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Dark matter models can give rise to specific signatures at particle physics experiments or in cosmology. The details of the cosmological history can also influence the new physics signals to be expected at e.g. collider experiments. In these proceedings, we briefly summarize the case of dark matter weakly to feebly coupled to Standard Model fermions through t-channel portal dividing the discussion into three main regimes. We also underline the interplay between cosmology and particle physics., Comment: 6pp, proceedings LFC22

We consider a scenario in which the dark matter is alone in a hidden sector and consists of a real scalar particle with a manifest or spontaneously broken $\mathbb{Z}_2$ symmetry, at a temperature which differs from the one of the visible sector, $T' \neq T$. While similar models with general couplings have already been studied in the literature, the special case of a model with spontaneous symmetry breaking constitutes a non-trivial limit of these results, since it features vanishing tree-level amplitudes for the processes $k \rightarrow 2$ with $k>2$ at threshold, thus making the cross-section governing dark-matter freeze-out velocity suppressed. We carefully determine the thermally averaged dark-matter annihilation cross-section in this scenario, including the possible effects of one-loop corrections and Bose-Einstein statistics, while also reporting our results in the domain of thermal dark matter candidates, $T'_\text{fo}/T$ vs. $m_\text{DM}$ with $T'_\text{fo}$ being the hidden-sector temperature at decoupling. We show that for fixed quartic coupling, due to entropy conservation, the thermal candidates lie along a curve $T'/T \propto m_\text{DM}^{-1/3 (1+\kappa)}$ with anomalous scaling $\kappa \sim \mathcal{O}(T'_\text{fo}/m_\text{DM}) > 0$. Furthermore, we demonstrate that this scaling is valid for a broad class of cannibal DM scenarios, with or without symmetry breaking. In addition, we also discuss the relevant cosmological and astrophysical constraints., Comment: 26 pages, 6 figures; v2: added discussion on domain-wall formation, matches published version

We present the experimental discovery of multiple simultaneous degeneracies in the spectrum of a Kerr oscillator subjected to a squeezing drive. This squeezing, in combination with the Kerr interaction creates an effective static two-well potential in the frame rotating at half the frequency of the sinusoidal driving force. Remarkably, these degeneracies can be turned on-and-off on demand, and their number is tunable. We find that when the detuning $\Delta$ between the frequency of the oscillator and characteristic frequency of the drive equals an even multiple of the Kerr coefficient $K$, $\Delta/K = 2m$, the oscillator displays $m + 1$ exact, parity-protected, spectral degeneracies, insensitive to the drive amplitude. The degeneracies stem from the unusual destructive interference of tunnel paths in the classically forbidden region of the double well static effective potential that models our experiment. Exploiting this interference, we measure a peaked enhancement of the incoherent well-switching lifetime creating a super-protected cat qubit in the ground state manifold of our oscillator. {Our results demonstrate the relationship between degeneracies and noise protection in quantum systems.

Transmon qubits are the predominant element in circuit-based quantum information processing, such as existing quantum computers, due to their controllability and ease of engineering implementation. But more than qubits, transmons are multilevel nonlinear oscillators that can be used to investigate fundamental physics questions. Here, they are explored as simulators of excited state quantum phase transitions (ESQPTs), which are generalizations of quantum phase transitions to excited states. We show that the spectral kissing (coalescence of pairs of energy levels) experimentally observed in the effective Hamiltonian of a driven SNAIL-transmon is an ESQPT precursor. We explore the dynamical consequences of the ESQPT, which include the exponential growth of out-of-time-ordered correlators, followed by periodic revivals, and the slow evolution of the survival probability due to localization. These signatures of ESQPT are within reach for current superconducting circuits platforms and are of interest to experiments with cold atoms and ion traps., Comment: 18 pages, 7 figures

We derive the static effective Lindbladian beyond the rotating wave approximation (RWA) for a driven nonlinear oscillator coupled to a bath of harmonic oscillators. The associated dissipative effects may explain orders of magnitude differences between the predictions of the ordinary RWA model and results from recent superconducting circuits experiments on the Kerr-cat qubit. The higher-order dissipators found in our calculations have important consequences for quantum error-correction protocols and parametric processses.

