One-loop MHV rules and pure yang-mills

It has been known for some time that the standard MHV diagram formulation of perturbative Yang-Mills theory is incomplete, as it misses rational terms in one-loop scattering amplitudes of pure Yang-Mills. We propose that certain Lorentz violating counterterms, when expressed in the field varibles which give rise to standard MHV vertices, produces precisely these missing terms. These counterterms appear when Yang-Mills is treated with a regulator, introdued by Thorn and collaborators, which arises in world-sheet formulations of Yang-Mills theory in the lightcone gauge. As an illustration of our proposal, we show that simple one-loop, two-point conterterm is the generating function for the infinite sequecne of one-loop, all-plus helicity amplitudes in pure Yang-Mills, in complete agreement with known expressions.