Search

Interactions between dark matter and ordinary matter will transfer momentum, and therefore give rise to a force on ordinary matter due to the dark matter `wind.' We show that this force can be maximal in a realistic model of dark matter, meaning that an order-1 fraction of the dark matter momentum incident on a target of ordinary matter is reflected. The model consists of light ($m_\phi \lsim \text{eV}$) scalar dark matter with an effective interaction $\phi^2 \bar{\psi}\psi$, where $\psi$ is an electron or nucleon field. If the coupling is repulsive and sufficiently strong, the field $\phi$ is excluded from ordinary matter, analogous to the Meissner effect for photons in a superconductor. We show that there is a large region of parameter space that is compatible with existing constraints, where the force is large enough to be detected by existing force probes, such as satellite tests of the equivalence principle and torsion balance experiments. However, shielding of the dark matter by ordinary matter prevents existing experiments from being sensitive to the dark matter force. We show that precise measurements of spacecraft trajectories proposed to test long distance modifications of gravity are sensitive to this force for a wide range of parameters., Comment: 29 pages, 5 figures, JHEP publication version

We consider the complete set of observables for collider searches for indirect effects of new heavy physics. They consist of $SU(3)_{\rm C}\times U(1)_{\rm EM}$ invariant interaction terms/operators that parameterize deviations from the Standard Model. We show that, under very general assumptions, the leading deviations from the Standard Model are given by a finite number of `primary' operators, with the remaining operators given by `Mandelstam descendants' whose effects are suppressed by powers of Mandelstam variables divided by the mass scale $M$ of the heavy physics. We explicitly determine all 3 and 4-point primary operators relevant for Higgs signals at colliders by using the correspondence between on-shell amplitudes and independent operators. We give a detailed discussion of the methods used to obtain this result, including a new analytical method for determining the independent operators. The results are checked using the Hilbert series that counts independent operators. We also give a rough sketch of the phenomenology, including unitarity bounds on the interaction strengths and rough estimates of their importance for Higgs decays at the HL-LHC. These results motivate further exploration of Higgs decays to $Z\bar{f}f$, $W\bar{f}f'$, $\gamma \bar{f}f$, and $Z\gamma\gamma$., Comment: 46 pages, 2 figures, 13 tables. Final published version in JHEP

In this Snowmass white paper, we describe how unitarity bounds can convert sensitivities for Higgs couplings at future colliders into sensitivities to the scale of new physics. This gives a model-independent consequence of improving these sensitivities and illustrate the impact they would have on constraining new physics. Drawing upon past successful applications of unitarity as a guide for future colliders (e.g. the Higgs mass bound and discovering it at the LHC), we hope this data will be useful in the planning for next generation colliders., Comment: v2, 5 pages, added Muon Collider numbers, 2 added plots, contribution to Snowmass 2021

Hamiltonian truncation is a non-perturbative numerical method for calculating observables of a quantum field theory. The starting point for this method is to truncate the interacting Hamiltonian to a finite-dimensional space of states spanned by the eigenvectors of the free Hamiltonian $H_0$ with eigenvalues below some energy cutoff $E_\text{max}$. In this work, we show how to treat Hamiltonian truncation systematically using effective field theory methodology. We define the finite-dimensional effective Hamiltonian by integrating out the states above $E_\text{max}$. The effective Hamiltonian can be computed by matching a transition amplitude to the full theory, and gives corrections order by order as an expansion in powers of $1/E_\text{max}$. The effective Hamiltonian is non-local, with the non-locality controlled in an expansion in powers of $H_0/E_\text{max}$. The effective Hamiltonian is also non-Hermitian, and we discuss whether this is a necessary feature or an artifact of our definition. We apply our formalism to 2D $\lambda \phi^4$ theory, and compute the the leading $1/E_\text{max}^2$ corrections to the effective Hamiltonian. We show that these corrections non-trivially satisfy the crucial property of separation of scales. Numerical diagonalization of the effective Hamiltonian gives residual errors of order $1/E_\text{max}^3$, as expected by our power counting. We also present the power counting for 3D $\lambda \phi^4$ theory and perform calculations that demonstrate the separation of scales in this theory., Comment: 51 pages, 9 figures, v2: Clarifications and additional discussion added in response to referee reports. Conclusions unchanged

A primary goal of present and future colliders is measuring the Higgs couplings to Standard Model (SM) particles. Any observed deviation from the SM predictions for these couplings is a sign of new physics whose energy scale can be bounded from above by requiring tree-level unitarity. In this paper, we extend previous work on unitarity bounds from the Higgs cubic coupling to Higgs couplings to vector bosons and top quarks. We find that HL-LHC measurements of these couplings compatible with current experimental bounds may point to a scale that can be explored at the HL-LHC or a next-generation collider. Our approach is completely model-independent: we assume only that there are no light degrees of freedom below the scale of new physics, and allow arbitrary values for the infinitely many couplings beyond the SM as long as they are in agreement with current measurements. We also extend and clarify the methodology of this analysis, and show that if the scale of new physics is above the TeV scale, then the deviations can be described by the leading higher-dimension gauge invariant operator, as in the SM effective field theory., Comment: 48 pages, 17 figures, added discussion on basis dependence of unitarity bounds. Final published version in JHEP

General principles of quantum field theory imply that there exists an operator product expansion (OPE) for Wightman functions in Minkowski momentum space that converges for arbitrary kinematics. This convergence is guaranteed to hold in the sense of a distribution, meaning that it holds for correlation functions smeared by smooth test functions. The conformal blocks for this OPE are conceptually extremely simple: they are products of 3-point functions. We construct the conformal blocks in 2-dimensional conformal field theory and show that the OPE in fact converges pointwise to an ordinary function in a specific kinematic region. Using microcausality, we also formulate a bootstrap equation directly in terms of momentum space Wightman functions., Comment: 25 pages, 4 figures

