caused by traversing a quark-gluon plasma produced in hadronic heavy ion collisions.

First-principles study of semicore electron excitation in the electronic energy loss of ZnO for protons

The electronic stopping power of zinc oxide for protons is presented over a wide range of velocities by using real-time time-dependent density functional theory. We calculated the electronic stopping power of energetic protons for both channeling and off-channeling trajectories, and revealed the microcosmic mechanism of semicore $3d$-electron excitation in ZnO. In the low-energy regime, the stopping power obtained from channeling geometry is in a quantitative agreement with the measured data, which reproduced not only the experimental threshold velocity of the stopping power, but also the deviation from velocity-proportional electronic stopping power which is considered to be caused by excitation of the tightly bound $3d$ electrons. In the high-energy regime, we examined the impact parameter dependence of semicore $3d$-electron excitation of ZnO, and showed that the stopping power obtained from off-channeling geometry greatly improves the simulation results in comparison with the channeling results. We also demonstrated that the electronic energy loss of protons is not only related to the number of electrons excited, but also associated with the energy distribution of excited electrons and holes after collisions.

Central elastic scattering

We comment on phase selection of the scattering amplitude, emphasizing that the elastic overlap function should have a central impact parameter profile at high energies and highlighting the role of the reflective scattering mode at the LHC energies. Emerging problems with the use of peripheral impact parameter dependence of the elastic overlap function are explicitly indicated. Their solution is an elimination of the phases connected to peripheral form of the elastic overlap function. Contrary, we adhere to a relative peripheral form of the inelastic overlap function with an additional new feature of a maximum at nonzero value of the impact parameter at the highest energies. Phenomenologically, the dynamics of hadron scattering is motivated by a hadron structure with a hard central core presence.