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This document is comprised of a collection of updated preliminary parameters for the key parts of the muon collider. The updated preliminary parameters follow on from the October 2023 Tentative Parameters Report. Particular attention has been given to regions of the facility that are believed to hold greater technical uncertainty in their design and that have a strong impact on the cost and power consumption of the facility. The data is collected from a collaborative spreadsheet and transferred to overleaf.

We study the theory of a scalar in the fundamental representation of the internal supergroup $SU(N|M)$. Remarkably, for $M=N+1$ its tree-level mass does not receive quantum corrections at one loop from either self-coupling or interactions with gauge bosons and fermions. This property comes at the price of introducing both degrees of freedom with wrong statistics and with wrong sign kinetic terms. We detail a method to break $SU(N|M)$ down to its bosonic subgroup through a Higgs-like mechanism, allowing for the partial decoupling of the dangerous modes, and study the associated vacuum structure up to one loop., Comment: 32 pages + appendices

We show that the mass of a scalar field transforming in the fundamental of an $SU(N|N+1)$ supergroup internal symmetry is protected against one-loop corrections from quartic, gauge, and yukawa interactions. Although the negative-norm states responsible for this protection are likely fatal to a unitary interpretation of the theory, such ultraviolet insensitivity may open a new avenue to understanding the lightness of the Higgs., Comment: 5 pages

The extra-dimensional axion solves the strong CP problem while largely circumventing the quality problem that plagues its four-dimensional counterparts. Such high quality can be clearly understood in terms of the generalized global symmetries of the higher-dimensional theory. We emphasize that an electric one-form symmetry is entirely responsible for protecting the potential of axions arising from 5D gauge theories and use this to systematically characterize the extra-dimensional axion quality problem. We identify three ways of breaking this one-form symmetry to generate an axion potential: adding electrically charged matter, gauging a magnetic higher-form symmetry, and turning on an ABJ anomaly. In the latter case, we identify new ways of generating an axion potential via extra-dimensional magnetic monopoles. We also discuss how the axion is modified if the protective electric one-form symmetry is itself gauged. Finally, we relate these effects to gravitational expectations for the quality problem via generalized weak gravity conjectures. The clarity that generalized symmetries bring to the extra-dimensional axion quality problem highlights their relevance to particle phenomenology., Comment: 10 pages, 1 table

How can one fully harness the power of physics encoded in relativistic $N$-body phase space? Topologically, phase space is isomorphic to the product space of a simplex and a hypersphere and can be equipped with explicit coordinates and a Riemannian metric. This natural structure that scaffolds the space on which all collider physics events live opens up new directions for machine learning applications and implementation. Here we present a detailed construction of the phase space manifold and its differential line element, identifying particle ordering prescriptions that ensure that the metric satisfies necessary properties. We apply the phase space metric to several binary classification tasks, including discrimination of high-multiplicity resonance decays or boosted hadronic decays of electroweak bosons from QCD processes, and demonstrate powerful performance on simulated data. Our work demonstrates the many benefits of promoting phase space from merely a background on which calculations take place to being geometrically entwined with a theory's dynamics., Comment: 39 pages, 15 figures; added references; corrected typos; minor clarification of some texts; added another possibility to generalize the metric

The baryon acoustic oscillation (BAO) analysis from the first year of data from the Dark Energy Spectroscopic Instrument (DESI), when combined with data from the cosmic microwave background (CMB), has placed an upper-limit on the sum of neutrino masses, $\sum m_\nu < 70$ meV (95%). In addition to excluding the minimum sum associated with the inverted hierarchy, the posterior is peaked at $\sum m_\nu = 0$ and is close to excluding even the minumum sum, 58 meV at 2$\sigma$. In this paper, we explore the implications of this data for cosmology and particle physics. The sum of neutrino mass is determined in cosmology from the suppression of clustering in the late universe. Allowing the clustering to be enhanced, we extended the DESI analysis to $\sum m_\nu < 0$ and find $\sum m_\nu = - 160 \pm 90$ meV (68%), and that the suppression of power from the minimum sum of neutrino masses is excluded at 99% confidence. We show this preference for negative masses makes it challenging to explain the result by a shift of cosmic parameters, such as the optical depth or matter density. We then show how a result of $\sum m_\nu =0$ could arise from new physics in the neutrino sector, including decay, cooling, and/or time-dependent masses. These models are consistent with current observations but imply new physics that is accessible in a wide range of experiments. In addition, we discuss how an apparent signal with $\sum m_\nu < 0$ can arise from new long range forces in the dark sector or from a primordial trispectrum that resembles the signal of CMB lensing., Comment: 42 pages, 6 figures, 1 table; v2: minor corrections

