Search

We study tetraquarks in large $N$ QCD with heavy quarks, in the domain where non-relativistic quantum mechanics offers an adequate approximation. Within the regime of validity of the Born-Oppenheimer approximation, we systematically study and explicitly construct tetraquark states. At leading order in the $1/N$ expansion, the bound spectrum consists of free mesons, while the $1/N$ corrections give rise to a Born-Oppenheimer potential that can bind the mesons into tetraquarks. We find two different types of tetraquarks, each endowed with distinct color-spatial wavefunctions. These states arise in the presence of an $\mathcal{O}(N)$ mass hierarchy between the quarks and the antiquarks. We provide a quantitative argument indicating that only for such a hierarchy is the ground state of the system a tetraquark. We discuss what the extrapolation of our results to realistic values of the parameters may imply for the QCD tetraquark states., Comment: 42 pages, 9 figures

We explore flavor dynamics in the broad scenario of a strongly interacting light Higgs (SILH). Our study focuses on the mechanism of partial fermion compositeness, but is otherwise as systematic as possible. Concretely, we classify the options for the underlying flavor (and CP) symmetries, which are necessary in order to bring this scenario safely within the range of present or future explorations. Our main goal in this context is to provide a practical map between the space of hypotheses (the models) and the experimental ground that will be explored in the medium and long term, in both indirect and direct searches, in practice at HL-LHC and Belle II, in EDM searches and eventually at FCC-hh. Our study encompasses scenarios with the maximal possible flavor symmetry, corresponding to minimal flavor violation (MFV), scenarios with no symmetry, corresponding to the so-called flavor anarchy, and various intermediate cases that complete the picture. One main result is that the scenarios that allow for the lowest new physics scale have intermediate flavor symmetry rather than the maximal symmetry of MFV models. Such optimal models are rather resilient to indirect exploration via flavor and CP violating observables, and can only be satisfactorily explored at a future high-energy collider. On the other hand, the next two decades of indirect exploration will significantly stress the parameter space of a large swath of less optimal but more generic models up to mass scales competing with those of the FCC-hh., Comment: Small fixes. 105 pages, 9 figures, 16 tables

We consider correlators for the flux of energy and charge in the background of operators with large global $U(1)$ charge in conformal field theory (CFT). It has recently been shown that the corresponding Euclidean correlators generically admit a semiclassical description in terms of the effective field theory (EFT) for a conformal superfluid. We adapt the semiclassical description to Lorentzian observables and compute the leading large charge behavior of the flux correlators in general $U(1)$ symmetric CFTs. We discuss the regime of validity of the large charge EFT for these Lorentzian observables and the subtleties in extending the EFT approach to subleading corrections. We also consider the Wilson-Fisher fixed point in $d=4-\epsilon$ dimensions, which offers a specific weakly coupled realization of the general setup, where the subleading corrections can be systematically computed without relying on an EFT., Comment: 33 pages, 8 figures

We determine the contribution of long-range pion interactions to the $X(3872)$ dynamics, assuming it is a loosely bound $D^0 \bar{D}^{*0}$ molecule. Our result is based on the distorted wave Born approximation in non-relativistic quantum mechanics. Despite their long-range nature, we find that pion interactions cannot produce a large and negative effective range. Nonetheless, they introduce imaginary parts. In particular, they contribute to the total decay width of the $X(3872)$ with a term associated with, but not precisely corresponding to, the $D^*$ width. Our approach can also be applied to the recently discovered $T_{cc}^+$ states., Comment: 9 pages, 1 figure. v2: minor changes. Comparison with ref. [26] improved

We explore an odd class of QFTs where a hierarchy problem is resolved with new dynamics as opposed to new particles. The essential element of our construction is a $U(1)$ pseudo-NG boson with symmetry breaking interactions all characterized by a large number $N$ of units of the fundamental charge. In the resulting effective theory, quantum corrections, like those to the effective potential and mass, which are normally power divergent and saturated at the UV cut-off, are instead saturated at a much lower scale. This critical scale, which does not involve any new particle, corresponds to the onset of unsuppressed multiparticle production in scattering processes. Remarkably this all happens within the tractable domain of weak coupling. Terms involving arbitrarily high powers of the Goldstone field must however be taken into account. In particular, a truncation to the renormalizable part of the effective Lagrangian would completely miss the physics., Comment: 22 pages, 2 figures, v2. fixed typos

