We study the scenario in which a massive particle is thrown into a rapidly rotating Kerr black hole in an attempt to spin it up beyond its extremal limit, challenging weak cosmic censorship. We work in black-hole perturbation theory, and focus on nonspinning, uncharged particles sent in on equatorial orbits. We first identify the complete parameter-space region in which overspinning occurs when backreaction effects from the particle’s self-gravity are ignored. We find, in particular, that overspinning can be achieved only with particles sent in from infinity. Gravitational self-force effects may prevent overspinning by radiating away a sufficient amount of the particle’s angular momentum (“dissipative effect”), and/or by increasing the effective centrifugal repulsion, so that particles with suitable parameters never get captured (“conservative effect”). We analyze the full effect of the self-force, thereby completing previous studies by Jacobson and Sotiriou (who neglected the self-force) and by Barausse, Cardoso and Khanna (who considered the dissipative effect on a subset of orbits). Our main result is an inequality, involving certain self-force quantities, which describes a necessary and sufficient condition for the overspinning scenario to be overruled. This “censorship” condition is formulated on a certain one-parameter family of geodesics in the limit of an extremal Kerr geometry. We find that the censorship condition is insensitive to the dissipative effect (within the first-order self-force approximation used here), except for a subset of perfectly fine-tuned orbits, for which a separate censorship condition is derived. We do not obtain here the self-force input needed to evaluate either of our two conditions, but discuss the prospects for producing the necessary data using state-of-the-art numerical codes.

Big bang nucleosynthesis in a modified gravity model of $f(R)\propto R^n$ is investigated. The only free parameter of the model is a power-law index $n$. We find cosmological solutions in a parameter region of $1<n\le (4+\sqrt{6})/5$. We calculate abundances of ${}^4\mathrm{He}$, D, ${}^3\mathrm{He}$, ${}^7\mathrm{Li}$, and ${}^6\mathrm{Li}$ during big bang nucleosynthesis. We compare the results with the latest observational data. It is then found that the power-law index is constrained to be $(n-1)=(-0.86\pm 1.19)\times 10^{-4}$ (95% C.L.) mainly from observations of deuterium abundance as well as ${}^4\mathrm{He}$ abundance.

A scheme of simplified smooth hybrid inflation is realized in the framework of supersymmetric $SU(5)$. The smooth model of hybrid inflation provides a natural solution to the monopole problem that appears in the breaking of $SU(5)$ gauge symmetry. The supergravity corrections with nonminimal Kähler potential are shown to play important role in realizing inflation with a red-tilted scalar spectral index $n_s<1$ within Planck’s latest bounds. As compared to shifted model of hybrid inflation, relatively large values of the tensor-to-scalar ratio $r\lesssim 0.01$ are achieved here, with nonminimal couplings $-0.05\lesssim {\kappa }_S\lesssim 0.01$ and $-1\lesssim {\kappa }_{SS}\lesssim 1$ and the gauge symmetry-breaking scale $M\simeq (2.0–16.7)\times {10}^{16}\mathrm{GeV}$.

We explore some particle physics implications of the growing evidence for a helical primordial magnetic field (PMF). From the interactions of magnetic monopoles and the PMF, we derive an upper bound on the monopole number density, $n(t_0)<1\times {10}^{-20}{\mathrm{cm}}^{-3}$, which is a “primordial” analog of the Parker bound for the survival of galactic magnetic fields. Our bound is weaker than existing constraints, but it is derived under independent assumptions. We also show how improved measurements of the PMF at different redshifts can lead to further constraints on magnetic monopoles. Axions interact with the PMF due to the $g_{a\gamma }\phi \mathbf{E}·\mathbf{B}/4\pi$ interaction. Including the effects of the cosmological plasma, we find that the helicity of the PMF is a source for the axion field. Although the magnitude of the source is small for the PMF, it could potentially be of interest in astrophysical environments. Earlier derived constraints from the resonant conversion of cosmic microwave background photons into axions lead to $g_{a\gamma }\lesssim 10^{-9}{\mathrm{GeV}}^{-1}$ for the suggested PMF strength $\sim {10}^{-14}\mathrm{G}$ and coherence length $\sim 10\mathrm{Mpc}$. Finally, we apply constraints on the neutrino magnetic dipole moment that arise from requiring successful big bang nucleosynthesis in the presence of a PMF, and we find ${\mu }_{\nu }\lesssim 10^{-16}{\mu }_B$.