Anomaly detection is a promising, model-agnostic strategy to find physics beyond the Standard Model. State-of-the-art machine learning methods offer impressive performance on anomaly detection tasks, but interpretability, resource, and memory concerns motivate considering a wide range of alternatives. We explore using the 2-Wasserstein distance from optimal transport theory, both as an anomaly score and as input to interpretable machine learning methods, for event-level anomaly detection at the Large Hadron Collider. The choice of ground space plays a key role in optimizing performance. We comment on the feasibility of implementing these methods in the L1 trigger system., Comment: 18 pages, 2 figures, 3 tables; added references, figure, and table entries; Submission to SciPost

Effective field theories (EFTs) of heavy particles coupled to the inflaton are rife with operator redundancies, frequently obscured by sensitivity to both boundary terms and field redefinitions. We initiate a systematic study of these redundancies by establishing a minimal operator basis for an archetypal example, the abelian gauge-Higgs-inflaton EFT. Working up to dimension 9, we show that certain low-dimensional operators are entirely redundant and identify new non-redundant operators with potentially interesting cosmological collider signals. Our methods generalize straightforwardly to other EFTs of heavy particles coupled to the inflaton., Comment: 31 pages, 4 figures

We develop a generalized field space geometry for higher-derivative scalar field theories, expressing scattering amplitudes in terms of a covariant geometry on the all-order jet bundle. The incorporation of spacetime and field derivative coordinates solves complications due to higher-order derivatives faced by existing approaches to field space geometry. We identify a jet bundle analog to the field space metric that, besides field redefinitions, exhibits invariance under total derivatives. The invariance consequently extends to its amplitude contributions and the canonical covariant geometry., Comment: 7+8 pages. v2: Journal version

We present a formulation of scalar effective field theories in terms of the geometry of Lagrange spaces. The horizontal geometry of the Lagrange space generalizes the Riemannian geometry on the scalar field manifold, inducing a broad class of affine connections that can be used to covariantly express and simplify tree-level scattering amplitudes. Meanwhile, the vertical geometry of the Lagrange space characterizes the physical validity of the effective field theory, as a torsion component comprises strictly higher-point Wilson coefficients. Imposing analyticity, unitarity, and symmetry on the theory then constrains the signs and sizes of derivatives of the torsion component, implying that physical theories correspond to a special class of vertical geometry., Comment: 35 pages, 1 figure. v2: Journal version

We develop a diagrammatic approach to effective field theories (EFTs) corresponding to deep neural networks at initialization, which dramatically simplifies computations of finite-width corrections to neuron statistics. The structures of EFT calculations make it transparent that a single condition governs criticality of all connected correlators of neuron preactivations. Understanding of such EFTs may facilitate progress in both deep learning and field theory simulations., Comment: 7+13 pages, 5 figures

We revisit the effective field theory of the two Higgs doublet model at tree level. The introduction of a novel basis in the UV theory allows us to derive matching coefficients in the effective description that resum important contributions from the Higgs vacuum expectation value. The new basis typically provides a significantly better approximation of the full theory prediction than the traditional approach that utilizes the Higgs basis, particularly for alignment away from the decoupling limit., Comment: 39 pages, 10 figures

The 2021-22 High-Energy Physics Community Planning Exercise (a.k.a. ``Snowmass 2021'') was organized by the Division of Particles and Fields of the American Physical Society. Snowmass 2021 was a scientific study that provided an opportunity for the entire U.S. particle physics community, along with its international partners, to identify the most important scientific questions in High Energy Physics for the following decade, with an eye to the decade after that, and the experiments, facilities, infrastructure, and R&D needed to pursue them. This Snowmass summary report synthesizes the lessons learned and the main conclusions of the Community Planning Exercise as a whole and presents a community-informed synopsis of U.S. particle physics at the beginning of 2023. This document, along with the Snowmass reports from the various subfields, will provide input to the 2023 Particle Physics Project Prioritization Panel (P5) subpanel of the U.S. High-Energy Physics Advisory Panel (HEPAP), and will help to guide and inform the activity of the U.S. particle physics community during the next decade and beyond., Comment: 75 pages, 3 figures, 2 tables. This is the first chapter and summary of the full report of the Snowmass 2021 Workshop. This version fixes an important omission from Table 2, adds two references that were not available at the time of the original version, fixes a minor few typos, and adds a small amount of material to section 1.1.3