The subject of radiation reaction in classical electromagnetism remains controversial over 120 years after the pioneering work of Lorentz. We give a simple but rigorous treatment of the subject at the textbook level that explains the apparent paradoxes that are much discussed in the literature on the subject. We first derive the equation of motion of a charged particle from conservation of energy and momentum, which includes the self-force term. We then show that this theory is unstable if charged particles are pointlike: the energy is unbounded from below, and charged particles self-accelerate (`over-react') due to their negative `bare' mass. This theory clearly does not describe our world, but we show that these instabilities are absent if the particle has a finite size larger than its classical radius. For such finite-size charged particles, the effects of radiation reaction can be computed in a systematic expansion in the size of the particle. The leading term in this expansion is the reduced-order Abraham-Lorentz equation of motion, which has no stability problems. We also discuss the apparent paradox that a particle with constant acceleration radiates, but does not suffer radiation reaction (`under-reaction'). Along the way, we introduce the ideas of renormalization and effective theories, which are important in many areas of modern theoretical physics. We hope that this will be a useful addition to the literature that will remove some of the air of mystery and paradox surrounding the subject., Comment: 21 pages

We consider modifications of the Higgs potential due to new physics at high energy scales. These upset delicate cancellations predicted by the Standard Model for processes involving Higgs bosons and longitudinal gauge bosons, and lead to a breakdown of the theory at high energies. We focus on modifications of the Higgs trilinear coupling and use the violation of tree-level unitarity as an estimate of the scale where the theory breaks down. We obtain a completely model-independent bound of ~ 13 TeV for an order-1 modification of the trilinear. We argue that this bound can be saturated only in fine-tuned models, and the scale of new physics is likely to be much lower. The most stringent bounds are obtained from amplitudes involving multiparticle states that are not conventional scattering states. Our results show that a future determination of the Higgs cubic coupling can point to a well-defined scale of new physics that can be targeted and explored at future colliders., Comment: 28 pages, 3 figures, added discussion. Final published version in JHEP

Non-minimal Higgs sectors are strongly constrained by the agreement of the measured couplings of the 125 GeV Higgs with Standard Model predictions. This agreement can be explained by an approximate $\mathbb{Z}_2$ symmetry under which the additional Higgs bosons are odd. This allows the additional Higgs bosons to be approximately inert, meaning that they have suppressed VEVs and suppressed mixing with the Standard Model Higgs. In this case, single production of the new Higgs bosons is suppressed, but electroweak pair production is unsuppressed. We study the phenomenology of a minimal 2 Higgs doublet model that realizes this scenario. In a wide range of parameters, the phenomenology of the model is essentially fixed by the masses of the exotic Higgs bosons, and can therefore be explored systematically. We study a number of different plausible signals in this model, and show that several LHC searches can constrain or discover additional Higgs bosons in this parameter space. We find that the reach is significantly extended at the high luminosity LHC., Comment: 30 pages, 8 figures. v2: clarifications and references added, version to be published in JHEP

Quirks are exotic particles charged under a new confining gauge group that can give rise to unique collider signatures, depending on their vector-like mass, quantum numbers, and the confinement scale. In this work, we consider the possibility that quirks produced at the LHC lose all of their kinetic energy through ionization loss before escaping the detector, and annihilate at a time when there are no active pp collisions. We recast an existing CMS search for out-of-time decays of R-hadrons to place new limits on quirk parameter space. We propose several simple modifications to the existing out-of-time search strategy that can give these searches sensitivity in regions of quirk parameter space not covered by any existing or proposed search strategy., Comment: 27 pages, 9 figures

4D CFTs have a scale anomaly characterized by the coefficient $c$, which appears as the coefficient of logarithmic terms in momentum space correlation functions of the energy-momentum tensor. By studying the CFT contribution to 4-point graviton scattering amplitudes in Minkowski space we derive a sum rule for $c$ in terms of $TT\mathcal{O}$ OPE coefficients. The sum rule can be thought of as a version of the optical theorem, and its validity depends on the existence of the massless and forward limits of the $\langle TTTT \rangle$ correlation functions that contribute. The finiteness of these limits is checked explicitly for free scalar, fermion, and vector CFTs. The sum rule gives $c$ as a sum of positive terms, and therefore implies a lower bound on $c$ given any lower bound on $TT\mathcal{O}$ OPE coefficients. We compute the coefficients to the sum rule for arbitrary operators of spin 0 and 2, including the energy-momentum tensor., Comment: 60 pages, 8 figures; v2: minor modifications, matches published version

We argue that conformal invariance in flat spacetime implies Weyl invariance in a general curved background metric for all unitary theories in spacetime dimensions $d \leq 10$. We also study possible curvature corrections to the Weyl transformations of operators, and show that these are absent for operators of sufficiently low dimensionality and spin. We find possible `anomalous' Weyl transformations proportional to the Weyl (Cotton) tensor for $d > 3$ ($d = 3$). The arguments are based on algebraic consistency conditions similar to the Wess-Zumino consistency conditions that classify possible local anomalies. The arguments can be straightforwardly extended to larger operator dimensions and higher $d$ with additional algebraic complexity., Comment: 30 pages, v3: Version accepted to JHEP, clarifications added and typos fixed

