Ph.D Thesis


Ph.D StudentWeiss Yaniv
SubjectCollider Probes of the Standard Model via Effective Field
Theory and On-Shell Methods
DepartmentDepartment of Physics
Supervisor PROF. Yael Shadmi
Full Thesis textFull thesis text - English Version


Abstract

This thesis is a collection of three papers exploring the use of on-shell methods to directly derive renormalizable and nonrenormalizable scattering amplitudes instead of starting from a Lagrangian.

Such an approach is particularly advantageous in the context of effective field theories (EFT).

On-shell methods avoid gauge and operator redundancies, which are hard-wired into the Lagrangian formalism, thus greatly simplifying the actual application of EFTs.

Scattering amplitudes are constrained by unitarity, spin-statistics, and Lorentz symmetry (the little group) which determine the allowed kinematical structures, up to unknown numerical coefficients.

The number of these numerical coefficients is determined by imposing kinematical and symmetry constraints, and matches the number of Wilson coefficients in the EFT Lagrangian.


In the first paper, we use on-shell methods to calculate the tree-level, four-point EFT amplitudes of a massive, SM-neutral, spin-0 (h) or spin-1 (Z`) state coupled to gluons.

In particular, we derive the hhgg, hggg and Z`ggg amplitudes, which are the relevant ones for the production and decay of the new states.

We then derive the massless Z` amplitude from the massive Z`ggg amplitude and show that in the high energy limit the massive vector decomposes into a scalar and a massless vector.


In the second paper, we use on-shell methods to construct all three-point amplitudes featuring an electroweak-like spectrum, as well as the ffZh four-point.

We then examine the constraints of perturbative unitarity, which are easily imposed due to the compact form of the amplitudes, and recover many of the familiar Higgs mechanism relations.


In the third paper, we systematically derive independent four-point contact terms, which are necessary ingredients in an on-shell construction of effective field theories.

The derivation relies on simple relations between massive and massless amplitudes.

We also list independent terms for all massive three-points up to spin-3.