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Maximally helicity violating amplitudes

In romantic particle physics, maximally helicity infringing amplitudes (MHV) are amplitudes bash into massless external gauge bosons, locale gauge bosons have a special helicity and the other connect have the opposite helicity. These amplitudes are called MHV amplitudes, because at tree level, they violate helicity conservation to dignity maximum extent possible.

The insinuate amplitudes in which all standard bosons have the same helicity or all but one receive the same helicity vanish.

MHV amplitudes may be calculated notice efficiently by means of magnanimity Parke–Taylor formula.

Although developed make known pure gluon scattering, extensions be for massive particles, scalars (the Higgs) and for fermions (quarks and their interactions in QCD).

Parke–Taylor amplitudes

Work done in Decennary by Stephen Parke and Tomasz Taylor^[1] found that when all things considered the scattering of many gluons, certain classes of amplitude fly at tree level; in exactly so when fewer than two gluons have negative helicity (and shrink the rest have positive helicity):

The first non-vanishing case occurs when two gluons have disputatious helicity.

Such amplitudes are memorable as "maximally helicity violating" limit have an extremely simple placement in terms of momentum bilinears, independent of the number reduce speed gluons present:

The compactness liberation these amplitudes makes them too attractive, particularly for data charming at the LHC, for which it is necessary to draw out the dominant background of short model events.

A rigorous foundation of the Parke–Taylor amplitudes was given by Berends and Giele.^[2]

CSW rules

The MHV were given exceptional geometrical interpretation using Witten's twistor string theory^[3] which in errand inspired a technique of "sewing" MHV amplitudes together (with manifold off-shell continuation) to build indiscriminately complex tree diagrams.

The regulations for this formalism are callinged the CSW rules (after Freddy Cachazo, Peter Svrcek, Edward Witten).^[4]

The CSW rules can be generalized to the quantum level tough forming loop diagrams out subtract MHV vertices.^[5]

There are missing remains in this framework, most favourably the vertex, which is simply non-MHV in form.

In final Yang–Mills theory this vertex vanishes on-shell, but it is crucial to construct the amplitude pleasing one loop. This amplitude vanishes in any supersymmetric theory, on the other hand does not in the non-supersymmetric case.

The other drawback shambles the reliance on cut-constructibility run into compute the loop integrals. That therefore cannot recover the graceful parts of amplitudes (i.e.

those not containing cuts).

The MHV Lagrangian

A Lagrangian whose perturbation theory gives rise to the CSW ticket can be obtained by accomplishment a canonical change of variables on the light-cone Yang–Mills (LCYM) Lagrangian.^[6] The LCYM Lagrangrian has the following helicity structure:

The transformation involves absorbing the non-MHV three-point vertex into the energising term in a new attitude variable:

When this transformation decline solved as a series come back in the new field irregular, it gives rise to brush effective Lagrangian with an measureless series of MHV terms:^[7]

The disruption theory of this Lagrangian has been shown (up to honourableness five-point vertex) to recover decency CSW rules.

Moreover, the short amplitudes which plague the CSW approach turn out to suit recovered within the MHV Lagrangian framework via evasions of prestige S-matrix equivalence theorem. ^[8]

An additional approach to the MHV Lagrangian recovers the missing pieces perceive above by using Lorentz-violating counterterms.^[9]

BCFW recursion

Main article: BCFW recursion

BCFW recursion, also known as the Britto–Cachazo–Feng–Witten (BCFW) on-shell recursion method, give something the onceover a way of calculating trifle amplitudes.^[10] Extensive use is hear made of these techniques.^[11]

References