We present a new phenomenological analysis of the inclusive rare decay B → X s ℓ + ℓ − . In particular, we present the first calculation of the NNLL contributions due to the leading two-loop matrix elements, evaluated for arbitrary dilepton invariant mass. This allows to obtain the first NNLL estimates of the dilepton mass spectrum and the lepton forward-backward asymmetry in the high M 2 ℓ + ℓ − region, and to provide an independent check of previously published results in the low M 2 ℓ + ℓ − region. The numerical impact of these NNLL corrections in the high-mass region (M 2 ℓ + ℓ − > 14.4 GeV 2 ) amounts to −13% in the integrated rate, and leads to a reduction of the scale uncertainty to ±3%. The impact of non-perturbative contributions in this region is also discussed in detail.

Using heavy quark effective field theory, exponentiation of Sudakov double logarithms, and perturbative factorization theorems for exclusive processes, we calculate the amplitude for the semileptonic decay of mesons with a single, very heavy quark into .rr and p for a large hadronic recoil momentum. A formula for these large-recoil widths is obtained in terms of two-particle wave functions of the heavy and light mesons and applied to semileptonic decays of the B.PACS number(s1: 13.20.He, 12.39.Hg

We report the results of a new calculation of soft-gluon corrections in B → X s ℓ + ℓ − decays. In particular, we present the first calculation of bremsstrahlung and corresponding virtual terms to the lepton forward-backward asymmetry, which allows us to systematically include all contributions to this observable beyond the lowest non-trivial order. The new terms are important, for instance the position of the zero of the asymmetry receives corrections of O(10%). Using a different method, we also provide an independent check of recently published results on bremsstrahlung and infrared virtual corrections to the dilepton-invariant mass distribution.

The effect of soft supersymmetry-breaking terms on one-loop finite N = 1 supersymmetric gauge theories is investigated, and the general conditions that finiteness be preserved given. Particular attention is paid to the kinds of breakings which arise in low energy supergravity models, and it is shown that in this case the susy-breaking gaugino and scalar masses and cubic scalar interactions are related.The search for finite supersymmetric theories in four dimensions began in 1974 when it was pointed out [l] that a N = 1 supersymmetric gau e theory with three matter multiplets in the adjoint representationhad vanishing one-loop gauge &function Gpi) -tial -0). Subsequently it was shown that; for a N = 1 theory with ~0 superpoten-there exists no choice of g&p and representation such that both /3 1) il) and the two-loop gauge p-function ) vanish [2]. Then in 1977 it was shown that, for the N = 4 supersymmetric gauge theory, P(l) = pC2) = 0 [3!. This theory corresponds in N = 1 language to a theory with three matter multiplets in the a4oint &presenta-tion and a superpotential w = &+$"l&"3 .This result was later extended to the three-loop level [4] and eventually to all orders [5]. More finite theories were found, when, using the susy no-renormalisation theorems [6], it was shown that @)vanished for n > 1 in N = 2 theories [7] *' . N = 2 theories are defined by the superpotential **where $, C;, 9 transform according t!, the R*, R and adjoint representation respectively. By choosing R so that fly) = 0 a class of fmite theories is obtained; the N = 4 case (eq. (1)