We present the third-order contributions to the quark-gluon and gluon-quark timelike splitting functions for the evolution of fragmentation functions in perturbative QCD. These quantities have been derived by studying physical evolution kernels for photon-and Higgs-exchange structure functions in deep-inelastic scattering and their counterparts in semi-inclusive annihilation, together with constraints from the momentum sum rule and the supersymmetric limit. For this purpose we have also calculated the second-order coefficient functions for one-hadron inclusive Higgs decay in the heavy-top limit. A numerically tolerable uncertainty remains for the quark-gluon splitting function, which does not affect the endpoint logarithms for small and large momentum fractions. We briefly discuss these limits and illustrate the numerical impact of the third-order corrections. Compact and accurate parametrizations are provided for all third-order timelike splitting functions.

We present all-order results for the highest three large-x logarithms of the splitting functions P qg and P gq and of the coefficient functions C φ,q , C 2,g and C L,g for structure functions in Higgs-and gauge-boson exchange DIS in massless perturbative QCD. The corresponding coefficients have been derived by studying the unfactorized partonic structure functions in dimensional regularization independently in terms of their iterative structure and in terms of the constraints imposed by the functional forms of the real-and virtual-emission contributions together with their Kinoshita-LeeNauenberg cancellations required by the mass-factorization theorem. The numerical resummation corrections are small for the splitting functions, but partly very large for the coefficient functions. The highest two (three for C L,g ) logarithms can be resummed in a closed form in terms of new special functions recently introduced in the context of the resummation of the leading logarithms.

We present all-order expressions for the leading double-logarithmic threshold contributions to the quark-gluon coefficient functions for inclusive Higgs-boson production in the heavy top-quark limit and for Drell-Yan lepton-pair production. These results have been derived using the structure of the unfactorized cross sections in dimensional regularization and the large-x resummation of the gluon-quark and quark-gluon splitting functions. The resummed coefficient functions, which are identical up to colour factor replacements, are similar to their counterparts in deep-inelastic scattering but slightly more complicated.

We have used the latest data from the ALEPH Collaboration to extract values for QCD condensates up to dimension d = 12 in the V − A channel and up to dimension d = 8 in the V , A and V + A channels. Performing 2-and 3-parameter fits, we obtain new results for the correlations of condensates. The results are consistent among themselves and agree with most of the previous results found in the literature. *

We generalize a recently proposed on-shell approach to renormalize the Cabibbo-Kobayashi-Maskawa quark-mixing matrix to the case of an extended leptonic sector that includes Dirac and Majorana neutrinos in the framework of the seesaw mechanism. An important property of this formulation is the gauge independence of both the renormalized and bare lepton mixing matrices. Also, the texture zero in the neutrino mass matrix is preserved.

Recently methods have been developed to extend the resummation of large-x double logarithms in inclusive deep-inelastic scattering (DIS) to terms not addressed by the soft-gluon exponentiation. Here we briefly outline our approach based on fixed-order results, the general large-x structure in dimensional regularization and the all-order factorization of mass singularities, which is directly applicable also to semi-inclusive e + e − annihilation (SIA). We then present some main results for the corresponding timelike splitting functions and transverse and longitudinal fragmentation functions. The close relation between DIS and SIA facilitates the determination of additional third-order results for the latter function which is fully known only at the next-to-leading order. Therefore all above quantities can be resummed at next-to-next-to-leading logarithmic accuracy. * Speaker.

Abstract:We present analytic all-order results for the highest three threshold logarithms of the space-like and time-like off-diagonal splitting functions and the corresponding coefficient functions for inclusive deep-inelastic scattering (DIS) and semi-inclusive e + e − annihilation. All these results, obtained through an order-by-order analysis of the structure of the corresponding unfactorized quantities in dimensional regularization, can be expressed in terms of the Bernoulli functions introduced by one of us and leading-logarithmic soft-gluon exponentials. The resulting numerical corrections are small for the splitting functions but large for the coefficient functions. In both cases more terms in the threshold expansion need to be determined in order to arrive at quantitatively reliable results.

Erratum: Quark-mixing renormalization effects in the determination of the CKM parameters jV ij j [Phys. Rev. D 79, 076007 (2009)] We uncovered errors in the computer codes employed in the calculations of Tables I and II. Since they involve the subtraction of very close numbers, we revised these calculations using quadruple precision and checked directly the contributions to Table II from the wave-function renormalization of the external quarks by means of a simple analytic algorithm. The last column of Table I represents a diagonal scheme that is employed in the calculations of Table II. It is obtained by replacing V ij ! ij in the external loops' couplings and replacing the mass of the up-(down-)type quark in such loops by the mass of the external up-(down-)type quark in the W-decay process. This diagonal scheme has the virtue of reproducing many of the important contributions of the complete calculations and, at the same time, prevents the emergence of unphysical UV divergences. The revised calculations show that, in the electroweak renormalization schemes of Refs. [1][2][3][4][5], the relative shifts Á ij in jV ij j 2 , induced by the quark-mixing renormalization effects, are extremely small, as may be seen in the corrected versions of Tables I and II. In particular, the precise test of Cabibbo-Kobayashi-Maskawa unitarity in Eq. (10) is not modified. In the MS scheme, the Á ij are considerably larger, reaching Oð1%Þ in the cases of jV ub j 2 and jV cb j 2 . This is due to the presence of significant finite corrections that are not removed by the MS subtraction.