We investigate models in which inflation is driven by an ultraviolet safe and interacting scalar sector stemming from a new class of nonsupersymmetric gauge field theories. These new theories, different from generic scalar models, are well defined to arbitrary short distances because of the existence of a controllable ultraviolet interacting fixed point. The scalar couplings at the ultraviolet fixed point and their overall running are predicted by the geometric structure of the underlying theory. We analyze the minimal and nonminimal coupling to gravity of these theories and the consequences for inflation. In the minimal coupling case the theory requires large nonperturbative quantum corrections to the quantum potential for the theory to agree with the data, while in the nonminimal coupling case the perturbative regime in the couplings of the theory is preferred. Requiring the theory to reproduce the observed amplitude of density perturbations constrains the geometric data of the theory such as the number of colors and flavors for generic values of the nonminimal coupling.

In a modified gravity theory, the propagation equation of gravitational waves will be presented in a nonstandard way. Therefore this tensor mode perturbation of time-space, as a complement to the scalar mode perturbation, provides a unique character distinguishing modified gravity from general relativity. To avoid the model-dependent issue, in this paper, we propose a parametrized modification to the propagation of gravitational waves. We show the effects on the angular power spectrum of cosmic microwave background radiation due to the parametrized modification and its degeneracy to the tensor mode power spectrum index $n_t$ and its running ${\alpha }_t$. Last, we report the current status on the detection of modified gravity through the currently available cosmic observations. Our results show no significant deviation to general relativity.

We consider the cross-correlation search for periodic gravitational waves and its potential application to the low-mass x-ray binary Sco X-1. This method coherently combines data not only from different detectors at the same time, but also data taken at different times from the same or different detectors. By adjusting the maximum allowed time offset between a pair of data segments to be coherently combined, one can tune the method to trade off sensitivity and computing costs. In particular, the detectable signal amplitude scales as the inverse fourth root of this coherence time. The improvement in amplitude sensitivity for a search with a maximum time offset of one hour, compared with a directed stochastic background search with 0.25-Hz-wide bins, is about a factor of 5.4. We show that a search of one year of data from the Advanced LIGO and Advanced Virgo detectors with a coherence time of one hour would be able to detect gravitational waves from Sco X-1 at the level predicted by torque balance over a range of signal frequencies from 30 to 300 Hz; if the coherence time could be increased to ten hours, the range would be 20 to 500 Hz. In addition, we consider several technical aspects of the cross-correlation method: We quantify the effects of spectral leakage and show that nearly rectangular windows still lead to the most sensitive search. We produce an explicit parameter-space metric for the cross-correlation search, in general, and as applied to a neutron star in a circular binary system. We consider the effects of using a signal template averaged over unknown amplitude parameters: The quantity to which the search is sensitive is a given function of the intrinsic signal amplitude and the inclination of the neutron-star rotation axis to the line of sight, and the peak of the expected detection statistic is systematically offset from the true signal parameters. Finally, we describe the potential loss of signal-to-noise ratio due to unmodeled effects such as signal phase acceleration within the Fourier transform time scale and gradual evolution of the spin frequency.

In a two-part system, the collapse of the wave function of one part can put the other part in a state which would be difficult or impossible to achieve otherwise, in particular, one sensitive to small effects in the “collapse” interaction. We present some applications to the very symmetric and experimentally accessible situations of the decays $\varphi (1020)\to K^o{K}^o$, $\psi (3770)\to D^o{D}^o$, or $\mathrm{\Upsilon }(4s)\to B^o{B}^o$, involving the internal state of the two-state $K^o$, $D^o$, or $B^o$ mesons. The collapse of the wave function occasioned by a decay of one member of the pair (away side) fixes the state vector of that side’s two-state system. Bose-Einstein statistics then determines the state of the recoiling meson (near side), whose evolution can then be followed further. In particular, the statistics requirement dictates that the “away side” and “near side” internal wave functions must be orthogonal at the time of the collapse. Thus a $CP$ violation in the away side decay implies a complementary $CP$ impurity on the near side, which can be detected in the further evolution. The $CP$ violation so manifested is necessarily direct $CP$ violation, since neither the mass matrix nor time evolution was involved in the collapse. A parametrization of the direct $CP$ violation is given, and various manifestations are presented. Certain rates or combination of rates are identified which are nonzero only if there is direct $CP$ violation. The very explicit and detailed use made of the collapse of the wave function makes the procedure interesting with respect to the fundamentals of quantum mechanics. We note an experimental consistency test for our treatment of the collapse of the wave function, which can be carried out by a certain measurement of partial decay rates.

