Luca Trentadue

Resummation of the QCD perturbative series for hard processes

Abstract We study the region of inhibited radiation in hard hadronic processes, as for jet cross sections and heavy flavour production near threshold. The cases of deep inelastic scattering and Drell-Yan annihilation are explicitly considered. A general method to exponentiate leading and next-to-leading logarithms to all orders in perturbation theory is developed. A complete formula for the large N -moments is given and shown to agree with previous two-loop calculations. The resummation procedure suggests how to connect the perturbative and nonperturbative regions. The natural limit within the perturbative phase is shown to be the intrinsic transverse momentum.

Resummation of large logarithms in e+e− event shape distributions

Abstract We describe a method for the resummation of leading and next-to-leading large logarithms to all orders in QCD perturbation theory, applicable to e + e − event shape distributions that have the property of exponentiation near the two-jet region. After a general discussion of the conditions for exponentiation and the evaluation of matrix elements and phase space to next-to-leading logarithmic accuracy, we give details of the application of the method to the thrust and heavy jet mass distributions. We show how the resummed expressions can be matched with known second-order results to obtain improved predictions throughout the whole of phase space, and how to suppress spurious higher-order terms generated by resummation outside the physical region. We also give the necessary ingredients for the improvement of third-order predictions by resummation when they become available.

THE RESUMMATION OF SOFT GLUONS IN HADRONIC COLLISIONS

Abstract We compute the effects of soft-gluon resummation for the production of high mass systems in hadronic collisions. We carefully analyse the growth of the perturbative expansion coefficients of the resummation formula. We propose an expression consistent with the known leading and next-to-leading resummation results, in which the coefficients grow much less than factorially. We apply our formula to Drell-Yan pair production, heavy flavour production, and the production of high invariant mass jet pairs in hadronic collisions. We find that, with our formula, resummation effects become important only fairly close to the threshold region. In the case of heavy flavour production we find that resummation effects are small in the experimental configurations of practical interest.

Comment on QCD exponentiation at large x

Abstract Agreement between two different approaches to exponentiate large logarithmic contributions in perturbative QCD is shown. The different parametrizations used suggest a rule to relate known and new coefficients.

Soft photons and second order radiative corrections to e+e−→Z0

Abstract We derive a second order expression for the electromagnetic radiation to the initial state in e + e − →Z 0 . Extending a formulation in terms of evolution equations we calculate dominant and non-dominant contributions by including further corrections. Total cross sections are computed and a comparison with previous results is made.

Thrust distribution in e+e- annihilation

Abstract We calculate the thrust distribution in e+e− annihilation including resummation of leading and next-to-leading logarithms of 1−T to all orders in QCD perturbation theory. This enables us to predict the distribution up to the largest values of T and reduces the renormalization scale dependence relative to the leading order at both large and small T. From a comparison with experimental data, we find Λ (5) MS =200±140 MeV , corresponding to α s (m 2 z )=0.116±0.012 .

The gluon form factor to higher orders: Gluon-gluon annihilation at small Qt

Abstract We study the region of small transverse momenta in the dynamics of the gluon-gluon annihilation channel. This is done by evaluating the gluon form factor at the single non-leading infrared and collinear logarithmic accuracy to all orders in α s . An explicit expression for the gluon form factor is obtained. The results are compared with those for the analogous quark case.

The top cross section in hadronic collisions

Abstract We reexamine the top quark production cross section at the Tevatron and LHC, in the light of recent progress on the resummation of logarithmic soft gluon corrections. We find that resummation effects are much smaller than previously thought. We also compute Coulombic threshold effects, and find them negligible. We update the discussion of uncertainties due to scale dependence, the value of the strong coupling constant, and the parton density parametrization. Our current best estimate of the top production cross section at the Tevatron and its error is σ(mt = 175 GeV) = 4.75 −0.62+0.73.

Hadronic cross sections in electron-positron annihilation with tagged photon

Events with tagged photons in the process of electron-positron annihilation into hadrons are considered. The initial state radiation is suggested to scan the hadronic cross section with the energy. QED radiative corrections are taken into account. The results for the total and exclusive cross sections are given in an analytic form. Some numerical estimates are presented.

Large angle QED processes at e+e− colliders at energies below 3 GeV

QED processes at electron-positron colliders are considerd. We present differential cross-sections for large--angle Bhabha scattering, annihilation into muons and photons. Radiative corrections in the first order are taken into account exactly. Leading logarithmic contributions are calculated in all orders by means of the structure-function method. An accuracy of the calculation can be estimated about 0.2%.