On-shell Recursion Relations for n-point QCD

We present on the use of on-shell recursion relations. These can be used not only for calculating tree amplitudes, including those with masses, but also to compute analytically the missing rational terms of one-loop QCD amplitudes. Combined with the cut-containing pieces calculated using a unitarity approach complete one-loop QCD amplitudes can be derived. This approach is discussed in the context of the adjacent 2-minus all-multiplicity QCD gluon amplitude.Comment: Talk presented at the 7th Workshop On Continuous Advances In QCD, 11-14 May 2006, Minneapolis, Minnesot

Direct extraction of one-loop integral coefficients

We present a general procedure for obtaining the coefficients of the scalar bubble and triangle integral functions of one-loop amplitudes. Coefficients are extracted by considering two-particle and triple unitarity cuts of the corresponding bubble and triangle integral functions. After choosing a specific parameterisation of the cut loop momentum we can uniquely identify the coefficients of the desired integral functions simply by examining the behaviour of the cut integrand as the unconstrained parameters of the cut loop momentum approach infinity. In this way we can produce compact forms for scalar integral coefficients. Applications of this method are presented for both QCD and electroweak processes, including an alternative form for the recently computed three-mass triangle coefficient in the six-photon amplitude $A_6(1^-,2^+,3^-,4^+,5^-,6^+)$. The direct nature of this extraction procedure allows for a very straightforward automation of the procedure.Comment: 42 pages, 7 figure

Multi-Parton Scattering Amplitudes via On-Shell Methods

We present an overview of recent developments, based on on-shell techniques, in the calculation of multi-parton scattering amplitudes at one loop that are relevant for phenomenological studies at hadron colliders. These new on-shell methods make efficient use of the physical properties of the hard scattering, such as unitarity and factorization.Comment: Invited review, Annual Review of Nuclear and Particle Science; v2: references adde

Constructing QCD one-loop amplitudes

In the context of constructing one-loop amplitudes using a unitarity bootstrap approach we discuss a general systematic procedure for obtaining the coefficients of the scalar bubble and triangle integral functions of one-loop amplitudes. Coefficients are extracted after examining the behaviour of the cut integrand as the unconstrained parameters of a specifically chosen parametersiation of the cut loop momentum approach infinity.Comment: 5 Pages. To appear in the proceedings of the 8th International Symposium on Radiative Corrections (RADCOR 2007): Application of Quantum Field Theory to Phenomenology, Florence, Italy, 1-6 Oct 200

All-Multiplicity One-Loop Corrections to MHV Amplitudes in QCD

We compute the complete one-loop corrections to the simplest class of QCD gluon amplitudes, those with two color-adjacent opposite-helicity external particles. We present results for an arbitrary number of external legs. The computation uses the recently-developed on-shell recursion relations for the rational parts, along with older unitarity-based results for the cut-containing terms.Comment: 5 pages; corrected typos, minor text addition; final Phys Rev versio

Infrared finite amplitudes

Soft and collinear singularities, known collectively as infrared singularities here, plague the calculation of scattering amplitudes in gauge theories with massless particles such as QCD. The aim of this thesis is to describe methods of deriving amplitudes that are infrared finite and therefore do not suffer from this problem. We begin with an overview of scattering theory which includes a detailed discussion of the source of infrared singularities and outlines approaches that can be used to avoid them. Taking one of these approaches, namely that of dressed states, we give a detailed description of how such states can be constructed. We then proceed to give an explicit example calculation of the total cross section of the process e+e(^-) →2 jets at NLO. In this example we construct dressed amplitudes and demonstrate their lack of infrared singularities and then go on to show that the total cross section is the same as that calculated using standard field theory techniques. We then move on and attempt to improve the efficiency of calculations using dressed states amplitudes. We describe some of the problems of the method, specifically the large numbers of diagrams produced and the multiple different delta functions present in each amplitude. In attempting to fix these issues we demonstrate the difficulties of producing covariant amplitudes from this formalism. Finally we propose the use of the asymptotic interaction representation as a solution to these difficulties and outline a method of producing covariant infrared finite scattering amplitudes using this

Twistor-Inspired Construction of Electroweak Vector Boson Currents

We present an extension of the twistor-motivated MHV vertices and accompanying rules presented by Cachazo, Svrvcek and Witten to the construction of vector-boson currents coupling to an arbitrary source. In particular, we give rules for constructing off-shell vector-boson currents with one fermion pair and n gluons of arbitrary helicity. These currents may be employed directly in the computation of electroweak amplitudes. The rules yield expressions in agreement with previously-obtained results for Z,W,\gamma^* --> qbar q + n gluons (analytically up to n=3, beyond via the Berends--Giele recursion relations). We also confirm that the contribution to a seven-point amplitude containing the non-abelian triple vector-boson coupling obtained using the next-to-MHV currents matches the previous result in the literature.Comment: 22 pages, 4 figures, v2 minor corrections and added commentary on multiple vector boson

Bootstrapping One-Loop QCD Amplitudes with General Helicities

The recently developed on-shell bootstrap for computing one-loop amplitudes in non-supersymmetric theories such as QCD combines the unitarity method with loop-level on-shell recursion. For generic helicity configurations, the recursion relations may involve undetermined contributions from non-standard complex singularities or from large values of the shift parameter. Here we develop a strategy for sidestepping difficulties through use of pairs of recursion relations. To illustrate the strategy, we present sets of recursion relations needed for obtaining n-gluon amplitudes in QCD. We give a recursive solution for the one-loop n-gluon QCD amplitudes with three or four color-adjacent gluons of negative helicity and the remaining ones of positive helicity. We provide an explicit analytic formula for the QCD amplitude A_{6;1}(1^-,2^-,3^-,4^+,5^+,6^+), as well as numerical results for A_{7;1}(1^-,2^-,3^-,4^+,5^+,6^+,7^+), A_{8;1}(1^-,2^-,3^-,4^+,5^+,6^+,7^+,8^+), and A_{8;1}(1^-,2^-,3^-,4^-,5^+,6^+,7^+,8^+). We expect the on-shell bootstrap approach to have widespread applications to phenomenological studies at colliders.Comment: 77 pages, 17 figures; v2, corrected minor typos in text and small equation

On-Shell Unitarity Bootstrap for QCD Amplitudes

We describe the recently developed on-shell bootstrap for computing one-loop amplitudes in non-supersymmetric theories such as QCD. The method combines the unitarity method with loop-level on-shell recursion. The unitarity method is used to compute cut-containing parts of amplitudes, and on-shell recursion is used for the remaining rational terms.Comment: 10 pages, 9 figures, write-up of talks given by Z. Bern and D. A. Kosower at Loops & Legs 2006, Eisenach, Germany; v2: added referenc

Infrared-Finite Amplitudes for Massless Gauge Theories

We present a method to construct infrared-finite amplitudes for gauge theories with massless fermions. Rather than computing $S$-matrix elements between usual states of the Fock space we construct order-by-order in perturbation theory dressed states that incorporate all long-range interactions. The $S$-matrix elements between these states are shown to be free from soft and collinear singularities. As an explicit example we consider the process $e^+ e^-\to 2$ jets at next-to-leading order in the strong coupling. We verify by explicit calculation that the amplitudes are infrared finite and recover the well-known result for the total cross section $e^+ e^-\to$ hadrons.Comment: 46 page