A muon collider would enable the big jump ahead in energy reach that is needed for a fruitful exploration of fundamental interactions. The challenges of producing muon collisions at high luminosity and 10~TeV centre of mass energy are being investigated by the recently-formed International Muon Collider Collaboration. This Review summarises the status and the recent advances on muon colliders design, physics and detector studies. The aim is to provide a global perspective of the field and to outline directions for future work., Comment: 118 pages, 103 figures

We consider the field theory that defines a perfect incompressible 2D fluid. One distinctive property of this system is that the quadratic action for fluctuations around the ground state features neither mass nor gradient term. Quantum mechanically this poses a technical puzzle, as it implies the Hilbert space of fluctuations is not a Fock space and perturbation theory is useless. As we show, the proper treatment must instead use that the configuration space is the area preserving Lie group $S\mathrm{Diff}$. Quantum mechanics on Lie groups is basically a group theory problem, but a harder one in our case, since $S\mathrm{Diff}$ is infinite dimensional. Focusing on a fluid on the 2-torus $T^2$, we could however exploit the well known result $S\mathrm{Diff}(T^2)\sim SU(N)$ for $N\to \infty$, reducing for finite $N$ to a tractable case. $SU(N)$ offers a UV-regulation, but physical quantities can be robustly defined in the continuum limit $N\to\infty$. The main result of our study is the existence of ungapped localized excitations, the vortons, satisfying a dispersion $\omega \propto k^2$ and carrying a vorticity dipole. The vortons are also characterized by very distinctive derivative interactions whose structure is fixed by symmetry. Departing from the original incompressible fluid, we constructed a class of field theories where the vortons appear, right from the start, as the quanta of either bosonic or fermionic local fields., Comment: 63 pages, 8 figures

The Large Charge sector of Conformal Field Theory (CFT) can generically be described through a semiclassical expansion around a superfluid background. In this work, focussing on $U(1)$ invariant Wilson-Fisher fixed points, we study the spectrum of spinning large charge operators. For sufficiently low spin these correspond to the phonon excitations of the superfluid state. We discuss the organization of these states into conformal multiplets and the form of the corresponding composite operators in the free field theory limit. The latter entails a mapping, built order-by-order in the inverse charge $n^{-1}$, between the Fock space of vacuum fluctuations and the Fock space of fluctuations around the superfluid state. We discuss the limitations of the semiclassical method, and find that the phonon description breaks down for spins of order $n^{1/2}$ while the computation of observables is valid up to spins of order $n$. Finally, we apply the semiclassical method to compute some conformal 3-point and 4-point functions, and analyze the conformal block decomposition of the latter with our knowledge of the operator spectrum., Comment: 45 pages + appendices, 5 figures

In the path towards a muon collider with center of mass energy of 10 TeV or more, a stage at 3 TeV emerges as an appealing option. Reviewing the physics potential of such muon collider is the main purpose of this document. In order to outline the progression of the physics performances across the stages, a few sensitivity projections for higher energy are also presented. There are many opportunities for probing new physics at a 3 TeV muon collider. Some of them are in common with the extensively documented physics case of the CLIC 3 TeV energy stage, and include measuring the Higgs trilinear coupling and testing the possible composite nature of the Higgs boson and of the top quark at the 20 TeV scale. Other opportunities are unique of a 3 TeV muon collider, and stem from the fact that muons are collided rather than electrons. This is exemplified by studying the potential to explore the microscopic origin of the current $g$-2 and $B$-physics anomalies, which are both related with muons., Comment: 73 pages, 28 figures; Contribution to Snowmass 2021

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 study the potential of lepton collisions with about $10\text{ TeV}$ center of mass energy to probe Electroweak, Higgs and Top short-distance physics at the $100\text{ TeV}$ scale, pointing out the interplay with the long-distance ($100\text{ GeV}$) phenomenon of Electroweak radiation. On one hand, we find that sufficiently accurate theoretical predictions require the resummed inclusion of radiation effects, which we perform at the double logarithmic order. On the other hand, we notice that short-distance physics does influence the emission of Electroweak radiation. Therefore the investigation of the radiation pattern can enhance the sensitivity to new short-distance physical laws. We illustrate these aspects by studying Effective Field Theory contact interactions in di-fermion and di-boson production, and comparing cross-section measurements that require or that exclude the emission of massive Electroweak bosons. The combination of the two types of measurements is found to enhance the sensitivity to the new interactions. Based on these results, we perform sensitivity projections to Higgs and Top Compositeness and to minimal $Z'$ new physics scenarios at future muon colliders., Comment: 48 pages, 17 figures

