t \bar{t} W production and decay at NLO

We present results for the production of a top pair in association with a W-boson at next-to-leading order. We have implemented this process into the parton-level integrator MCFM including the decays of both the top quarks and the W-bosons with full spin correlations. Although the cross section for this process is small, it is a Standard Model source of same-sign lepton events that must be accounted for in many new physics searches. For a particular analysis of same-sign lepton events in which b-quarks are also present, we investigate the effect of the NLO corrections as a function of the signal region cuts.Comment: 10 pages, 7 figure

Counting loop diagrams: computational complexity of higher-order amplitude evaluation

We discuss the computational complexity of the perturbative evaluation of scattering amplitudes, both by the Caravaglios-Moretti algorithm and by direct evaluation of the individual diagrams. For a self-interacting scalar theory, we determine the complexity as a function of the number of external legs. We describe a method for obtaining the number of topologically inequivalent Feynman graphs containing closed loops, and apply this to one- and two-loop amplitudes. We also compute the number of graphs weighted by their symmetry factors, thus arriving at exact and asymptotic estimates for the average symmetry factor of diagrams. We present results for the asymptotic number of diagrams up to 10 loops, and prove that the average symmetry factor approaches unity as the number of external legs becomes large.Comment: 27 pages, 17 table

Automatic Integral Reduction for Higher Order Perturbative Calculations

We present a program for the reduction of large systems of integrals to master integrals. The algorithm was first proposed by Laporta; in this paper, we implement it in MAPLE. We also develop two new features which keep the size of intermediate expressions relatively small throughout the calculation. The program requires modest input information from the user and can be used for generic calculations in perturbation theory.Comment: 23 page

Diagrammatic proof of the BCFW recursion relation for gluon amplitudes in QCD

We present a proof of the Britto-Cachazo-Feng-Witten tree-level recursion relation for gluon amplitudes in QCD, based on a direct equivalence between BCFW decompositions and Feynman diagrams. We demonstrate that this equivalence can be made explicit when working in a convenient gauge. We exhibit that gauge invariance and the particular structure of Yang-Mills vertices guarantees the validity of the BCFW construction.Comment: 24 pages, 33 figure

Evaluating multi-loop Feynman diagrams with infrared and threshold singularities numerically

We present a method to evaluate numerically Feynman diagrams directly from their Feynman parameters representation. We first disentangle overlapping singularities using sector decomposition. Threshold singularities are treated with an appropriate contour deformation. We have validated our technique comparing with recent analytic results for the gg->h two-loop amplitudes with heavy quarks and scalar quarks.Comment: 8 pages, 3 figures; references added, version to appear in JHE

On the Deformation of a Hyperelastic Tube Due to Steady Viscous Flow Within

In this chapter, we analyze the steady-state microscale fluid--structure interaction (FSI) between a generalized Newtonian fluid and a hyperelastic tube. Physiological flows, especially in hemodynamics, serve as primary examples of such FSI phenomena. The small scale of the physical system renders the flow field, under the power-law rheological model, amenable to a closed-form solution using the lubrication approximation. On the other hand, negligible shear stresses on the walls of a long vessel allow the structure to be treated as a pressure vessel. The constitutive equation for the microtube is prescribed via the strain energy functional for an incompressible, isotropic Mooney--Rivlin material. We employ both the thin- and thick-walled formulations of the pressure vessel theory, and derive the static relation between the pressure load and the deformation of the structure. We harness the latter to determine the flow rate--pressure drop relationship for non-Newtonian flow in thin- and thick-walled soft hyperelastic microtubes. Through illustrative examples, we discuss how a hyperelastic tube supports the same pressure load as a linearly elastic tube with smaller deformation, thus requiring a higher pressure drop across itself to maintain a fixed flow rate.Comment: 19 pages, 3 figures, Springer book class; v2: minor revisions, final form of invited contribution to the Springer volume entitled "Dynamical Processes in Generalized Continua and Structures" (in honour of Academician D.I. Indeitsev), eds. H. Altenbach, A. Belyaev, V. A. Eremeyev, A. Krivtsov and A. V. Porubo

Numerical evaluation of one-loop QCD amplitudes

We present the publicly available program NGluon allowing the numerical evaluation of primitive amplitudes at one-loop order in massless QCD. The program allows the computation of one-loop amplitudes for an arbitrary number of gluons. The focus of the present article is the extension to one-loop amplitudes including an arbitrary number of massless quark pairs. We discuss in detail the algorithmic differences to the pure gluonic case and present cross checks to validate our implementation. The numerical accuracy is investigated in detail.Comment: Talk given at ACAT 2011 conference in London, 5-9 Septembe

Feynman Rules for the Rational Part of the QCD 1-loop amplitudes

We compute the complete set of Feynman Rules producing the Rational Terms of kind R_2 needed to perform any QCD 1-loop calculation. We also explicitly check that in order to account for the entire R_2 contribution, even in case of processes with more than four external legs, only up to four-point vertices are needed. Our results are expressed both in the 't Hooft Veltman regularization scheme and in the Four Dimensional Helicity scheme, using explicit color configurations as well as the color connection language.Comment: 18 pages, 11 figures. Misprints corrected in Appendix A. Version to be published in JHE

NLO QCD corrections to pp -> ttbb+X via quark anti-quark annihilation

The process pp -> top anti-top bottom anti-bottom + X represents a very important background reaction to searches at the LHC, in particular to top anti-top H production where the Higgs boson decays into a bottom anti-bottom pair. A successful analysis of top anti-top H at the LHC requires the knowledge of direct top anti-top bottom anti-bottom production at NLO in QCD. We take the first step in this direction upon calculating the NLO QCD corrections to the subprocess initiated by quark anti-quark annihilation.Comment: 6 pages, LaTeX, 4 postscript figures, to appear in proceedings of the "9th Workshop on Elementary Particle Theory: Loops and Legs in Quantum Field Theory", Sondershausen, Germany, April 20-25, 200