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Elizabeth H. Simmons

Publications and source records attributed to Elizabeth H. Simmons.

At least 19 recordsLinked to original sources

Radion Portal Freeze-Out Dark-Matter

We show that, in a consistent model of a stabilized extra-dimensional theory, the radion can serve as a natural portal between ordinary matter and WIMP dark matter. With an effective coupling scale of the Kaluza-Klein theory of 20-100 TeV, the radion portal can produce the observed relic abundance through resonant annihilation for dark matter masses up to a TeV. Existing and planned direct dark matter detection experiments cannot constrain this model. However, indirect detection limits exclude dark matter masses between 5 and 80 GeV, where the radion mediator primarily decays into b-quarks.

hep-ph

Incentivizing supplemental math assignments and using AI-generated hints is associated with improved exam performance

Inequities in student access to trigonometry and calculus are often associated with racial and socioeconomic privilege, and often influence introductory physics course performance. To mitigate these disparities in student preparedness, we developed a two-pronged intervention consisting of (1) incentivized supplemental math assignments and (2) AI-generated learning support tools in the form of optional hints embedded in the physics homework assignments. Both interventions are grounded in the Situated Expectancy-Value Theory of Achievement Motivation, which posits that students are more likely to complete a task that they expect to do well in and whose outcomes they think are valuable. For the supplemental math assignments, the extra credit was scaled to make it worth more points for students with lower exam scores, thereby creating even greater value for students who might benefit most from the assignments. AI-generated hints were integrated into the homework assignments, thereby reducing or eliminating the cost to the student, in terms of time, energy, and social barriers or fear of judgment. Our findings indicate that both these interventions are associated with increased exam scores; in particular, the scaled extra credit reduced disparities in completion of supplemental math assignments. These interventions, which are relatively simple for any instructor to implement, are therefore very promising for creating more equitable undergraduate quantitative courses.

physics.ed-ph

Limits on Kaluza-Klein Portal Dark Matter Models

We revisit the phenomenology of dark-matter (DM) scenarios within radius-stabilized Randall-Sundrum models. Specifically, we consider models where the dark matter candidates are Standard Model (SM) singlets confined to the TeV brane and interact with the SM via spin-2 and spin-0 gravitational Kaluza-Klein (KK) modes. We compute the thermal relic density of DM particles in these models by applying recent work showing that scattering amplitudes of massive spin-2 KK states involve an intricate cancellation between various diagrams. Considering the resulting DM abundance, collider searches, and the absence of a signal in direct DM detection experiments, we show that spin-2 KK portal DM models are highly constrained. We confirm that within the usual thermal freeze-out scenario, scalar dark matter models are essentially ruled out. In contrast, we show that fermion and vector dark matter models are viable in a region of parameter space in which dark matter annihilation through a KK graviton is resonant. Specifically, vector models are viable for dark matter masses ranging from 1.1 TeV to 5.5 TeV for theories in which the scale of couplings of the KK modes is of order 40 TeV or lower. Fermion dark matter models are viable for a similar mass region, but only for KK coupling scales of order 20 TeV. In this work, we provide a complete description of the calculations needed to arrive at these results and, in an appendix, a discussion of new KK-graviton couplings needed for the computations, which have not previously been discussed in the literature. Here, we focus on models in which the radion is light, and the back-reaction of the radion stabilization dynamics on the gravitational background can be neglected. The phenomenology of a model with a heavy radion and the consideration of the effects of the radion stabilization dynamics on the DM abundance are being addressed in forthcoming work.

hep-ph

Scattering amplitudes in the Randall-Sundrum model with brane-localized curvature terms