We find the complete set of conditions satisfied by the forward $2\to2$ scattering amplitude in unitarity and causal theories. These are based on an infinite set of energy dependent quantities -- the arcs -- which are dispersively expressed as moments of a positive measure defined at (arbitrarily) higher energies. We identify optimal finite subsets of constraints, suitable to bound Effective Field Theories (EFTs), at any finite order in the energy expansion. At tree-level arcs are in one-to-one correspondence with Wilson coefficients. We establish under which conditions this approximation applies, identifying seemingly viable EFTs where it never does. In all cases, we discuss the range of validity in both couplings and energy. We also extend our results to the case of small but finite~$t$. A consequence of our study is that EFTs in which the scattering amplitude in some regime grows in energy faster than $E^6$ cannot be UV-completed., Comment: 15 pages, v2 matches published version

At finite density, the spontaneous breakdown of an internal non-Abelian symmetry dictates, along with gapless modes, modes whose gap is fixed by the algebra and proportional to the chemical potential: the gapped Goldstones. Generically the gap of these states is comparable to that of other non-universal excitations or to the energy scale where the dynamics is strongly coupled. This makes it non-straightforward to derive a universal ef effective field theory (EFT) description realizing all the symmetries. Focusing on the illustrative example of a fully broken SU (2) group, we demonstrate that such an EFT can be constructed by carving out around the Goldstones, gapless and gapped, at small 3-momentum. The rules governing the EFT, where the gapless Goldstones are soft while the gapped ones are slow, are those of standard nonrelativistic EFTs, like for instance nonrelativistic QED. In particular, the EFT Lagrangian formally preserves gapped Goldstone number, and processes where such number is not conserved are described inclusively by allowing for imaginary parts in the Wilson coefficients. Thus, while the symmetry is manifestly realized in the EFT, unitarity is not. We comment on the application of our construction to the study of the large charge sector of conformal field theories with non-Abelian symmetries., Comment: 32 pages+appendices, 3 figures, v2 matches journal version

In arXiv:1909.01269 it was shown that the scaling dimension of the lightest charge $n$ operator in the $U(1)$ model at the Wilson-Fisher fixed point in $d=4-\varepsilon$ can be computed semiclassically for arbitrary values of $\lambda n$, where $\lambda$ is the perturbatively small fixed point coupling. Here we generalize this result to the fixed point of the $U(1)$ model in $3-\varepsilon$ dimensions. The result interpolates continuously between diagrammatic calculations and the universal conformal superfluid regime for CFTs at large charge. In particular it reproduces the expectedly universal $O(n^0)$ contribution to the scaling dimension of large charge operators in $3d$ CFTs., Comment: 7 pages, v2 typos fixed, match journal version

We study the scaling dimension $\Delta_{\phi^n}$ of the operator $\phi^n$ where $\phi$ is the fundamental complex field of the $U(1)$ model at the Wilson-Fisher fixed point in $d=4-\varepsilon$. Even for a perturbatively small fixed point coupling $\lambda_*$, standard perturbation theory breaks down for sufficiently large $\lambda_*n$. Treating $\lambda_* n$ as fixed for small $\lambda_*$ we show that $\Delta_{\phi^n}$ can be successfully computed through a semiclassical expansion around a non-trivial trajectory, resulting in $$ \Delta_{\phi^n}=\frac{1}{\lambda_*}\Delta_{-1}(\lambda_* n)+\Delta_{0}(\lambda_* n)+\lambda_* \Delta_{1}(\lambda_* n)+\ldots $$ We explicitly compute the first two orders in the expansion, $\Delta_{-1}(\lambda_* n)$ and $\Delta_{0}(\lambda_* n)$. The result, when expanded at small $\lambda_* n$, perfectly agrees with all available diagrammatic computations. The asymptotic at large $\lambda_* n$ reproduces instead the systematic large charge expansion, recently derived in CFT. Comparison with Monte Carlo simulations in $d=3$ is compatible with the obvious limitations of taking $\varepsilon=1$, but encouraging., Comment: 24 pages + appendices, 2 figures v2 fixed typos

