HERA Energies Research Articles

Exclusive emissions of rho-mesons and the unintegrated gluon distribution

Exclusive emissions of vector mesons in forward directions of rapidity offer us a faultless chance to probe the proton structure at small xx. A high-energy factorization formula is established within BFKL, given as the convolution of an impact factor depicting the forward-meson emission and of an unintegrated gluon distribution (UGD) driving the gluon evolution at small xx. As a nonperturbative quantity, the UGD is not well known and several models for it exist. We present recent progresses on the study of the exclusive forward \rhoρ-meson leptoproduction at HERA and EIC energies, showing how osbervables sensitive to different polarization states of the \rhoρ-particle act as discriminators for the existing UGD models.

Running coupling effect in next-to-leading order Balitsky-Kovchegov evolution equations * *Supported by the National Natural Science Foundation of China (12165004, 12061141008, 11975005); the Fund of Science and Technology Department of Guizhou Province ([2019]5653); the Education Department of Guizhou Province (KY[2021]131); the National Key Research and Development Program of China (2018YFE0104700, 2018YFE0104800)

Balitsky-Kovchegov equations in projectile and target rapidity representations are analytically solved for fixed and running coupling cases in the saturation domain. Interestingly, we find that the respective analytic S-matrices in the two rapidity representations have almost the same rapidity dependence in the exponent in the running coupling case, which provides a method to explain why the equally good fits to HERA data were obtained when using three different Balitsky-Kovchegov equations formulated in the two representations. To test the analytic outcomes, we solve the Balitsky-Kovchegov equations and numerically compute the ratios between these dipole amplitudes in the saturation region. The ratios are close to one, which confirms the analytic results. Moreover, the running coupling, collinearly-improved, and extended full collinearly-improved Balitsky-Kovchegov equations are used to fit the HERA data. We find that all of them provide high quality descriptions of the data, and the obtained from the fits are similar. Both the analytic and numerical calculations imply that the Balitsky-Kovchegov equation at the running coupling level is robust and has a sufficiently strong predictive power at HERA energies; however, higher order corrections could be significant for future experiments, such as those at the EIC or LHeC.

Confronting the impact parameter dependent JIMWLK evolution with HERA data

The small-$x$ evolution of protons is determined from numerical solutions of the JIMWLK equations, starting from an initial condition at moderate $x$ for a finite size proton. The resulting dipole amplitude is used to calculate the total reduced cross section $\sigma_r$ and charm reduced cross section $\sigma_{rc}$, as well as diffractive vector meson production. We compare results to experimental data from HERA and discuss fundamental problems arising from the regime sensitive to non-perturbative physics. We emphasize that information on the gluonic content of the proton, gluon spatial distributions and correlations over wide ranges in $x$, which can in principle be constrained by our study, are essential ingredients for describing the initial state in proton-proton and proton-ion collisions. Future electron nucleus collisions at an electron-ion collider will provide important additional insight for heavier nuclei. We further demonstrate that it is not possible to probe gluon saturation in electron-proton collision at HERA energies and that electron-heavy ion collisions will be essential to access the saturation regime.

Exclusive J/ψ photoproduction off protons in ultraperipheral p-Pb collisions at √(s(NN))=5.02 TeV.

We present the first measurement at the LHC of exclusive J/ψ photoproduction off protons, in ultraperipheral proton-lead collisions at sqrt[s_{NN}]=5.02 TeV. Events are selected with a dimuon pair produced either in the rapidity interval, in the laboratory frame, 2.5<y<4 (p-Pb) or -3.6<y<-2.6 (Pb-p), and no other particles observed in the ALICE acceptance. The measured cross sections σ(γ+p→J/ψ+p) are 33.2±2.2(stat)±3.2(syst)±0.7(theor) nb in p-Pb and 284±36(stat)_{-32}^{+27}(syst)±26(theor) nb in Pb-p collisions. We measure this process up to about 700GeV in the γp center of mass, which is a factor of two larger than the highest energy studied at HERA. The data are consistent with a power law dependence of the J/ψ photoproduction cross section in γp energies from about 20 to 700GeV, or equivalently, from Bjorken x scaling variable between ∼2×10^{-2} and ∼2×10^{-5}, thus indicating no significant change in the gluon density behavior of the proton between HERA and LHC energies.