We summarize recent progress in the development, application, and understanding of effective field theories and highlight promising directions for future research. This Report is prepared as the TF02 "Effective Field Theory" topical group summary for the Theory Frontier as part of the Snowmass 2021 process., Comment: 12 pages

We summarize the state of Beyond the Standard Model (BSM) model building in particle physics for Snowmass 2021, focusing mainly on several whitepaper contributions to BSM model building (TF08) and closely related areas., Comment: 44 pages, 1 figure, Submitted to the Proceedings of the US Community Study on the Future of Particle Physics (Snowmass 2021). Topical Group Report for TF08 - BSM Model Building

This is the Snowmass2021 Energy Frontier (EF) Beyond the Standard Model (BSM) report. It combines the EF topical group reports of EF08 (Model-specific explorations), EF09 (More general explorations), and EF10 (Dark Matter at Colliders). The report includes a general introduction to BSM motivations and the comparative prospects for proposed future experiments for a broad range of potential BSM models and signatures, including compositeness, SUSY, leptoquarks, more general new bosons and fermions, long-lived particles, dark matter, charged-lepton flavor violation, and anomaly detection., Comment: 108 pages + 38 pages references and appendix, 37 figures, Report of the Topical Group on Beyond the Standard Model Physics at Energy Frontier for Snowmass 2021. The first nine authors are the Conveners, with Contributions from the other authors

We assess the state of naturalness in high-energy physics and summarize recent approaches to the three major naturalness problems: the cosmological constant problem, the electroweak hierarchy problem, and the strong CP problem., Comment: 43 pages, contribution to Snowmass 2021

Many well-motivated extensions of the Standard Model predict the existence of new light species that may have been produced in the early universe. Prominent examples include axions, sterile neutrinos, gravitinos, dark photons, and more. The gravitational influence of light relics leaves imprints in the cosmic microwave background fluctuations, the large-scale structure of the universe and the primordial element abundances. In this paper, we detail the physics of cosmological light relics, and describe how measurements of their relic density and mass serve as probes of physics beyond the Standard Model. A measurement of the light relic density at the precision of upcoming cosmological surveys will point the way toward new physics or severely constrain the range of viable extensions to the Standard Model., Comment: Contribution to Snowmass 2021. 59 pages, 12 figures

A program to build a lepton-collider Higgs factory, to precisely measure the couplings of the Higgs boson to other particles, followed by a higher energy run to establish the Higgs self-coupling and expand the new physics reach, is widely recognized as a primary focus of modern particle physics. We propose a strategy that focuses on a new technology and preliminary estimates suggest that can lead to a compact, affordable machine. New technology investigations will provide much needed enthusiasm for our field, resulting in trained workforce. This cost-effective, compact design, with technologies useful for a broad range of other accelerator applications, could be realized as a project in the US. Its technology innovations, both in the accelerator and the detector, will offer unique and exciting opportunities to young scientists. Moreover, cost effective compact designs, broadly applicable to other fields of research, are more likely to obtain financial support from our funding agencies., Comment: 11 pages, 2 figures, contribution to Snowmass 2021

The International Linear Collider (ILC) is on the table now as a new global energy-frontier accelerator laboratory taking data in the 2030s. The ILC addresses key questions for our current understanding of particle physics. It is based on a proven accelerator technology. Its experiments will challenge the Standard Model of particle physics and will provide a new window to look beyond it. This document brings the story of the ILC up to date, emphasizing its strong physics motivation, its readiness for construction, and the opportunity it presents to the US and the global particle physics community., Comment: 356 pages, Large pdf file (40 MB) submitted to Snowmass 2021; v2 references to Snowmass contributions added, additional authors; v3 references added, some updates, additional authors

The perspective of designing muon colliders with high energy and luminosity, which is being investigated by the International Muon Collider Collaboration, has triggered a growing interest in their physics reach. We present a concise summary of the muon colliders potential to explore new physics, leveraging on the unique possibility of combining high available energy with very precise measurements., Comment: 21 pages, 7 figures; Contribution to Snowmass 2021

