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.

The dynamics of a cosmological (de)confinement phase transition is studied in nearly conformally invariant field theories, where confinement is predominantly spontaneously generated and associated with a light "dilaton" field. We show how the leading contribution to the transition rate can be computed within the dilaton effective theory. In the context of Composite Higgs theories, we demonstrate that a simple scenario involving two renormalization-group fixed points can make the transition proceed much more rapidly than in the minimal scenario, thereby avoiding excessive dilution of matter abundances generated before the transition. The implications for gravitational wave phenomenology are discussed. In general, we find that more (less) rapid phase transitions are associated with weaker (stronger) gravitational wave signals. The various possible features of the strongly coupled composite Higgs phase transition discussed here can be concretely modeled at weak coupling within the AdS/CFT dual Randall-Sundrum extra-dimensional description, which offers important insights into the nature of the transition and its theoretical control. These aspects will be presented in a companion paper.

The appealing feature of inverse seesaw models is that the Standard Model (SM) neutrino mass emerges from the exchange of TeV scale singlets with sizable Yukawa couplings, which can be tested at colliders. However, the tiny Majorana mass splitting between TeV singlets, introduced to accommodate small neutrino masses, is left unexplained. Moreover, we argue that these models suffer from a structural limitation that prevents a successful leptogenesis if one insists on having unsuppressed Yukawa couplings and TeV scale singlets. In this work we propose a hybrid seesaw model, where we replace the mass splitting with a coupling to a high scale seesaw module including a TeV scalar. We show that this structure achieves the goal of filling both the above gaps with couplings of order unity.The necessary structure automatically arises embedding the seesaw mechanism in composite Higgs models, but may also be enforced by new gauge symmetries in a weakly-coupled theory. Our hybrid seesaw models have distinguishing features compared to the standard high scale type-I seesaw and inverse seesaw. Firstly, they have much richer phenomenology. Indeed, they generally predict new TeV scale physics (including scalars) potentially accessible at present and future colliders, whereas weakly-coupled versions may also have astrophysical and cosmological signatures due to the presence of a light Nambu-Goldstone boson coupled to neutrinos. Secondly, our scenario features an interesting interplay between high scale and TeV scale physics in leptogenesis and enlarges the range of allowed high scale singlet masses beyond the usual ∼ 10 9 − 10 15 GeV, without large hierarchies in the Yukawa couplings nor small mass splitting among the singlets.

We study the cosmological transition of 5D warped compactifications, from the high-temperature black-brane phase to the low-temperature Randall-Sundrum I phase. The transition proceeds via percolation of bubbles of IR-brane nucleating from the black-brane horizon. The violent bubble dynamics can be a powerful source of observable stochastic gravitational waves. While bubble nucleation is non-perturbative in 5D gravity, it is amenable to semiclassical treatment in terms of a “bounce” configuration interpolating between the two phases. We demonstrate how such a bounce configuration can be smooth enough to maintain 5D effective field theory control, and how a simple ansatz for it places a rigorous lower-bound on the transition rate in the thin-wall regime, and gives plausible estimates more generally. When applied to the Hierarchy Problem, the minimal Goldberger-Wise stabilization of the warped throat leads to a slow transition with significant supercooling. We demonstrate that a simple generalization of the Goldberger-Wise potential modifies the IR-brane dynamics so that the transition completes more promptly. Supercooling determines the dilution of any (dark) matter abundances generated before the transition, potentially at odds with data, while the prompter transition resolves such tensions. We discuss the impact of the different possibilities on the strength of the gravitational wave signals. Via AdS/CFT duality the warped transition gives a theoretically tractable holographic description of the 4D Composite Higgs (de)confinement transition. Our generalization of the Goldberger-Wise mechanism is dual to, and concretely models, our earlier proposal in which the composite dynamics is governed by separate UV and IR RG fixed points. The smooth 5D bounce configuration we introduce complements the 4D dilaton/radion dominance derivation presented in our earlier work.

