Resummation of non-global QCD observables

We discuss issues related to the resummation of non-global observables in QCD, those that are sensitive to radiation in only a part of phase space. Examples of such observables are certain single-hemisphere event shapes in e+e- and DIS. Compared to global observables (those sensitive to all emissions, e.g. the e+e- thrust) a new class of single-logarithmic terms arises. These have been neglected in recent calculations in the literature. For a whole set of single hemisphere e+e- and DIS event shapes, we analytically evaluate the first such term, at order alpha_s^2, and give numerical results for the resummation of these terms in the large-Nc limit.Comment: 10 page

Perturbative QCD analysis of near-to-planar three jet events

We present the all-order resummed thrust minor distribution as a measure of aplanarity in three-jet events.Comment: 5 pages, 2 figures, Talk presented by Andrea Banfi at QCD 00 Euroconference, Montpellier, July 200

Sudakov resummation of multiparton QCD cross sections

We present the general expressions for the resummation, up to next-to-leading logarithmic accuracy, of Sudakov-type logarithms in processes with an arbirtrary number of hard-scattering partons. These results document the formulae used by the authors in several previous phenomenological studies. The resummation formulae presented here, which are valid for phase-space factorizable observables, determine the resummation correction in a process-independent fashion. All process dependence is encoded in the colour and flavour structure of the leading order and virtual one-loop amplitudes, and in Sudakov weights associated to the cross section kinematics. We explicitly illustrate the application to the case of Drell--Yan and prompt-photon production.Comment: 13 pages, LaTe

Determination of alpha_s from F_2^p at HERA

We compute the proton structure function F_2^p at small x and large Q^2 at next-to-leading order in alpha_s(Q^2), including summations of all leading and subleading logarithms of Q^2 and 1/x in a way consistent with momentum conservation. We perform a detailed comparison to the 1993 HERA data, and show that they may be used to determine alpha_s(M_Z^2)=0.120 pm 0.005(exp) pm 0.009(th). The theoretical error is dominated by the renormalization and factorization scheme ambiguities.Comment: 24 pages, TeX with harvmac and epsf, 10 figures in compressed postscript. Final (published) versio

A novel subtraction scheme for double-real radiation at NNLO

A general subtraction scheme, STRIPPER (SecToR Improved Phase sPacE for real Radiation), is derived for the evaluation of next-to-next-to-leading order (NNLO) QCD contributions from double-real radiation to processes with at least two particles in the final state at leading order. The result is a Laurent expansion in the parameter of dimensional regularization, the coefficients of which should be evaluated by numerical Monte Carlo integration. The two main ideas are a two-level decomposition of the phase space, the second one factorizing the singular limits of amplitudes, and a suitable parameterization of the kinematics allowing for derivation of subtraction and integrated subtraction terms from eikonal factors and splitting functions without non-trivial analytic integration.Comment: 14 pages, 3 figures, matches published version, includes new name for the scheme, extended discussion of massless final states, and some new reference

Heavy top limit and double-logarithmic contributions to Higgs production at m_H^2 / s << 1

Next-to-next-to-leading order (NNLO) QCD corrections to Higgs boson hadroproduction have recently been calculated in the heavy top-quark limit m_t -> \infty. The m_t -> \infty limit introduces double-logarithmic corrections in ln x, with x = m_H^2 / s. We identify these corrections order by order in alpha_s. As an application, we derive an analytic expression for the dominant x << 1 part of the NNLO coefficient.Comment: 7 page

The soft-gluon current at one-loop order

We study the soft limit of one-loop QCD amplitudes and we derive the process-independent factorization formula that controls the singular behaviour in this limit. This is obtained from the customary eikonal factorization formula valid at tree (classical) level by introducing a generalized soft-gluon current that embodies the quantum corrections. We compute the explicit expression of the soft-gluon current at one-loop order. It contains purely non-abelian correlations between the colour charges of each pair of hard-momentum partons in the matrix element. This leads to colour correlations between (two and) three hard partons in the matrix element squared. Exploiting colour conservation, we recover QED-like factorization for the square of the matrix elements with two and three hard partons.Comment: latex, 20 pages, 4 eps figure

Soft-Gluon Resummation for the Fragmentation of Light and Heavy Quarks at Large x

We present a QCD study of fragmentation processes for light and heavy quarks in the semi-inclusive region of large x. Large logarithmic terms, due to soft-gluon radiation, are evaluated and resummed to all perturbative orders in the QCD coupling alpha_s. Complete analytical results to next-to-leading logarithmic accuracy are given for one-particle and two-particle inclusive distributions in e+e- annihilation and DIS. Factorization of parton radiation at low transverse momenta is exploited to identify the universal (process-independent) perturbative fragmentation function that controls heavy-quark processes, and to perform next-to-leading logarithmic resummation of its soft-gluon contributions. To gauge the quantitative impact of resummation, we perform numerical studies of light- and heavy-quark fragmentation in e+e- collisions.Comment: 37 pages, Latex, axodraw, epsfig, 11 figure

A numerical method for NNLO calculations

A method to isolate the poles of dimensionally regulated multi-loop integrals and to calculate the pole coefficients numerically is extended to be applicable to phase space integrals as well.Comment: 5 pages, Talk presented at Radcor/Loops and Legs 2002, to appear in the proceeding

One-loop Singular Behaviour of QCD and SUSY QCD Amplitudes with Massive Partons

We discuss the structure of infrared and ultraviolet singularities in on-shell QCD and supersymmetric QCD amplitudes at one-loop order. Previous results, valid for massless partons, are extended to the case of massive partons. Using dimensional regularization, we present a general factorization formula that controls both the singular epsilon-poles and the logarithmic contributions that become singular for vanishing masses. We introduce generalized Altarelli--Parisi splitting functions and discuss their relations with the singular terms in the amplitudes. The dependence on the regularization scheme is also considered.Comment: 15 pages, 1 Latex fil