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

Progress in NNLO calculations for scattering processes

The various motivations for improving the perturbative prediction to next-to-next-to-leading order (NNLO) for basic scattering processes in proton-(anti)proton, electron-proton and electron-positron scattering are discussed in detail. Recent progress in the field of next-to-next-to-leading order calculations is reviewed.Comment: Latex 9 pages, 2 postscript embedded figures, JHEP class, Based on invited talks at 6th International Symposium on Radiative Corrections, Application of Quantum Field Theory to Phenomenology (RADCOR 2002) and 6th Zeuthen Workshop on Elementary Particle Theory (Loops and Legs in Quantum Field Theory) Kloster Banz, Germany, 8th - 13th Sep 2002 and 14th Topical Conference on Hadron Collider Physics (HCP 2002), Karlsruhe, Germany, 29th Sep - 4th Oct 200

Analytical Result for Dimensionally Regularized Massless Master Non-planar Double Box with One Leg off Shell

The dimensionally regularized massless non-planar double box Feynman diagram with powers of propagators equal to one, one leg off the mass shell, i.e. with p_1^2=q^2\neq 0, and three legs on shell, p_i^2=0, i=2,3,4, is analytically calculated for general values of q^2 and the Mandelstam variables s,t and u (not necessarily restricted by the physical condition s+t+u=q^2). An explicit result is expressed through (generalized) polylogarithms, up to the fourth order, dependent on rational combinations of q^2,s,t and u, and simple finite two- and three fold Mellin--Barnes integrals of products of gamma functions which are easily numerically evaluated for arbitrary non-zero values of the arguments.Comment: 9 pages, LaTeX with axodraw.sty, minor changes in references, to appear in Physics Letters

Bounds for the normal approximation of the maximum likelihood estimator

While the asymptotic normality of the maximum likelihood estimator under regularity conditions is long established, this paper derives explicit bounds for the bounded Wasserstein distance between the distribution of the maximum likelihood estimator (MLE) and the normal distribution. For this task, we employ Stein's method. We focus on independent and identically distributed random variables, covering both discrete and continuous distributions as well as exponential and non-exponential families. In particular, a closed form expression of the MLE is not required. We also use a perturbation method to treat cases where the MLE has positive probability of being on the boundary of the parameter space.Comment: Published at http://dx.doi.org/10.3150/15-BEJ741 in the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm

Holographic correlation functions in Critical Gravity

We compute the holographic stress tensor and the logarithmic energy-momentum tensor of Einstein-Weyl gravity at the critical point. This computation is carried out performing a holographic expansion in a bulk action supplemented by the Gauss-Bonnet term with a fixed coupling. The renormalization scheme defined by the addition of this topological term has the remarkable feature that all Einstein modes are identically cancelled both from the action and its variation. Thus, what remains comes from a nonvanishing Bach tensor, which accounts for non-Einstein modes associated to logarithmic terms which appear in the expansion of the metric. In particular, we compute the holographic $1$-point functions for a generic boundary geometric source.Comment: 21 pages, no figures,extended discussion on two-point functions, final version to appear in JHE

Method of Brackets and Feynman diagrams evaluation

In this work we present the relation between method of brackets and the master theorem of Ramanujan in the evaluation of multivariable integrals, in this case Feynman diagrams.Comment: 6 pages, 2 figures. Published in Proc. of 'Loops and Legs in Quantum Field Theory'', April, 2010, W\'orlitz, German

Analytic Continuation of Massless Two-Loop Four-Point Functions

We describe the analytic continuation of two-loop four-point functions with one off-shell external leg and internal massless propagators from the Euclidean region of space-like $1\to 3$ decay to Minkowskian regions relevant to all $1\to 3$ and $2\to 2$ reactions with one space-like or time-like off-shell external leg. Our results can be used to derive two-loop master integrals and unrenormalized matrix elements for hadronic vector-boson-plus-jet production and deep inelastic two-plus-one-jet production, from results previously obtained for three-jet production in electron--positron annihilation.Comment: 26 pages, LaTe

Scattering amplitudes for e^+e^- --> 3 jets at next-to-next-to-leading order QCD

We present the calculation of the fermionic contribution to the QCD two-loop amplitude for e^+e^- --> q qbar g.Comment: 5 pages, 4 figures, espcrc2.sty (included), Talk given at QCD '02, Montpellier, France, 2-9th July 200

Bounds for the asymptotic normality of the maximum likelihood estimator using the Delta method

The asymptotic normality of the Maximum Likelihood Estimator (MLE) is a cornerstone of statistical theory. In the present paper, we provide sharp explicit upper bounds on Zolotarev-type distances between the exact, unknown distribution of the MLE and its limiting normal distribution. Our approach to this fundamental issue is based on a sound combination of the Delta method, Stein's method, Taylor expansions and conditional expectations, for the classical situations where the MLE can be expressed as a function of a sum of independent and identically distributed terms. This encompasses in particular the broad exponential family of distributions.Comment: 15 pages, 1 tabl