Gluon number fluctuations with heavy quarks at HERA

We study the effect of gluon number fluctuations (Pomeron loops) on the proton structure function at HERA. It is shown that the description of charm and bottom quarks and longitudinal structure functions are improved, with χ2/d.o.f=0.803 (fluctuations) as compared with χ2/d.o.f=0.908 (without fluctuations), once the gluon number fluctuations are included. We find that in the gluon number fluctuation case the heavy quarks do not play an important role in the proton structure function as the saturation model. The successful description of the HERA data indicates that the gluon number fluctuation could be one of the key mechanisms to describe the proton structure function at HERA energies.

DGLAP versus perturbative Pomeron in large momentum transfer hard diffractive processes at HERA and LHC

We evaluate within the LO DGLAP approximation the dependence on energy of the cross section of the photo(electro)production of vector meson V (V=J/ψ,…) in the hard elastic processes off a parton γ∗+g→V+g as the function of momentum transfer t=(qγ−pV)2. We demonstrate that in the limit −t⩾mV2+Q2 the cross section does not contain double logarithmic terms in any order of the DGLAP approximation leading to the energy independent cross section. Thus the energy dependence of cross section γ∗+p→J/ψ+rapidity gap+X is governed at large t by the gluon distribution within a proton, i.e. it is unambiguously predicted within the DGLAP approximation including the stronger WγN dependence at larger −t. This prediction explains recent HERA data. The calculations which follow perturbative Pomeron logic predict opposite trend of a weaker WγN dependence at larger t. We explain that at the HERA energies double logarithmic terms characteristic for DGLAP approximation dominate in the hard processes as the consequence of the constraints due to the energy–momentum conservation. We give predictions for the ultraperipheral hard diffractive processes at the LHC and show that these processes are well suited for looking for the contribution of the single logarithmic terms due to the gluon emission in the multi-Regge kinematics. We also comment on the interrelation between energy and t dependence of the cross sections of the hard exclusive processes.

XF (or y)-Dependence of Nuclear Absorption and Energy Loss Effects on J/Ψ Production

By means of the nuclear parton distribution studied only with lepton deep-inelastic scattering experimental data, the J/Ψ “normal nuclear absorption" and energy loss effects are studied in a Glauber formalism at HERA and RHIC energies. Assuming that the absorption cross section σabs increases with the charmonium-nucleon center of mass energy, the results reveal a significant dependence of the σabs on rapidity y at RHIC energies. The initial-state energy loss effect, which is found important only at HERA energies, is also considered, and its influence should be eliminated when we studied the absorption effect at low collision energies. Finally, we also present the theoretical prediction for LHC.

DIS and the effects of fluctuations: a momentum space analysis

Among the dipole models of deep inelastic scattering at small values of the Bjorken variable $x$, one has been recently proposed which relates the virtual photon-proton cross section to the dipole-proton forward scattering amplitude in momentum space. The latter is parametrized by an expression which interpolates between its behavior at saturation and the travelling wave, ultraviolet, amplitudes predicted by perturbative QCD from the Balitsky-Kovchegov equation. Inspired by recent developments in coordinate space, we use this model to parametrize the proton structure function and confront it to HERA data on $ep$ deep inelastic scattering. Both event-by-event and the physical amplitudes are considered, the latter used to investigate the effect of gluon number fluctuations, beyond the mean-field approximation. We conclude that fluctuations are not present in DIS at HERA energies.