By applying a microwave drive to a specially designed Josephson circuit, we have realized an elementary quantum optics model, the squeezed Kerr oscillator. This model displays, as the squeezing amplitude is increased, a cross-over from a single ground state regime to a doubly-degenerate ground state regime. In the latter case, the ground state manifold is spanned by Schr\"odinger-cat states, i.e. quantum superpositions of coherent states with opposite phases. For the first time, having resolved up to the tenth excited state in a spectroscopic experiment, we confirm that the proposed emergent static effective Hamiltonian correctly describes the system, despite its driven character. We also find that the lifetime of the coherent state components of the cat states increases in steps as a function of the squeezing amplitude. We interpret the staircase pattern as resulting from pairwise level kissing in the excited state spectrum. Considering the Kerr-cat qubit encoded in this ground state manifold, we achieve for the first time quantum nondemolition readout fidelities greater than 99%, and enhancement of the phase-flip lifetime by more than two orders of magnitude, while retaining universal quantum control. Our experiment illustrates the crucial role of parametric drive Hamiltonian engineering for hardware-efficient quantum computation.

We explore the possible phases of a condensed dark matter (DM) candidate taken to be in the form of a fermion with a Yukawa coupling to a scalar particle, at zero temperature but at finite density. This theory essentially depends on only four parameters, the Yukawa coupling, the fermion mass, the scalar mediator mass, and the DM density. At low fermion densities we delimit the Bardeen-Cooper-Schrieffer (BCS), Bose-Einstein Condensate (BEC) and crossover phases as a function of model parameters using the notion of scattering length. We further study the BCS phase by consistently including emergent effects such as the scalar density condensate and superfluid gaps. Within the mean field approximation, we derive the consistent set of gap equations, retaining their momentum dependence, and valid in both the non-relativistic and relativistic regimes. We present numerical solutions to the set of gap equations, in particular when the mediator mass is smaller and larger than the DM mass. Finally, we discuss the equation of state (EoS) and possible astrophysical implications for asymmetric DM., Comment: 10+19 pages, 6+8 figures

Single-charge tunneling is a decoherence mechanism affecting superconducting qubits, yet the origin of excess quasiparticle excitations (QPs) responsible for this tunneling in superconducting devices is not fully understood. We measure the flux dependence of charge-parity (or simply, ``parity'') switching in an offset-charge-sensitive transmon qubit to identify the contributions of photon-assisted parity switching and QP generation to the overall parity-switching rate. The parity-switching rate exhibits a qubit-state-dependent peak in the flux dependence, indicating a cold distribution of excess QPs which are predominantly trapped in the low-gap film of the device. Moreover, we find that the photon-assisted process contributes significantly to both parity switching and the generation of excess QPs by fitting to a model that self-consistently incorporates photon-assisted parity switching as well as inter-film QP dynamics.

Among the upgrades in current high energy physics (HEP) experiments and the new facilities coming online, solving software challenges has become integral for the success of the collaborations, The demand for human resources highly-skilled in both HEP and software domains is increasing. With a highly distributed environment in human resources, the sustainability of the HEP ecosystem requires a continuous effort in the equipment of physicists with the required abilities in software development. In this paper, the collective software training program in HEP and its activities led by the HEP Software Foundation (HSF) and the Institute for Research and Innovation in Software in HEP (IRIS-HEP) are presented. Experiment-agnostic, open, and accessible modules for training have been developed, focusing on common software material with ranges from core software skills needed by everyone to advanced training required to produce high-quality sustainable software. A basic software curriculum was built, and an introductory software training event has been prepared to serve HEP entrants. This program serves individuals with transferable skills that are becoming increasingly important to careers in the realm of software and computing, whether inside or outside HEP., Comment: Submitted to Proceedings of ACAT2021 (20th International Workshop on Advanced Computing and Analysis Techniques in Physics Research)