We sketch recent progress and promising future directions for research connected with the strong CP problem. Topics surveyed include axion dark matter substructure and its gravitational detection; axion model building and the quality problem; experimental tests of ultraviolet solutions; and connections to lattice QCD., Comment: 5 pages, contribution to Snowmass 2021

Scattering amplitudes in quantum field theory are independent of the field parameterization, which has a natural geometric interpretation as a form of `coordinate invariance.' Amplitudes can be expressed in terms of Riemannian curvature tensors, which makes the covariance of amplitudes under non-derivative field redefinitions manifest. We present a generalized geometric framework that extends this manifest covariance to $all$ allowed field redefinitions. Amplitudes satisfy a recursion relation that closely resembles the application of covariant derivatives to increase the rank of a tensor. This allows us to argue that (tree-level) amplitudes possess a notion of `on-shell covariance,' in that they transform as a tensor under any allowed field redefinition up to a set of terms that vanish when the equations of motion and on-shell momentum constraints are imposed. We highlight a variety of immediate applications to effective field theories., Comment: 6 pages

Selection rules arising from accidental or broken symmetries may be sufficiently obscure that their agency is hidden, leading to the appearance of "magic zeroes" -- quantities that are suppressed without apparent recourse to a symmetry explanation. Magic zeroes and their corresponding hidden symmetries may shed new light on parametric hierarchies in the Standard Model and beyond. We identify the hidden symmetry responsible for a recently-discovered magic zero, the vanishing of the putative leading contribution to the anomalous dipole moments of the muon upon integrating out weak doublet and singlet vector-like fermions. Some of the tools involved -- spurion analysis leveraging discrete symmetries of the free theory, field redefinitions, spectator fields, and non-supersymmetric non-renormalization theorems -- may prove useful in the hunt for new magic zeroes and their hidden symmetries., Comment: 23 pages + appendix

Which is the best metric for the space of collider events? Motivated by the success of the Energy Mover's Distance in characterizing collider events, we explore the larger space of unbalanced optimal transport distances, of which the Energy Mover's Distance is a particular case. Geometric and computational considerations favor an unbalanced optimal transport distance known as the Hellinger-Kantorovich distance, which possesses a Riemannian structure that lends itself to efficient linearization. We develop the particle linearized unbalanced Optimal Transport (pluOT) framework for collider events based on the linearized Hellinger-Kantorovich distance and demonstrate its efficacy in boosted jet tagging. This provides a flexible and computationally efficient optimal transport framework ideally suited for collider physics applications., Comment: 17 pages, 5 figures, 3 tables

We initiate the study of a new class of beyond the Standard Model states that we call "Loryons." They have the defining characteristic of being non-decoupling, in the sense that their physical mass is dominated by a contribution from the vacuum expectation value of the Higgs boson. The stakes are high: the discovery of a Loryon would tell us that electroweak symmetry must be non-linearly realized in the effective field theory of the Standard Model. Loryons have their masses bounded from above by perturbative unitarity considerations and thus define a finite parameter space for exploration. After providing a complete catalog of Loryon representations under mild assumptions, we turn to examining the constraints on the parameter space from Higgs couplings measurements, precision electroweak tests, and direct collider searches. We show that most fermionic candidates are already ruled out (with some notable exceptions), while much of the scalar Loryon parameter space is still wide open for discovery., Comment: 55 pages, 11 figures, 13 tables

We derive the scale of unitarity violation from the geometry of Effective Field Theory (EFT) extensions of the Standard Model Higgs sector. The high-energy behavior of amplitudes with more than four scalar legs depends on derivatives of geometric invariants with respect to the physical Higgs field $h$, such that higher-point amplitudes begin to reconstruct the scalar manifold away from our vacuum. In theories whose low-energy limit can be described by the Higgs EFT (HEFT) but not the Standard Model EFT (SMEFT), non-analyticities in the vicinity of our vacuum limit the radius of convergence of geometric invariants, leading to unitarity violation at energies below $4\pi v$. Our results unify approaches to the HEFT/SMEFT dichotomy based on unitarity, analyticity, and geometry, and more broadly illustrate the sense in which observables probe the geometry of an EFT. Along the way, we provide novel basis-independent results for Goldstone/Higgs boson scattering amplitudes expressed in terms of geometric covariant quantities., Comment: 42+12 pages, 6 figures. v2: Added references. v3: Journal version