Dipole scattering amplitude in momentum space: investigating fluctuations at HERA

not included in the original Balitsky-JIMWLK hierarchy and obviously missed in its mean field version, the BK equation. The fluctuations have been exhaustively investigated in recent years and their effects in the high energy evolution will be discussed in the next sections of this contribution. What one can antecipate is that they dramatically influence the high energy scattering, at least in the case when the strong coupling constant as is fixed. Among these investigations, one can cite a recent study [6] of the possible implications of the gluon number fluctuations in the measurements of the F2 proton structure function of deep inelastic scattering (DIS) at HERA, through well known models for the dipole-proton cross section in coordinate space [7,8]. The results show that, although they may be present in the DIS measurements, they seem not to strongly influence the evolution at HERA energies. In these proceedings we use the first model for the dipoleproton cross section developed in momentum space [9] with fluctuation effects included to fit the last HERA data. This model has shown to be successful in the description of DIS data, specially with heavy quark (charm) contributions included, by using a mean-field (BK) inspired parametrization for the scattering amplitude, which enters in the expression for the dipole-proton cross section. Some preliminary results are presented and some future expectations on the effects of fluctuations at HERA are discussed.

Leading-twist nuclear shadowing and suppression of hard coherent diffraction in proton-nucleus scattering

We use the Glauber-Gribov multiple scattering formalism and the theory of leading twist nuclear shadowing to develop a method for the calculation of leading twist hard coherent diffraction in hadron-nucleus processes. We demonstrate that soft multiple rescatterings lead to the factorization breaking of hard diffraction in proton-nucleus scattering, which is larger than in hadron-nucleon scattering. At the LHC and RHIC kinematics, we compare the hard diffractive to e.m. mechanisms of hard coherent production of two jets in proton-nucleus scattering. We study the xIP, � and Adependence of the ratio of the dijet production cross sections due to the two effects, R. We demonstrate that in proton-heavy nucleus hard coherent diffraction at the LHC, R is small, which offers a clean method to study hard photon-proton scattering at the energies exceeding the HERA energies by the factor of ten. On the other hand, the use of lighter nuclei, such as 40 Ca, will allow to study the screened nuclear diffractive parton distribution. Moreover, a comparison of the dijet diffractive production to the heavy-quark-jet diffractive production will estimate the screened nuclear diffractive gluon PDF, which will be measured in nucleus-nucleus ultraperipheral collisions at the LHC.

Probing small x QCD in ultraperipheral collisions at LHC

We summarize current evidence for onset of the Black Disk limit at the HERA energies and and argue that ultraperipheral collisions at LHC will provide unique new oportunities for studing of small x phenomena in the interactions with nucleons and nuclei in the energy range W ⩽ TeV allowing to extend the x range of HERA by a factor of ten.

Dynamics of pp collisions at small impact parameters, universality of cross sections of hadron-hadron collisions and critical phenomena at superhigh energies

Studies of the small x dynamics at HERA energies allow one to quantify the range of momentum transfers and energies for which strength of the interaction approaches the maximum strength allowed by the unitarity in the gluon channel (black disk limit-BDL). Implications for the proton-proton interactions at collider energies (Tevatron, LHC) include a dominance of BDL up to transverse momenta of hadrons (jets) in the final state of a few GeV for collisions at small impact parameters, and explanation of proximity of the profile function of pp interaction to one at small impact parameters, leading to the universality of cross sections at superhigh energies. We discuss briey theoretical challenges in the applications of pQCD to small x phenomena, the onset of BDL for hard processes at large energies and universal limiting behavior: F 2, xG ∝ ln3(x o/x), σ(γ T) ∝ ln3(s/s o). We explain that the onset of BDL should be accompanied by generic nonlinear phenomena for the produced states such as kinks, different symmetry of final states, etc and related tunneling transitions. Characteristic features of QCD physics of central collisions at ultrahigh energies correspond to a new regime: (i) interaction is dominated by hard interactions of quarks and gluons leading to disappearance of the soft physics and hadronic degrees of freedom, (ii) change with energy of the space-time evolution of produced quark-gluon states, (iii) change of the avor composition of the produced system, (iv) formation of a color network, etc. Hence, such collisions are likely to result in the production of new forms of the QCD matter. We also comment on the implications of the discussed physics for cosmic ray interactions at ultrahigh energies and on the methods to get information necessary for modeling cosmic rays at energies much higher than LHC using planned experiments at LHC.

LOW X SATURATION DYNAMICS AT HERA?

We compare the predictions of two distinct dipole models for inclusive and exclusive diffractive processes. While only one of these dipole models contains perturbative saturation dynamics, we show that the predictions of both models are fully consistent with the available HERA data, indicating no compelling evidence for saturation at present HERA energies.