Weak vector-boson $W,Z$ scattering at high energy probes the Higgs sector and is most sensitive to any new physics associated with electroweak symmetry breaking. We show that in the presence of the 125 GeV Higgs boson, a conventional effective-theory analysis fails for this class of processes. We propose to extrapolate the effective-theory ansatz by an extension of the parameter-free $K$-matrix unitarization prescription, which we denote as direct $T$-matrix unitarization. We generalize this prescription to arbitrary nonperturbative models and describe the implementation as an asymptotically consistent reference model matched to the low-energy effective theory. We present exemplary numerical results for full six-fermion processes at the LHC.

For the foreseeable future, the analysis and design of the complex systems needed to generate intense beams of radiation via the process of coherent emission into free-space will depend on the principles and methods of classical electrodynamics (CED). But the fields and forces predicted by the currently accepted CED theory are manifestly incompatible with Maxwell’s equations’ energy integral as applied to the process of coherent emission into free-space. It is the purpose of this paper to review the evidence for these limitations of conventional CED, to identify an alternative formulation of CED that does not suffer from these defects, and to describe how the predictions of this more physically realistic formulation of electrodynamics, including the role of the advanced interactions allowed by Maxwell’s equations and thermodynamics, might be tested by experiment and applied to enhance the capabilities of devices and systems employing the mechanism of “radiation into free-space.”

ATLAS recently reported a $3\sigma$ excess in a leptonic-$Z+E_T^{\text{miss}}$ channel. This was interpreted in the literature in a simplified general gauge mediation model containing a gluino, a Higgsino next-to-lightest supersymmetric particle and a gravitino lightest supersymmetric particle. We test the consistency of this explanation in lieu of the results of the corresponding search in CMS, and other LHC searches for new physics. Due to nondecoupling effects from squarks the parameter space of these models is split into two regions; in one region additional leptons via top quark production are expected, while the other region sees a large probability for zero-lepton events. After combining the relevant constraints we find that these models cannot explain the ATLAS excess.

The $3.6\sigma$ discrepancy between the predicted and measured values of the anomalous magnetic moment of positive muons can be explained by the existence of a new dark boson $Z_{\mu }$ with a mass in the sub-GeV range, which is coupled predominantly to the second and third lepton generations through the $L_{\mu }-L_{\tau }$ current. After a discussion of the present phenomenological bounds on the $Z_{\mu }$ coupling, we show that if the $Z_{\mu }$ exists, it could be observed in the reaction $\mu +Z\to \mu +Z+Z_{\mu }$ of a muon scattering off nuclei by looking for an excess of events with large missing muon beam energy in a detector due to the prompt bremsstrahlung $Z_{\mu }$ decay $Z_{\mu }\to \nu \nu$ into a couple of neutrinos. We describe the experimental technique and the preliminary study of the feasibility for the proposed search. We show that this specific signal allows for a search for the $Z_{\mu }$ with a sensitivity in the coupling constant ${\alpha }_{\mu }\gtrsim 10^{-11}$, which is 3 orders of magnitude higher than the value required to explain the discrepancy. We point out that the availability of high-energy and -intensity muon beams at CERN SPS provides a unique opportunity to either discover or rule out the $Z_{\mu }$ in the proposed search in the near future. The experiment is based on the missing-energy approach developed for the searches for invisible decays of dark photons and (pseudo)scalar mesons at CERN and is complementary to these experiments.

