Narrow Results

We briefly review some selected topics in the small x physics. In particular, we discuss the progress in the problem related to the resummation at small x and the parton saturation phenomena. Finally we discuss some phenomenological applications to deep inelastic scattering, hadron and heavy ion collisions.

Ultrahigh energy neutrinos can provide important information about the distant astronomical objects and the origin of the Universe. Precise knowledge about neutrino interactions and production rates is essential for estimating background, expected fluxes and detection probabilities. In this paper we review the applications of the high energy QCD to the calculations of the interaction cross-sections of the neutrinos. We also study the production of the ultrahigh energy neutrinos in the atmosphere due to the charm and beauty decays.

The relation between diffraction in lepton-proton collisions and shadowing of nuclear structure functions which arises from Gribov inelastic shadowing, is described. A model realizing such relation, which produces a parameter-free description of experimental data on nuclear structure functions at small x, is presented. The application to the description of multiplicities in nuclear collisions is discussed and related to other approaches.

We construct a model for double parton distribution functions (dPDFs) based on the notion of self-similarity, pursued earlier for small x physics at HERA. The most general form of dPDFs contains total 13 parameters to be fitted from data of proton–proton collision at LHC. It is shown that the constructed dPDF does not factorize into two single PDFs in conformity with QCD expectation, and it satisfies the condition that at the kinematic boundary x₁+x₂ = 1 (where x₁ and x₂ are the longitudinal fractional momenta of two partons), the dPDF vanishes.

In the present paper we summarize our recent results on the structure function g₁ and present explicit expressions for the nonsinglet and singlet components of g₁, which can be also used at arbitrary x and Q². These expressions combine the well-known DGLAP-results for the anomalous dimensions and coefficient functions with the total resummation of the leading logarithmic contributions and the shift of Q² →Q² + μ². In contrast to DGLAP, these expressions do not require the introduction of singular parametrizations for the initial parton densities. We have also applied our results to describe the experimental data in the kinematic region of the COMPASS experiment, which is beyond the reach of DGLAP. For a more detailed review of our results see Ref. 1.

In this paper, the evolutions of longitudinal proton structure function have been obtained at small x up to next-to-next-to-leading order using a hard Pomeron behavior. In our paper, evolutions of gluonic as well as heavy longitudinal structure functions have been obtained separately and the total contributions have been calculated. The total longitudinal structure functions have been compared with results of Donnachie–Landshoff (DL) model, Color Dipole (CD) model, k_T factorization and H1 data.

We present an analytic formula to extract the longitudinal structure function in the next-to-leading order of the perturbation theory at low x, from the Regge-like behavior of the gluon distribution and the structure function at this limit. In this approach, the longitudinal structure function has the hard-Pomeron behavior. The determined values are compared with the H1 data and MRST model. All results can consistently be described within the framework of perturbative QCD, which essentially show increases as x decreases.

Ultra-high energy neutrinos are an enigma; among their many poorly understood aspects are their origins and how they interact with nucleons when they reach the Earth. Due to the hard scale ($Q\sim M_{W,Z}$) involved in neutrino-nucleon scattering and for a large range of neutrino energies, it is appropriate to describe the target nucleon in terms of its partons — quarks and gluons — and their evolution with $Q^2$ as governed by the Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) evolution equations of perturbative Quantum ChromoDynamics (pQCD). Nevertheless, at the highest neutrino energies, the scattering cross-section is dominated by the contribution of small $x$ gluons of the target where one expects DGLAP evolution equations to break down due to high gluon density effects (gluon saturation). Here, we give a brief overview of gluon saturation physics in QCD and its effects on ultra-high energy neutrino-nucleon (nucleus) scattering cross-section.

At high energy (small x) n-point coorelators of Wilson lines appear in calculation of physical observables. The energy dependence of these observables is determined by the solution of the evolution equations these correlators satisfy. The most common correlator is the two-point function, the imaginary part of the forward scattering amplitude of a quark anti-quark dipole scattering on a target. This appears in structure functions in DIS as well as single inclusive hadron production in proton-nucleus collisions. Higher point correlators of Wilson lines appear in less inclusive processes, such as two-hadron angular and rapidity correlations and satisfy the Balitski-JIMWLK evolution equation. Here we derive the evolution equation satisfied by the six point correlator of Wilson lines which appears in di-hadron angular correlations in proton-nucleus collisions at high energy.

Nonlinear evolution at small x was evaluated numerically with full dependence on impact parameter using the BK equation. several distinct behaviors were found and are presented for the leading logarithmic kernel in the BK evolution equation with both fixed and running coupling. The value of the saturation scale at various dipole sizes was found to agree with analytic expectations. Calculation of the F₂ structure function from the numerical solution of the evolution with running coupling were then compared to the HERA data and qualitative agreement found. The agreement is improved with inclusion of soft contributions and these are discussed.