Pairwise Multiparticle States and the Monopole Unitarity Puzzle.

We suggest a novel resolution for a decades old mystery-what happens when a positron scatters off a minimal grand-unification-theory monopole in an s wave, a puzzle first discussed by Callan in 1983. Using the language of on shell amplitudes and pairwise helicity we suggest that the final state contains two up quarks and a down quark in an entangled "pairwise" multiparticle state-the only particle final state that satisfies angular momentum and gauge charge conservation. The cross section for this process is as large as in the original Rubakov-Callan effect, only suppressed by the QCD scale. The final state we find cannot be seen in Callan's truncated 2D theory, since our new pairwise state appears only in more than two dimensions.

Z-Portal Continuum Dark Matter.

We examine the possibility that dark matter (DM) consists of a gapped continuum, rather than ordinary particles. A weakly interacting continuum (WIC) model, coupled to the standard model via a Z portal, provides an explicit realization of this idea. The thermal DM relic density in this model is naturally consistent with observations, providing a continuum counterpart of the "WIMP miracle." Direct detection cross sections are strongly suppressed compared to ordinary Z-portal WIMP, thanks to a unique effect of the continuum kinematics. Continuum DM states decay throughout the history of the Universe, and observations of cosmic microwave background place constraints on potential late decays. Production of WICs at colliders can provide a striking cascade-decay signature. We show that a simple Z-portal WIC model provides a fully viable DM candidate consistent with all current experimental constraints.

Completing Multiparticle Representations of the Poincaré Group.

We extend the definition of asymptotic multiparticle states of the S-matrix beyond the tensor products of one-particle states. We identify new quantum numbers called pairwise helicities, or q_{ij}, associated with asymptotically separated pairs of particles. We first treat all single particles and particle pairs independently, allowing us to generalize the Wigner construction, and ultimately projecting onto the physical states. Our states reduce to tensor product states for vanishing q_{ij}, while for vanishing spins they reproduce Zwanziger's scalar dyon states. This construction yields the correct asymptotic states for the scattering of electric and magnetic charges, with pairwise helicity identified as q_{ij}=e_{i}g_{j}-e_{j}g_{i}.

Crunching Dilaton, Hidden Naturalness.

We introduce a new approach to the Higgs naturalness problem. The Higgs mixes with the dilaton of a conformal field theory (CFT) sector whose true ground state has a large negative vacuum energy. If the Higgs vacuum expectation value is nonzero and below O(TeV), the CFT admits a second metastable vacuum, where the expansion history of the Universe is conventional. As a result, only Hubble patches with unnaturally small values of the Higgs mass do not immediately crunch. The main experimental prediction of this mechanism is a dilaton in the 0.1-10 GeV range that mixes with the Higgs and can be detected at future colliders and experiments searching for weakly coupled particles.

Demonstration of Confinement and Chiral Symmetry Breaking in SO(N_{c}) Gauge Theories.

We demonstrate that SO(N_{c}) gauge theories with matter fields in the vector representation confine due to monopole condensation and break the SU(N_{F}) chiral symmetry to SO(N_{F}) via the quark bilinear. Our results are obtained by perturbing the N=1 supersymmetric theory with anomaly-mediated supersymmetry breaking.

Generating a Higgs Potential Quartic Term.

We present a simple mechanism for generating a Higgs quartic in composite Higgs models without a corresponding quadratic term. This quartic term will originate from a Higgs dependent kinetic mixing between additional fermionic states. The mechanism can be naturally embedded to models with maximal symmetry as well as twin Higgs models. The resulting twin Higgs models will have a fully natural realistic Higgs potential, where the quartic mechanism will serve as the only source for the Z_{2} breaking, while the top and gauge sectors can remain exactly Z_{2} invariant.

Emergence of Maximal Symmetry.

An emergent global symmetry of the composite sector (called maximal symmetry) can soften the ultraviolet behavior of the Higgs potential and also significantly modify its structure. We explain the conditions for the emergence of maximal symmetry as well as its main consequences and present two simple implementations. In both cases the emergence of maximal symmetry is enforced by the structure of the gauge symmetries.