In chemical reactions, the interplay between coherent evolution and dissipation is central to determining key properties such as the rate and yield. Of particular interest are cases where two potential energy surfaces cross at features known as conical intersections (CIs), resulting in nonadiabatic dynamics that may promote ultrafast and highly efficient reactions when rovibrational damping is present. A prominent chemical reaction that involves a CI is the cis-trans isomerization reaction in rhodopsin, which is crucial to vision. CIs in real molecular systems are typically investigated via optical pump-probe spectroscopy, which has demanding spectral bandwidth and temporal resolution requirements, and where precise control of the environment is challenging. A complementary approach for understanding chemical reactions is to use quantum simulators that can provide access to a wider range of observables, though thus far combining strongly interacting linear (rovibrational) and nonlinear (electronic) degrees of freedom with engineered dissipation has yet to be demonstrated. Here, we create a tunable CI in a hybrid qubit-oscillator circuit QED processor and simultaneously track both a reactive wave-packet and electronic qubit in the time-domain. We identify dephasing of the electronic qubit as the mechanism that drives wave-packet branching along the reactive coordinate in our model. Furthermore, we directly observe enhanced branching when the wave-packet passes through the CI. Thus, the forces that influence a chemical reaction can be viewed as an effective measurement induced dephasing rate that depends on the position of the wave-packet relative to the CI. Our results set the groundwork for more complex simulations of chemical dynamics, offering deeper insight into the role of dissipation in determining macroscopic quantities of interest such as the quantum yield of a chemical reaction.

We propose a new wavelet-based method for density estimation when the data are size-biased. More specifically, we consider a power of the density of interest, where this power exceeds 1/2. Warped wavelet bases are employed, where warping is attained by some continuous cumulative distribution function. A special case is the conventional orthonormal wavelet estimation, where the warping distribution is the standard continuous uniform. We show that both linear and nonlinear wavelet estimators are consistent, with optimal and/or near-optimal rates. Monte Carlo simulations are performed to compare four special settings which are easy to interpret in practice. An application with a real dataset on fatal traffic accidents involving alcohol illustrates the method. We observe that warped bases provide more flexible and superior estimates for both simulated and real data. Moreover, we find that estimating the power of a density (for instance, its square root) further improves the results., Comment: 45 pages, 9 figures

A controlled evolution generated by nonlinear interactions is required to perform full manipulation of a quantum system, and such control is only coherent when the rate of nonlinearity is large compared to the rate of decoherence. As a result, engineered quantum systems typically rely on a bare nonlinearity much stronger than all decoherence rates, and this hierarchy is usually assumed to be necessary. In this work, we challenge this assumption by demonstrating the universal control of a quantum system where the relevant rate of bare nonlinear interaction is comparable to the fastest rate of decoherence. We do this by introducing a novel noise-resilient protocol for the universal quantum control of a nearly-harmonic oscillator that takes advantage of an in-situ enhanced nonlinearity instead of harnessing a bare nonlinearity. Our experiment consists of a high quality-factor microwave cavity with weak-dispersive coupling to a much lower quality superconducting qubit. By using strong drives to temporarily excite the oscillator, we realize an amplified three-wave-mixing interaction, achieving typical operation speeds over an order of magnitude faster than expected from the bare dispersive coupling. Our demonstrations include preparation of a single-photon state with $98\pm 1(\%)$ fidelity and preparation of squeezed vacuum with a squeezing level of $11.1$ dB, the largest intracavity squeezing reported in the microwave regime. Finally, we also demonstrate fast measurement-free preparation of logical states for the binomial and Gottesman-Kitaev-Preskill (GKP) quantum error-correcting codes., Comment: 31 pages, 14 figures

We present a recursive formula for the computation of the static effective Hamiltonian of a system under a fast-oscillating drive. Our analytical result is well-suited to symbolic calculations performed by a computer and can be implemented to arbitrary order, thus overcoming limitations of existing time-dependent perturbation methods and allowing computations that were impossible before. We also provide a simple diagrammatic tool for calculation and treat illustrative examples. By construction, our method applies directly to both quantum and classical systems; the difference is left to a low-level subroutine. This aspect sheds light on the relationship between seemingly disconnected independently developed methods in the literature and has direct applications in quantum engineering., Comment: 5 pages, 3 figures

We develop a theory for the dynamics of an Andreev bound state hosted by a weak link of finite length for which charging effects are important. We derive the linear response of both the current through the link and charge accumulated in it with respect to the phase and gate voltage biases. The resulting matrix encapsulates the spectroscopic properties of a weak link embedded in a microwave resonator. In the low-frequency limit, we obtain the response functions analytically using an effective low-energy Hamiltonian, which we derive. This Hamiltonian minimally accounts for Coulomb interaction and is suitable for a phenomenological description of a weak link having a finite length., Comment: 26 pages, 7 figures. Added a footnote

