Abstract: Calculation of amplitudes in perturbative quantum field theory involve large loop integrals. The complexity of those integrals, in combination with the large number of Feynman diagrams, make the calculations very difficult. Reduction methods proved to be very helpful, lowering the number of integrals that need to be actually calculated. Especially reduction at the integrand level improves the speed and set-up of these calculations. In this article we demonstrate, by counting the numbers of tensor structures and independent coefficients, how to write such relations at the integrand level for one-and two-loop amplitudes. We clarify their connection to the so-called spurious terms at one loop and discuss their structure in the two-loop case. This method is also applicable to higher loops, and the results obtained apply to both planar and non-planar diagrams.

Abstract: String theory constructions using D-brane physics offer a framework where ingredients like extra abelian factors in the gauge group, more than one Higgs doublet and a generalized Green-Schwarz mechanism appear at the same time. Motivated by works towards the direction of obtaining the Standard Model in orientifold constructions, we study in the present work a Stueckelberg extension of the two-Higgs-doublet model. The distinctive features of our model are i) a sharp decay width for the heavy gauge boson, and ii) a charged Higgs boson having two main decay channels at tree level with equal branching ratios.

Abstract: A measurement of the production cross-section for Z bosons that decay to muons is presented. The data were recorded by the LHCb detector during pp collisions at a centre-of-mass energy of 7 TeV, and correspond to an integrated luminosity of 1.0 fb(-1). The cross-section is measured for muons in the pseudorapidity range 2.0 < eta < 4.5 with transverse momenta p(T) >20 GeV/e. The dimuon mass is restricted to 60 < M mu+mu- < 120 GeV/c(2). The measured cross-section is sigma(Z ->mu+mu-) = (76.0 +/- 0.3 +/- 0.5 +/- 1.0 +/- 1.3) pb where the uncertainties are due to the sample size, systematic effects, the beam energy and the luminosity. This result is in good agreement with theoretical predictions at next-to-next-to-leading order in perturbative quantum chromodynamics. The cross-section is also measured differentially as a function of kinematic variables of the Z boson. Ratios of the production cross-sections of electroweak bosons are presented using updated LHCb measurements of W boson production. A precise test of the Standard Model is provided by the measurement of the ratio sigma(W+) -> mu(+) nu(mu) + sigma(W) -> mu(+) (nu) over bar (mu)/sigma(Z ->mu+mu-) = 0.09 +/- 0.12 +/- 0.05, where the uncertainty due to luminosity cancels.