Long-lived particles at the energy frontier: the MATHUSLA physics case.

We examine the theoretical motivations for long-lived particle (LLP) signals at the LHC in a comprehensive survey of standard model (SM) extensions. LLPs are a common prediction of a wide range of theories that address unsolved fundamental mysteries such as naturalness, dark matter, baryogenesis and neutrino masses, and represent a natural and generic possibility for physics beyond the SM (BSM). In most cases the LLP lifetime can be treated as a free parameter from the [Formula: see text]m scale up to the Big Bang Nucleosynthesis limit of [Formula: see text] m. Neutral LLPs with lifetimes above [Formula: see text]100 m are particularly difficult to probe, as the sensitivity of the LHC main detectors is limited by challenging backgrounds, triggers, and small acceptances. MATHUSLA is a proposal for a minimally instrumented, large-volume surface detector near ATLAS or CMS. It would search for neutral LLPs produced in HL-LHC collisions by reconstructing displaced vertices (DVs) in a low-background environment, extending the sensitivity of the main detectors by orders of magnitude in the long-lifetime regime. We study the LLP physics opportunities afforded by a MATHUSLA-like detector at the HL-LHC, assuming backgrounds can be rejected as expected. We develop a model-independent approach to describe the sensitivity of MATHUSLA to BSM LLP signals, and compare it to DV and missing energy searches at ATLAS or CMS. We then explore the BSM motivations for LLPs in considerable detail, presenting a large number of new sensitivity studies. While our discussion is especially oriented towards the long-lifetime regime at MATHUSLA, this survey underlines the importance of a varied LLP search program at the LHC in general. By synthesizing these results into a general discussion of the top-down and bottom-up motivations for LLP searches, it is our aim to demonstrate the exceptional strength and breadth of the physics case for the construction of the MATHUSLA detector.

Trigonometric Parity for Composite Higgs Models.

We identify trigonometric parity as the key ingredient behind models of neutral naturalness for the Higgs potential and show how to construct the minimal model realizing trigonometric parity. We show that any symmetric coset space readily includes such a trigonometric parity, which is simply a combination of a π/2 rotation along a broken direction and a Higgs parity transformation. The top sector can be extended such that this Z_{2} remains intact, which ensures the cancelation of the quadratic divergences in the Higgs potential, yielding the simplest model of neutral naturalness.

Kaluza-Klein Monopoles and their Zero Modes.

We find the conditions for the existence of fermionic zero modes of the fundamental representation in the background of a Kaluza-Klein (KK) monopole. We show that while there is no zero mode without a real mass, a normalizable zero mode appears once the real mass is sufficiently large. This provides an elegant explanation for the known decoupling of KK monopole effects in supersymmetric theories when a large real mass term is added. We also present an application where the correct counting of KK zero modes plays an essential role in understanding the nonperturbative effects determining the low-energy dynamics.

Maximally Symmetric Composite Higgs Models.

Maximal symmetry is a novel tool for composite pseudo Goldstone boson Higgs models: it is a remnant of an enhanced global symmetry of the composite fermion sector involving a twisting with the Higgs field. Maximal symmetry has far-reaching consequences: it ensures that the Higgs potential is finite and fully calculable, and also minimizes the tuning. We present a detailed analysis of the maximally symmetric SO(5)/SO(4) model and comment on its observational consequences.

Inflation from broken scale invariance.

We construct a model of inflation based on a low-energy effective theory of spontaneously broken global scale invariance. This provides a shift symmetry that protects the inflaton potential from quantum corrections. Since the underlying scale invariance is noncompact, arbitrarily large inflaton field displacements are readily allowed in the low-energy effective theory. A weak breaking of scale invariance by almost marginal operators provides a nontrivial inflaton minimum, which sets and stabilizes the final low-energy value of the Planck scale. The underlying scale invariance ensures that the slow-roll approximation remains valid over large inflaton displacements, and yields a scale invariant spectrum of perturbations, as required by the cosmic microwave background observations.