This paper presents two methods to compute scale anomaly coefficients in conformal field theories (CFTs), such as the c anomaly in four dimensions, in terms of the CFT data. We first use Euclidean position space to show that the anomaly coefficient of a four-point function can be computed in the form of an operator product expansion (OPE), namely a weighted sum of OPE coefficients squared. We compute the weights for scale anomalies associated with scalar operators and show that they are not positive. We then derive a different sum rule of the same form in Minkowski momentum space where the weights are positive. The positivity arises because the scale anomaly is the coefficient of a logarithm in the momentum space four-point function. This logarithm also determines the dispersive part, which is a positive sum over states by the optical theorem. The momentum space sum rule may be invalidated by UV and/or IR divergences, and we discuss the conditions under which these singularities are absent. We present a detailed discussion of the formalism required to compute the weights directly in Minkowski momentum space. A number of explicit checks are performed, including a complete example in an 8-dimensional free field theory., Comment: 39 pages, 7 figures

The discovery of a 125 GeV Higgs boson at the Large Hadron Collider strongly motivates direct searches for additional Higgs bosons. In a type I two Higgs doublet model there is a large region of parameter space at $\tan\beta > 5$ that is currently unconstrained experimentally. We show that the process $gg \to H \to A Z \to ZZh$ can probe this region, and can be the discovery mode for an extended Higgs sector at the LHC. We analyze 9 promising decay modes for the $ZZh$ state, and we find that the most sensitive final states are $\ell\ell\ell\ell bb$, $\ell\ell jjbb$, $\ell\ell\nu\nu\gamma\gamma$ and $\ell\ell\ell\ell +{}$missing energy., Comment: 24 pages, 12 figures

We argue that all consistent 4D quantum field theories obey a spacetime-averaged weak energy inequality $\langle T^{00} \rangle \ge -C/L^4$, where $L$ is the size of the smearing region, and $C$ is a positive constant that depends on the theory. If this condition is violated, the theory has states that are indistinguishable from states of negative total energy by any local measurement, and we expect instabilities or other inconsistencies. We apply this condition to 4D conformal field theories, and find that it places constraints on the OPE coefficients of the theory. The constraints we find are weaker than the "conformal collider" constraints of Hofman and Maldacena. We speculate that there may be theories that violate the Hofman-Maldacena bounds, but satisfy our bounds. In 3D CFTs, the only constraint we find is equivalent to the positivity of 2-point function of the energy-momentum tensor, which follows from unitarity. Our calculations are performed using momentum-space Wightman functions, which are remarkably simple functions of momenta, and may be of interest in their own right., Comment: 33 pages, 1 figure v2: adding clarifying information and fixed typos

We present a mechanism that allows a large Higgsino mass without large fine-tuning. The Higgs is a pseudo Nambu-Goldstone boson (PNGB) of the global symmetry breaking pattern $SO(5) \to SO(4)$. Because of the PNGB nature of the light Higgs, the $SO(5)$ invariant Higgsino mass does not directly contribute to the Higgs mass. Large couplings in the Higgs sector that spontaneously breaks $SO(5)$ minimize the tuning, and are also motivated by the requirements of generating a sufficiently large Higgs quartic coupling and of maintaining a natural approximate global $SO(5)$ symmetry. When these conditions are imposed, theories of this type predict heavy Higgsinos. This construction differs from composite Higgs models in that no new particles are introduced to form complete $SO(5)$ multiplets involving the top quark---the stop is the only top partner. Compatibility with Higgs coupling measurements requires cancelations among contributions to the Higgs mass squared parameter at the 10% level. An important implication of this construction is that the compressed region of stop and sbottom searches can still be natural., Comment: 22 pages, 2 figures; v2: references added

We study the phenomenology of models of electroweak symmetry breaking where the Higgs potential is dominated by a positive quadratic term destabilized by a tadpole arising from the coupling to an "auxiliary" Higgs sector. The auxiliary Higgs sector can be either perturbative or strongly coupled, similar to technicolor models. Since electroweak symmetry breaking is driven by a tadpole, the cubic and quartic Higgs couplings can naturally be significantly smaller than their values in the standard model. The theoretical motivation for these models is that they can explain the 125 GeV Higgs mass in supersymmetry without fine-tuning. The auxiliary Higgs sector contains additional Higgs states that cannot decouple from standard model particles, so these models predict a rich phenomenology of Higgs physics beyond the standard model. In this paper we analyze a large number of direct and indirect constraints on these models. We present the current constraints after the 8 TeV run of the LHC, and give projections for the sensitivity of the upcoming 14 TeV run. We find that the strongest constraints come from the direct searches $A^0 \to Zh$, $A^0 \to t\bar{t}$, with weaker constraints from Higgs coupling fits. For strongly-coupled models, additional constraints come from $\rho^+ \to WZ$ where $\rho^+$ is a vector resonance. Our overall conclusion is that a significant parameter space for such models is currently open, allowing values of the Higgs cubic coupling down to 0.4 times the standard model value for weakly coupled models and vanishing cubic coupling for strongly coupled models. The upcoming 14 TeV run of the LHC will stringently test this scenario and we identify several new searches with discovery potential for this class of models., Comment: 35 pages, 10 figures

Effective WIMP models are minimal extensions of the standard model that explain the relic density of dark matter by the ``WIMP miracle.'' In this paper we consider the phenomenology of effective WIMPs with trilinear couplings to leptons and a new ``lepton partner'' particle. The observed relic abundance fixes the strength of the cubic coupling, so the parameters of the models are defined by the masses of the WIMP and lepton partner particles. This gives a simple parameter space where collider and direct detection experiments can be compared under well-defined physical minimality assumptions. The most sensitive collider probe is the search for leptons + MET, while the most sensitive direct detection channel is scattering from nuclei arising from loop diagrams. Collider and direct detection searches are highly complementary: colliders give the only meaningful constraint when dark matter is its own antiparticle, while direct detection is generally more sensitive if the dark matter is not its own antiparticle., Comment: 22 pages, 10 figures

