General Split Helicity Gluon Tree Amplitudes in Open Twistor String Theory

We evaluate all split helicity gluon tree amplitudes in open twistor string theory. We show that these amplitudes satisfy the BCFW recurrence relations restricted to the split helicity case and, hence, that these amplitudes agree with those of gauge theory. To do this we make a particular choice of the sextic constraints in the link variables that determine the poles contributing to the contour integral expression for the amplitudes. Using the residue theorem to re-express this integral in terms of contributions from poles at rational values of the link variables, which we determine, we evaluate the amplitudes explicitly, regaining the gauge theory results of Britto et al.Comment: 30 pages, minor misprints correcte

Maximally Supersymmetric Planar Yang-Mills Amplitudes at Five Loops

We present an ansatz for the planar five-loop four-point amplitude in maximally supersymmetric Yang-Mills theory in terms of loop integrals. This ansatz exploits the recently observed correspondence between integrals with simple conformal properties and those found in the four-point amplitudes of the theory through four loops. We explain how to identify all such integrals systematically. We make use of generalized unitarity in both four and D dimensions to determine the coefficients of each of these integrals in the amplitude. Maximal cuts, in which we cut all propagators of a given integral, are an especially effective means for determining these coefficients. The set of integrals and coefficients determined here will be useful for computing the five-loop cusp anomalous dimension of the theory which is of interest for non-trivial checks of the AdS/CFT duality conjecture. It will also be useful for checking a conjecture that the amplitudes have an iterative structure allowing for their all-loop resummation, whose link to a recent string-side computation by Alday and Maldacena opens a new venue for quantitative AdS/CFT comparisons.Comment: 52 pages, 20 figures, revte

Three-jet cross sections in hadron-hadron collisions at next-to-leading order

We present a new QCD event generator for hadron collider which can calculate one-, two- and three-jet cross sections at next-to-leading order accuracy. In this letter we study the transverse energy spectrum of three-jet hadronic events using the kT algorithm. We show that the next-to-leading order correction significantly reduces the renormalization and factorization scale dependence of the three-jet cross section.Comment: 4 pages, 4 figures, REVTEX

Next-to-Maximal Helicity Violating Amplitudes in Gauge Theory

Using the novel diagrammatic rules recently proposed by Cachazo, Svrcek, and Witten, I give a compact, manifestly Lorentz-invariant form for tree-level gauge-theory amplitudes with three opposite helicities.Comment: 12 pages, 1 figur

Yangian Symmetry at Two Loops for the su(2|1) Sector of N=4 SYM

We present the perturbative Yangian symmetry at next-to-leading order in the su(2|1) sector of planar N=4 SYM. Just like the ordinary symmetry generators, the bi-local Yangian charges receive corrections acting on several neighboring sites. We confirm that the bi-local Yangian charges satisfy the necessary conditions: they transform in the adjoint of su(2|1), they commute with the dilatation generator, and they satisfy the Serre relations. This proves that the sector is integrable at two loops.Comment: 13 pages, v2: minor correction

Expansion around half-integer values, binomial sums and inverse binomial sums

I consider the expansion of transcendental functions in a small parameter around rational numbers. This includes in particular the expansion around half-integer values. I present algorithms which are suitable for an implementation within a symbolic computer algebra system. The method is an extension of the technique of nested sums. The algorithms allow in addition the evaluation of binomial sums, inverse binomial sums and generalizations thereof.Comment: 21 page

Recursion Rules for Scattering Amplitudes in Non-Abelian Gauge Theories

We present a functional derivation of recursion rules for scattering amplitudes in a non-Abelian gauge theory in a form valid to arbitrary loop order. The tree-level and one-loop recursion rules are explicitly displayed.Comment: 18 pages, RevTeX, 2 postscript figures, a reference added, minor typographical errors correcte