The lagrangian origin of MHV rules

Abstract

We construct a canonical transformation that takes the usual Yang-Mills action into one whose Feynman diagram expansion generates the MHV rules. The off-shell continuation appears as a natural consequence of using light-front quantisation surfaces. The construction extends to include massless fermions.

Gravitation and quadratic forms

“…We are left with This is a clear point of contrast from Yang-Mills theory where both the pure and maximally supersymmetric theories are described by quadratic form structures composed of covariant derivatives [1]. From the MHV literature [15][16][17][18][19][20], we know that all treelevel scattering amplitudes in Yang-Mills theory may be expressed entirely in terms of the "square" or "angular" brackets. In gravity, the cubic amplitude does indeed have the same property but the quartic and higher vertices involve a mixture of both brackets.The derivatives we have introduced in the quadratic form for gravity do not transform covariantly beyond order κ and this is very likely, another way of stating what the amplitude structures have already taught us.…”

Twistor-inspired construction of massive quark amplitudes

“…The method for the derivation of the CSW rules introduced in [17,18] and applied to quarks in [25] uses the light-cone approach to Yang-Mills theory. In this section the treatment of massive quarks in light-cone Yang-Mills is reviewed and streamlined compared to [25].…”

“…To incorporate massive quarks it is convenient to follow closely the setup used in the construction of soft-collinear effective theory [30] for massive quarks [31]. The treatment of quarks in [17,25] emerges as a special case for the choice n ± = 2 −1/2 (1, 0, 0, ±1). A Dirac spinor Ψ and it's conjugate are decomposed as…”

“…Particular interesting for the extension towards massive particles are derivations of the CSW rules based on field redefinitions in the framework of light-cone gauge Yang-Mills [17] or the lift of the Yang-Mills action to twistor space [19,20]. Both of these action-based methods have been used to construct CSW rules for a propagating massive, colored scalar φ [21,22].…”

CSW rules for massive matter legs and glue loops

“…In a development initiated by Mansfield [10] and pushed further by Ettle and Morris [11], the starting point is the lightcone Yang-Mills Lagrangian. In terms of helicities, the action roughly takes the form…”