Dynamical R-parity violation.

We present a new paradigm for supersymmetric theories with R-parity violation (RPV). At high scale, R parity is conserved in the visible sector but spontaneously broken in the supersymmetry-breaking sector. The breaking is then dynamically mediated to the visible sector and is manifested via nonrenormalizable operators at low energy. Consequently, RPV operators originate from the Kähler potential rather than the superpotential, and are naturally suppressed by the supersymmetry-breaking scale, explaining their small magnitudes. A new set of nonholomorphic RPV operators is identified and found to often dominate over the standard RPV ones. We study the relevant low-energy constraints arising from baryon-number violating processes, proton decay, and flavor changing neutral currents, which may all be satisfied if a solution to the standard model flavor puzzle is incorporated. The chiral structure of the RPV operators implies new and distinct collider signatures, indicating the need to alter current techniques in searching for RPV at the LHC.

A naturally light dilaton and a small cosmological constant.

We present a non-supersymmetric theory with a naturally light dilaton. It is based on a 5D holographic description of a conformal theory perturbed by a close-to-marginal operator of dimension [Formula: see text] which develops a condensate. As long as the dimension of the perturbing operator remains very close to marginal (even for large couplings) a stable minimum at hierarchically small scales is achieved, where the dilaton mass squared is suppressed by [Formula: see text]. At the same time the cosmological constant in this sector is also suppressed by [Formula: see text], and thus it is parametrically smaller than in a broken SUSY theory. As a byproduct we also present an exact solution to the scalar-gravity system that can be interpreted as a new holographic realization of spontaneously broken conformal symmetry. Even though this metric deviates substantially from AdS space in the deep IR it still describes a non-linearly realized exactly conformal theory. We also display the effective potential for the dilaton for arbitrary holographic backgrounds.

Electroweak symmetry breaking from monopole condensation.

We argue that the electroweak symmetry of the standard model (SM) could be broken via condensation of magnetic monopole bilinears. We present an extension of the SM where this could indeed happen, and where the heavy top mass is also a consequence of the magnetic interactions.

New approach to the micro--Bmicro problem of gauge-mediated supersymmetry breaking.

We present a new approach to the microBmicro problem of gauge-mediated supersymmetry breaking. Rather than reducing the generically large contribution to Bmicro we point out that acceptable electroweak symmetry breaking can be achieved with micro{2}<

Towards a realistic model of Higgsless electroweak symmetry breaking.

We present a 5D gauge theory in warped space based on a bulk SU(2)L x SU(2)R x U(1)(B-L) gauge group where the gauge symmetry is broken by boundary conditions. The symmetry breaking pattern and the mass spectrum resemble that in the standard model (SM). To leading order in the warp factor the rho parameter and the coupling of the Z (S parameter) are as in the SM, while corrections are expected at the level of a percent. From the anti-de Sitter (AdS) conformal field theory point of view the model presented here can be viewed as the AdS dual of a (walking) technicolorlike theory, in the sense that it is the presence of the IR brane itself that breaks electroweak symmetry, and not a localized Higgs on the IR brane (which should be interpreted as a composite Higgs model). This model predicts the lightest W, Z, and gamma resonances to be at around 1.2 TeV, and no fundamental (or composite) Higgs particles.

Dimming supernovae without cosmic acceleration.

We present a simple model where photons propagating in extragalactic magnetic fields can oscillate into very light axions. The oscillations may convert some of the photons, departing a distant supernova, into axions, making the supernova appear dimmer and hence more distant than it really is. Averaging over different configurations of the magnetic field we find that the dimming saturates at about one-third of the light from the supernovae at very large redshifts. This results in a luminosity distance versus redshift curve almost indistinguishable from that produced by the accelerating Universe, if the axion mass and coupling scale are m approximately 10(-16) eV, M approximately 4 x 10(11) GeV. This phenomenon may be an alternative to the accelerating Universe for explaining supernova observations.