We consider, in general terms, the possible parameter space of thermal dark matter candidates. We assume that the dark matter particle is fundamental and was in thermal equilibrium in a hidden sector with a temperature $T'$, which may differ from that of the Standard Model temperature, $T$. The candidates lie in a region in the $T'/T$ vs. $m_{\rm dm}$ plane, which is bounded by both model-independent theoretical considerations and observational constraints. The former consists of limits from dark matter candidates that decoupled when relativistic (the relativistic floor) and from those that decoupled when non-relativistic with the largest annihilation cross section allowed by unitarity (the unitarity wall), while the latter concerns big bang nucleosynthesis ($N_{\rm eff}$ ceiling) and free streaming. We present three simplified dark matter scenarios, demonstrating concretely how each fits into the domain., Comment: 15 pages, 8 figures

This paper proposes a generalization of Gaussian mixture models, where the mixture weight is allowed to behave as an unknown function of time. This model is capable of successfully capturing the features of the data, as demonstrated by simulated and real datasets. It can be useful in studies such as clustering, change-point and process control. In order to estimate the mixture weight function, we propose two new Bayesian nonlinear dynamic approaches for polynomial models, that can be extended to other problems involving polynomial nonlinear dynamic models. One of the methods, called here component-wise Metropolis-Hastings, apply the Metropolis-Hastings algorithm to each local level component of the state equation. It is more general and can be used in any situation where the observation and state equations are nonlinearly connected. The other method tends to be faster, but is applied specifically to binary data (using the probit link function). The performance of these methods of estimation, in the context of the proposed dynamic Gaussian mixture model, is evaluated through simulated datasets. Also, an application to an array Comparative Genomic Hybridization (aCGH) dataset from glioblastoma cancer illustrates our proposal, highlighting the ability of the method to detect chromosome aberrations.

Long term sustainability of the high energy physics (HEP) research software ecosystem is essential for the field. With upgrades and new facilities coming online throughout the 2020s this will only become increasingly relevant throughout this decade. Meeting this sustainability challenge requires a workforce with a combination of HEP domain knowledge and advanced software skills. The required software skills fall into three broad groups. The first is fundamental and generic software engineering (e.g. Unix, version control,C++, continuous integration). The second is knowledge of domain specific HEP packages and practices (e.g., the ROOT data format and analysis framework). The third is more advanced knowledge involving more specialized techniques. These include parallel programming, machine learning and data science tools, and techniques to preserve software projects at all scales. This paper dis-cusses the collective software training program in HEP and its activities led by the HEP Software Foundation (HSF) and the Institute for Research and Innovation in Software in HEP (IRIS-HEP). The program equips participants with an array of software skills that serve as ingredients from which solutions to the computing challenges of HEP can be formed. Beyond serving the community by ensuring that members are able to pursue research goals, this program serves individuals by providing intellectual capital and transferable skills that are becoming increasingly important to careers in the realm of software and computing, whether inside or outside HEP, Comment: For CHEP 2021 conference,sent for publication to CSBS Springer

Bosonic modes have wide applications in various quantum technologies, such as optical photons for quantum communication, magnons in spin ensembles for quantum information storage and mechanical modes for reversible microwave-to-optical quantum transduction. There is emerging interest in utilizing bosonic modes for quantum information processing, with circuit quantum electrodynamics (circuit QED) as one of the leading architectures. Quantum information can be encoded into subspaces of a bosonic superconducting cavity mode with long coherence time. However, standard Gaussian operations (e.g., beam splitting and two-mode squeezing) are insufficient for universal quantum computing. The major challenge is to introduce additional nonlinear control beyond Gaussian operations without adding significant bosonic loss or decoherence. Here we review recent advances in universal control of a single bosonic code with superconducting circuits, including unitary control, quantum feedback control, driven-dissipative control and holonomic dissipative control. Various approaches to entangling different bosonic modes are also discussed., Comment: 23 pages, 9 figures, 1 table (+2 pages supplement with 1 figure)

