Britto, Cachazo and Feng have recently derived a recursion relation for tree-level scattering amplitudes in Yang-Mills. This relation has a bilinear structure inherited from factorisation on multi-particle poles of the scattering amplitudes -a rather generic feature of field theory. Motivated by this, we propose a new recursion relation for scattering amplitudes of gravitons at tree level. Using this, we derive a new general formula for the MHV tree-level scattering amplitude for n gravitons. Finally, we comment on the existence of recursion relations in general field theories.

We show how the MHV diagram description of Yang-Mills theories can be used to study non-supersymmetric loop amplitudes. In particular, we derive a compact expression for the cut-constructible part of the general one-loop MHV multi-gluon scattering amplitude in pure Yang-Mills theory. We show that in special cases this expression reduces to known amplitudes -the amplitude with adjacent negative-helicity gluons, and the five gluon non-adjacent amplitude. Finally, we briefly discuss the twistor space interpretation of our result. ♣ {j.a.p.bedford, a.brandhuber, w.j.spence, g.travaglini}@qmul.ac.uk 1 The paper [5] discusses the twistor structure of some non-supersymmetric one-loop amplitudes and the possible role of additional vertices in these models. A recent paper [18] has also developed a generalised MHV diagram construction for scattering amplitudes involving a Higgs boson and gluons. These amplitudes are described in terms of a tree-level, non-supersymmetric effective interaction which arises by integrating out a heavy top quark in one-loop diagrams.

The Delta(4) diode array phantom (Scandidos, Uppsala, Sweden) was evaluated for verification of segmental intensity-modulated radiation therapy (IMRT) and volumetric modulated arc therapy (VMAT) on an Elekta linear accelerator (Crawley UK). The device was tested for angular sensitivity by irradiating it from 36 different gantry angles, and the responses of the device to various step-and-shoot segment doses and dose rates were evaluated using an ionization chamber as a comparison. The phantom was then compared with ionization chamber and film results for two prostate and pelvic nodes IMRT plans, two head and neck IMRT plans and two lung VMAT plans. These plans were calculated using Pinnacle(3) (Philips Radiation Oncology Systems, Madison, WI). The uniformity of angular response was better than 0.5% over the range of gantry angles. The uniformity of response of the Delta(4) to different segment monitor units and dose rates was better than 0.5%. The assessment of the IMRT and VMAT plans showed that the Delta(4) measured a dose within 2.5% of the ionization chamber, and compared to film recorded a slightly larger region (range -2% to +7%) agreeing with the planned dose to within 3% and 3 mm. The Delta(4) is a complex device and requires careful benchmarking, but following the successful completion of these measurements, the Delta(4) has been introduced into clinical use.

Depending upon the emphasis in the treatment planning, VMAT provides treatment plans which are higher in quality and/or faster to deliver than IMRT. The scheme described has been successfully introduced into clinical use.