In this paper we investigate the scattering amplitudes of spin-2 Kaluza-Klein (KK) states in Randall-Sundrum models with brane-localized curvature terms. We show that the presence of brane-localized curvature interactions modifies the properties of (4D) scalar fluctuations of the metric, resulting in scattering amplitudes of the massive spin-2 KK states which grow as ${\cal O}(s^3)$ instead of ${\cal O}(s)$. We discuss the constraints on the size of the brane-localized curvature interactions based on the consistency of the Sturm-Liouville mode systems of the spin-2 and spin-0 metric fluctuations. We connect the properties of the scattering amplitudes to the diffeomorphism invariance of the compactified KK theory with brane-localized curvature interactions. We verify that the scattering amplitudes involving brane-localized external sources (matter) are diffeomorphism-invariant, but show that those for matter localized at an arbitrary point in the bulk are not. We demonstrate that, in Feynman gauge, the spin-0 Goldstone bosons corresponding to helicity-0 states of the massive spin-2 KK bosons behave as a tower of Galileons, and that it is their interactions that produce the high-energy behavior of the scattering amplitudes. We also outline the correspondence between our results and those in the Dvali-Gabadadze-Porrati (DGP) model. In an appendix we discuss the analogous issue in extra-dimensional gauge theory, and show that the presence of a brane-localized gauge kinetic-energy term does not change the high-energy behavior of corresponding KK vector boson scattering amplitudes.

hep-ph

Scattering Amplitudes of Massive Spin-2 Kaluza-Klein States with Matter

We perform a comprehensive analysis of the scattering of matter and gravitational Kaluza-Klein (KK) modes in five-dimensional gravity theories. We consider matter localized on a brane as well as in the bulk of the extra dimension for scalars, fermions and vectors respectively, and consider an arbitrary warped background. While naive power-counting suggests that there are amplitudes which grow as fast as ${\cal O}(s^3)$ [where $s$ is the center-of-mass scattering energy-squared], we demonstrate that cancellations between the various contributions result in a total amplitude which grows no faster than ${\cal O}(s)$. Extending previous work on the self-interactions of the gravitational KK modes, we show that these cancellations occur due to sum-rule relations between the couplings and the masses of the modes that can be proven from the properties of the mode equations describing the gravity and matter wavefunctions. We demonstrate that these properties are tied to the underlying diffeomorphism invariance of the five-dimensional theory. We discuss how our results generalize when the size of the extra dimension is stabilized via the Goldberger-Wise mechanism. Our conclusions are of particular relevance for freeze-out and freeze-in relic abundance calculations for dark matter models including a spin-2 portal arising from an underlying five-dimensional theory.

hep-ph

Symmetries, Spin-2 Scattering Amplitudes, and Equivalence theorems in Warped Five-Dimensional Gravitational Theories

Building on work by Hang and He, we show how the residual five-dimensional diffeomorphism symmetries of compactified gravitational theories with a warped extra dimension imply Equivalence theorems which ensure that the scattering amplitudes of helicity-0 and helicity-1 spin-2 Kaluza-Klein states equal (to leading order in scattering energy) those of the corresponding Goldstone bosons present in the `t-Hooft-Feynman gauge. We derive a set of Ward identities that lead to a transparent power-counting of the scattering amplitudes involving spin-2 Kaluza-Klein states. We explicitly calculate these amplitudes in terms of the Goldstone bosons in the Randall-Sundrum model, check the correspondence to previous unitary-gauge computations, and demonstrate the efficacy of `t-Hooft-Feynman gauge for accurately computing amplitudes for scattering of the spin-2 states both among themselves and with matter. Power-counting for the Goldstone boson interactions establishes that the scattering amplitudes grow no faster than $O(s)$, explaining the origin of the behavior previously shown to arise from intricate cancellations between different contributions to these scattering amplitudes in unitary gauge. We describe how our results apply to more general warped geometries, including models with a stabilized extra dimension. In an appendix we explicitly identify the symmetry algebra of the residual 5D diffeomorphisms of a Randall-Sundrum extra-dimensional theory.

hep-ph

Vector-Like Top Quark Production via an Electroweak Dipole Moment at a Muon Collider

