Publications
Spin-2 Kaluza-Klein scattering in a stabilized warped background
| Title | Spin-2 Kaluza-Klein scattering in a stabilized warped background |
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| Authors | R. Sekhar Chivukula, Dennis Foren, Kirtimaan A. Mohan, Dipan Sengupta, and Elizabeth H. Simmons |
| Abstract | 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 appendixes, the full set of sum rules ensuring proper high-energy growth of all $2\rightarrow2$ massive spin-2 scattering amplitudes. |
| Publish Date | 16 February 2023 |
| Links | Phys. Rev. D 107, 035015, arXiv:2206.10628 |
Spin-2 Kaluza-Klein mode scattering in models with a massive radion
| Title | Spin-2 Kaluza-Klein mode scattering in models with a massive radion |
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| Authors | R. Sekhar Chivukula, Dennis Foren, Kirtimaan A. Mohan, Dipan Sengupta, and Elizabeth H. Simmons |
| Abstract | 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. |
| Publish Date | 24 May 2021 |
| Links | Phys. Rev. D 103, 095024, arXiv:2104.08169 |
Scattering Amplitudes in Theories of Compactified Gravity
| Title | Scattering Amplitudes in Theories of Compactified Gravity |
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| Authors | Dennis Foren |
| Abstract | In this dissertation we discuss the properties of matrix elements describing the scattering of massive spin-2 particles in theories of compactified gravity. Our primary result is the calculation of 2-to-2 massive spin-2 Kaluza-Klein (KK) mode scattering matrix elements in the Randall-Sundrum 1 (RS1) model and the demonstration that those matrix elements grow no faster than $\mathcal{O}(s)$ irrespective of the KK mode numbers and helicities considered. Because this calculation requires summing infinitely-many spin-2 mediated diagrams which each diverge like $\mathcal{O}(s^5)$, overall $\mathcal{O}(s)$ growth is only attained through cancellations between these diagrams. This in turn requires intricate cancellations between infinitely-many KK mode masses and couplings. We derive these sum rules, including their generalization to fully inelastic processes. We also consider these matrix elements in the five-dimensional orbifolded torus (5DOT) and large $kr_c$ limits, investigate the impact of including only finitely-many diagrams in the calculation (as measured via truncation error), and calculate the five-dimensional strong coupling scale $\Lambda_{\pi}\equiv M_{\text{Pl}}\,e^{-kr_c\pi}$ via the four-dimensional scattering calculation. |
| Publish Date | 01 August 2020 |
| Links | Michigan State University, arXiv:2008.09996 |
Massive spin-2 scattering amplitudes in extra-dimensional theories
| Title | Massive spin-2 scattering amplitudes in extra-dimensional theories |
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| Authors | R. Sekhar Chivukula, Dennis Foren, Kirtimaan A. Mohan, Dipan Sengupta, and Elizabeth H. Simmons |
| Abstract | 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 $\mathcal{O}(s^5)$, the full results grow only as $\mathcal{O}(s)$. 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. |
| Publish Date | 08 April 2020 |
| Links | Phys. Rev. D 101, 075013, arXiv:2002.12458 |
Scattering Amplitudes of Massive Spin-2 Kaluza-Klein States Grow Only as $\mathcal{O}(s)$
| Title | Scattering Amplitudes of Massive Spin-2 Kaluza-Klein States Grow Only as $\mathcal{O}(s)$ |
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| Authors | R. Sekhar Chivukula, Dennis Foren, Kirtimaan A. Mohan, Dipan Sengupta, and Elizabeth H. Simmons |
| Abstract | We present the results of the first complete calculation of the tree-level $2\rightarrow2$ high-energy scattering amplitudes of the longitudinal modes of massive spin-2 Kaluza-Klein (KK) states, both in the case where the internal space is a torus and in the Randall-Sundrum model where the internal space has constant negative curvature. While individual contributions to this amplitude grow as $\mathcal{O}(s^5)$, we demonstrate explicitly that intricate cancellations occur between different contributions, reducing the growth to $\mathcal{O}(s)$, a slower rate of growth than previously argued in the literature. These cancellations require subtle relationships between the masses of the Kaluza-Klein states and their interactions, and reflect the underlying higher-dimensional diffeomorphism invariance. Our results provide fresh perspective on the range of validity of (effective) field theories involving massive spin-2 KK particles, with significant implications for the theory and phenomenology of these states. |
| Publish Date | 06 March 2020 |
| Links | Phys. Rev. D 101, 055013, arXiv:1906.11098 |
Sum rules for massive spin-2 Kaluza-Klein elastic scattering amplitudes
| Title | Sum rules for massive spin-2 Kaluza-Klein elastic scattering amplitudes |
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| Authors | R. Sekhar Chivukula, Dennis Foren, Kirtimaan A. Mohan, Dipan Sengupta, and Elizabeth H. Simmons |
| Abstract | 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 five-dimensional gravity, which would naively grow like $\mathcal{O}(s^5)$, grow only like $\mathcal{O}(s)$. Since the individual contributions to these amplitudes do grow like $\mathcal{O}(s^5)$, 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 $\mathcal{O}(s^5)$ and $\mathcal{O}(s^4)$ 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 $\mathcal{O}(s^3)$ and $\mathcal{O}(s^2)$ illustrate the essential role of the radion mode of the extradimensional metric, which is the dynamical mode related to the size of the internal space. |
| Publish Date | 18 December 2019 |
| Links | Phys. Rev. D 100, 115033, arXiv:1910.06159 |
Colorphilic spin-2 resonances in the LHC dijet channel
| Title | Colorphilic spin-2 resonances in the LHC dijet channel |
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| Authors | R. Sekhar Chivukula, Dennis Foren, and Elizabeth H. Simmons |
| Abstract | 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, mass resolution of the detector, 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, a dimensionless combination of quantities (production cross-section, total decay width, and invariant mass) that can be quickly measured after the discovery of a dijet resonance. Previous publications have demonstrated the color discriminant variable's utility when applied to theories containing vector bosons (colorons, $Z^{\prime}$), excited quarks, and diquarks. We extend this analysis to the case of the colorphilic graviton by applying the color discriminant variable 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 $Z^{\prime}$ models, and can be distinguished from those originating from coloron, excited quark, and diquark models. |
| Publish Date | 28 September 2018 |
| Links | Phys. Scr. 93 115301, arXiv:1706.02502 |
Direct search implications for a custodially-embedded composite top
| Title | Direct search implications for a custodially-embedded composite top |
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| Authors | R. Sekhar Chivukula, Roshan Foadi, Dennis Foren, and Elizabeth H. Simmons |
| Abstract | We assess current experimental constraints on the bidoublet + singlet model of top compositeness previously proposed in the literature. This model extends the Standard Model’s spectrum by adding a custodially embedded vectorlike electroweak bidoublet of quarks and a vectorlike electroweak singlet quark. While either of those states alone would produce a model in tension with constraints from precision electroweak data, in combination they can produce a viable model. We show that current precision electroweak data, in the wake of the Higgs discovery, accommodate the model and we explore the impact of direct collider searches for the partners of the top quark. |
| Publish Date | 05 July 2016 |
| Links | Phys. Rev. D 94, 014002, arXiv:1605.06088 |