This paper addresses the question of whether there are 4D Lorentz invariant unitary quantum field theories with scale invariance but not conformal invariance. An important loophole in the arguments of Luty-Polchinski-Rattazzi and Dymarsky-Komargodski-Schwimmer-Theisen is that trace of the energy-momentum tensor $T$ could be a generalized free field. In this paper we rule out this possibility. The key ingredient is the observation that a unitary theory with scale but not conformal invariance necessarily has a non-vanishing anomaly for global scale transformations. We show that this anomaly cannot be reproduced if $T$ is a generalized free field unless the theory also contains a dimension-2 scalar operator. In the special case where such an operator is present it can be used to redefine ("improve") the energy-momentum tensor, and we show that there is at least one energy-momentum tensor that is not a generalized free field. In addition, we emphasize that, in general, large momentum limits of correlation functions cannot be understood from the leading terms of the coordinate space OPE. This invalidates a recent argument by Farnsworth-Luty-Prilepina (FLP). Despite the invalidity of the general argument of FLP, some of the techniques turn out to be useful in the present context., Comment: 14 pages

We give a non-perturbative proof that any 4D unitary and Lorentz-invariant quantum field theory with a conserved scale current is in fact conformally invariant. We show that any scale invariant theory (unitary or not) must have either a vanishing anomaly for global scale transformations or an operator of spin 2 and dimension 2. Neither of these possibilities is allowed for unitary theories, proving the result. This is also a strong constraint on non-unitary Euclidean theories with scale but not conformal invariance, suggesting the conjecture that all such theories are free field theories., Comment: This paper has been withdrawn by the authors. Paper withdrawn. This paper claimed to give a proof that scale invariance implies conformal invariance using only the OPE and unitarity. This cannot be correct due to a counterexample. The mistake in the present paper is the use of the OPE in momentum space, which does not hold in the cases it was used in the argument. A detailed discussion of this point can be found in arXiv:1402.3208 and arXiv:1402.6322

The 'WIMP miracle' for the relic abundance of thermal dark matter motivates weak scale dark matter with renormalizable couplings to standard model particles. We study minimal models with such couplings that explain dark matter as a thermal relic. The models contain a singlet dark matter particle with cubic renormalizable couplings between standard model particles and 'partner' particles with the same gauge quantum numbers as the standard model particle. The dark matter has spin 0, 1/2, or 1, and may or may not be its own antiparticle. Each model has 3 parameters: the masses of the dark matter and standard model partners, and the cubic coupling. Requiring the correct relic abundance gives a 2-dimensional parameter space where collider and direct detection constraints can be directly compared. We focus on the case of dark matter interactions with colored particles. We find that collider and direct detection searches are remarkably complementary for these models. Direct detection limits for the cases where the dark matter is not its own antiparticle require dark matter masses to be in the multi-TeV range, where they are extremely difficult to probe in collider experiments. The models where dark matter is its own antiparticle are strongly constrained by collider searches for monojet and jets + MET signals. These models are constrained by direct detection mainly near the limit where the dark matter and partner masses are nearly degenerate, where collider searches become more difficult., Comment: 37 pages, 11 figures

In this paper we study a new class of supersymmetric models that can explain a 125 GeV Higgs without fine-tuning. These models contain additional `auxiliary Higgs' fields with large tree-level quartic interaction terms but no Yukawa couplings. These have electroweak-breaking vacuum expectation values, and contribute to the VEVs of the MSSM Higgs fields either through an induced quartic or through an induced tadpole. The quartic interactions for the auxiliary Higgs fields can arise from either D-terms or F-terms. The tadpole mechanism has been previously studied in strongly-coupled models with large D-terms, referred to as `superconformal technicolor.' The perturbative models studied here preserve gauge coupling unification in the simplest possible way, namely that all new fields are in complete SU(5) multiplets. The models are consistent with the observed properties of the 125 GeV Higgs-like boson as well as precision electroweak constraints, and predict a rich phenomenology of new Higgs states at the weak scale. The tuning is less than 10% in almost all of the phenomenologically allowed parameter space. If electroweak symmetry is broken by an induced tadpole, the cubic and quartic Higgs self-couplings are significantly smaller than in the standard model., Comment: 37 pages, 11 figures

The entanglement entropy associated with a spatial boundary in quantum field theory is UV divergent, with the leading term proportional to the area of the boundary. For a class of quantum states defined by a path integral, the Callan-Wilczek formula gives a geometrical definition of the entanglement entropy. We show that, for this class of quantum states, the entanglement entropy is rendered UV-finite by precisely the counterterms required to cancel the UV divergences in the gravitational effective action. In particular, the leading contribution to the entanglement entropy is given by the renormalized Bekenstein-Hawking formula, in accordance with a proposal of Susskind and Uglum. We show that the subleading UV-divergent terms in the entanglement entropy depend nontrivially on the quantum state. We compute new subleading terms in the entanglement entropy and find agreement with the Wald entropy formula for black hole spacetimes with bifurcate Killing horizons. We speculate that the entanglement entropy of an arbitrary spatial boundary may be a well-defined observable in quantum gravity., Comment: 26 pages, 2 figures. v2: minor corrections and clarifications