Vectorial partners of the Standard Model quarks and leptons are predicted in many dynamical models of electroweak symmetry breaking. The most easily accessible of these new particles, either due to mass or couplings, are typically expected to be the partners of the third-generation fermions. It is therefore essential to explore the signatures of these particles at future high-energy colliders. We study the potential of a high-energy muon collider to singly produce a vector-like top-quark partner via an electroweak dipole moment operator, such an operator being typical of composite constructions beyond the Standard Model. We use a phenomenological model for third-generation quarks and their partners that satisfies an extended custodial symmetry. This automatically protects the $W$-boson and $Z$-boson masses from receiving large electroweak corrections, and it allows the model to be viable given current electroweak data. We demonstrate that cross sections associated with dipole-induced vector-like quark production can easily exceed those inherent to more conventional single-production modes via ordinary electroweak couplings. We then explore the associated phenomenology, and we show that at least one (and often more than one) of the extra vector-like states can be studied at high-energy muon colliders. Typical accessible masses are found to range up to close to the kinematic production threshold, when the vector-like partners are produced in combination with an ordinary top quark.

hep-ph

Vector-Like top quark production via a chromo-magnetic moment at the LHC

Theories which provide a dynamical explanation for the large top-quark mass often include TeV-scale vector-like top-quark and bottom-quark partner states which can be potentially discovered at the LHC. These states are currently probed through model-independent searches for pair-production via gluon fusion, as well as through model-dependent complementary electroweak single production. In this paper we study the potential to extend those searches for the partners of the third-generation Standard Model quarks on the basis of their expected chromomagnetic interactions. We discuss how current searches for "excited" bottom-quarks produced via $b$-gluon fusion through chromomagnetic interactions are relevant, and provide significant constraints. We then explore the region of the parameter space in which the bottom-quark partner is heavier than the top-quark partner, in which case the top-partner can be primarily produced via the decay of the bottom-partner. Next, we probe the potential of the production of a single top-quark partner in association with an ordinary top-quark by gluon-fusion. Kinematically these two new processes are similar, and they yield the production of a heavy top partner and a lighter Standard Model state, a pattern which allows for the rejection of the associated dominant Standard Model backgrounds. We examine the sensitivity of these modes in the case where the top-partner subsequently decays to a Higgs boson and an ordinary top-quark, and we demonstrate that these new channels have the potential of extending and complementing the conventional strategies at LHC run III and at the high-luminosity phase of the LHC. In this last case, we find that partner masses that range up to about 3 TeV can be reached. This substantially expands the expected mass reach for these new states, including regions of parameter space that are inaccessible by traditional searches.

hep-ph

Single Vector-Like top quark production via chromomagnetic interactions at present and future hadron colliders $-$A Snowmass 2021 White Paper

In our recent paper, we have investigated the potential for the LHC to discover vector-like quark partner states singly produced via their chromomagnetic moment interactions. These production mechanisms extend traditional searches which rely on pair-production of top-quark partner states or on the single production of these states through electroweak interactions, in the sense of providing greatly increased reach in parameter space regions where traditional searches are insensitive. In this study we determine the potential of both the 14 TeV high-luminosity LHC (HL-LHC) and a 100 TeV proton-proton collider to probe new vector-like quarks produced in this mode. We focus on the single production of a top-quark partner in association with an ordinary top-quark, as well as on the resonant production of the bottom-quark partner with its subsequent decay to a top-quark partner and a $W$ boson. For both cases we consider a top-partner decay to the Higgs boson and an ordinary top-quark. We find that HL-LHC and a future 100 TeV proton collider can probe vector-like partner masses up to about 3 TeV and 15-20 TeV respectively, visibly extending the range of the traditional vector like quark partner searches.

hep-ph

Supersymmetry and Sum Rules in the Goldberger-Wise Model

In this work we demonstrate that the mixed gravitational and scalar sectors of the five-dimensional Goldberger-Wise (GW) model, in which the size of a warped extra dimension is dynamically determined, has a "hidden" dual $N=2$ supersymmetric structure. This symmetry structure, a generalization of one found in the unstabilized Randall-Sundrum model, is a result of the spontaneously broken five-dimensional diffeomorphism invariance of the underlying gravitational theory. The supersymmetries relate the properties of the spin-1 and spin-0 modes "eaten" by the massive spin-2 Kaluza-Klein states of the theory to the mode functions of the spin-2 modes. Because the symmetries relate the couplings and masses of the massive spin-2 states to those of the tower of physical spin-0 states of the GW model, they enable us to analytically prove the sum rule relations which ensure the tree-level scattering amplitudes of the massive spin-2 states will grow no faster than ${\cal O}(s)$. The analysis given here also explains the unconventional forms of the spin-0 mode equation, boundary condition(s), and normalization found in the GW model.