We classify effective field theory (EFT) deformations of the Standard Model (SM) according to the analyticity property of the Lagrangian as a function of the Higgs doublet H. Our distinction in analytic and non-analytic corresponds to the more familiar one between linearly and non-linearly realized electroweak symmetry, but offers deeper physical insight. From the UV perspective, non-analyticity occurs when the new states acquire mass from electroweak symmetry breaking, and thus cannot be decoupled to arbitrarily high scales. This is reflected in the IR by the anomalous growth of the interaction strength for processes involving many Higgs bosons and longitudinally polarized massive vectors, with a breakdown of the EFT description below a scale $O(4 \pi v)$. Conversely, analyticity occurs when new physics can be pushed parametrically above the electroweak scale. We illustrate the physical distinction between these two EFT families by discussing Higgs boson self-interactions. In the analytic case, at the price of some unnaturalness in the Higgs potential, there exists space for $O(1)$ deviations of the cubic coupling, compatible with single Higgs and electroweak precision measurements, and with new particles out of the direct LHC reach. Larger deviations are possible, but subject to less robust assumptions about higher-dimensional operators in the Higgs potential. On the other hand, when the cubic coupling is produced by a non-analytic deformation of the SM, we show by an explicit calculation that the theory reaches strong coupling at $O(4 \pi v)$, quite independently of the magnitude of the cubic enhancement., Comment: 17 pages; v2: comments and references added, published version

Conventional scenarios of electroweak (EW) baryogenesis are strongly constrained by experimental searches for CP violation beyond the SM. We propose an alternative scenario where the EW phase transition and baryogenesis occur at temperatures of the order of a new physics threshold $\Lambda$ far above the Fermi scale, say, in the $100-1000$ TeV range. This way the needed new sources of CP-violation, together with possible associated flavor-violating effects, decouple from low energy observables. The key ingredient is a new CP- and flavor-conserving sector at the Fermi scale that ensures the EW symmetry remains broken and sphalerons suppressed at all temperatures below $\Lambda$. We analyze a minimal incarnation based on a linear $O(N)$ model. We identify a specific large-$N$ limit where the effects of the new sector are vanishingly small at zero temperature while being significant at finite temperature. This crucially helps the construction of realistic models. A number of accidental factors, ultimately related to the size of the relevant SM couplings, force $N$ to be above $\sim 100$. Such a large $N$ may seem bizarre, but it does affect the simplicity of the model and in fact it allows us to carry out a consistent re-summation of the leading contributions to the thermal effective potential. Extensions of the SM Higgs sector can be compatible with smaller values $N\sim 20-30$. Collider signatures are all parametrically suppressed by inverse powers of $N$ and may be challenging to probe, but present constraints from direct dark matter searches cannot be accommodated in the minimal model. We discuss various extensions that satisfy all current bounds. One of these involves a new gauge force confining at scales between $\sim1$ GeV and the weak scale., Comment: V2 matches published version

We calculate the scaling dimensions of operators with large global charge and spin in 2+1 dimensional conformal field theories. By the state-operator correspondence, these operators correspond to superfluids with vortices and can be systematically studied using effective field theory. As the spin increases from zero to the unitarity bound, the superfluid state corresponding to the lowest dimension operator passes through three distinct regimes: (1) a single phonon, (2) two vortices, and (3) multiple vortices. We also calculate correlation functions with two such operators and the Noether current., Comment: 7 pages

The spectrum of primordial gravitational waves is one of the most robust inflationary observables, often thought of as a direct probe of the energy scale of inflation. We present a simple model, where the dynamics controlling this observable is very different than in the standard paradigm of inflation. The model is based on a peculiar finite density phase---the magnetic gaugid---which stems from a highly non-linear effective theory of a triplet of abelian gauge fields. The gaugid extends the notion of homogeneous isotropic solid, in that its spectrum of fluctuations includes helicity-2 phonons. We show how, upon implementing the gaugid to drive inflation, the helicity-2 phonon mixes with the graviton, significantly affecting the size of the primordial tensor spectrum. The rest of the features of the theory, in particular the vector and scalar perturbations, closely resemble those of solid inflation., Comment: 35+8 pages

We analyze the parametric structure of Twin Higgs (TH) theories and assess the gain in fine tuning which they enable compared to extensions of the Standard Model with colored top partners. Estimates show that, at least in the simplest realizations of the TH idea, the separation between the mass of new colored particles and the electroweak scale is controlled by the coupling strength of the underlying UV theory, and that a parametric gain is achieved only for strongly-coupled dynamics. Motivated by this consideration we focus on one of these simple realizations, namely composite TH theories, and study how well such constructions can reproduce electroweak precision data. The most important effect of the Twin states is found to be the infrared contribution to the Higgs quartic coupling, while direct corrections to electroweak observables are sub-leading and negligible. We perform a careful fit to the electroweak data including the leading-logarithmic corrections to the Higgs quartic up to three loops. Our analysis shows that agreement with electroweak precision tests can be achieved with only a moderate amount of tuning, in the range 5-10\%, in theories where colored states have mass of order 3-5 TeV and are thus out of reach of the LHC. For these levels of tuning, larger masses are excluded by a perturbativity bound, which makes these theories possibly discoverable, hence falsifiable, only at a future 100 TeV collider., Comment: 50 pages (29 + appendices), 9 figures; v2: the section and appendix on the Higgs potential have been updated, the results are unchanged

