arXiv subjects
Publications and source records attributed to Richard D. Ball.
We summarize our recent results on the small x resummation of the singlet anomalous dimension. We recall the main features of our approach, and briefly describe some work in progress on the inclusion of subleading corrections to it.
We summarize our recent result for a splitting function for small x evolution which includes resummed small x logarithms deduced from the leading order BFKL equation with the inclusion of running coupling effects. We compare this improved splitting function with alternative approaches.
We construct an anomalous dimension for small x evolution which goes beyond standard fixed order perturbative evolution by including resummed small x logarithms deduced from the leading order BFKL equation with running coupling. Surprisingly, we find that once running coupling effects are properly taken into account, the leading approximation is very close to standard perturbative evolution in the range of x accessible at HERA, in overall agreement with the data, with no need for phenomenological parameters to summarise subleading effects. We also show that further corrections due to subleading small x logarithms derived from the Fadin-Lipatov kernel can be kept under control, but that they involve substantial resummation ambiguities which limit their practical usefulness.
We discuss the theoretical underpinnings for the extraordinary success of perturbative QCD in the description of HERA data. In particular, we examine recent progress in the understanding of perturbative QCD at small x. We explain the relation between evolution equations in Q^2 and x, and how they can be used for simultaneous resummation of the relevant large logs at HERA. We show that while the HERA data can be understood within our current knowledge of the perturbative expansion of QCD, they pose stringent constraints on the perturbatively inaccessible behaviour of QCD in the Regge limit.
We discuss the inclusion of running coupling effects in perturbative small x evolution equations. We show that a running coupling BFKL-like x-evolution equation is fully compatible, up to higher twist corrections, with the standard factorized perturbative evolution of parton distributions. We then use this result, combined with the well-known Airy asymptotics, to prove that the oscillations which are present in the running-coupling BFKL solution do not affect the associated splitting functions, which instead remain smooth in the small x limit. This allows us to give a prescription to include running-coupling corrections in the small-x resummation of scaling violations. We show that these corrections are small in the HERA region.
We explore the possibilities for measuring the quark content of the proton and neutron using neutrino beams produced at a muon storage ring. Because of the nature of the beams, small nuclear targets such as hydrogen and deuterium can be considered, as well as polarized targets. The statistics expected from these targets are calculated using nominal muon storage ring intensities, and the resulting statistical errors on the numerous structure functions available are given, for both polarized and unpolarized targets. It is shown that with a relatively small target, the structure functions F_2, xF_3, xg_1 and xg_5 for neutrinos and antineutrinos on protons and deuterium, either unpolarized or polarized, could be determined with excellent precision over most of the accessible kinematic range.
We review small $x$ contributions to perturbative evolution equations for parton distributions, and their resummation. We emphasize in particular the resummation technique recently developed in order to deal with the apparent instability of naive small $x$ evolution kernels and understand the empirical sucess of fixed--order perturbation theory. We give predictions for the gluon distribution and the structure functions F_2(x,Q^2) and F_L(x,Q^2) in an extended kinematic region, such as would be relevant for THERA or LEP+LHC ep colliders.
We apply our systematic NLO small x resummation of singlet splitting functions to the scaling violations of structure functions and compare the results with data. We develop various theoretical tools which are needed in order to relate resummed parton distributions to measurable structure functions, and we present results from a variety of fits to HERA data for the structure functions F_2 and F_L using the resummation. The behaviour of the singlet splitting functions at small x and fixed Q^2 is effectively parametrized as x^{-lambda}. We find that, for lambda small or negative, the resummed description of scaling violations may be phenomenologically as good as or even better than the standard next-to-leading order treatment. However, the best fit gluon density and value of alpha_s can be significantly modified by the resummation.
The asymptotic behaviour at large N of the MS-bar quark anomalous dimensions is derived to all orders assuming only MS-bar factorization and standard results for the exponentiation of soft logarithms in the quark initiated bare cross sections for deep inelastic scattering and Drell-Yan. The result is then used to write the MS-bar quark coefficient functions in a form in which all terms of $O(\ln^m N)$ are resummed.
We propose an improvement of the splitting functions at small x which overcomes the apparent problems encountered by the BFKL approach. We obtain a stable expansion for the x-evolution function chi(M) near M=0 by including in it a sequence of terms derived from the one- and two-loop anomalous dimension gamma. The requirement of momentum conservation is always satisfied. The residual ambiguity on the splitting functions is effectively parameterized in terms of the value of lambda, which fixes the small x asymptotic behaviour x^-lambda of the singlet parton distributions. We derive from this improved evolution function an expansion of the splitting function which leads to good apparent convergence, and to a description of scaling violations valid both at large and small x.
This is an extended and pedagogically oriented version of our recent work, in which we proposed an improvement of the splitting functions at small x which overcomes the apparent problems encountered by the BFKL approach.
We extract the small x asymptotic behaviour of the Altarelli-Parisi splitting functions from their expansion in leading logarithms of 1/x. We show in particular that the nominally next-to-leading correction extracted from the Fadin-Lipatov kernel is enhanced asymptotically by an extra ln 1\x over the leading order. We discuss the origin of this problem, its dependence on the choice of factorization scheme, and its all-order generalization. We derive necessary conditions which must be fulfilled in order to obtain a well behaved perturbative expansion, and show that they may be satisfied by a suitable reorganization of the original series.
We review the current situation in polarized scattering experiments. We describe the theoretical interpretation of inclusive deep inelastic processes, the current experimental situation and perturbative analyses which extract structure functions and parton distribution functions. We also discuss various issues such as positivity constraints, small x and the possibility of polarized colliding beam experiments at HERA, semi-inclusive processes, the separation of flavors and the measurement of the gluon polarization, and the possibility of using polarisation experiments to put constraints on new physics.
We show that the all order summation of small x logarithms cannot be included in the Q^2 evolution of structure functions because the NLLx corrections overwhelm the LLx contribution.
We summarise the perturbative QCD analysis of the structure function data for g_1 from longitudinally polarized deep inelastic scattering from proton, deuteron and neutron targets, with particular emphasis on testing sum rules, determining helicity fractions, and extracting the strong coupling from both scaling violations and the Bjorken sum rule.
We describe how perturbative QCD may be applied to inelastic e-p scattering at high center-of-mass energies, i.e. at small x and fixed Q^2.
We present a NLO perturbative analysis of all available data on the polarized structure function g_1(x,Q^2) with the aim of making a quantitative test of the validity of the Bjorken sum rule, of measuring α_s, and of deriving helicity fractions. We take particular care over the small x extrapolation, since it is now known that Regge behaviour is unreliable at perturbative scales. For fixed α_s we find that if all the most recent data are included g_A=1.18\pm0.09, confirming the Bjorken sum rule at the 8% level. We further show that the value of α_s is now reasonably well constrained by scaling violations in the structure function data, despite the fact that it cannot yet be reliably fixed by the value of the Bjorken sum: our final result is α_s(m_Z) = 0.120+0.010-0.008. We also confirm earlier indications of a sizeable positive gluon polarization in the nucleon.
We review recent HERA data on the structure function F_2 at small x and large Q^2. We show that the salient features of the data are revealed by comparing them to the double asymptotic scaling behaviour which F_2 is predicted to satisfy in perturbative QCD.