Charm quark–antiquark correlations in photon–proton scattering

Correlation of charm-quark–charm-antiquark in γp scattering are calculated in the kt-factorization approach. We apply different unintegrated gluon distributions (uGDF) used in the literature. The results of our calculations are compared with very recent experimental results from the FOCUS Collaboration. The CCFM uGDF developed recently by Kwieciński et al. gives a good description of the data. New observables are suggested for future studies. Predictions and perspectives for the HERA energies are presented.

SEARCHES FOR NEW PHENOMENA AT COLLIDERS

An overview of recent experimental results on searches for new phenomena at the LEP, HERA and Tevatron high energy colliders is presented, including in particular new results obtained from the analysis of the Run II data at the Tevatron. No significant evidence for physics beyond the Standard Model has been found and limits at the 95% confidence level have been set on the mass and couplings of several new particles. The complementarity between the different experiments is discussed, as well as future prospects for ongoing and future experiments.

Compilation of cross sections for proton–nucleus interactions at the HERA energy

This work compiles information concerning the total, inelastic and diffractive cross sections for proton–nucleus interactions. The values are fitted together with the expression σ= σ 0 A α , where A is the target atomic mass number. Also discussed is the amplitude of the diffractive components of the inelastic cross section.

Nonperturbative QCD treatment of $J/\Psi$ photoproduction

We present a nonperturbative QCD calculation of elastic $J/\psi$ meson production in photon-proton scattering at high energies. Using light cone wave functions of the photon and vector mesons, and the framework of the model of the stochastic QCD vacuum, we calculate the differential and integrated elastic cross sections for $\gamma p \goto J/\psi p $ . With an energy dependence following the two-pomeron model we are able to give a consistent description of the integrated cross sections and the differential cross sections at low $|t|$ in the range from 20 GeV up to the highest HERA energies. We discuss different approaches to introduce saturation and find no specific effects up to energies presently available. We also calculate and compare to experiments the cross section for $\upsilon$ photoproduction.

On charmonia and charmed mesons photoproduction at high energy

We compare the predictions of the collinear parton model and the kT-factorization approach in J/Ψ and D★ meson photoproduction at HERA energies. It is shown that obtained D★ meson spectra over pT and η are very similar in the parton model and kT-factorization approach and they underestimate the experimental data. Opposite, the predictions of the both approaches for pT- and z-spectra in the J/Ψ photoproduction are very different as well as the prediction obtained for the spin parameter α(pT).

Erratum: PolarizedJ/ψproduction in deep inelastic scattering at DESY HERA [Phys. Rev. D 63, 034017 (2001)

We perform a calculation on the polarization of J/psi production in deep inelastic scattering in the HERA energy range. For the inclusive production distributions, we find that the color-singlet contributions are consistent with the experimental data in the major region of z (z>0.4). Only in low z regions, there are some hints of the need of the color-octet contributions to describe the experimental data. For the polarization of J/psi in DIS processes, we find the parameter alpha changes with Q^2. Especially, at higher Q^2, difference on alpha between color-singlet and color-octet contributions become more distinctive. In the two regions of lower and larger z, the polarization parameter alpha have different features. These properties can provide important information on the polarization mechanism for J/psi production.

The non-forward BFKL amplitude and rapidity gap physics

We discuss the BFKL approach to processes with large momentum transferred through a rapidity gap. The Mueller and Tang scheme to the BFKL non-forward parton-parton elastic scattering amplitude at large $t$, is extended to include higher conformal spins. The new contributions are found to decrease with increasing energy, as follows from the gluon reggeisation phenomenon, and to vanish for asymptotically high energies. However, at moderate energies and high $|t|$, the higher conformal spins dominate the amplitude. We illustrate the effects by studying the production of two high $E_T$ jets separated by a rapidity gap at HERA energies. In a simplified framework, we find excellent agreement with the HERA photoproduction data once we incorporate the rapidity gap survival probability against soft rescattering effects. We emphasize that measurements of the analogous process in electroproduction may probe different summations over conformal spins.