Aachen 2019 – scientific programme

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T: Fachverband Teilchenphysik

T 46: Theorie: QCD

T 46.8: Talk

Tuesday, March 26, 2019, 17:45–18:00, ST 8

Recursion Relations for Massive Scattering Amplitudes — •Robert Franken — Julius-Maximilians-Universität, Würzburg

In this talk I will show that scattering amplitudes with massive or massless particles of spin s ≤ 1 in renormalisable theories can be constructed recursively out of amplitudes with a lesser number of external legs. The basic idea is to deform the momenta of the external particles by shifting them into the complex plane in such a manner that on-shellness and overall momentum conservation are preserved. The precise shifting procedure depends on the kind of the involved particles and their spin projected along a reference axis.

Using Cauchy’s residue theorem leads to connect the physical amplitude to emerging poles in the complex plane and a contour integral which is forced to vanish by deforming enough external momenta.

It turns out that shifting 5 external legs is always sufficient, shifting 3 external legs is sufficient except all external particles are scalars or longitudinally polarised vector bosons.

Furthermore the introduction of special reference frames to guarantee a good behaviour of the contour integral and hence recursive constructibility involves some subtleties. Especially the reference frames for individual particles are different. To overcome these problems a formalism to convert a posteriori between different reference frames is introduced, leading to a description in a common frame.

Together with construction rules, that forbid certain helicity combinations in the 3-point amplitudes, a set of selection and suppression rules can be derived.