We propose a framework for natural breaking of electroweak symmetry in supersymmetric models, where elementary Higgs fields are semi-perturbatively coupled to a strong superconformal sector. The Higgs VEVs break conformal symmetry in the strong sector at the TeV scale, and the strong sector in turn gives important contributions to the Higgs potential, giving rise to a kind of Higgs bootstrap. A Higgs with mass $125\GeV$ can be accommodated without any fine tuning. A Higgsino mass of order the Higgs mass is also dynamically generated in these models. The masses in the strong sector generically violate custodial symmetry, and a good precision electroweak fit requires tuning of order $\sim 10%$. The strong sector has an approximately supersymmetric spectrum of hadrons at the TeV scale that can be observed by looking for a peak in the $WZ$ invariant mass distribution, as well as final states containing multiple $W$, $Z$, and Higgs bosons. The models also generically predict large corrections (either enhancement or suppression) to the $h \to \ga\ga$ width., Comment: 31 pages

We study the possible IR and UV asymptotics of 4D Lorentz invariant unitary quantum field theory. Our main tool is a generalization of the Komargodski-Schwimmer proof for the $a$-theorem. We use this to rule out a large class of renormalization group flows that do not asymptote to conformal field theories in the UV and IR. We show that if the IR (UV) asymptotics is described by perturbation theory, all beta functions must vanish faster than $(1/|\ln\mu|)^{1/2}$ as $\mu \to 0$ ($\mu \to \infty$). This implies that the only possible asymptotics within perturbation theory is conformal field theory. In particular, it rules out perturbative theories with scale but not conformal invariance, which are equivalent to theories with renormalization group pseudocycles. Our arguments hold even for theories with gravitational anomalies. We also give a non-perturbative argument that excludes theories with scale but not conformal invariance. This argument holds for theories in which the stress-energy tensor is sufficiently nontrivial in a technical sense that we make precise., Comment: 41 pages, 2 figures. v2: Arguments clarified, some side comments corrected, connection to previous work by Jack and Osborn described, conclusions unaffected

In extended Higgs sectors, heavy Higgs bosons can decay via cascades to a light Higgs boson plus $W$ and $Z$ bosons. We study signals of such sectors at the Tevatron and LHC that result from resonant production of a heavy $H^0$ followed by the decay $H^0 \to H^\pm W^\mp$ with $H^+ \to W^+ h^0 \to W^+ b\bar{b}$ or $H^+ \to t\bar{b} \to W^+ b\bar{b}$. The final states have the same particle content as that of $t\bar{t}$ production, but with a resonant structure that can be used to distinguish signal events from background events. We propose analysis techniques and estimate the experimental sensitivity of the Tevatron and LHC experiments to these signals., Comment: For submission to PRD

Particle physics models with more than one Higgs boson occur in many frameworks for physics beyond the standard model, including supersymmetry, technicolor, composite Higgs, and "little Higgs" models. If the Higgs sector contains couplings stronger than electroweak gauge couplings, there will be heavy Higgs particles that decay to lighter Higgs particles plus heavy particles such as $W$, $Z$, and $t$. This motivates searches for final states involving multiple $W$, $Z$, $t$, and $\bar{b}b$ pairs. A two Higgs doublet model with custodial symmetry is a useful simplified model to describe many of these signals. The model can be parameterized by the physical Higgs masses and the mixing angles $\al$ and $\be$, so discovery or exclusion in this parameter space has a straightforward physical interpretation. We illustrate this with a detailed analysis of the process $gg \to A$ followed by $A \to h Z$ and $h \to WW$. For $m_{A} \simeq 330\GeV$, $m_{h} \simeq 200\GeV$ we can get a $4.5\si$ signal with 1 fb${}^{-1}$ of integrated luminosity at the Large Hadron Collider., Comment: 4 pages, 3 figures

In supersymmetric theories with a strong conformal sector, soft supersymmetry breaking naturally gives rise to confinement and chiral symmetry breaking in the strong sector at the TeV scale. We construct and analyze models where such a sector dynamically breaks electroweak symmetry, and take the first steps in studying their phenomenology. We consider two scenarios, one where the strong dynamics induces vacuum expectation values for elementary Higgs fields, and another where the strong dynamics is solely responsible for electroweak symmetry breaking. In both cases there is no fine tuning required to explain the absence of a Higgs boson below the LEP bound, solving the supersymmetry naturalness problem. Quark and lepton masses arise from conventional Yukawa couplings to elementary Higgs bosons, so there are no additional flavor-changing effects associated with the strong dynamics. A good precision electroweak fit can be obtained because the strong sector is an SU(2) gauge theory with one weak doublet, and has adjustable parameters that control the violation of custodial symmetry. In addition to the the standard supersymmetry signals, these models predict production of multiple heavy standard model particles (t, W, Z, and b) from decays of resonances in the strong sector. The strong sector has no approximate parity symmetry, so WW scattering is unitarized by states that can decay to WWW as well as WW., Comment: 34 pages, 3 figures; v2: minor changes, references added

In supersymmetric theories with a strong conformal sector, soft supersymmetry breaking at the TeV scale naturally gives rise to confinement and chiral symmetry breaking at the same scale. We investigate models where such a sector dynamically breaks electroweak symmetry. We consider two scenarios, one where the strong dynamics induces vacuum expectation values for elementary Higgs fields, and another where the strong dynamics is solely responsible for electroweak symmetry breaking. In both cases there is no fine tuning required to explain the absence of a Higgs boson below the LEP bound, solving the supersymmetry naturalness problem. A good precision electroweak fit can be obtained, and quark and lepton masses are generated without flavor-changing neutral currents. Electroweak symmetry breaking may be dominated either by the elementary Higgs bosons or by the strong dynamics. In addition to standard superymmetry collider signals, these models predict production of multiple heavy standard model particles (t, W, Z, and b) from decays of resonances in the strong sector., Comment: 4 pages; v2: minor changes, references added