Superconducting microwave circuits incorporating nonlinear devices, such as Josephson junctions, are one of the leading platforms for emerging quantum technologies. Increasing circuit complexity further requires efficient methods for the calculation and optimization of the spectrum, nonlinear interactions, and dissipation in multi-mode distributed quantum circuits. Here, we present a method based on the energy-participation ratio (EPR) of a dissipative or nonlinear element in an electromagnetic mode. The EPR, a number between zero and one, quantifies how much of the energy of a mode is stored in each element. It obeys universal constraints--valid regardless of the circuit topology and nature of the nonlinear elements. The EPR of the elements are calculated from a unique, efficient electromagnetic eigenmode simulation of the linearized circuit, including lossy elements. Their set is the key input to the determination of the quantum Hamiltonian of the system. The method provides an intuitive and simple-to-use tool to quantize multi-junction circuits. It is especially well-suited for finding the Hamiltonian and dissipative parameters of weakly anharmonic systems, such as transmon qubits coupled to resonators, or Josephson transmission lines. We experimentally tested this method on a variety of Josephson circuits, and demonstrated agreement within several percents for nonlinear couplings and modal Hamiltonian parameters, spanning five-orders of magnitude in energy, across a dozen samples., Comment: 15 Figures, 39 pages, 4 tables; See also http://github.com/zlatko-minev/pyEPR Send feedback to zlatko.minev@aya.yale.edu

We discuss the phenomenology of a dark matter scenario in which we extend the Standard Model by a real scalar particle and a vector-like heavy quark. Such a model can be seen as a simplified version of a composite setup in which the scalar field, that couples to the top quark via a Yukawa interaction with the new heavy quark, is a viable dark matter candidate. We emphasize that QCD corrections are important not only for predictions at colliders but also for direct and indirect dark matter searches and the relic abundance. We moreover show that a large fraction of the model parameter space remains unconstrained., Comment: 6 pages, 4 figures, presented at LFC19 (Strong dynamics for physics within and beyond the Standard Model at LHC and Future Colliders)

We analyse how dark matter (DM) can be produced in the early universe, working in the framework of a hidden sector charged under a U(1)' gauge symmetry and interacting with the Standard Model through kinetic mixing. Depending on the masses of the dark matter particle and of the dark photon, as well as on the hidden U(1)' gauge coupling and the kinetic mixing parameter, we classify all the distinct regimes along which the observed dark matter relic density can be accounted for. We find that 9 regimes are potentially operative to produce the DM particles and this along 5 distinct dynamical mechanisms. Among these, 4 regimes are new and correspond to regimes in which the DM particles are produced by on-shell dark photons. One of them proceeds along a new dynamical mechanism, which we dub sequential freeze-in. We argue that such regimes and the associated dynamical mechanisms are characteristic of DM models for which, on top of the Standard Model and the dark sector, there are other massive, but relatively light particles -- akin to the dark photon -- that interact both with the SM and the DM sectors., Comment: 18 pages, 14 figures

Quantum superpositions of macroscopically distinct classical states, so-called Schr\"{o}dinger cat states, are a resource for quantum metrology, quantum communication, and quantum computation. In particular, the superpositions of two opposite-phase coherent states in an oscillator encode a qubit protected against phase-flip errors. However, several challenges have to be overcome in order for this concept to become a practical way to encode and manipulate error-protected quantum information. The protection must be maintained by stabilizing these highly excited states and, at the same time, the system has to be compatible with fast gates on the encoded qubit and a quantum non-demolition readout of the encoded information. Here, we experimentally demonstrate a novel method for the generation and stabilization of Schr\"{o}dinger cat states based on the interplay between Kerr nonlinearity and single-mode squeezing in a superconducting microwave resonator. We show an increase in transverse relaxation time of the stabilized, error-protected qubit over the single-photon Fock-state encoding by more than one order of magnitude. We perform all single-qubit gate operations on time-scales more than sixty times faster than the shortest coherence time and demonstrate single-shot readout of the protected qubit under stabilization. Our results showcase the combination of fast quantum control with the robustness against errors intrinsic to stabilized macroscopic states and open up the possibility of using these states as resources in quantum information processing., Comment: Corrected typos. See journal reference for accepted version

Motivated by the swampland conjectures, we study cosmological signatures of a quintessence potential which induces time variation in the low energy effective field theory. After deriving the evolution of the quintessence field, we illustrate its possible ramifications by exploring putative imprints in a number of directions of particle phenomenology. We first show that a dark matter self-interaction rate increasing with time gives a novel way of reconciling the large self interactions required to address small scale structure issues with the constraint coming from clusters. Next, we study the effects of kinetic mixing variation during the radiation dominated era on freeze-in dark matter production. Last, we elucidate quintessence effects on the restoration of the electroweak symmetry at finite temperature and the lifetime of the electroweak vacuum through a modification of the effective Higgs mass and quartic coupling., Comment: 13 pages, 10 figures. V2: references added, accepted for publication in PRD

