<p>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. In particular, 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 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, provide 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 backreaction 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 will be addressed in forthcoming work.</p>

United States

R. Sekhar Chivukula

Australia

Joshua A. Gill

Kirtimaan A. Mohan

George Sanamyan

Dipan Sengupta

Elizabeth H. Simmons

Italy

Xing Wang

Limits on Kaluza-Klein portal dark matter models

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 <math><mi>O</mi><mo>(</mo><msup><mi>s</mi><mn>3</mn></msup><mo>)</mo></math> instead of <math><mi>O</mi><mo>(</mo><mi>s</mi><mo>)</mo></math>. 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 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.

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

SuperWIMPs are extremely weakly interacting massive particles that inherit their relic abundance from late decays of frozen-out parent particles. Within supersymmetric models, gravitinos and axinos represent two of the most well motivated superWIMPs. In this paper we revisit constraints on these scenarios from a variety of cosmological observations that probe their production mechanisms as well as the superWIMP kinematic properties in the early Universe. We consider in particular observables of Big Bang Nucleosynthesis and the Cosmic Microwave Background (spectral distortion and anisotropies), which limit the fractional energy injection from the late decays, as well as warm and mixed dark matter constraints derived from the Lyman- $$\alpha $$  <math> <mi>α</mi> </math>   forest and other small-scale structure observables. We discuss complementary constraints from collider experiments, and argue that cosmological considerations rule out a significant part of the gravitino and the axino superWIMP parameter space.

Meera Deshpande

Jan Hamann

Martin White

Anthony Williams

Yvonne Wong

Revisiting cosmological constraints on supersymmetric SuperWIMPs

A detailed and systematic formulation of Carrollian relativity is provided. Based on the transformations, first provided by Sengupta (Nuovo Cim, 54:512, 1966), we construct a mapping between Lorentz relativistic and Carrollian relativistic vectors. Using this map the Carroll theory is built from the standard Maxwell action. We show that we get self-consistent equations of motion from the action, both in electric and magnetic limits. We introduce Carroll electric and magnetic fields. A new set of maps is derived that connects Carroll electric and magnetic fields with the usual Maxwell ones and yields Carroll equations in terms of fields. Consistency of results with the potential formulation is shown. Carroll version of symmetries like duality, gauge, shift, Noether and boost are treated in details and their implications elaborated. Especially, boost symmetry provides a link to the various maps used in this paper.

India

Rabin Banerjee

Soumya Bhattacharya

Bibhas Majhi

Sengupta transformations and Carrollian relativistic theory

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 leads 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 <math><mi>O</mi><mo>(</mo><mi>s</mi><mo>)</mo></math>, 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. We explicitly identify the symmetry algebra of the residual 5D diffeomorphisms of a Randall-Sundrum extra-dimensional theory.

Symmetries, spin-2 scattering amplitudes, and equivalence theorems in warped five-dimensional gravitational theories

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 <math><mi>O</mi><mo>(</mo><msup><mi>s</mi><mn>3</mn></msup><mo>)</mo></math> [where <math><mi>s</mi></math> 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 <math><mi>O</mi><mo>(</mo><mi>s</mi><mo>)</mo></math>. 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 wave functions. 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.

Scattering amplitudes of massive spin-2 Kaluza-Klein states with matter

A recent paper [1] within a phenomenological dark matter framework with a massive graviton in the external state argued that a divergence with increasing center-of-momentum energy arising from the longitudinal polarizations of the graviton. In this paper we point out that in processes such as graviton-photon production from matter annihilation, <math><mrow><mi>f</mi><mover><mrow><mi>f</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>→</mo><mi>G</mi><mi>γ</mi></mrow></math>, no such anomalous divergences occur at tree level. This then applies to other tree-level amplitudes related by crossing symmetry such as <math><mrow><mi>γ</mi><mi>f</mi><mo>→</mo><mi>G</mi><mi>f</mi></mrow></math>, <math><mrow><mi>G</mi><mi>f</mi><mo>→</mo><mi>γ</mi><mi>f</mi></mrow></math>, <math><mrow><mi>γ</mi><mover><mrow><mi>f</mi></mrow><mrow><mo>¯</mo></mrow></mover><mo>→</mo><mi>G</mi><mover><mrow><mi>f</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow></math>, <math><mi>f</mi><mo>→</mo><mi>f</mi><mi>G</mi><mi>γ</mi></math> and so on. We show this by explicitly computing the relevant tree-level diagrams, where we find that delicate cancellations ensure that all anomalously growing terms are well-regulated. Effectively at tree level this is consistent with the operation of a Ward identity associated with the external photon for such amplitudes. The same tree-level results apply if the photon is replaced by a gluon. These results have important consequences for model construction in areas including dark matter, gravity and high-energy physics.

Anthony G. Williams

Graviton-photon production with a massive spin-2 particle

Kirtimaan Mohan

Tim Tait

Bin Yan

C.P. Yuan

Erratum to: Direct detection and LHC constraints on a t-channel simplified model of Majorana dark matter at one loop

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 <math><mn>2</mn><mo>→</mo><mn>2</mn></math> massive spin-2 scattering amplitudes.

Dennis Foren

Spin-2 Kaluza-Klein scattering in a stabilized warped background

Leptonic signatures of Dark Matter (DM) are one of the cleanest ways to discover such a secluded form of matter at high energy colliders. We explore the full parameter space relevant to multi-lepton (2- and 3-lepton) signatures at the Large Hadron Collider (LHC) from representative minimal consistent models with scalar and fermion DM. In our analysis, we suggest a new parametrisation of the model parameter spaces in terms of the DM mass and mass differences between DM and its multiplet partners. This parametrisation allows us to explore properties of DM models in their whole parameter space. This approach is generic and quite model-independent since the mass differences are related to the couplings of the DM to the Standard Model (SM) sector. We establish the most up-to-date LHC limits on the inert 2-Higgs Doublet Model (i2HDM) and Minimal Fermion DM (MFDM) model parameter spaces, by using the complementary information stemming from 2- and 3-lepton signatures. We provide a map of LHC efficiencies and cross-section limits for such 2- and 3-lepton signatures allowing one to easily make model-independent reinterpretations of LHC results for analogous classes of models. We also present combined constraints from the LHC, DM relic density and direct search experiments indicating the current status of the i2HDM and MFDM model.