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Timothy Trott

Publications and source records attributed to Timothy Trott.

9 recordsLinked to original sources
arXiv2026

Supersymmetry, Supergravity and the Consistency of On-Shell Massive Superamplitudes

I study constraints from consistent complex factorisation of $2\rightarrow 2$ scattering amplitudes in $4d$ and their relationship with supersymmetry. I complete the argument demonstrating that a massless helicity-$3/2$ particle must be a gravitino in a theory of supergravity and derive the structure and couplings of massive supermultiplets from first principles. For massive BPS particles in theories with extended supersymmetry, further constraints on the couplings are derived from consistent factorisation of massive superamplitudes. Among these is the requirement that BPS vector bosons must have couplings conforming to Lie algebra structure constants or generalised Chern-Simons terms. The gravitational coupling is shown to participate and draws the graviphotons into the Lie algebra. All $2\rightarrow 2$ tree-level amplitudes of massive particles with spin $s\leq 1$ are calculated in (super)gravity using on-shell methods and the double copy. These are assembled and decomposed into (super)amplitudes with varying amounts of supersymmetry. Finally, I study scattering of BPS gravitinos with unbroken $\mathcal{N}\geq 4$ supergravity and show that consistent factorisation leads to the full reconstruction of the super-Higgs mechanism. This argument completely determines the perturbative structure of all $\mathcal{N}=4$ Minkowski vacua of gauged maximal supergravity. Gravitinos in theories not admitting a super-Higgs mechanism are ruled-out.

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arXiv2026

Consistent Scattering Amplitudes, Yang-Mills, the Higgs Mechanism and the EFTs Beyond

I study constraints on fundamental physics emerging from consistency of a unitary, local and perturbative $S$-matrix in $4d$. For massless particles, some new constraints arising from consistent complex factorisation of $2\rightarrow 2$ amplitudes are derived, leading, in particular, to the complete structure of the gluon three-particle amplitudes, including the geometric restrictions on the Lie algebra, parity and time-reversal symmetry, among other details. For massive particles, a hierarchy of constraints may be derived instead by imposing a maximum rate of unitarity-violating growth in the high energy limit. All $2\rightarrow 2$ tree-level amplitudes of massive particles with spin $s\leq 1$ are calculated in generality using on-shell methods and presented with manifest high energy dependence. The anatomy of these amplitudes' helicity sectors is dissected in order to identify conditions under which their energy growth is limited or eliminated. Using these results, it is shown that the scattering of massive vector bosons has suppressed, but not fully unitarised, high energy dependence if the parity-conserving parts of their self-couplings are Lie algebra structure constants, possibly non-semisimple or non-compact, and the parity-violating parts are ``generalised Chern-Simons terms''. Full unitarisation then requires the standard Yang-Mills Lie algebra properties and, for a gapped spectrum, the Higgs mechanism. These amplitudes are assembled, embedded and unified into elegant superamplitudes in theories with extended supersymmetry when the particles are BPS. More generally, a broader landscape of EFTs is charted through various combinations of constraints and coupling hierarchies.

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arXiv2021

The Muon Smasher's Guide

We lay out a comprehensive physics case for a future high-energy muon collider, exploring a range of collision energies (from 1 to 100 TeV) and luminosities. We highlight the advantages of such a collider over proposed alternatives. We show how one can leverage both the point-like nature of the muons themselves as well as the cloud of electroweak radiation that surrounds the beam to blur the dichotomy between energy and precision in the search for new physics. The physics case is buttressed by a range of studies with applications to electroweak symmetry breaking, dark matter, and the naturalness of the weak scale. Furthermore, we make sharp connections with complementary experiments that are probing new physics effects using electric dipole moments, flavor violation, and gravitational waves. An extensive appendix provides cross section predictions as a function of the center-of-mass energy for many canonical simplified models.