We report a first-principles study of the driven dissipative dynamics for Kerr oscillators in the mesoscopic regime. This regime is characterized by large Kerr nonlinearity, realized here using the nonlinear kinetic inductance of a large array of Josephson junctions. The experimentally measured nonlinear resonance lineshapes of the junction array modes show significant deviations from steady-state numerical predictions, and necessitate time-dependent numerical simulations indicative of strong measurement-induced dephasing in the system arising from the large cross-Kerr effect between array modes. Analytical and numerical calculations of switching rate corroborate this by showing the emergence of a slow time scale, which is much longer than the linear decay rate and is set by fluctuation-induced switching times in the bistable regime. Furthermore, our analysis shows that the usual quantum-activated escape treatment is inadequate for prediction of the switching rates at large frequency shifts caused by strong nonlinearities, necessitating a quantum treatment that utilizes the full system Liouvillian. Based on our analysis, we identify a universal crossover parameter that delineates the regimes of validity of semiclassical and quantum descriptions, respectively. Our work shows how dynamical switching effects in strongly nonlinear systems provide a platform to study quantum-to-classical transitions., Comment: 16 pages, 9 figures

This paper describes the Polarimetric and Helioseismic Imager on the Solar Orbiter mission (SO/PHI), the first magnetograph and helioseismology instrument to observe the Sun from outside the Sun-Earth line. It is the key instrument meant to address the top-level science question: How does the solar dynamo work and drive connections between the Sun and the heliosphere? SO/PHI will also play an important role in answering the other top-level science questions of Solar Orbiter, as well as hosting the potential of a rich return in further science. SO/PHI measures the Zeeman effect and the Doppler shift in the FeI 617.3nm spectral line. To this end, the instrument carries out narrow-band imaging spectro-polarimetry using a tunable LiNbO_3 Fabry-Perot etalon, while the polarisation modulation is done with liquid crystal variable retarders (LCVRs). The line and the nearby continuum are sampled at six wavelength points and the data are recorded by a 2kx2k CMOS detector. To save valuable telemetry, the raw data are reduced on board, including being inverted under the assumption of a Milne-Eddington atmosphere, although simpler reduction methods are also available on board. SO/PHI is composed of two telescopes; one, the Full Disc Telescope (FDT), covers the full solar disc at all phases of the orbit, while the other, the High Resolution Telescope (HRT), can resolve structures as small as 200km on the Sun at closest perihelion. The high heat load generated through proximity to the Sun is greatly reduced by the multilayer-coated entrance windows to the two telescopes that allow less than 4% of the total sunlight to enter the instrument, most of it in a narrow wavelength band around the chosen spectral line., Comment: 36 pages, 41 figures

Quantum state transfer between microwave and optical frequencies is essential for connecting superconducting quantum circuits to coherent optical systems and extending microwave quantum networks over long distances. To build such a hybrid `quantum Internet,' an important experiment in the quantum regime is to entangle microwave and optical modes. Based on the model of a generic cavity electro-optomechanical system, we present a heralded scheme to generate entangled microwave--optical photon pairs, which can bypass the efficiency threshold for quantum channel capacity in direct transfer protocols. The parameter regime for entanglement verification is identified that is compatible with realistic experimental settings. Our scheme is feasible given the latest experimental progress on electro-optomechanics, and can be potentially generalized to various physical systems.

The grand-unification gauge group SO(10) contains matter parity as a discrete subgroup. This symmetry could be at the origin of dark matter stability. The properties of the dark matter candidates depend on the path along which SO(10) is broken, in particular through Pati-Salam or left-right symmetric subgroups. We systematically determine the non-supersymmetric dark matter scenarios that can be realized along the various paths. We emphasize that the dark matter candidates may have colored or electrically charged partners at low scale that belong to the same SO(10) multiplet. These states, which in many cases are important for co-annihilation, could be observed more easily than the dark matter particle. We determine the structure of the tree-level and loop-induced mass splittings between the dark matter candidate and their partners and discuss the possible phenomenological implications., Comment: 44 pages; added references, to appear in PRD