Bread and Butter Standard Model

Lectures given at the International School of Subnuclear Physics: 37th Course: Basics and Highlights of Fundamental Physics, Erice, Italy, 29 Aug - 7 Sep 1999

One-loop effective lagrangians after matching

We discuss the limitations of the covariant derivative expansion prescription advocated to compute the one-loop Standard Model (SM) effective lagrangian when the heavy fields couple linearly to the SM. In particular, one-loop contributions resulting from the exchange of both heavy and light fields must be explicitly taken into account through matching because the proposed functional approach alone does not account for them. We review a simple case with a heavy scalar singlet of charge $-1$ to illustrate the argument. As two other examples where this matching is needed and this functional method gives a vanishing result, up to renormalization of the heavy sector parameters, we re-evaluate the one-loop corrections to the T--parameter due to a heavy scalar triplet with vanishing hypercharge coupling to the Brout-Englert-Higgs boson and to a heavy vector-like quark singlet of charged $2/3$ mixing with the top quark, respectively. In all cases we make use of a new code for matching fundamental and effective theories in models with arbitrary heavy field additions.Comment: 22 pages; v2: comments and references added; v3: published version, typos correcte

One-loop radiative corrections to the helicity amplitudes of QCD processes involving four quarks and one gluon

We present analytic results for the one-loop corrections of the helicity amplitudes of the QCD five-parton subprocesses involving four quarks and one gluon obtained with a standard Feynman diagram calculation using dimensional reduction.Comment: 9 pages LaTeX, ETH-TH/94-14, KLTE-DTP/94-

Two-loop amplitudes and master integrals for the production of a Higgs boson via a massive quark and a scalar-quark loop

We compute all two-loop master integrals which are required for the evaluation of next-to-leading order QCD corrections in Higgs boson production via gluon fusion. Many two-loop amplitudes for 2 -> 1 processes in the Standard Model and beyond can be expressed in terms of these integrals using automated reduction techniques. These integrals also form a subset of the master integrals for more complicated 2 -> 2 amplitudes with massive propagators in the loops. As a first application, we evaluate the two-loop amplitude for Higgs boson production in gluon fusion via a massive quark. Our result is the first independent check of the calculation of Spira, Djouadi, Graudenz and Zerwas. We also present for the first time the two-loop amplitude for gg -> h via a massive squark

Unitarity cuts and reduction to master integrals in d dimensions for one-loop amplitudes

We present an alternative reduction to master integrals for one-loop amplitudes using a unitarity cut method in arbitrary dimensions. We carry out the reduction in two steps. The first step is a pure four-dimensional cut-integration of tree amplitudes with a mass parameter, and the second step is applying dimensional shift identities to master integrals. This reduction is performed at the integrand level, so that coefficients can be read out algebraically.Comment: 38 Pages. v2: reference added, typos fixe

Singular terms of helicity amplitudes at one-loop in QCD and the soft limit of the cross sections of multi-parton processes

We describe a general method that enables us to obtain all the singular terms of helicity amplitudes of n-parton processes at one loop. The algorithm uses helicity amplitudes at tree level and simple color algebra. We illustrate the method by calculating the singular part of the one loop helicity amplitudes of all $2\to 3$ parton subprocesses. The results are used to derive the soft gluon limit of the cross sections of all $2\to 4$ parton scattering subprocesses which provide a useful initial condition for the angular ordering approximation to coherent multiple soft gluon emission, incorporated in existing Monte Carlo simulation programs.Comment: Latex,13 pages, ETH-TH/94-

One-loop helicity amplitudes for all 2 -> 2 processes in QCD and N=1 supersymmetric Yang-Mills theory

One loop corrections to the helicity amplitudes of all 2 -> 2 subprocesses are calculated in QCD and in N=1 supersymmetric Yang-Mills theory using two versions of dimensional regularization: the `t~Hooft-Veltman scheme and dimensional reduction. Studying the structure of the soft and collinear singularities, we found universal transition rules for the squared matrix element which can be used to translate the results obtained in these schemes to the results valid in the conventional dimensional regularization scheme. With explicit calculation it is demonstrated that the one loop helicity amplitudes of the 2 -> 2 subprocesses calculated using dimensional reduction in the N=1 supersymmetric $SU(N)$ gauge theory respect the supersymmetry Ward identities. Our transition rules can also be used to calculate the next-to-leading order Altarelli-Parisi kernels in the dimensional reduction scheme when they satisfy supersymmetry Ward identities as well.Comment: 40 pages + 1 table, uses LaTeX and table.tex, ETH-TH/93-1

Jet physics at hadron colliders

I give a short summary of jet definition algorithms and recent progress in the quantitative description of jet production.Comment: 9 pages, LaTex, 6 postscript figures, Proceedings of Quark Matter 2002, Nantes, France, July 18-24, 200