New techniques for one-loop scattering amplitudes

We review the main features of the Ossola, Papadopoulos and Pittau (OPP) method for the evaluation of one-loop amplitudes of arbitrary scattering processes. In this approach, the coefficients of the scalar integrals are extracted by means of simple algebraic equations constructed by numerically evaluating the numerator of the integrand for specific choices of the integration momentum. After a discussion of the first results obtained with this method, we will focus on the latest developments in the direction of a fully automatized approach to multi-loop NLO calculation

Multiloop Integrand Reduction for Dimensionally Regulated Amplitudes

We present the integrand reduction via multivariate polynomial division as a natural technique to encode the unitarity conditions of Feynman amplitudes. We derive a recursive formula for the integrand reduction, valid for arbitrary dimensionally regulated loop integrals with any number of loops and external legs, which can be used to obtain the decomposition of any integrand analytically with a finite number of algebraic operations. The general results are illustrated by applications to two-loop Feynman diagrams in QED and QCD, showing that the proposed reduction algorithm can also be seamlessly applied to integrands with denominators appearing with arbitrary powers.Comment: Published version. 5 pages, 2 figure

Search for fermiophobic Higgs bosons in final states with photons at LEP 2

Higgs boson production with subsequent decay to photons was searched for in the data collected by the DELPHI detector at centre-of-mass energies between 183 GeV and 209 GeV, corresponding to a total integrated luminosity of nearly 650 pb^{-1}. No evidence for a signal was found, and limits were set on h0Z0 and h0A0 production with h0 decay to photons. These results were used to exclude regions in the parameter space of fermiophobic scenarios of Two Higgs Doublet Models.Comment: 24 pages, 6 figures, Accepted by Eur. Phys. J.

On the Numerical Evaluation of One-Loop Amplitudes: the Gluonic Case

We develop an algorithm of polynomial complexity for evaluating one-loop amplitudes with an arbitrary number of external particles. The algorithm is implemented in the Rocket program. Starting from particle vertices given by Feynman rules, tree amplitudes are constructed using recursive relations. The tree amplitudes are then used to build one-loop amplitudes using an integer dimension on-shell cut method. As a first application we considered only three and four gluon vertices calculating the pure gluonic one-loop amplitudes for arbitrary external helicity or polarization states. We compare our numerical results to analytical results in the literature, analyze the time behavior of the algorithm and the accuracy of the results, and give explicit results for fixed phase space points for up to twenty external gluons.Comment: 22 pages, 9 figures; v2: references added, version accepted for publicatio

Complete (O_7,O_8) contribution to B -> X_s gamma at order alpha_s^2

We calculate the set of O(alpha_s^2) corrections to the branching ratio and to the photon energy spectrum of the decay process B -> X_s gamma originating from the interference of diagrams involving the electromagnetic dipole operator O_7 with diagrams involving the chromomagnetic dipole operator O_8. The corrections evaluated here are one of the elements needed to complete the calculations of the B -> X_s gamma branching ratio at next-to-next-to-leading order in QCD. We conclude that this set of corrections does not change the central value of the Standard Model prediction for Br(B -> X_s gamma) by more than 1 %.Comment: 19 pages, 8 figure

The Integrand Reduction of One- and Two-Loop Scattering Amplitudes

The integrand-level methods for the reduction of scattering amplitudes are well-established techniques, which have already proven their effectiveness in several applications at one-loop. In addition to the automation and refinement of tools for one-loop calculations, during the past year we observed very interesting progress in developing new techniques for amplitudes at two- and higher-loops, based on similar principles. In this presentation, we review the main features of integrand-level approaches with a particular focus on algebraic techniques, such as Laurent series expansion which we used to improve the one-loop reduction, and multivariate polynomial division which unveils the structure of multi-loop amplitudes.Comment: 7 pages, v2: fixed typos, added references. Presented at "Loops and Legs in Quantum Field Theory", Wernigerode, Germany, 15-20 April 201

Biomasse da praterie seminaturali come fonte di energia: un fuoco di paglia?

Biomass from seminatural grasslands as energy source: flash in the pan? - The aim of the study is to evaluate the potentiality of four seminatural herbaceous communities (grasslands of Arrhenatherion, Nardo-Agrostion tenuis, Bromion erecti and Polygono-Trisetion alliances) in the Prealpine Lombardy. We quantified the biomass production (stubble height 5 cm), the main bioenergetic features, such as ash, carbon, hydrogen and nitrogen content, and the Higher Heating Value. Biomass values vary greatly, with means between 513 (Arrhenatherion) to 227 g m-2 (Bromion erecti). The mean ash content ranges between 4.3-7.7% and mean HHV from 18.3 to 19.6 MJ kg-1. The mean energy per unit area varies between 4.5-9.5 MJ m-2.We suggest that the management of seminatural grasslands could provide biomass suitable for bioenergy production instead of common energy crops and at the same time promote conservation of habitats and their biodiversity, mostly in protected areas

On the Rational Terms of the one-loop amplitudes

The various sources of Rational Terms contributing to the one-loop amplitudes are critically discussed. We show that the terms originating from the generic (n-4)-dimensional structure of the numerator of the one-loop amplitude can be derived by using appropriate Feynman rules within a tree-like computation. For the terms that originate from the reduction of the 4-dimensional part of the numerator, we present two different strategies and explicit algorithms to compute them.Comment: 14 pages, 3 figures, uses axodraw.st