Helicity amplitudes on the light-front
Open Access
- Author:
- Cruz-santiago, Christian Alexander
- Graduate Program:
- Physics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- May 11, 2015
- Committee Members:
- Anna Stasto, Dissertation Advisor/Co-Advisor
Anna Stasto, Committee Chair/Co-Chair
Eugenio Bianchi, Committee Member
John C Collins, Committee Member
Victor Nistor, Committee Member - Keywords:
- scattering amplitudes
helicity amplitudes
maximum helicity violating
MHV
light front
light cone
off-shell
gauge invariance - Abstract:
- Significant progress has been made recently in the field of helicity amplitudes. Currently there are on-shell recursion relations with shifted complex momenta, geometric interpretations of amplitudes and gauge invariant off-shell amplitudes. All this points to helicity amplitudes being a rich field with much more to say. In this work we take initial steps in understanding amplitudes through the light-front formalism for the first time. We begin by looking at crossing symmetry. In the light-front it is not obvious that crossing symmetry should be present as there are non-local energy denominators that mix energies of different states. Nevertheless, we develop a systematic approach to relate, for example, 1 → N gluon processes to 2 → N − 1 processes. Using this method, we give a perturbative proof of crossing symmetry on the light-front. One important caveat is that the proof requires the amplitudes to be on-shell. We also saw that the analytic continuation from outgoing to incoming particle produces a phase that’s dependent on the choice of polarizations. Next, we reproduce the Parke-Taylor amplitudes. For this purpose we found a recursion relation for an off-shell object called the fragmentation function. This recursion relies on the factorization property of the fragmentation functions, and it becomes apparent that this recursion is the light-front analog of the Berends-Giele recursion relation. We also found this object’s connection to off-shell and on-shell amplitudes. The solution for the off-shell amplitude, which does reproduce the Parke-Taylor amplitudes in the on-shell limit, turns out to be very interesting. It can be written as a linear sum of off-shell objects with the same structure as MHV amplitudes. Finally, we look at the Wilson line approach to generate gauge invariant off-shell amplitudes. It turns out that the exact same recursion relation appears on both frameworks, thereby providing the interpretation that our recursion relation has it’s origins in gauge invariance. This also proved that the interesting, off-shell, MHV-like object that appeared algebraically in our solution is gauge invariant. We also show that for a Ward identity calculation the light-front rules must be modified. The Ward identity involves an extra instantaneous term that has the effect of conserving full four-momentum in the numerator of the amplitude.