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arXiv2020

Causality, Unitarity and Symmetry in Effective Field Theory

Sum rules in effective field theories, predicated upon causality, place restrictions on scattering amplitudes mediated by effective contact interactions. Through unitarity of the $S$-matrix, these imply that the size of higher dimensional corrections to transition amplitudes between different states is bounded by the strength of their contributions to elastic forward scattering processes. This places fundamental limits on the extent to which hypothetical symmetries can be broken by effective interactions. All analysis is for dimension $8$ operators in the forward limit. Included is a thorough derivation of all positivity bounds for a chiral fermion in $SU(2)$ and $SU(3)$ global symmetry representations resembling those of the Standard Model, general bounds on flavour violation, new bounds for interactions between particles of different spin, inclusion of loops of dimension $6$ operators and illustration of the resulting strengthening of positivity bounds over tree-level expectations, a catalogue of supersymmetric effective interactions up to mass dimension $8$ and $4$ legs and the demonstration that supersymmetry unifies the positivity theorems as well as the new bounds.

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arXiv2019

Constructing $\mathcal{N}=4$ Coulomb Branch Superamplitudes

We study scattering amplitudes of massive BPS states on the Coulomb branch of $4d$ $\mathcal{N}=4$ super-Yang-Mills, utilising a little group covariant on-shell superspace for massive particles. Super-BCFW recursion for massive amplitudes is constructed and its validity is proven for all Coulomb branch superamplitudes. We then determine the exact three-particle superamplitudes for massive states. These ingredients allow us to explicitly compute the four- and five-particle superamplitudes, which is the first non-trivial usage of BCFW recursion for amplitudes with entirely massive external states. The manifest little group covariance helps clarify both the role of special kinematic properties of BPS states and the organizational structures of the superamplitudes.

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arXiv2019

Massive On-Shell Supersymmetric Scattering Amplitudes

We introduce a manifestly little group covariant on-shell superspace for massive particles in four dimensions using the massive spinor helicity formalism. This enables us to construct massive on-shell superfields and fully utilize on-shell symmetry considerations to derive all possible $\mathcal{N}=1$ three-particle amplitudes for particles of spin as high as one, as well as some simple amplitudes for particles of any spin. Throughout, the conceptual and computational simplicity of this approach is exhibited.

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arXiv2016

Cosmological Signals of a Mirror Twin Higgs

We investigate the cosmology of the minimal model of neutral naturalness, the mirror Twin Higgs. The softly-broken mirror symmetry relating the Standard Model to its twin counterpart leads to significant dark radiation in tension with BBN and CMB observations. We quantify this tension and illustrate how it can be mitigated in several simple scenarios that alter the relative energy densities of the two sectors while respecting the softly-broken mirror symmetry. In particular, we consider both the out-of-equilibrium decay of a new scalar as well as reheating in a toy model of twinned inflation, Twinflation. In both cases the dilution of energy density in the twin sector does not merely reconcile the existence of a mirror Twin Higgs with cosmological constraints, but predicts contributions to cosmological observables that may be probed in current and future CMB experiments. This raises the prospect of discovering evidence of neutral naturalness through cosmology rather than colliders.

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arXiv2015

SUSY Implications from WIMP Annihilation into Scalars at the Galactic Centre

An excess in gamma-rays emanating from the galactic centre has recently been observed in the Fermi-LAT data. This signal can be interpreted as resulting from WIMP annihilation, with the spectrum well-fit by dark matter annihilating dominantly into either bottom-quark or Higgs pairs. Supersymmetric models provide a well-motivated framework to study the implications of this signal in these channels. With a neutralino dark matter candidate, the gamma-ray excess cannot be easily accommodated in the minimal supersymmetric model, which in any case requires tuning below the percent level to explain the observed Higgs mass. Instead we are naturally led to consider the next-to-minimal model with a singlet superfield. This not only allows for the annihilation channel into bottom-quark pairs to be implemented, but also provides new possibilities for annihilation into Higgs-pseudoscalar pairs. We show that the fit to the gamma-ray excess for the Higgs-pseudoscalar channel can be just as good as for annihilation into bottom-quark pairs. Moreover, in the parameter range of interest, the next-to-minimal supersymmetric model solves the mu-problem and can explain the 125 GeV Higgs mass with improved naturalness. We also consider an extension by adding a right-handed neutrino superfield with the right-handed sneutrino acting as a dark matter candidate. Interestingly, this allows for the annihilation into pseudoscalar pairs which also provide a good fit to the gamma-ray excess. Furthermore, in the case of a neutralino LSP, the late decay of a sneutrino NLSP can non-thermally produce the observed relic abundance. Finally, the WIMP annihilation into scalar pairs allows for the possibility of detecting the Higgs or pseudoscalar decay into two photons, providing a smoking-gun signal of the model.

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