Hellerman et al. (arXiv:1505.01537) have shown that in a generic CFT the spectrum of operators carrying a large U(1) charge can be analyzed semiclassically in an expansion in inverse powers of the charge. The key is the operator state correspondence by which such operators are associated with a finite density superfluid phase for the theory quantized on the cylinder. The dynamics is dominated by the corresponding Goldstone hydrodynamic mode and the derivative expansion coincides with the inverse charge expansion. We illustrate and further clarify this situation by first considering simple quantum mechanical analogues. We then systematize the approach by employing the coset construction for non-linearly realized space-time symmetries. Focussing on CFT3 we illustrate the case of higher rank and non-abelian groups and the computation of higher point functions. Three point function coefficients turn out to satisfy universal scaling laws and correlations as the charge and spin are varied., Comment: 40+8 pages, 2 figures

Even though the Standard Model (SM) is weakly coupled at the Fermi scale, a new strong dynamics involving its degrees of freedom may conceivably lurk at slightly higher energies, in the multi TeV range. Approximate symmetries provide a structurally robust context where, within the low energy description, the dimensionless SM couplings are weak, while the new strong dynamics manifests itself exclusively through higher-derivative interactions. We present an exhaustive classification of such scenarios in the form of effective field theories, paying special attention to new classes of models where the strong dynamics involves, along with the Higgs boson, the SM gauge bosons and/or the fermions. The IR softness of the new dynamics suppresses its effects at LEP energies, but deviations are in principle detectable at the LHC, even at energies below the threshold for production of new states. Our construction provides the so far unique structurally robust context where to motivate several searches in Higgs physics, diboson production, or WW scattering, which were so far poorly justified. Perhaps surprisingly, the interplay between weak coupling, strong coupling and derivatives, which is controlled by symmetries, can override the naive expansion in operator dimension, providing instances where dimension-8 dominates dimension-6, well within the domain of validity of the low energy effective theory. This result reveals the limitations of an analysis that is both ambitiously general and restricted to dimension-6 operators., Comment: 37 pages, 1 figure

Run 2 LHC data show hints of a new resonance in the diphoton distribution at an invariant mass of 750 GeV. We analyse the data in terms of a new boson, extracting information on its properties and exploring theoretical interpretations. Scenarios covered include a narrow resonance and, as preliminary indications suggest, a wider resonance. If the width indications persist, the new particle is likely to belong to a strongly-interacting sector. We also show how compatibility between Run 1 and Run 2 data is improved by postulating the existence of an additional heavy particle, whose decays are possibly related to dark matter., Comment: v2: 45 pages, 12 figures, final. Factor of 2 changed in table 1, 4th row

We present a renormalizable theory of scalars in which the low energy effective theory contains a pseudo-Goldstone Boson with a compact field space of 2{\pi} F and an approximate discrete shift symmetry Z_Q with Q>>1, yet the number of fields in the theory goes as log(Q). Such a model can serve as a UV completion to models of relaxions and is a new source of exponential scale separation in field theory. While the model is local in `theory space', it appears to not have a continuum generalization (i.e., it cannot be a deconstructed extra dimension). Our framework shows that super-Planckian field excursions can be mimicked while sticking to renormalizable four-dimensional quantum field theory. We show that a supersymmetric extension is straightforwardly obtained and we illustrate possible UV completions based on a compact extra-dimension, where all global symmetries arise accidentally as a consequence of gauge invariance and 5D locality., Comment: 6 pages

Based on an explicit model, we propose and discuss the generic features of a possible implementation of the Twin Higgs program in the context of composite Higgs models. We find that the Twin Higgs quadratic divergence cancellation argument can be uplifted to a genuine protection of the Higgs potential, based on symmetries and selection rules, but only under certain conditions which are not fulfilled in some of the existing models. We also find that a viable scenario, not plagued by a massless Twin Photon, can be obtained by not gauging the Twin Hypercharge and taking this as the only source of Twin Symmetry breaking at a very high scale., Comment: 19 pages; v2: typos and notation corrected, results unchanged; v3: published version

