Anna M. Staśto

Renormalization group improved small- x Green’s function

We investigate the basic features of the gluon density predicted by a renormalisation group improved small-x equation which incorporates both the gluon splitting function at leading collinear level and the exact BFKL kernel at next-to-leading level. We provide resummed results for the Greens function and its hard Pomeron exponent

A matrix formulation for small-x singlet evolution

\omega_s(\alpha_s)

The gluon splitting function at moderately small x

, and for the splitting function and its critical exponent

Expanding running coupling effects in the hard Pomeron

\omega_c(\alpha_s)

Extending QCD perturbation theory to higher energies

. We find that non-linear resummation effects considerably extend the validity of the hard Pomeron regime by decreasing diffusion corrections to the Greens function exponent and by slowing down the drift towards the non-perturbative Pomeron regime. As in previous analyses, the resummed exponents are reduced to phenomenologically interesting values. Furthermore, significant preasymptotic effects are observed. In particular, the resummed splitting function departs from the DGLAP result in the moderate small-x region, showing a shallow dip followed by the expected power increase in the very small-x region. Finally, we outline the extension of the resummation procedure to include the photon impact factors.

Towards the test of saturation physics beyond leading logarithm.

We propose a matrix evolution equation in (x,kt)-space for flavour singlet, unintegrated quark and gluon densities, which generalizes DGLAP and BFKL equations in the relevant limits. The matrix evolution kernel is constructed so as to satisfy renormalization group constraints in both the ordered and antiordered regions of exchanged momenta kt, and incorporates the known NLO anomalous dimensions in the MSbar scheme as well as the NLx BFKL kernel. We provide a hard Pomeron exponent and effective eigenvalue functions that include the n_f-dependence, and give also the matrix of resummed DGLAP splitting functions. The results connect smoothly with those of the single-channel approach. The novel P_{qa} splitting functions show resummation effects delayed down to x=0.0001, while both P_{ga} entries show a shallow dip around x=0.001, similarly to the gluon-gluon single-channel results. We remark that the matrix formulation poses further constraints on the consistency of a BFKL framework with the MSbar scheme, which are satisfied at NLO, but marginally violated by small n_f/N_c^2-suppressed terms at NNLO.

Tunneling transition to the pomeron regime

Abstract It is widely believed that at small x , the BFKL resummed gluon splitting function should grow as a power of 1/ x . But in several recent calculations it has been found to decrease for moderately small- x before eventually rising. We show that this ‘dip’ structure is a rigorous feature of the P gg splitting function for sufficiently small α s , the minimum occurring formally at log (1/x)∼1/ α s . We calculate the properties of the dip, including corrections of relative order α s , and discuss how this expansion in powers of α s , which is poorly convergent, can be qualitatively matched to the fully resummed result of a recent calculation, for realistic values of α s . Finally, we note that the dip position, as a function of α s , provides a lower bound in x below which the NNLO fixed-order expansion of the splitting function breaks down and the resummation of small- x terms is mandatory.

Next-to-leading and resummed BFKL evolution with saturation boundary

We study QCD hard processes at scales of order k^2>Lambda^2 in the limit in which the beta-function coefficient - b is taken to be small, but alphas(k) is kept fixed. The (nonperturbative) Pomeron is exponentially suppressed in this limit, making it possible to define purely perturbative high-energy Greens functions. The hard Pomeron exponent acquires diffusion and running coupling corrections which can be expanded in the b parameter and turn out to be dependent on the effective coupling b alphas^2 Y. We provide a general setup for this b-expansion and we calculate the first few terms both analytically and numerically.

Matching collinear and small

On the basis of the results of a new renormalisation group improved small-x resummation scheme, we argue that the range of validity of perturbative calculations is considerably extended in rapidity with respect to leading log expectations. We thus provide predictions for the energy dependence of the gluon Green function in its perturbative domain and for the resummed splitting function. As in previous analyses, high-energy exponents are reduced to phenomenologically acceptable values. Additionally, interesting preasymptotic effects are observed. In particular, the splitting function shows a shallow dip in the moderate small-x region, followed by the expected power increase.

x

We present results from the first next-to-leading-order (NLO) numerical analysis of forward hadron production in pA and dA collisions in the small-x saturation formalism. Using parton distributions and fragmentation functions at NLO, as well as the dipole amplitude from the solution to the Balitsky-Kovchegov equation with running coupling, together with the NLO corrections to the hard coefficients, we obtain a good description of the available RHIC data in dAu collisions. In the large p⊥ region beyond the saturation scale, we find that the NLO correction becomes dominant and negative, which indicates that other physics beyond NLO becomes important and should also be taken into account. Furthermore, we make predictions for forward hadron production in pPb collisions at the LHC. This analysis not only incorporates the important NLO corrections for all partonic channels, but also reduces the renormalization scale dependence and helps to significantly reduce the theoretical uncertainties. It therefore provides a precise test of saturation physics beyond the leading logarithmic approximation.