Sevillano Munoz, Sergio
(2023)
FeynMG: Automating particle physics calculations in scalar-tensor theories.
PhD thesis, University of Nottingham.
Abstract
This thesis explores the automation of the analysis of scalar-tensor theories at subatomic scales. For this, we make use of the fact that, when appended to the Standard Model, these theories can be expressed as standard gravity plus a Beyond the Standard Model theory. Therefore, studying the modifications that scalar-tensor theories have on a matter sector in this description requires the use of quantum field theory.
For this, we first investigate the origin of long-range interactions (fifth forces) in scalar-tensor theories of gravity both working in the Einstein and the Jordan-frames. We focus on theories of Brans-Dicke type in which an additional scalar field is coupled directly to the Ricci scalar of General Relativity. In our exploration of the Jordan frame calculation, we find that a specific gauge choice called scalar-harmonic gauge is convenient to perform a consistent linearization of the gravitational sector in the weak-field limit, which gives rise to a kinetic mixing between the non-minimally coupled scalar field and the graviton. It is through this mixing that a fifth force can arise between matter fields. We are then able to compute the matrix elements for fifth-force exchanges obtaining frame-independent results. Moreover, we also show the pivotal role that sources of explicit scale symmetry breaking in the matter sector play in admitting fifth-force couplings.
Irrespectively of the selected frame, we find the calculation to be very time-consuming and model dependent, motivating the development of computational tools for these derivations. The ability to represent perturbative expansions of interacting quantum field theories in terms of simple diagrammatic rules has revolutionized calculations in particle physics (and elsewhere). Moreover, these rules are readily automated, a process that has catalysed the rise of symbolic algebra packages. However, in the case of extended theories of gravity, such as scalar-tensor theories, it is necessary to precondition the Lagrangian to apply this automation or, at the very least, to take advantage of existing software pipelines.
In this context, we present the Mathematica package FeynMG, which works in conjunction with the well-known package FeynRules. FeynMG takes as inputs the FeynRules model file for a non-gravitational theory and a user-supplied gravitational Lagrangian. FeynMG provides functionality that inserts the minimal gravitational couplings of the degrees of freedom specified in the model file, determines the couplings of the additional tensor and scalar degrees of freedom (the metric and the scalar field from the gravitational sector), and preconditions the resulting Lagrangian so that it can be passed to FeynRules, either directly or by outputting an updated FeynRules model file. The Feynman rules can then be determined and output through FeynRules, using existing universal output formats and interfaces to other analysis packages, such as MadGraph. Therefore, in combination with these additional analysis packages, FeynMG will make possible to test for modifications to the Standard Model due to scalar-tensor theories in particle colliders.
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