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., Comment: 105 pages, 41 figures, 5 tables

Parity solutions to the strong CP problem are a compelling alternative to approaches based on Peccei-Quinn symmetry, particularly given the expected violation of global symmetries in a theory of quantum gravity. The most natural of these solutions break parity at a low scale, giving rise to a host of experimentally accessible signals. We assess the status of the simplest parity-based solution in light of LHC data and flavor constraints, highlighting the prospects for near-future tests at colliders, tabletop experiments, and gravitational wave observatories. The origin of parity breaking and associated gravitational effects play crucial roles, providing new avenues for discovery through EDMs and gravity waves. These experimental opportunities underline the promise of generalized parity, rather than Peccei-Quinn symmetry, as a robust and testable solution to the strong CP problem.

We initiate the study of gravitational wave (GW) signals from first-order phase transitions in supersymmetry-breaking hidden sectors. Such phase transitions often occur along a pseudo-flat direction universally related to supersymmetry (SUSY) breaking in hidden sectors that spontaneously break $R$-symmetry. The potential along this pseudo-flat direction imbues the phase transition with a number of novel properties, including a nucleation temperature well below the scale of heavy states (such that the temperature dependence is captured by the low-temperature expansion) and significant friction induced by the same heavy states as they pass through bubble walls. In low-energy SUSY-breaking hidden sectors, the frequency of the GW signal arising from such a phase transition is guaranteed to lie within the reach of future interferometers given existing cosmological constraints on the gravitino abundance. Once a mediation scheme is specified, the frequency of the GW peak correlates with the superpartner spectrum. Current bounds on supersymmetry are compatible with GW signals at future interferometers, while the observation of a GW signal from a SUSY-breaking hidden sector would imply superpartners within reach of future colliders., Comment: 66 pages latex, fifteen figures incorporated

We introduce an efficient framework for computing the distance between collider events using the tools of Linearized Optimal Transport (LOT). This preserves many of the advantages of the recently-introduced Energy Mover's Distance, which quantifies the "work" required to rearrange one event into another, while significantly reducing the computational cost. It also furnishes a Euclidean embedding amenable to simple machine learning algorithms and visualization techniques, which we demonstrate in a variety of jet tagging examples. The LOT approximation lowers the threshold for diverse applications of the theory of optimal transport to collider physics., Comment: 16 pages, 5 figures

There are two canonical approaches to treating the Standard Model as an Effective Field Theory (EFT): Standard Model EFT (SMEFT), expressed in the electroweak symmetric phase utilizing the Higgs doublet, and Higgs EFT (HEFT), expressed in the broken phase utilizing the physical Higgs boson and an independent set of Goldstone bosons. HEFT encompasses SMEFT, so understanding whether SMEFT is sufficient motivates identifying UV theories that require HEFT as their low energy limit. This distinction is complicated by field redefinitions that obscure the naive differences between the two EFTs. By reformulating the question in a geometric language, we derive concrete criteria that can be used to distinguish SMEFT from HEFT independent of the chosen field basis. We highlight two cases where perturbative new physics must be matched onto HEFT: (i) the new particles derive all of their mass from electroweak symmetry breaking, and (ii) there are additional sources of electroweak symmetry breaking. Additionally, HEFT has a broader practical application: it can provide a more convergent parametrization when new physics lies near the weak scale. The ubiquity of models requiring HEFT suggests that SMEFT is not enough., Comment: 69+28 pages, 6 figures, 33 footnotes. v2: Added minor clarifications, matches JHEP version

In a supersymmetric (SUSY) theory, the IR-contributions to the Higgs mass are calculable below the mediation scale $\Lambda_{\text{UV}}$ in terms of the IR field content and parameters. However, logarithmic sensitivity to physics at $\Lambda_{\text{UV}}$ remains. In this work we present a first example of a framework, dictated by symmetries, to supersoften these logarithms from the matter sector. The result is a model with finite, IR-calculable corrections to the Higgs mass. This requires the introduction of new fields -- the `lumberjacks' -- whose role is to screen the UV-sensitive logs. These models have considerably reduced fine-tuning, by more than an order of magnitude for high scale supersymmetry. This impacts interpretations of the natural parameter space, suggesting it may be premature to declare a naturalness crisis for high-scale SUSY., Comment: 5 pages