We classify condensed matter systems in terms of the spacetime symmetries they spontaneously break. In particular, we characterize condensed matter itself as any state in a Poincar\'e-invariant theory that spontaneously breaks Lorentz boosts while preserving at large distances some form of spatial translations, time-translations, and possibly spatial rotations. Surprisingly, the simplest, most minimal system achieving this symmetry breaking pattern---the "framid"---does not seem to be realized in Nature. Instead, Nature usually adopts a more cumbersome strategy: that of introducing internal translational symmetries---and possibly rotational ones---and of spontaneously breaking them along with their space-time counterparts, while preserving unbroken diagonal subgroups. This symmetry breaking pattern describes the infrared dynamics of ordinary solids, fluids, superfluids, and---if they exist---supersolids. A third, "extra-ordinary", possibility involves replacing these internal symmetries with other symmetries that do not commute with the Poincar\'e group, for instance the galileon symmetry, supersymmetry or gauge symmetries. Among these options, we pick the systems based on the galileon symmetry, the "galileids", for a more detailed study. Despite some similarity, all different patterns produce truly distinct physical systems with different observable properties. For instance, the low-energy $2\to 2$ scattering amplitudes for the Goldstone excitations in the cases of framids, solids and galileids scale respectively as $E^2$, $E^4$, and $E^6$. Similarly the energy momentum tensor in the ground state is "trivial" for framids ($\rho +p=0$), normal for solids ($\rho+p>0$) and even inhomogenous for galileids., Comment: 58 pages, 1 table, 1 free cut-and-paste project for rainy days in Appendix

The local Callan-Symanzik equation describes the response of a quantum field theory to local scale transformations in the presence of background sources. The consistency conditions associated with this anomalous equation imply non-trivial relations among the $\beta$-function, the anomalous dimensions of composite operators and the short distance singularities of correlators. In this paper we discuss various aspects of the local Callan-Symanzik equation and present new results regarding the structure of its anomaly. We then use the equation to systematically write the n-point correlators involving the trace of the energy-momentum tensor. We use the latter result to give a fully detailed proof that the UV and IR asymptotics in a neighbourhood of a 4D CFT must also correspond to CFTs. We also clarify the relation between the matrix entering the gradient flow formula for the $\beta$-function and a manifestly positive metric in coupling space associated with matrix elements of the trace of the energy momentum tensor., Comment: v2: Modified discussion of the amplitude; v3: typos fixed

We study the impact of Higgs precision measurements at a high-energy and high-luminosity linear electron positron collider, such as CLIC or the ILC, on the parameter space of a strongly interacting Higgs boson. Some combination of anomalous couplings are already tightly constrained by current fits to electroweak observables. However, even small deviations in the cross sections of single and double Higgs production, or the mere detection of a triple Higgs final state, can help establish whether it is a composite state and whether or not it emerges as a pseudo-Nambu-Goldstone boson from an underlying broken symmetry. We obtain an estimate of the ILC and CLIC sensitivities on the anomalous Higgs couplings from a study of WW scattering and hh production which can be translated into a sensitivity on the compositeness scale 4\pi f, or equivalently on the degree of compositeness \xi=v^2/f^2. We summarize the current experimental constraints, from electroweak data and direct resonance searches, and the expected reach of the LHC and CLIC on \xi and on the scale of the new resonances., Comment: 47 pages, 11 figures. v2: eq. 25 has been fixed and the sensitivities quoted in the conclusions slightly revised. Final version to appear on JHEP

Goldstone's theorem does not apply straightforwardly to the case of spontaneously broken scale invariance. We elucidate under what conditions a light scalar degree of freedom, identifiable with the dilaton, can naturally arise. Our construction can be considered an explicit dynamical solution to the cosmological constant problem in the scalar version of gravity., Comment: v2: published version

We provide a systematic effective lagrangian description of the phenomenology of the lightest top-partners in composite Higgs models. Our construction is based on symmetry, on selection rules and on plausible dynamical assumptions. The structure of the resulting simplified models depends on the quantum numbers of the lightest top partner and of the operators involved in the generation of the top Yukawa. In all cases the phenomenology is conveniently described by a small number of parameters, and the results of experimental searches are readily interpreted as a test of naturalness. We recast presently available experimental bounds on heavy fermions into bounds on top partners: LHC has already stepped well inside the natural region of parameter space., Comment: 44 pages, 12 figures. Minor corrections to match published version

We clarify questions related to the convergence of the OPE and conformal block decomposition in unitary Conformal Field Theories (for any number of spacetime dimensions). In particular, we explain why these expansions are convergent in a finite region. We also show that the convergence is exponentially fast, in the sense that the operators of dimension above Delta contribute to correlation functions at most exp(-a Delta). Here the constant a>0 depends on the positions of operator insertions and we compute it explicitly., Comment: 26 pages, 6 figures; v2: a clarifying note and two refs added; v3: note added concerning an extra constant factor in the main error estimate, misprint corrected