We analyze signals at the Large Hadron Collider (LHC) from production and decay of Kaluza-Klein (KK) gravitons in the context of “extended” warped extra-dimensional models, where the standard model (SM) Higgs and fermion fields are restricted to be in-between the usual ultraviolet/Planck brane and a ∼ O(10) TeV (new, “intermediate”) brane, whereas the SM gauge fields (and gravity) propagate further down to the ∼ O(TeV) infrared brane. Such a framework suppresses flavor violation stemming from KK particle effects, while keeping the KK gauge bosons and gravitons accessible to the LHC. We find that the signals from KK graviton are significantly different than in the standard warped model. This is because the usually dominant decay modes of KK gravitons into top quark, Higgs and longitudinal W/Z particles are suppressed by the above spatial separation between these two sets of particles, thus other decay channels are allowed to shine themselves. In particular, we focus on two novel decay channels of the KK graviton. The first one is the decay into a pair of radions, each of which decays (dominantly) into a pair of SM gluons, resulting in a resonant 4-jet final state consisting of two pairs of dijet resonance. On the other hand, if the radion is heavier and/or KK gluon is lighter, then the KK graviton mostly decays into a KK gluon and a SM gluon. The resulting KK gluon has a significant decay branching fraction into radion and SM gluon, thereby generating (again) a 4-jet signature, but with a different underlying event topology, i.e., featuring now three different resonances. We demonstrate that the High-Luminosity LHC (HL-LHC) has sensitivity to KK graviton of (up to) ∼ 4 TeV in both channels, in the specific model with only gluon field (and gravity) propagating in the extended bulk, whereas it is unlikely to have sensitivity in the standard dijet resonance search channel from KK graviton decay into two gluons.

We develop an extension of the basic inverse seesaw model which addresses simultaneously two of its drawbacks, namely, the lack of explanation of the tiny Majorana mass term µ for the TeV-scale singlet fermions and the difficulty in achieving successful leptogenesis.Firstly, we investigate systematically leptogenesis within the inverse (and the related linear) seesaw models and show that a successful scenario requires either small Yukawa couplings, implying loss of experimental signals, and/or quasi-degeneracy among singlets mass of different generations, suggesting extra structure must be invoked. Then we move to the analysis of our new framework, which we refer to as hybrid seesaw. This combines the TeV degrees of freedom of the inverse seesaw with those of a high-scale (M N TeV) seesaw module in such a way as to retain the main features of both pictures: naturally small neutrino masses, successful leptogenesis, and accessible experimental signatures. We show how the required structure can arise from a more fundamental theory with a gauge symmetry or from warped extra dimensions/composite Higgs. We provide a detailed derivation of all the analytical formulae necessary to analyze leptogenesis in this new framework, and discuss the entire gamut of possibilities our scenario encompasses-including scenarios with singlet masses in the enlarged range M N ∼ 10 6 − 10 16 GeV. The idea of hybrid seesaw was proposed by us in arXiv:1804.06847; here, we substantially elaborate upon and extend earlier results.

We study an attractive scenario, “Sleptonic SUSY”, which reconciles the 125 GeV Higgs scalar and the non-observation of superpartners thus far with potentially pivotal roles for slepton phenomenology: providing viable ongoing targets for LHC discovery, incorporating a co-annihilation partner for detectable thermal relic dark matter, and capable of mediating the potential muon g − 2 anomaly. This is accomplished by a modestly hierarchical spectrum, with sub-TeV sleptons and electroweakinos and with multi-TeV masses for the other new states. We study new elements in the UV MSSM realization of Sleptonic SUSY based on higher-dimensional sequestering and the synergy between the resulting gaugino-mediation, hypercharge D-term mediation and Higgs-mediation of SUSY-breaking, so as to more fully capture the range of possibilities. This framework stands out by harmoniously solving the flavor, CP and μ − Bμ problems of the supersymmetric paradigm. We discuss its extension to orbifold GUTs, including gauge-coupling and b-tau unification. We also develop a non-minimal model with extra Higgs fields, in which the electroweak vacuum is more readily cosmologically stable against decay to a charge-breaking vacuum, allowing a broader range of sleptonic spectra than in the MSSM alone. We survey the rich set of signals possible at the LHC and future colliders, covering both R-parity conservation and violation, as well as for dark matter detection. While the multi-TeV squarks imply a Little Hierarchy Problem, intriguingly, small changes in parameter space to improve naturalness result in dramatic phase transitions to either electroweak-preservation or charge-breaking. In a Multiverse setting, the modest unnaturalness may then be explained by the “principle of living dangerously”.

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