This document proposes a collection of simplified models relevant to the design of new-physics searches at the LHC and the characterization of their results. Both ATLAS and CMS have already presented some results in terms of simplified models, and we encourage them to continue and expand this effort, which supplements both signature-based results and benchmark model interpretations. A simplified model is defined by an effective Lagrangian describing the interactions of a small number of new particles. Simplified models can equally well be described by a small number of masses and cross-sections. These parameters are directly related to collider physics observables, making simplified models a particularly effective framework for evaluating searches and a useful starting point for characterizing positive signals of new physics. This document serves as an official summary of the results from the "Topologies for Early LHC Searches" workshop, held at SLAC in September of 2010, the purpose of which was to develop a set of representative models that can be used to cover all relevant phase space in experimental searches. Particular emphasis is placed on searches relevant for the first ~50-500 pb-1 of data and those motivated by supersymmetric models. This note largely summarizes material posted at http://lhcnewphysics.org/, which includes simplified model definitions, Monte Carlo material, and supporting contacts within the theory community. We also comment on future developments that may be useful as more data is gathered and analyzed by the experiments., Comment: 40 pages, 2 figures. This document is the official summary of results from "Topologies for Early LHC Searches" workshop (SLAC, September 2010). Supplementary material can be found at http://lhcnewphysics.org

If R hadrons are discovered at the LHC, investigation of their properties will be of paramount importance. One important question is how much of the R-hadron mass is due to electroweak symmetry breaking, i.e. the coupling of the Higgs to R-hadrons. In this paper we show that in models where the Higgs has a sizable coupling to R-hadrons we can readily observe Higgs production in association with a pair of R-hadrons ("Higgsstrahlung"). This process can be used to distinguish between different models of R-hadrons. It may be the discovery mode of the Higgs for low mass Higgs bosons, and provides a low-background Higgs sample to study h to bb., Comment: 9 pages, 3 figures, 2 tables

We construct a complete, realistic, and natural UV completion of minimal conformal technicolor that explains the origin of quark and lepton masses and mixing angles. As in "bosonic technicolor", we embed conformal technicolor in a supersymmetric theory, with supersymmetry broken at a high scale. The exchange of heavy scalar doublets generates higher-dimension interactions between technifermions and quarks and leptons that give rise to quark and lepton masses at the TeV scale. Obtaining a sufficiently large top quark mass requires strong dynamics at the supersymmetry breaking scale in both the top and technicolor sectors. This is natural if the theory above the supersymmetry breaking also has strong conformal dynamics. We present two models in which the strong top dynamics is realized in different ways. In both models, constraints from flavor-changing effects can be easily satisfied. The effective theory below the supersymmetry breaking scale is minimal conformal technicolor with an additional light technicolor gaugino. We argue that this light gaugino is a general consequence of conformal technicolor embedded into a supersymmetric theory. If the gaugino has mass below the TeV scale it will give rise to an additional pseudo Nambu-Goldstone boson that is observable at the LHC., Comment: 37 pages; references added

We construct a simple and natural supersymmetric model where the dominant Higgs decay is h -> aa followed by a -> gg. In this case m_h < m_Z is compatible with all experimental searches, completely eliminating the fine tuning otherwise required to satisfy Higgs search limits. The model extends the MSSM with singlet Higgs fields as well as vector-like colored particles that mediate the decay a -> gg. The a is a pseudo-Nambu Goldstone boson of a new global U(1) symmetry, and can naturally have any mass from a few GeV to m_h/2. All interactions can be perturbative up to the GUT scale, and gauge coupling unification is preserved if the colored mediators come in complete GUT representations. In this case a -> gamma gamma has a ~1% branching ratio, so h -> gg gamma gamma may be observable. The colored particles that mediate the h -> gg decay must be below the TeV scale, and can therefore be produced at the LHC. If these particles are stable on collider timescales, they will appear as R-hadrons, a signal visible in early LHC running. A smoking-gun signal that the stable colored particles are mediators of h -> 4j is R-hadron production in association with an a. We show that this signal with a -> gamma gamma is observable at LHC with as little as 10 fb^{-1} of integrated luminosity. Observation of R-hadrons plus missing energy can show that the superpartner of the R-hadron is R-parity odd, and therefore not an ordinary quark or gluon., Comment: 12 pages

Mixed anomaly and gauge mediation ("gaugomaly'' mediation) gives a natural solution to the SUSY flavor problem with a conventional LSP dark matter candidate. We present a minimal version of gaugomaly mediation where the messenger masses arise directly from anomaly mediation, automatically generating a messenger scale of order 50 TeV. We also describe a simple relaxation mechanism that gives rise to realistic mu and B mu terms. B is naturally dominated by the anomaly-mediated contribution from top loops, so the mu/B mu sector only depends on a single new parameter. In the minimal version of this scenario the full SUSY spectrum is determined by two continuous parameters (the anomaly- and gauge-mediated SUSY breaking masses) and one discrete parameter (the number of messengers). We show that these simple models can give realistic spectra with viable dark matter., Comment: 18 pages, 4 figures; v2: corrected example generating non-holomorphic Kahler terms

