Planar Radiation Zeros and Scattering Equations in Field Theory Amplitudes
Author
Medrano Jiménez, DiegoEntity
UAM. Departamento de Física TeóricaDate
2019-09-06Subjects
Campos, Teoría de (Física) - Tesis doctorales; FísicaNote
Tesis Doctoral inédita leída en la Universidad Autónoma de Madrid, Facultad de Ciencias, Departamento de Física Teórica. Fecha de Lectura: 06-09-2019Esta obra está bajo una licencia de Creative Commons Reconocimiento-NoComercial-SinObraDerivada 4.0 Internacional.
Abstract
We have presented for the rst time a detailed description of planar radiation zeros as
a novel mathematical structure giving rise to new insights on the internal behavior of a
theory, such as the biadjoint scalar theory, the Yang-Mills theory or the Einstein-Hilbert
gravity. The concept \radiation zero" makes reference to all the con gurations in phase
space for which the full scattering amplitude of a given process vanishes. In our case, we
have studied \planar zeros", meaning that our characterization applies to those processes
where all particle momenta lie in the same spatial plane. Although being a rather naive
concept, the obtained results are far from incidental. On one side, we have found that the
conditions of emergence of gauge planar zeros in the maximally helicity violating sector live
inside the projective space spanned by the stereographic coordinates labelling the direction
of
ight of the outgoing momenta. The existence of such a projective characterization
implies that planar zeros are always realized inside the soft limit of any of the emitted particles,
which might be of relevance for the infrared structure or the asymptotic symmetries
of the theory. On a di erent side, we have found that gravitational amplitudes always
vanish inside this planar limit for non-helicity conserving con gurations without imposing
any further kinematic conditions. String 0-corrections of these behaviors have also been
obtained. All the computations have been done in the context of the color-kinematics du-
ality, used as a procedure to compute gravitational amplitudes from their gauge analogues;
and the Cachazo-He-Yuan formalism, as a novel integral representation to write scattering
amplitudes in contrast to the traditional Feynman diagram decomposition. In particular,
the latter relies upon a rational map between the space of null D-dimensional momentum
vectors and the moduli space of punctured Riemann spheres, given the name of scattering
equations. Considered to be a challenging task, we have shown the advantages of using
the Sudakov parametrization of particle momenta to simplify the computation of their
exact solutions. In particular, we have shown that both punctures in the Riemann sphere
and scattering amplitudes themselves adopt rather compact formulas when expressed in
terms of Sudakov variables, suggesting the parametrization to be a natural candidate for an e cient description of scattering amplitudes inside the formalism.
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