hep-ph

Spin-2 Kaluza-Klein Scattering in a Stabilized Warped Background

Scattering amplitudes involving massive spin-2 particles typically grow rapidly with energy. In this paper we demonstrate that the anomalous high-energy growth of the scattering amplitudes cancel for the massive spin-2 Kaluza-Klein modes arising from compactified five-dimensional gravity in a stabilized warped geometry. Generalizing previous work, we show that the two sum rules which enforce the cancellations between the contributions to the scattering amplitudes coming from the exchange of the (massive) radion and those from the exchange of the tower of Goldberger-Wise scalar states (admixtures of the original gravitational and scalar fields of the theory) still persist in the case of the warping which would be required to produce the hierarchy between the weak and Planck scales in a Randall-Sundrum model. We provide an analytic proof of one combination of these generalized scalar sum rules, and show how the sum rule depends on the Einstein equations determining the background geometry and the mode-equations and normalization of the tower of physical scalar states. Finally, we provide a consistent and self-contained derivation of the equations governing the physical scalar modes and we list, in appendices, the full set of sum rules ensuring proper high-energy growth of all $2 \to 2$ massive spin-2 scattering amplitudes.

hep-ph

Spin-2 KK Mode Scattering in Models with a Massive Radion

We calculate tree-level scattering amplitudes of massive spin-2 KK particles in models of stabilized compact extra-dimensional theories. Naively introducing a mass for the radion in an extra-dimensional model without accounting for the dynamics responsible for stabilizing the extra dimension upsets the cancellations relating the masses and couplings of the spin-2 modes, resulting in KK scattering amplitudes which grow like $E^{4}$ instead of $E^{2}$. We therefore investigate scattering of the Kaluza-Klein states in theories incorporating the Goldberger-Wise mechanism to stabilize the size of the extra dimension. We demonstrate that the cancellations occur only when one includes not only the massive radion, but also the massive spin-0 modes arising from the Goldberger-Wise scalar. We compute the revised sum rules which are satisfied in a stabilized model to ensure a consistent high-energy scattering amplitude. We introduce a simple model of a stabilized extra dimension which is a small deformation of a flat (toroidal) five-dimensional model, and demonstrate the cancellations in computations performed to leading nontrivial order in the deformation. These results are the first complete KK scattering computation in an extra-dimensional model with a stabilized extra dimension, with implications for the theory and phenomenology of these models.

hep-ph

Narrow Resonances Revisited -- Simplifying Multidimensional Constraints

As we amass more LHC data, we continue to search for new and improved methods of visualizing search results, in ways that are as model-independent as possible. The simplified limits framework is an approach developed to recast limits on searches for narrow resonances in terms of products of branching ratios (BRs) corresponding to the resonance's production and decay modes. In this work, we extend the simplified limits framework to a multidimensional parameter space of BRs, which can be used to unfold an ambiguity in the simplified parameter $ζ$ introduced when more than one channel contributes to the production of the resonance. It is also naturally applicable to combining constraints from experimental searches with different observed final states. Constraints can be visualized in a three-dimensional space of branching ratios by employing ternary diagrams, triangle plots which utilize the inherent unitarity of the sum of the resonance's BRs. To demonstrate this new methodology, we recast constraints from recent ATLAS searches in diboson final states for spin-0, 1, and 2 narrow resonances into constraints on the resonance's width-to-mass ratio and display them in the space of relevant branching ratios. We also demonstrate how to generalize the method to cases where more than three branching ratios are relevant by using N-simplex diagrams, and we suggest a broader application of the general method to digital data sets.

