We present next-to-next-to-leading order corrections to the inclusive production of the Higgs bosons at the CERN Large Hadron Collider (LHC) including finite top quark mass effects. Expanding our analytic results for the partonic cross section around the soft limit we find agreement with a very recent publication by Harlander and Ozeren \cite{Harlander:2009mq}.Comment: 15 page

We present an algorithm that reveals relevant contributions in non-threshold-type asymptotic expansion of Feynman integrals about a small parameter. It is shown that the problem reduces to finding a convex hull of a set of points in a multidimensional vector space.

Quantum chromodynamics (QCD) effects in the semileptonic decay b → cℓν are evaluated to the second order in the coupling constant, O`α 2 s´, and to several orders in the expansion in quark masses, mc/m b . Corrections are calculated for the total decay rate as well as for the first two moments of the lepton energy and the hadron system energy distributions. Applied to the muon decay, they decrease its predicted rate by −0.43 ppm.PACS numbers: 13.35. Bv,13.25.Hw,12.38.Bx Decays of heavy fermions are an abundant source of information about fundamental interactions. Particularly important among them is the muon (µ) decay. Insensitive to strong interactions, it can be very precisely described by the electroweak model. The experiment MuLan at the Paul Scherrer Institute will likely measure the rate of the muon decay with an uncertainty better than 1 ppm and thus improve the determination of the Fermi constant G F that describes the strength of the charged-current weak interaction [1]. Along with the fine structure constant α and the Z-boson mass, G F is one of the three pillars of electroweak Standard Model tests [2].In a separate effort, the TWIST experiment at TRI-UMF measures energy and angular distributions of positrons in the µ + decay, testing the Standard Model and searching for new interactions, notably new bosons predicted by left-right symmetric models [3,4,5].To match this experimental progress, both the rate [6] and the energy distribution [7] have been calculated in quantum electrodynamics (QED) with O α 2 accuracy. Two-loop weak corrections have also been calculated [8]. In the decay rate studies, the electron mass m e was assumed negligible in the already small O α 2 effects. Here we show that the finite m e effect decreases the muon decay rate by about half ppm, exceeding previous estimates [10] and approaching the expected MuLan precision.The final-state fermion mass effects are much larger in the heavy-quark decay b → cℓν. Studied in Bfactories and the Tevatron, this process provides information about the Cabibbo-Kobayashi-Maskawa (CKM) matrix element V cb , as well as about parameters governing heavy-quark dynamics (see [9] for an up to date review and references). Also in this case, theoretical studies at O α produced in this decay [20]. In this paper we present corresponding analytical results obtained as an expansion in powers and logarithms of ρ ≡ m c /m b .The construction of such mass expansion is illustrated with an O(α s ) example in Fig. 1. Real and virtual corrections are calculated together as cuts of the diagram 1(a). Depending on virtualities of momenta flowing into and through the charm quark lines, m c can be treated as small compared to those momenta, or else those momenta can be treated as small compared to the b-quark mass in other lines of the diagram. The most interesting case is shown in Fig. 1(d), where two loop momenta are of order m c . This configuration generates odd powers of ρ and will be discussed in some detail below.At O(α 2 s ) the number of diagrams is larger and...

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We describe three algorithms for computer-aided symbolic multi-loop calculations that facilitated some recent novel results. First, we discuss an algorithm to derive the canonical form of an arbitrary Feynman integral in order to facilitate their identification. Second, we present a practical solution to the problem of multi-loop analytical tensor reduction. Finally, we discuss the partial fractioning of polynomials with external linear relations between the variables. All algorithms have been tested and used in real calculations.