S-matrix equivalence theorem evasion and dimensional regularisation with the canonical MHV lagrangian

We demonstrate that the canonical change of variables that yields the MHVlagrangian, also provides contributions to scattering amplitudes that evade theequivalence theorem. This `ET evasion' in particular provides the tree-level(-++) amplitude, which is non-vanishing off shell, or on shell with complexmomenta or in (2,2) signature, and is missing from the MHV (aka CSW) rules. Atone loop there are ET-evading diagrammatic contributions to the amplitudes withall positive helicities. We supply the necessary regularisation in order todefine these contributions (and quantum MHV methods in general) by startingfrom the light-cone Yang-Mills lagrangian in D dimensions and making acanonical change of variables for all D-2 transverse degrees of freedom of thegauge field. In this way, we obtain dimensionally regularised three- andfour-point MHV amplitudes. Returning to the one-loop ( ) amplitude, wedemonstrate that its quadruple cut coincides with the known result, and showhow the original light-cone Yang-Mills contributions can in fact bealgebraically recovered from the ET-evading contributions. We conclude that thecanonical MHV lagrangian, supplemented with the extra terms brought tocorrelation functions by the non-linear field transformation, providecontributions which are just a rearrangement of those from light-coneYang-Mills and thus coincide with them both on and off shell.Comment: 32 pages, 9 figures. v2: corrects typos and Fig. 8; adds further citations and acknowledgement