We study the minimal model of conformal technicolor, an SU(2) gauge theory near a strongly coupled conformal fixed point, with conformal symmetry softly broken by technifermion mass terms. Conformal symmetry breaking triggers chiral symmetry breaking in the pattern SU(4) -> Sp(4), which gives rise to a pseudo-Nambu-Goldstone boson that can act as a composite Higgs boson. The top quark is elementary, and the top and electroweak gauge loop contributions to the Higgs mass are cut off entirely by Higgs compositeness. In particular, the model requires no top partners and no "little Higgs" mechanism. A nontrivial vacuum alignment results from the interplay of the top loop and technifermion mass terms. The composite Higgs mass is completely determined by the top loop, in the sense that m_h/m_t is independent of the vacuum alignment and is computable by a strong-coupling calculation. There is an additional composite pseudoscalar A with mass larger than m_h and suppressed direct production at LHC. We discuss the electroweak fit in this model in detail. Corrections to Z -> bb and the T parameter from the top sector are suppressed by the enhanced Sp(4) custodial symmetry. Even assuming that the strong contribution to the S parameter is positive and usuppressed, a good electroweak fit can be obtained for v/f ~ 0.25, where v and f are the electroweak and chiral symmetry breaking scales respectively. This requires fine tuning at the 10% level., Comment: 34 pages, 4 figures; v2: updated precision electroweak fit

Particles with TeV mass and strong self-interactions generically have the right annihilation cross section to explain an observed excess of cosmic electrons and positrons if the end-product of the annihilation is charged leptons. We present an explicit model of strongly-coupled TeV-scale dark matter whose relic abundance related to the matter-antimatter asymmetry of the observed universe. The B - L asymmetry of the standard model is transfered to the dark sector by an operator carrying standard model lepton number. Lepton number violation naturally induces dark matter particle-antiparticle oscillations at late times, allowing dark matter-antimatter annihilations today. The dark matter annihilates into lighter strongly-interacting particles in the dark sector that decay to leptons via the transfer operator. The strong dynamics in the dark sector is at the weak scale due to supersymmetry breaking. The correct dark matter abundance is automatically obtained for natural values of dimensionless parameters, analogous to the situation for conventional WIMPs., Comment: 4 pages, revtex, 1 figure; v2: corrected discussion of relic density, bounds on dark matter Majorana mass

Models in which the dark matter is very weakly coupled to the observable sector may explain the observed dark matter density, either as a "superWIMP" or as "asymmetric dark matter." Both types of models predict displaced vertices at colliders, with a rich variety of possible phenomenology. We classify the cases in which the decays can naturally occur inside particle detectors at the LHC, with particular focus on the nontrivial scenarios where the decaying particle is invisible. Identification of the position and timing of these invisible displaced vertices significantly improves the prospects of reconstructing the new physics in models such as supersymmetry. In many cases, reconstruction of the visible products of the displaced decay can determine the dark matter mass, allowing the dark matter density to be predicted from collider data., Comment: 5 pages, 1 figure, revtex

We argue that theories of strong electroweak symmetry breaking sector necessarily contain new spin 0 states at the TeV scale in the tbar-t and tbar-b/bbar-t channels, even if the third generation quarks are not composite at the TeV scale. These states couple sufficiently strongly to third generation quarks to have significant production at LHC via gg \to X or gb \to X. The existence of narrow resonances in QCD suggests that the strong electroweak breaking sector contains narrow resonances that decay to tbar-t or tbar-b/bbar-t, with significant branching fractions to 3 or more longitudinal W and Z bosons. These may give new "smoking gun" signals of strong electroweak symmetry breaking., Comment: 4 pages, 1 figure

We consider a simple class of models in which the relic density of dark matter is determined by the baryon asymmetry of the universe. In these models a $B - L$ asymmetry generated at high temperatures is transfered to the dark matter, which is charged under $B - L$. The interactions that transfer the asymmetry decouple at temperatures above the dark matter mass, freezing in a dark matter asymmetry of order the baryon asymmetry. This explains the observed relation between the baryon and dark matter densities for dark matter mass in the range 5--15 GeV. The symmetric component of the dark matter can annihilate efficiently to light pseudoscalar Higgs particles $a$, or via $t$-channel exchange of new scalar doublets. The first possibility allows for $h^0 \to aa$ decays, while the second predicts a light charged Higgs-like scalar decaying to $\tau\nu$. Direct detection can arise from Higgs exchange in the first model, or a nonzero magnetic moment in the second. In supersymmetric models, the would-be LSP can decay into pairs of dark matter particles plus standard model particles, possibly with displaced vertices., Comment: 22 pages, no figures

Conformal technicolor is a paradigm for new physics at LHC that may solve the problems of strong electroweak symmetry breaking for quark masses and precision electroweak data. We give explicit examples of conformal technicolor theories based on a QCD-like sector. We suggest a practical method to test the conformal dynamics of these theories on the lattice., Comment: v2: Generalized discussion of lattice measurement of hadron masses, references added, minor clarifications v3: references added, minor changes

We consider extensions of the standard model containing additional heavy particles ("quirks") charged under a new unbroken non-abelian gauge group as well as the standard model. We assume that the quirk mass m is in the phenomenologically interesting range 100 GeV--TeV, and that the new gauge group gets strong at a scale Lambda < m. In this case breaking of strings is exponentially suppressed, and quirk production results in strings that are long compared to 1/Lambda. The existence of these long stable strings leads to highly exotic events at colliders. For 100 eV < Lambda < keV the strings are macroscopic, giving rise to events with two separated quirk tracks with measurable curvature toward each other due to the string interaction. For keV < Lambda < MeV the typical strings are mesoscopic: too small to resolve in the detector, but large compared to atomic scales. In this case, the bound state appears as a single particle, but its mass is the invariant mass of a quirk pair, which has an event-by-event distribution. For MeV < Lambda < m the strings are microscopic, and the quirks annihilate promptly within the detector. For colored quirks, this can lead to hadronic fireball events with 10^3 hadrons with energy of order GeV emitted in conjunction with hard decay products from the final annihilation., Comment: Added discussion of photon-jet decay, fixed minor typos

