A. Gehrmann-De Ridder

NNLO corrections to event shapes in e+ e- annihilation

We compute the next-to-next-to-leading order (NNLO) QCD corrections to the six most important event shape variables related to three-particle final states in electron- positron annihilation. The corrections are sizeable for all variables, however their magni- tude is substantially different for different observables. We observe that the NNLO correc- tions yield a considerably better agreement between theory and experimental data both in shape and normalisation of the event shape distributions. The renormalisation scale de- pendence of the theoretical prediction is substantially reduced compared to the previously existing NLO results. Our results will allow a precise determination of the strong coupling constant from event shape data collected at LEP.

Infrared structure of e+ e- ---> 2 jets at NNLO

Abstract The production of two jets is the simplest exclusive quantum chromodynamics process in electron–positron annihilation. Using this process, we examine the structure of next-to-next-to-leading order (NNLO) corrections to jet production observables. We derive a subtraction formalism including double real radiation at tree level and single real radiation at one loop. For two-jet production, these subtraction terms coincide with the full matrix elements, thus highlighting the phase space structure of the subtraction procedure. We then analytically compute the infrared singularities arising from each partonic channel. For the purely virtual (two-parton) NNLO corrections, these take the well known form predicted by Catanis infrared factorization formula. We demonstrate that individual terms in the infrared factorization formula can be identified with infrared singular terms from three- and four-parton final states, leaving only single poles and a contribution from the one-loop soft gluon current, which subsequently cancels between the three- and four-parton final states. Summing over all different final states, we observe an explicit cancellation of all infrared poles and recover the known two-loop correction to the hadronic R -ratio.

Second-order QCD corrections to the thrust distribution in electron-positron annihilation.

We compute the next-to-next-to-leading-order (NNLO) QCD corrections to the thrust distribution in electron-positron annihilation. The corrections turn out to be sizable, enhancing the previously known next-to-leading-order prediction by about 15%. Inclusion of the NNLO corrections significantly reduces the theoretical renormalization scale uncertainty on the prediction of the thrust distribution.

Second order QCD corrections to jet production at hadron colliders: the all-gluon contribution

We report the calculation of next-to-next-to-leading order QCD corrections in the purely gluonic channel to dijet production and related observables at hadron colliders. Our result represents the first next-to-next-to-leading order calculation of a massless jet observable at hadron colliders, and opens the path towards precision QCD phenomenology with the LHC.

Four-particle phase space integrals in massless QCD

The inclusive four-particle phase space integral of any 1→4 matrix element in massless QCD contains divergences due to the soft and collinear emission of up to two particles in the final state. We show that any term appearing in this phase space integral can be expressed as linear combination of only four master integrals. These four master integrals are all computed in dimensional regularisation up to their fourth order terms, relevant to next-to-next-to-leading order jet calculations, both in an analytic form and purely numerically. New analytical and numerical techniques are developed in this context. We introduce the tripole parametrisation of the four-parton phase space. Furthermore, we exploit unitarity relations between multi-parton phase space integrals and multi-loop integrals. For the numerical calculation, the iterated sector decomposition of loop integrals is extended to phase space integrals. The results in this paper lead to infrared subtraction terms needed for the double real radiation contributions to jet physics in e+e− annihilation at the next-to-next-to-leading order.

Gluon–gluon antenna functions from Higgs boson decay

Abstract Antenna functions describe the infrared singular behaviour of colour-ordered QCD matrix elements due to the emission of unresolved partons inside an antenna formed by two hard partons. In this Letter, we show that antenna functions for hard gluon–gluon pairs can be systematically derived from the effective Lagrangian describing Higgs boson decay into gluons, and compute the infrared structure of the colour-ordered Higgs boson decay matrix elements at NLO and NNLO.

Quark-gluon antenna functions from neutralino decay

Abstract The computation of exclusive QCD jet observables at higher orders requires a method for the subtraction of infrared singular configurations arising from multiple radiation of real partons. One commonly used method at next-to-leading order (NLO) is based on the antenna factorization of colour-ordered matrix elements, and uses antenna functions to subtract the real radiation singularities. Up to now, NLO antenna functions could be derived in a systematic manner only for hard quark–antiquark pairs, while the gluon–gluon and quark–gluon antenna functions were constructed from their limiting behaviour. In this Letter, we show that antenna functions for hard quark–gluon pairs can be systematically derived from an effective Lagrangian describing heavy neutralino decay. The infrared structure of the colour-ordered neutralino decay matrix elements at NLO and NNLO is shown to agree with the structure observed for parton radiation off a quark–gluon antenna.

Jet rates in electron-positron annihilation at O(alpha(s)**3) in QCD

We compute production rates for two, three, four, and five jets in electron-positron annihilation at the third order in the QCD coupling constant. At this order, three-jet production is described to next-to-next-to-leading order in perturbation theory while the two-jet rate is obtained at next-to-next-to-next-to-leading order. Our results yield an improved perturbative description of the dependence of jet multiplicity on the jet resolution parameter y{cut}, particularly at small values of y{cut}.

Determination of the strong coupling constant using matched NNLO+NLLA predictions for hadronic event shapes in e+e− annihilations

We present a determination of the strong coupling constant from a fit of QCD predictions for six event-shape variables, calculated at next-to-next-to-leading order (NNLO) and matched to resummation in the next-to-leading-logarithmic approximation (NLLA). These event shapes have been measured in e+e? annihilations at LEP, where the data we use have been collected by the ALEPH detector at centre-of-mass energies between 91 and 206 GeV. Compared to purely fixed order NNLO fits, we observe that the central fit values are hardly affected, but the systematic uncertainty is larger because the NLLA part re-introduces relatively large uncertainties from scale variations. By combining the results for six event-shape variables and eight centre-of-mass energies, we find ?s(MZ) = 0.1224???0.0009?(stat)???0.0009?(exp)???0.0012?(had)???0.0035?(theo), which improves previously published measurements at NLO+NLLA. We also carry out a detailed investigation of hadronisation corrections, using a large set of Monte Carlo generator predictions.

A Complete O (alpha alpha-s) calculation of the photon + 1 jet rate in e+ e- annihilation

Abstract We present a complete calculation of the photon + 1 jet rate in e+ e− annihilation up to O (ααs). Although formally of next-to-leading order in perturbation theory, this calculation contains several ingredients appropriate to a next-to-next-to-leading order calculation of jet observables. In particular, we describe a generalization of the commonly used phase space slicing method to isolate the singularities present when more than one particle is unresolved. Within this approach, we analytically evaluate the singularities associated with the following double unresolved regions: triple collinear, soft/collinear and double single collinear configurations as well as those from the collinear limit of virtual graphs. By comparing the results of our calculation with the existing data on the photon + 1 jet rate from the ALEPH Collaboration at CERN, we make a next-to-leading order determination of the process-independent non-perturbative quark-to-photon fragmentation function Dq→γ(z, μF) at O (ααs). As a first application of this measurement allied with our improved perturbative calculation, we determine the dependence of the isolated photon + 1 jet cross section in a democratic clustering approach on the jet resolution parameter ycut at next-to-leading order. The next-to-leading order corrections to this observable are moderate but improve the agreement between theoretical prediction and experimental data.