hep-ph

Massive Spin-2 Scattering Amplitudes in Extra-Dimensional Theories

In this paper we describe in detail the computation of the scattering amplitudes of massive spin-2 Kaluza-Klein excitations in a gravitational theory with a single compact extra dimension, whether flat or warped. These scattering amplitudes are characterized by intricate cancellations between different contributions: although individual contributions may grow as fast as ${\cal O}(s^5)$, the full results grow only as ${\cal O}(s)$. We demonstrate that the cancellations persist for all incoming and outgoing particle helicities and examine how truncating the computation to only include a finite number of intermediate states impacts the accuracy of the results. We also carefully assess the range of validity of the low energy effective Kaluza-Klein theory. In particular, for the warped case we demonstrate directly how an emergent low energy scale controls the size of the scattering amplitude, as conjectured by the AdS/CFT correspondence.

hep-ph

Sum Rules for Massive Spin-2 Kaluza-Klein Elastic Scattering Amplitudes

It has recently been shown explicitly that the high-energy scattering amplitude of the longitudinal modes of massive spin-2 Kaluza Klein states in compactified 5-dimensional gravity, which would naively grow like O(s^5), grow only like O(s). Since the individual contributions to these amplitudes do grow like O(s^5), the required cancellations between these individual contributions result from intricate relationships between the masses of these states and their couplings. Here we report the explicit form of these sum-rule relationships which ensure the necessary cancellations for elastic scattering of spin-2 Kaluza Klein states in a Randall-Sundrum model. We consider an Anti-de-Sitter space of arbitrary curvature, including the special case of a toroidal compactification in which the curvature vanishes. The sum rules demonstrate that the cancellations at O(s^5) and O(s^4) are generic for a compact extra dimension, and arise from the Sturm-Liouville structure of the eigenmode system in the internal space. Separately, the sum rules at O(s^3) and O(s^2) illustrate the essential role of the radion mode of the extra-dimensional metric, which is the dynamical mode related to the size of the internal space.

hep-ph

Colorphilic Spin-2 Resonances in the LHC Dijet Channel

Experiments at the LHC may yet discover a dijet resonance indicative of Beyond the Standard Model (BSM) physics. In this case, the question becomes: what BSM theories are consistent with the unexpected resonance? One possibility would be a spin-2 object called the colorphilic graviton--a spin-2 color-singlet particle which couples exclusively to the quark and gluon stress-energy tensors. We assess the possibility of this state's discovery in the dijet channel as an s-channel resonance, and report the regions of parameter space where colorphilic gravitons have not yet been excluded by LHC-13 data but still may be discovered in the dijet channel at LHC-14 for integrated luminosities of 0.3, 1, and 3 ab$^{-1}$. We then delineate which of those regions remain accessible to future collider searches, once one accounts for applicability of the narrow-width approximation, detector mass resolution, and self-consistency according to tree-level partial-wave unitarity. We discover that--despite the strong constraints unitarity imposes on collider searches--the colorphilic graviton remains potentially discoverable in the LHC dijet channel. A means of investigation would be to apply the color discriminant variable (CDV), a dimensionless combination of quantities (cross-section, decay width, and invariant mass) that can be quickly measured after the discovery of a dijet resonance. Previous publications have demonstrated the CDV's utility when applied to theories containing Z', colorons, excited quarks, and diquarks. We extend this analysis to the colorphilic graviton by applying the CDV to the appropriate region of parameter space. We conclude that resolvable, discoverable dijet resonances consistent with colorphilic gravitons span a narrower range of masses than those consistent with leptophobic Z' models, and can be distinguished from those originating from coloron, excited quark, and diquark models.

hep-ph

$R_K$ anomalies and simplified limits on $Z'$ models at the LHC

The LHCb collaboration has recently reported a 2.5 $σ$ discrepancy with respect to the predicted value in a test of lepton universality in the ratio $R_{K^*}= \hbox{BR}(B \to K^* μ^+ μ^-) / \hbox{BR}(B \to K^* e^+ e^-)$. Coupled with an earlier observation of a similar anomaly in $R_{K}$, this has generated significant excitement. A number of new physics scenarios have been proposed to explain the anomaly. In this work we consider simplified limits on $Z'$ models from ATLAS and CMS searches for new resonances in dilepton and dijet modes, and we use the simplified limits variable $ζ$ to correlate the results of the resonance and B-decay experiments. By examining minimal $Z'$ models that can accomodate the observed LHCb results, we show that the high-mass resonance search results are begining to be sensitive to these models and that future results will be more informative.

hep-ph