Large-x structure of physical evolution kernels in Deep Inelastic Scattering

The modified evolution equation for parton distributions of Dokshitzer, Marchesini and Salam is extended to non-singlet Deep Inelastic Scattering coefficient functions and the physical evolution kernels which govern their scaling violation. Considering the x->1 limit, it is found that the leading next-to-eikonal logarithmic contributions to the physical kernels at any loop order can be expressed in term of the one-loop cusp anomalous dimension, a result which can presumably be extended to all orders in (1-x), and has eluded so far threshold resummation. Similar results are shown to hold for fragmentation functions in semi-inclusive e+ e- annihilation. Gribov-Lipatov relation is found to be satisfied by the leading logarithmic part of the modified physical evolution kernels.Comment: 12 pages; version 2: eq.(4.6) and comment below corrected (main results unchanged), section on fragmentation functions added; version 3: new results added: all-order relation in section 3.5, O(1-x) terms adressed in section 5; version 4: incorrect suggestion on Gribov-Lipatov reciprocity removed; version 5: slight extension of the version to be published in Physics Letters B, contains a discussion of O((1-x)^2) terms and added reference

Dispersive approach in Sudakov resummation

The dispersive approach to power corrections is given a precise implementation, valid beyond single gluon exchange, in the framework of Sudakov resummation for deep inelastic scattering and the Drell-Yan process. It is shown that the assumption of infrared finite Sudakov effective couplings implies the universality of the corresponding infrared fixed points. This property is closely tied to the universality of the virtual contributions to space-like and time-like processes, encapsulated in the second logarithmic derivative of the quark form factor.Comment: 3 pages, talk given at Quark Confinement and the Hadron Spectrum 7, Ponta Delgada, Azores, Portugal, 2-7 Sep 2006, LaTeX, uses aip-6s.clo, aipproc.cls and aipxfm.sty (included

Conformal window and Landau singularities

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 below N_f^* is suggested. Assuming an infrared fixed point is present in the perturbative part of the QCD coupling even in some range below N_f^* leads to the condition gamma(N_f^*)=1, where gamma is the critical exponent. This result is incompatible with the existence of an analogue of Seiberg free dual magnetic phase in QCD. Using the Banks-Zaks expansion, one gets 4<N_f^*<6. The low value of N_f^* gives some justification to the infrared finite coupling approach to power corrections, and suggests a way to compute their normalization from perturbative input. If the perturbative series are still asymptotic in the negative coupling region, the presence of a negative ultraviolet fixed point is required both in QCD and in supersymmetric QCD to preserve causality within the conformal window. Some evidence for such a fixed point in QCD is provided through a modified Banks-Zaks expansion. Conformal window amplitudes, which contain power contributions, are shown to remain generically finite in the N_f=-\infty one-loop limit in simple models with infrared finite perturbative coupling.Comment: 35 pages, 1 figure, JHEP style. A new section added to point out the results give some justification to the infrared finite coupling approach to power corrections, and suggest a way to compute their normalization from perturbative inpu

Integrality of Open Instantons Numbers

We prove the integrality of the open instanton numbers in two examples of counting holomorphic disks on local Calabi-Yau threefolds: the resolved conifold and the degenerate $\P \times \P$. Given the B-model superpotential, we extract by hand all Gromow-Witten invariants in the expansion of the A-model superpotential. The proof of their integrality relies on enticing congruences of binomial coefficients modulo powers of a prime. We also derive an expression for the factorial $(p^k-1)!$ modulo powers of the prime $p$. We generalise two theorems of elementary number theory, by Wolstenholme and by Wilson.Comment: 13 page