We consider aspects of tree and one-loop behavior in a generic 4d EFT of massless scalars, fermions, and vectors, with a particular eye to the high-energy limit of the Standard Model EFT at operator dimensions 6 and 8. First, we classify the possible Lorentz structures of operators and the subset of these that can arise at tree-level in a weakly coupled UV completion, extending the tree/loop classification through dimension 8 using functional methods. Second, we investigate how operators contribute to tree and one-loop helicity amplitudes, exploring the impact of non-renormalization theorems through dimension 8. We further observe that many dimension 6 contributions to helicity amplitudes, including rational parts, vanish exactly at one-loop level. This suggests the impact of helicity selection rules extends beyond one loop in non-supersymmetric EFTs., Comment: 29+1 pages, 5 figures, 6 tables

Massive $U(1)$ gauge theories featuring parametrically light vectors are suspected to belong in the Swampland of consistent EFTs that cannot be embedded into a theory of quantum gravity. We study four-dimensional, chiral $U(1)$ gauge theories that appear anomalous over a range of energies up to the scale of anomaly-cancelling massive chiral fermions. We show that such theories require to be UV-completed at a finite cutoff below which a radial mode must appear, and cannot be decoupled -- a St\"uckelberg limit does not exist. When the infrared fermion spectrum contains a mixed $U(1)$-gravitational anomaly, this class of theories provides a toy model of a boundary into the Swampland, for sufficiently small values of the vector mass. In this context, we show that the limit of a parametrically light vector comes at the cost of a quantum gravity scale that lies parametrically below $M_{Pl}$, and our result provides field theoretic evidence for the existence of a Swampland of EFTs that is disconnected from the subset of theories compatible with a gravitational UV-completion. Moreover, when the low energy theory also contains a $U(1)^3$ anomaly, the Weak Gravity Conjecture scale makes an appearance in the form of a quantum gravity cutoff for values of the gauge coupling above a certain critical size., Comment: 25 pages, 7 figures; v2: extended introduction

The persistence of the hierarchy problem points to a violation of effective field theory expectations. A compelling possibility is that this results from a physical breakdown of EFT, which may arise from correlations between ultraviolet (UV) and infrared (IR) physics. To this end, we study noncommutative field theory (NCFT) as a toy model of UV/IR mixing which generates an emergent infrared scale from ultraviolet dynamics. We explore the range of such theories where ultraviolet divergences are transmogrified into infrared scales, focusing particularly on the properties of Yukawa theory, where we identify a new infrared pole accessible in the $s$-channel of the Lorentzian theory. We further investigate the interplay between UV-finiteness and UV/IR mixing by studying properties of the softly-broken noncommutative Wess-Zumino model as soft terms are varied relative to the cutoff. While the Lorentz violation inherent to noncommutative theories may limit their direct application to the hierarchy problem, these toy models provide general lessons to guide the realization of UV/IR mixing in more realistic theories., Comment: 28+11 pages

We explore the prospects for bounding the weak scale using the weak gravity conjecture (WGC), addressing the hierarchy problem by violating the expectations of effective field theory. Building on earlier work by Cheung and Remmen, we construct models in which a super-extremal particle satisfying the electric WGC for a new Abelian gauge group obtains some of its mass from the Higgs, setting an upper bound on the weak scale as other UV-insensitive parameters are held fixed. Avoiding undue sensitivity of the weak scale to the parameters entering the bound implies that the super-extremal particle must lie at or below the weak scale. While the magnetic version of the conjecture implies additional physics entering around the same scale, we demonstrate that this need not correspond to a cutoff for the Higgs potential or otherwise trivialize the bound. We stress that linking the WGC to the weak scale necessarily involves new light particles coupled to the Higgs, implying a variety of experimentally accessible signatures including invisible Higgs decays and radiative corrections in the electroweak sector. These models also give rise to natural dark matter candidates, providing additional paths to discovery. In particular, collective effects in the dark matter plasma may provide a telltale sign of the Abelian gauge group responsible for bounding the weak scale., Comment: 28 pages, 3 figures

