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.

Integrand Reduction for Two-Loop Scattering Amplitudes through Multivariate Polynomial Division

We describe the application of a novel approach for the reduction of scattering amplitudes, based on multivariate polynomial division, which we have recently presented. This technique yields the complete integrand decomposition for arbitrary amplitudes, regardless of the number of loops. It allows for the determination of the residue at any multiparticle cut, whose knowledge is a mandatory prerequisite for applying the integrand-reduction procedure. By using the division modulo Groebner basis, we can derive a simple integrand recurrence relation that generates the multiparticle pole decomposition for integrands of arbitrary multiloop amplitudes. We apply the new reduction algorithm to the two-loop planar and nonplanar diagrams contributing to the five-point scattering amplitudes in N=4 super Yang-Mills and N=8 supergravity in four dimensions, whose numerator functions contain up to rank-two terms in the integration momenta. We determine all polynomial residues parametrizing the cuts of the corresponding topologies and subtopologies. We obtain the integral basis for the decomposition of each diagram from the polynomial form of the residues. Our approach is well suited for a seminumerical implementation, and its general mathematical properties provide an effective algorithm for the generalization of the integrand-reduction method to all orders in perturbation theory.Comment: 32 pages, 4 figures. v2: published version, text improved, new subsection 4.4 adde

MOCVD of Cr3(C,N)2 and CrSixCy Films Growth and Characterization

CrCxNy and CrSixCy thin films were deposited under low pressure by metallorganic chemical vapor deposition (MOCVD) in the temperature ranges 380-450°C and 450-500°C, respectively, using Cr(NEt2)4 and CrCH2SiMe34 as single-source precursors.The growth was achieved in a cold-wall vertical reactor using, respectively, H2 and He as the carrier gases. Both types of films exhibit a mirrorlike surface morphology and are amorphous asdeposited. The CrCxNy layers start to crystallize at 600°C after annealing for 1 h under vacuum,whereas it is necessary to reach 650°C under H2 atmosphere. In both cases, the original ternary phase Cr3(C0.8N0.2)2 crystallizes. The resistivity of as-deposited amorphous CrCxNy films is typically 600. cm, and it decreases to 150 #. cm after annealing upon the formation of polycrystalline Cr3#C,N#2 films. The CrSixCy layers have a very stable amorphous structure until 850°C for 4 h. In spite of their metallic appearance, they exhibit a high resistivity compared to the Cr3#C,N#2 films. The main characteristics of these Cr-based layers is presented and discussed