Recently, the LHCb and CDF collaborations reported the measure of an unexpectedly large direct CP asymmetry in D meson decays. In this paper we ask if new physics associated with Partial Compositeness could plausibly explain this result. We find that Composite Higgs models with mass scale around 10 TeV can account for it, while marginally satisfying all other flavor constraints in the quark sector. The minimal framework is however inadequate in the lepton sector due to the strong constraint from \mu\ to e \gamma. This tension can be efficiently alleviated by realizing Partial Compositeness within Supersymmetry. The resulting models can saturate the CP asymmetry in D decays for superpartner masses close to the TeV scale and somewhat large A-terms. The supersymmetric realization of Partial Compositeness also offers a predictive and phenomenologically viable organizing principle for R-Parity violation, and may result in very distinctive signatures at hadron colliders. With or without Supersymmetry, the neutron EDM is expected to be around the present experimental sensitivity., Comment: 35 pages, 2 tables, 3 figures. v2: published version

Dark matter, gauge coupling unification, and the strong CP problem find a common and simple solution (in the absence of naturalness) within axion models. We show that such solution, even without specifying the details of the model implementation, makes testable predictions for the experimentally measurable axion parameters: the axion mass and its coupling to photons., Comment: 16 pages, 5 figures

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

We analyze the kinematic conditions under which the scattering of equivalent massive spin-1 vector bosons factorizes out of the complete process. In practice, we derive the conditions for the validity of the effective W approximation, proposed long ago but never established on a firm basis. We also present a parametric estimate of the corrections to the approximation and explicitly check its validity in two examples., Comment: 36 pages, 14 figures, references added

We consider a generic composite Higgs model based on the coset SO(5)/SO(4) and study its phenomenology beyond the leading low-energy effective lagrangian approximation. Our basic goal is to introduce in a controllable and simple way the lowest-lying, possibly narrow, resonances that may exist is such models. We do so by proposing a criterion that we call partial UV completion. We characterize the simplest cases, corresponding respectively to a scalar in either singlet or tensor representation of SO(4) and to vectors in the adjoint of SO(4). We study the impact of these resonances on the signals associated to high-energy vector boson scattering, pointing out for each resonance the characteristic patterns of depletion and enhancement with respect to the leading-order chiral lagrangian. En route we derive the O(p^4) general chiral lagrangian and discuss its peculiar accidental and approximate symmetries., Comment: v3: a few typos corrected. Conclusions unchanged

We characterize models where electroweak symmetry breaking is driven by two light Higgs doublets arising as pseudo-Nambu-Goldstone bosons of new dynamics above the weak scale. They represent the simplest natural two Higgs doublet alternative to supersymmetry. We construct their low-energy effective Lagrangian making only few specific assumptions about the strong sector. These concern their global symmetries, their patterns of spontaneous breaking and the sources of explicit breaking. In particular we assume that all the explicit breaking is associated with the couplings of the strong sector to the Standard Model fields, that is gauge and (proto)-Yukawa interactions. Under those assumptions the scalar potential is determined at lowest order by very few free parameters associated to the top sector. Another crucial property of our scenarios is the presence of a discrete symmetry, in addition to custodial SO(4), that controls the $T$-parameter. That can either be simple CP or a $Z_2$ that distinguishes the two Higgs doublets. Among various possibilities we study in detail models based on SO(6)/SO(4)$\times$ SO(2), focussing on their predictions for the structure of the scalar spectrum and the deviations of their couplings from those of a generic renormalizable two Higgs doublet model., Comment: 54 pages

It has been recently pointed out that the unavoidable tuning among supersymmetric parameters required to raise the Higgs boson mass beyond its experimental limit opens up new avenues for dealing with the so called $\mu$-$B_\mu$ problem of gauge mediation. In fact, it allows for accommodating, with no further parameter tuning, large values of $B_\mu$ and of the other Higgs-sector soft masses, as predicted in models where both $\mu$ and $B_\mu$ are generated at one-loop order. This class of models, called Lopsided Gauge Mediation, offers an interesting alternative to conventional gauge mediation and is characterized by a strikingly different phenomenology, with light higgsinos, very large Higgs pseudoscalar mass, and moderately light sleptons. We discuss general parametric relations involving the fine-tuning of the model and various observables such as the chargino mass and the value of $\tan\beta$. We build an explicit model and we study the constraints coming from LEP and Tevatron. We show that in spite of new interactions between the Higgs and the messenger superfields, the theory can remain perturbative up to very large scales, thus retaining gauge coupling unification., Comment: 28 pages, 2 appendices, 10 figures

