Evolution Of Parton Distributions Research Articles

Gluons and sea quarks in the proton at low scales

We study the evolution of parton distributions down to low scales by considering several of their Mellin moments. For the initial conditions, we use a broad array of current parton density fits. Confirming earlier findings in the literature, we conclude that current determinations of parton distributions are incompatible with the idea that gluon or antiquark densities are generated by purely perturbative radiation as it is encoded in the DGLAP evolution equations.

Q 2 evolution of parton distributions at small values of x: Effective scale for combined H1 and ZEUS data on the structure function F 2

An expression for the structure function F2 in the form of Bessel functions at small values of the Bjorken variable x is used. This expression was derived for a flat initial condition in the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) evolution equations. The argument of the strong coupling constant was chosen in such a way as to annihilate the singular part of the anomalous dimensions in the next-to-leading-order of perturbation theory. This choice, together with the frozen and analytic versions of the strong coupling constant, is used to analyze combined data of the H1 and ZEUS Collaborations obtained recently for the structure function F2.

Applications of a nonlinear evolution equation II: The EMC effect

The EMC effect is studied by using the DGLAP equation with the ZRS corrections and minimum number of free parameters, where the nuclear shadowing effect is a dynamical evolution result of the equation, the nucleon swelling and Fermi motion in the nuclear environment deform the input parton distributions. Parton distributions of both proton and nucleus are predicted in a unified framework. We show that the parton recombination as a higher twist correction plays an essential role in the evolution of parton distributions either of proton or nucleus. We find that the nuclear anti-shadowing contributes a part of enhancement of the ratio of the structure functions around x ~ 0.1, while the other part origins from the deformation of the nuclear valence quark distributions. In particular, the nuclear gluon distributions are dynamically predicted, which are important information for the recherche of the high energy nuclear physics.

BFKL next-to-next-to-leading order

We determine an approximate expression for the O ( α s 3 ) contribution χ 2 to the kernel of the BFKL equation, which includes all collinear and anticollinear singular contributions. This is derived using recent results on the relation between the GLAP and BFKL kernels (including running-coupling effects to all orders) and on small- x factorization schemes. We present the result in various schemes, relevant both for applications to the BFKL equation and to small- x evolution of parton distributions.

Saturation Momentum: From Fixed to Running Coupling

Of late, it has been possible to establish and exploit connections between the evolution of parton distribution functions in quantum chromodynamics (QCD) and reaction diffusion systems in statistical physics. On that side stands the well studied Fischer-Kolmogorov-Petrovsky-Piscounov (FKPP) equation in its deterministic and stochastic (sFKPP) variants, respectively. On the side of QCD stand the JIMWLK equation, its recent extensions, and the Balitsky-Kovchegov (BK) equation. The key to extracting information on the solutions of the equation of motion in both fields is primarily the fact that both groups of equations describe the propagation into an unstable state. Unfortunately, the translation works mostly for the case of a fixed coupling constant only. Here, it is shown that, because the system is evolving away from an unstable fix point, it is possible to translate information from the fixed to the running coupling case. This is demonstrated for the saturation momentum in the regime of asymptotically high rapidities [1].

The color glass condensate and hadron production in the forward region

We consider one loop corrections to single inclusive particle production in parton–nucleus scattering at high energies, treating the target nucleus as a color glass condensate. We prove by explicit computation that in the leading log Q 2 approximation, these corrections lead to collinear factorization and DGLAP evolution of the projectile parton distribution and hadron fragmentation functions. In single-inclusive cross sections, only two-point functions of Wilson lines in the adjoint and fundamental representations (Mueller's dipoles) arise, which can be obtained from the solution of the JIMWLK equations. The application of our results to forward-rapidity production shows that, in general, recoil effects are large. Hence, the forward rapidity region at RHIC is rather different from the central region at LHC, despite comparable gluon densities in the target. We show that both the quantum x-evolution of the high-density target as well as the DGLAP Q 2 -evolution of the parton distribution and fragmentation functions are clearly seen in the BRAHMS data. This provides additional strong evidence for the color glass condensate at RHIC.

QED corrections to the evolution of parton distributions

We study the systematic inclusion of QED corrections in the evolution of parton distributions. O(α) corrections modify the evolution equation for parton distributions. They introduce additional parton distributions, like the photon distribution in the nucleon, and lead to additional mixing effects. We discuss the modifications for a realistic model of Nf,up up-type flavours and Nf,down down-type flavours. We have implemented these corrections into a numerical program and we quantify the size of these effects in a toy model. The corrections reach the order of 1%.

Leading logarithmic approximation in QCD

The leading logarithmic approximation (LLA) for the scattering amplitudes in QCD is reviewed. The double-logarithmic asymptotics of scattering amplitudes is obtained as a solution to nonlinear evolution equations in the infrared cutoff. The DGLAP equation describes an evolution of parton distributions with increasing parton virtuality. The evolution of the amplitudes with respect to the scale in the longitudinal subspace is given by the BFKL equation. The gluon and quarks in QCD lie on the Regge trajectories calculable in perturbation theory. Mesons and baryons are composite states of Reggeized quarks. Similarly the Pomeron and Odderon are colorless ground states of Reggeized gluons. In the case of multicolor QCD, the Reggeon field theory in LLA is completely integrable. The Reggeon interactions in QCD are derived from a gauge-invariant effective action. In particular, next-to-leading corrections to the BFKL equation in QCD and in supersymmetric gauge models are obtained in this way.

The evolution of parton distributions at small x

We investigate parton distributions at small x using moments of the Gribov-Lipatov-Altarelli-Parisi (GLAP) evolution equation with respect to x. In this representation the kernel of the GLAP equation contains singularities in the moment variable ω at ω = 0. We show that the importance of these singularities at small x depends on the form of the starting distributions. We examine the range of x in which the GLAP equation is valid. The restrictions on the range of x depend on the form of the starting distributions. We investigate whether the GLAP equation can be used to interpolate data in the HERA region. Results are given for the structure function F 2 at small x. A possible method of determining the gluon distribution from F 2 is discussed.

QCD EVOLUTION BY FINITE ELEMENT METHODS

A simple, new method for solving the Q2 evolution of parton distributions in perturbative QCD using cubic splines is described and applied to the evolution of non-singlet quark distributions.

Parton evolution as a branching process

The evolution of parton distributions in high-energy scattering is described using the methods of branching processes. Exclusive, inclusive and multiplicity distributions can be simply obtained from a functional form of the evolution equations. Previous results derived from leading logarithmic terms in perturbation theory are verified. As a new application, we calculate the multiplicity distribution of partons with momenta above a given cutoff.