Heavy-Quark Fragmentation

We study perturbative and non-perturbative aspects of heavy-quark fragmentation into hadrons, emphasizing the large-x region, where x is the energy fraction of the detected hadron. We first prove that when the moment index N and the quark mass m get large simultaneously with the ratio (N Lambda/m) fixed, the fragmentation function depends on this ratio alone. This opens up the way to formulate the non-perturbative contribution to the fragmentation function at large N as a shape function of m(1-x) which is convoluted with the Sudakov-resummed perturbative result. We implement this resummation and the parametrization of the corresponding shape function using Dressed Gluon Exponentiation. The Sudakov exponent is calculated in a process independent way from a generalized splitting function which describes the emission probability of an off-shell gluon off a heavy quark. Non-perturbative corrections are parametrized based on the renormalon structure of the Sudakov exponent. They appear in moment space as an exponential factor, with a leading contribution scaling as (N Lambda/m) and corrections of order (N Lambda/m)^3 and higher. Finally, we analyze in detail the case of B-meson production in e+e- collisions, confronting the theoretical predictions with LEP experimental data by fitting them in moment space

Massive quark scattering at strong coupling from AdS/CFT

We extend the analysis of Alday and Maldacena for obtaining gluon scattering amplitudes at strong coupling to include external massive quark states. Our quarks are actually the N=2 hypermultiplets which arise when D7-brane probes are included in the AdS_5 x S^5 geometry. We work in the quenched approximation, treating the N=2 matter multiplets as external sources coupled to the N=4 SYM fields. We first derive appropriate massive-particle boundary conditions for the string scattering worldsheets. We then find an exact worldsheet which corresponds to the scattering of two massive quarks and two massless gluons and extract from this the associated scattering amplitude. We also find the worldsheet and amplitude for the scattering of four massive quarks. Our worldsheet solutions reduce to the four massless gluon solution of Alday and Maldacena in the limit of zero quark mass. The amplitudes we compute can also be interpreted in terms of 2-2 scattering involving gluons and massive W-bosons.Comment: 46 pages, 11 figures, v4: additional comments added to intr

Fixing the conformal window in QCD

A physical characterization of Landau singularities is emphasized, which should trace the lower boundary N_f^* of the conformal window in QCD and supersymmetric QCD. A natural way to disentangle ``perturbative'' from ``non-perturbative'' contributions to amplitudes below N_f^* is suggested. Assuming an infrared fixed point persists in the perturbative part of the QCD coupling even below N_f^* leads to the condition \gamma(N_f^*)=1, where \gamma is the critical exponent. Using the Banks-Zaks expansion, one gets 4<N_f^*<6. This result is incompatible with the existence of an analogue of Seiberg duality in QCD. The presence of a negative ultraviolet fixed point is required both in QCD and in supersymmetric QCD to preserve causality within the conformal window. Evidence for the existence of such a fixed point in QCD is provided.Comment: 10 pages, 1 figure, extended version of a talk given at the QCDNET2000 meeting, Paris, September 11-14 2000; main new material added is evidence for negative ultraviolet fixed point in QC

On the renormalization of multiparton webs

We consider the recently developed diagrammatic approach to soft-gluon exponentiation in multiparton scattering amplitudes, where the exponent is written as a sum of webs - closed sets of diagrams whose colour and kinematic parts are entangled via mixing matrices. A complementary approach to exponentiation is based on the multiplicative renormalizability of intersecting Wilson lines, and their subsequent finite anomalous dimension. Relating this framework to that of webs, we derive renormalization constraints expressing all multiple poles of any given web in terms of lower-order webs. We examine these constraints explicitly up to four loops, and find that they are realised through the action of the web mixing matrices in conjunction with the fact that multiple pole terms in each diagram reduce to sums of products of lower-loop integrals. Relevant singularities of multi-eikonal amplitudes up to three loops are calculated in dimensional regularization using an exponential infrared regulator. Finally, we formulate a new conjecture for web mixing matrices, involving a weighted sum over column entries. Our results form an important step in understanding non-Abelian exponentiation in multiparton amplitudes, and pave the way for higher-loop computations of the soft anomalous dimension.Comment: 60 pages, 15 figure

The C parameter distribution in e+e- annihilation

We study perturbative and non-perturbative aspects of the distribution of the C parameter in e+e- annihilation using renormalon techniques. We perform an exact calculation of the characteristic function, corresponding to the C parameter differential cross section for a single off-shell gluon. We then concentrate on the two-jet region, derive the Borel representation of the Sudakov exponent in the large-beta_0 limit and compare the result to that of the thrust T. Analysing the exponent, we distinguish two ingredients: the jet function, depending on Q^2C, summarizing the effects of collinear radiation, and a function describing soft emission at large angles, with momenta of order QC. The former is the same as for the thrust upon scaling C by 1/6, whereas the latter is different. We verify that the rescaled C distribution coincides with that of 1-T to next-to-leading logarithmic accuracy, as predicted by Catani and Webber, and demonstrate that this relation breaks down beyond this order owing to soft radiation at large angles. The pattern of power corrections is also similar to that of the thrust: corrections appear as odd powers of Lambda/(QC). Based on the size of the renormalon ambiguity, however, the shape function is different: subleading power corrections for the C distribution appear to be significantly smaller than those for the thrust.Comment: 24 pages, Latex (using JHEP3.cls), 1 postscript figur

Next-to-next-to-leading soft-gluon corrections for the top quark cross section and transverse momentum distribution

I present results for top quark production in hadronic collisions at LHC and Tevatron energies. The soft-gluon corrections to the differential cross section are resummed at next-to-next-to-leading-logarithm (NNLL) accuracy via the two-loop soft anomalous dimension matrices. Approximate next-to-next-to-leading-order (NNLO) differential and total cross sections are calculated. Detailed theoretical predictions are shown for the t tbar cross section and the top quark p_T distribution at the Tevatron and the LHC.Comment: 23 pages, 14 figures; additional results and figure

Next-to-eikonal corrections to soft gluon radiation: a diagrammatic approach

We consider the problem of soft gluon resummation for gauge theory amplitudes and cross sections, at next-to-eikonal order, using a Feynman diagram approach. At the amplitude level, we prove exponentiation for the set of factorizable contributions, and construct effective Feynman rules which can be used to compute next-to-eikonal emissions directly in the logarithm of the amplitude, finding agreement with earlier results obtained using path-integral methods. For cross sections, we also consider sub-eikonal corrections to the phase space for multiple soft-gluon emissions, which contribute to next-to-eikonal logarithms. To clarify the discussion, we examine a class of log(1 - x) terms in the Drell-Yan cross-section up to two loops. Our results are the first steps towards a systematic generalization of threshold resummations to next-to-leading power in the threshold expansion.Comment: 66 pages, 19 figure