Long-lived colored particles with masses m > 200 GeV are allowed by current accelerator searches, and are predicted by a number of scenarios for physics beyond the standard model. We argue that such "heavy partons'' effectively have a geometrical cross section (of order 10 mb) for annihilation at temperatures below the QCD deconfinement transition. The annihilation process involves the formation of an intermediate bound state of two heavy partons with large orbital angular momentum. The bound state subsequently decays by losing energy and angular momentum to photon or pion emission, followed by annihilation of the heavy partons. This decay occurs before nucleosynthesis for m < 10^{11} GeV for electrically charged partons and m < TeV for electrically neutral partons. This implies that heavy parton lifetimes as long as 10^{14} sec are allowed even for heavy partons with m ~ TeV decaying to photons or hadrons with significant branching fraction., Comment: 13 pages, 4 figures. Minor revisions

We present a consistent effective theory that violates the null energy condition (NEC) without developing any instabilities or other pathological features. The model is the ghost condensate with the global shift symmetry softly broken by a potential. We show that this system can drive a cosmological expansion with dH/dt > 0. Demanding the absence of instabilities in this model requires dH/dt <~ H^2. We then construct a general low-energy effective theory that describes scalar fluctuations about an arbitrary FRW background, and argue that the qualitative features found in our model are very general for stable systems that violate the NEC. Violating the NEC allows dramatically non-standard cosmological histories. To illustrate this, we construct an explicit model in which the expansion of our universe originates from an asymptotically flat state in the past, smoothing out the big-bang singularity within control of a low-energy effective theory. This gives an interesting alternative to standard inflation for solving the horizon problem. We also construct models in which the present acceleration has w < -1; a periodic ever-expanding universe and a model with a smooth ``bounce'' connecting a contracting and expanding phase., Comment: 27 pages, 3 figures; v2: comments added about blue spectrum of GWs from inflation and the relation between NEC and modification of gravity, JHEP published version

In the context of anomaly-mediated supersymmetry breaking, it is natural for vectorlike fields and singlets to have supersymmetry breaking masses of order 10 TeV, and therefore act as messengers of supersymmetry breaking. We show that this can give rise to phenomenologically viable spectra compatible with perturbative gauge coupling unification. The minimal model interpolates continuously between pure anomaly mediation and gauge mediation with a messenger scale of order 10 TeV. It is also possible to have non-minimal models with more degenerate specta, with some squarks lighter than sleptons. These models reduce to the MSSM at low energies and incorporate a natural solution of the mu problem. The minimal model has four continuous parameters and one discrete parameter (the number of messengers). The LEP Higgs mass bound can be satisfied in the minimal model by tuning parameters at the GUT scale to one part in 50., Comment: 17 pages, 4 figures

Theories that spontaneously break Lorentz invariance also violate diffeomorphism symmetries, implying the existence of extra degrees of freedom and modifications of gravity. In the minimal model (``ghost condensation'') with only a single extra degree of freedom at low energies, the scale of Lorentz violation cannot be larger than about M ~ 100GeV due to an infrared instability in the gravity sector. We show that Lorentz symmetry can be broken at much higher scales in a non-minimal theory with additional degrees of freedom, in particular if Lorentz symmetry is broken by the vacuum expectation value of a vector field. This theory can be constructed by gauging ghost condensation, giving a systematic effective field theory description that allows us to estimate the size of all physical effects. We show that nonlinear effects become important for gravitational fields with strength \sqrt{\Phi} > g, where g is the gauge coupling, and we argue that the nonlinear dynamics is free from singularities. We then analyze the phenomenology of the model, including nonlinear dynamics and velocity-dependent effects. The strongest bounds on the gravitational sector come from either black hole accretion or direction-dependent gravitational forces, and imply that the scale of spontaneous Lorentz breaking is M < Min(10^{12}GeV, g^2 10^{15}GeV). If the Lorentz breaking sector couples directly to matter, there is a spin-dependent inverse-square law force, which has a different angular dependence from the force mediated by the ghost condensate, providing a distinctive signature for this class of models., Comment: 60 pages, 6 figures; version accepted for publication in JHEP

These lectures give an introduction to the problem of finding a realistic and natural extension of the standard model based on spontaneously broken supersymmetry. Topics discussed at some length include the effective field theory paradigm, coupling constants as superfield spurions, gauge mediated supersymmetry breaking, and anomaly mediated supersymmetry breaking, including an extensive introduction to supergravity relevant for phenomenology., Comment: 86 pages, LaTeX2e

We investigate the universal low-energy dynamics of the simplest Higgs phase for gravity, `ghost condensation.' We show that the nonlinear dynamics of the `ghostone' field dominate for all interesting gravitational sources. Away from caustic singularities, the dynamics is equivalent to the irrotational flow of a perfect fluid with equation of state p \propto \rho^2, where the fluid particles can have negative mass. We argue that this theory is free from catastrophic instabilities due to growing modes, even though the null energy condition is violated. Numerical simulations show that solutions generally have singularities in which negative energy regions shrink to zero size. We exhibit partial UV completions of the theory in which these singularities are smoothly resolved, so this does not signal any inconsistency in the effective theory. We also consider the bounds on the symmetry breaking scale M in this theory. We argue that the nonlinear dynamics cuts off the Jeans instability of the linear theory, and allows M \lsim 100GeV., Comment: 54 pages, 15 figures; postscript figures downloadable from http://schwinger.harvard.edu/~wiseman/Ghost/ghostepsfigs.tar.gz ; v2: substantial revision to section 5 on bounds