We consider the canonical quantization of an ordinary fluid. The resulting long-distance effective field theory is derivatively coupled, and therefore strongly coupled in the UV. The system however exhibits a number of peculiarities, associated with the vortex degrees of freedom. On the one hand, these have formally a vanishing strong-coupling energy scale, thus suggesting that the effective theory's regime of validity is vanishingly narrow. On the other hand, we prove an analog of Coleman's theorem, whereby the semiclassical vacuum has no quantum counterpart, thus suggesting that the vortex premature strong-coupling phenomenon stems from a bad identification of the ground state and of the perturbative degrees of freedom. Finally, vortices break the usual connection between short distances and high energies, thus potentially impairing the unitarity of the effective theory., Comment: 35 pages

We explore the constraining power of OPE associativity in 4D Conformal Field Theory with a continuous global symmetry group. We give a general analysis of crossing symmetry constraints in the 4-point function , where Phi is a primary scalar operator in a given representation R. These constraints take the form of 'vectorial sum rules' for conformal blocks of operators whose representations appear in R x R and R x Rbar. The coefficients in these sum rules are related to the Fierz transformation matrices for the R x R x Rbar x Rbar invariant tensors. We show that the number of equations is always equal to the number of symmetry channels to be constrained. We also analyze in detail two cases - the fundamental of SO(N) and the fundamental of SU(N). We derive the vectorial sum rules explicitly, and use them to study the dimension of the lowest singlet scalar in the Phi x Phi* OPE. We prove the existence of an upper bound on the dimension of this scalar. The bound depends on the conformal dimension of Phi and approaches 2 in the limit dim(Phi)-->1. For several small groups, we compute the behavior of the bound at dim(Phi)>1. We discuss implications of our bound for the Conformal Technicolor scenario of electroweak symmetry breaking., Comment: 30 pages

We derive model-independent lower bounds on the stress tensor central charge C_T in terms of the operator content of a 4-dimensional Conformal Field Theory. More precisely, C_T is bounded from below by a universal function of the dimensions of the lowest and second-lowest scalars present in the CFT. The method uses the crossing symmetry constraint of the 4-point function, analyzed by means of the conformal block decomposition., Comment: 16 pages, 6 figures

The hierarchy problem and the electroweak data, together, provide a plausible motivation for considering a light Higgs emerging as a pseudo-Goldstone boson from a strongly-coupled sector. In that scenario, the rates for Higgs production and decay differ significantly from those in the Standard Model. However, one genuine strong coupling signature is the growth with energy of the scattering amplitudes among the Goldstone bosons, the longitudinally polarized vector bosons as well as the Higgs boson itself. The rate for double Higgs production in vector boson fusion is thus enhanced with respect to its negligible rate in the SM. We study that reaction in pp collisions, where the production of two Higgs bosons at high pT is associated with the emission of two forward jets. We concentrate on the decay mode hh -> WW^(*)WW^(*) and study the semi-leptonic decay chains of the W's with 2, 3 or 4 leptons in the final states. While the 3 lepton final states are the most relevant and can lead to a 3 sigma signal significance with 300 fb^{-1} collected at a 14 TeV LHC, the two same-sign lepton final states provide complementary information. We also comment on the prospects for improving the detectability of double Higgs production at the foreseen LHC energy and luminosity upgrades., Comment: 54 pages, 26 figures. v2: typos corrected, a few comments and one table added. Version published in JHEP

In QFT, the null energy condition (NEC) for a classical field configuration is usually associated with that configuration's stability against small perturbations, and with the sub-luminality of these. Here, we exhibit an effective field theory that allows for stable NEC-violating solutions with exactly luminal excitations only. The model is the recently introduced `galileon', or more precisely its conformally invariant version. We show that the theory's low-energy S-matrix obeys standard positivity as implied by dispersion relations. However we also show that if the relevant NEC-violating solution is inside the effective theory, then other (generic) solutions allow for superluminal signal propagation. While the usual association between sub-luminality and positivity is not obeyed by our example, that between NEC and sub-luminality is, albeit in a less direct way than usual., Comment: 21 pages. v2: Typos in eq. (2.41) and (2.41) corrected; discussion of section 2.3 modified accordingly. Other sections and conclusions unchanged. Matches the Erratum published in JHEP