The hot dense environment of the early universe is known to have produced large numbers of baryons, photons, and neutrinos. These extreme conditions may have also produced other long-lived species, including new light particles (such as axions or sterile neutrinos) or gravitational waves. The gravitational effects of any such light relics can be observed through their unique imprint in the cosmic microwave background (CMB), the large-scale structure, and the primordial light element abundances, and are important in determining the initial conditions of the universe. We argue that future cosmological observations, in particular improved maps of the CMB on small angular scales, can be orders of magnitude more sensitive for probing the thermal history of the early universe than current experiments. These observations offer a unique and broad discovery space for new physics in the dark sector and beyond, even when its effects would not be visible in terrestrial experiments or in astrophysical environments. A detection of an excess light relic abundance would be a clear indication of new physics and would provide the first direct information about the universe between the times of reheating and neutrino decoupling one second later., Comment: 5 pages + references; 1 figure; science white paper submitted to the Astro2020 decadal survey

Particles beyond the Standard Model (SM) can generically have lifetimes that are long compared to SM particles at the weak scale. When produced at experiments such as the Large Hadron Collider (LHC) at CERN, these long-lived particles (LLPs) can decay far from the interaction vertex of the primary proton-proton collision. Such LLP signatures are distinct from those of promptly decaying particles that are targeted by the majority of searches for new physics at the LHC, often requiring customized techniques to identify, for example, significantly displaced decay vertices, tracks with atypical properties, and short track segments. Given their non-standard nature, a comprehensive overview of LLP signatures at the LHC is beneficial to ensure that possible avenues of the discovery of new physics are not overlooked. Here we report on the joint work of a community of theorists and experimentalists with the ATLAS, CMS, and LHCb experiments --- as well as those working on dedicated experiments such as MoEDAL, milliQan, MATHUSLA, CODEX-b, and FASER --- to survey the current state of LLP searches at the LHC, and to chart a path for the development of LLP searches into the future, both in the upcoming Run 3 and at the High-Luminosity LHC. The work is organized around the current and future potential capabilities of LHC experiments to generally discover new LLPs, and takes a signature-based approach to surveying classes of models that give rise to LLPs rather than emphasizing any particular theory motivation. We develop a set of simplified models; assess the coverage of current searches; document known, often unexpected backgrounds; explore the capabilities of proposed detector upgrades; provide recommendations for the presentation of search results; and look towards the newest frontiers, namely high-multiplicity "dark showers", highlighting opportunities for expanding the LHC reach for these signals.

We assess the current coverage and the future discovery potential of LHC searches for heavy Higgs bosons decaying into long-lived particles (LLPs), focusing primarily on the production of pairs of LLPs with hadronic final states. These signatures are generic in dark sectors where a heavy scalar decays into pairs of lighter states which subsequently mix with the Standard Model Higgs. We show that a handful of existing analyses provide broad coverage of LLP decay lengths ranging from millimeters to tens of meters, and explore the complementarity between searches for displaced and prompt final states in several simplified models. For both heavy singlet and heavy doublet scalars, LLP searches typically provide the leading sensitivity in current data and exhibit the strongest discovery potential in future LHC runs. We further translate the impact of these searches into the parameter space of various Twin Higgs models, demonstrating that LLP searches are a promising avenue for discovering a Twin Higgs with displaced decays. Finally, we propose a variety of additional search channels that would improve coverage of the second Higgs at the lifetime frontier., Comment: 37 pages, 12 figures. Matches version published in JHEP

In theories with discrete Abelian gauge groups, requiring that black holes be able to lose their charge as they evaporate leads to an upper bound on the product of a charged particle's mass and the cutoff scale above which the effective description of the theory breaks down. This suggests that a non-trivial version of the Weak Gravity Conjecture (WGC) may also apply to gauge symmetries that are discrete, despite there being no associated massless field, therefore pushing the conjecture beyond the slogan that `gravity is the weakest force'. Here, we take a step towards making this expectation more precise by studying $\mathbb{Z}_N$ and $\mathbb{Z}_2^N$ gauge symmetries realised via theories of spontaneous symmetry breaking. We show that applying the WGC to a dual description of an Abelian Higgs model leads to constraints that allow us to saturate but not violate existing bounds on discrete symmetries based on black hole arguments. In this setting, considering the effect of discrete hair on black holes naturally identifies the cutoff of the effective theory with the scale of spontaneous symmetry breaking, and provides a mechanism through which discrete hair can be lost without modifying the gravitational sector. We explore the possible implications of these arguments for understanding the smallness of the weak scale compared to $M_{Pl}$., Comment: 15 pages; introduction and conclusions extended; matches published version