QCD recursion relations from the largest time equation

We show how by reassembling the tree level gluon Feynman diagrams in a convenient gauge, space-cone, we can explicitly derive the BCFW recursion relations. Moreover, the proof of the gluon recursion relations hinges on an identity in momentum space which we show to be nothing but the Fourier transform of the largest time equation. Our approach lends itself to natural generalizations to include massive scalars and even fermions.Comment: 18 pages, 2 figures, minor changes to Sect.

On Tree Amplitudes in Gauge Theory and Gravity

The BCFW recursion relations provide a powerful way to compute tree amplitudes in gauge theories and gravity, but only hold if some amplitudes vanish when two of the momenta are taken to infinity in a particular complex direction. This is a very surprising property, since individual Feynman diagrams all diverge at infinite momentum. In this paper we give a simple physical understanding of amplitudes in this limit, which corresponds to a hard particle with (complex) light-like momentum moving in a soft background, and can be conveniently studied using the background field method exploiting background light-cone gauge. An important role is played by enhanced spin symmetries at infinite momentum--a single copy of a "Lorentz" group for gauge theory and two copies for gravity--which together with Ward identities give a systematic expansion for amplitudes at large momentum. We use this to study tree amplitudes in a wide variety of theories, and in particular demonstrate that certain pure gauge and gravity amplitudes do vanish at infinity. Thus the BCFW recursion relations can be used to compute completely general gluon and graviton tree amplitudes in any number of dimensions. We briefly comment on the implications of these results for computing massive 4D amplitudes by KK reduction, as well understanding the unexpected cancelations that have recently been found in loop-level gravity amplitudes.Comment: 22 pages, 3 figure

A direct proof of the CSW rules

Using recursion methods similar to those of Britto, Cachazo, Feng and Witten (BCFW) a direct proof of the CSW rules for computing tree-level gluon amplitudes is given.Comment: 11 pages, uses axodraw.st

MHV Techniques for QED Processes

Significant progress has been made in the past year in developing new `MHV' techniques for calculating multiparticle scattering amplitudes in Yang-Mills gauge theories. Most of the work so far has focussed on applications to Quantum Chromodynamics, both at tree and one-loop level. We show how such techniques can also be applied to abelian theories such as QED, by studying the simplest tree-level multiparticle process, e^+e^- to n \gamma. We compare explicit results for up to n=5 photons using both the Cachazo, Svrcek and Witten `MHV rules' and the related Britto-Cachazo-Feng `recursion relation' approaches with those using traditional spinor techniques.Comment: 19 pages, 10 figures. References adde

On-shell recursion relations for all Born QCD amplitudes

We consider on-shell recursion relations for all Born QCD amplitudes. This includes amplitudes with several pairs of quarks and massive quarks. We give a detailed description on how to shift the external particles in spinor space and clarify the allowed helicities of the shifted legs. We proof that the corresponding meromorphic functions vanish at z --> infinity. As an application we obtain compact expressions for helicity amplitudes including a pair of massive quarks, one negative helicity gluon and an arbitrary number of positive helicity gluons.Comment: 30 pages, minor change

Recursion relations, Helicity Amplitudes and Dimensional Regularization

Using the method of on-shell recursion relations we compute tree level amplitudes including D-dimensional scalars and fermions. These tree level amplitudes are needed for calculations of one-loop amplitudes in QCD involving external quarks and gluons.Comment: 28 pages, 6 figures, clarifications adde

SUSY Ward identities for multi-gluon helicity amplitudes with massive quarks

We use supersymmetric Ward identities to relate multi-gluon helicity amplitudes involving a pair of massive quarks to amplitudes with massive scalars. This allows to use the recent results for scalar amplitudes with an arbitrary number of gluons obtained by on-shell recursion relations to obtain scattering amplitudes involving top quarks.Comment: 22 pages, references adde

Multigluon tree amplitudes with a pair of massive fermions

We consider the calculation of n-point multigluon tree amplitudes with a pair of massive fermions in QCD. We give the explicit transformation rules of this kind of massive fermion-pair amplitudes with respect to different reference momenta and check the correctness of them by SUSY Ward identities. Using these rules and onshell BCFW recursion relation, we calculate the analytic results of several n-point multigluon amplitudes.Comment: 15page

Seven parton amplitudes from recursion relations

We present the first calculation of two-quark and five-gluon tree amplitudes using on-shell recursion relations. These amplitudes are needed for tree level 5-jet cross-section and an essential ingredient for next-to-leading order 4-jet and next-to-next-to-leading order 3-jet production at hadronic colliders. Very compact expressions for all possible helicity configurations are provided, allowing for direct implementation in Monte-Carlo codes.Comment: 11 page

Absolute Intensities of the Discrete and Continuous Absorption Bands of Oxygen Gas at 1.26 and 1.065 µ and the Radiative Lifetime of the 1Δg State of Oxygen

Laboratory measurements have been made of the absolute intensities of the discrete-line absorption band at 1.26 µ, and of the continuous bands at 1.26 and 1.065 µ in oxygen gas at pressures up to 4.3 atm. It has been shown that discrete and continuous absorptions are quite independent features, the one being a measure of the intrinsic transition probability in isolated molecules, the other of its enhancement in collision complexes. In the former the lines show significant pressure broadening, but the integral molecular absorption coefficients are constant; in the latter they are proportional to pressure and continuous absorption dominates in the 1.26-µ region at about ½ atm oxygen pressure.The radiative half-life of isolated 1Δg oxygen molecules is estimated to be 45 min, and the effect of gas pressure on the rate of decay has been predicted