We systematically construct tetraquark currents of $I^{\mathrm{G}}{J}^{\mathrm{PC}}=1^{-}{1}^{++}$ and classify them into types $\mathbf{A}$ (antisymmetric), $\mathbf{S}$ (symmetric) and $\mathbf{M}$ (mixed), based on flavor symmetries of diquarks and antidiquarks composing the tetraquark currents. We use tetraquark currents of type $\mathbf{M}$ to perform QCD sum rule analyses, and find a tetraquark current ${\eta }_{5\mu }^M$ with quark content $qs\overline{q}\overline{s}$ ($q=u$ or $d$) leading to a mass of $1.44\pm 0.08\mathrm{GeV}$ consistent with the $a_1(1420)$ state recently observed by the COMPASS Collaboration. Our results support tetraquark explanations for both $a_1(1420)$ and $f_1(1420)$, assuming that they are isospin partners. We also study their possible decay patterns. As tetraquark candidates, the possible decay modes of $a_1(1420)$ are $S$-wave $a_1(1420)\to K^{*}(892)K$ and $P$-wave $a_1(1420)\to f_0(980)\pi$, while the possible decay patterns of $f_1(1420)$ are $S$-wave $f_1(1420)\to K^{*}(892)K$ and $P$-wave $f_1(1420)\to a_0(980)\pi$. We speculate that $a_1(1420)$ is partly responsible for the large isospin violation in the $\eta (1405)\to f_0(980){\pi }_0$ decay mode, which is reported by BESIII Collaboration in the $J/\psi \to \gamma 3\pi$ process.

In this paper, we thoroughly investigate the LHC phenomenology of the type II seesaw mechanism for neutrino masses in the nondegenerate case where the triplet scalars of various charge ($H^{\pm \pm },H^{\pm },H^0,A^0$) have different masses. Compared with the degenerate case, the cascade decays of scalars lead to many new, interesting signal channels. In the positive scenario where $M_{H^{\pm \pm }}<M_{H^{\pm }}<M_{H^0/A^0}$, the four-lepton signal is still the most promising discovery channel for the doubly charged scalars $H^{\pm \pm }$. The five-lepton signal is crucial to probe the mass spectrum of the scalars, for which, for example, a $5\sigma$ reach at 14 TeV LHC for $M_{H^{\pm }}=430\mathrm{GeV}$ with $M_{H^{\pm \pm }}=400\mathrm{GeV}$ requires an integrated luminosity of $76{\mathrm{fb}}^{-1}$. And the six-lepton signal can be used to probe the neutral scalars $H^0/A^0$, which are usually hard to detect in the degenerate case. In the negative scenario where $M_{H^{\pm \pm }}>M_{H^{\pm }}>M_{H^0/A^0}$, the detection of $H^{\pm \pm }$ is more challenging, when the cascade decay $H^{\pm \pm }\to H^{\pm }{W}^{\pm *}$ is dominant. The most important channel is the associated $H^{\pm }{H}^0/A^0$ production in the final state ${\ell }^{\pm }{\cancel{E}}_{T}b\overline{b}b\overline{b}$, which requires a luminosity of $109{\mathrm{fb}}^{-1}$ for a $5\sigma$ discovery, while the final state ${\ell }^{\pm }{\cancel{E}}_{T}b\overline{b}{\tau }^{+}{\tau }^{-}$ is less promising. Moreover, the associated $H^0{A}^0$ production can give the same signals as the standard model Higgs pair production. With a much larger cross section, the $H^0{A}^0$ production in the final state $b\overline{b}{\tau }^{+}{\tau }^{-}$ could reach $3\sigma$ significance at 14 TeV LHC with a luminosity of $300{\mathrm{fb}}^{-1}$. In summary, with an integrated luminosity $\sim \mathcal{O}(500{\mathrm{fb}}^{-1})$, the triplet scalars can be fully reconstructed at 14 TeV LHC in the negative scenario.

In models with extended scalar sectors with several Higgs multiplets, such as Higgs triplet models, the $Z$ gauge boson can have nondiagonal couplings to charged Higgs bosons. In a model-independent way, we study the potential contributions arising from such theories to the $CP$-violating trilinear neutral gauge boson couplings $Z{Z}^{*}\gamma$, $ZZ{\gamma }^{*}$, and $ZZ{Z}^{*}$, which are parametrized by four form factors: $h_{1,2}^Z$, $f_4^{\gamma }$, and $f_4^Z$, respectively. Such form factors can only be induced if there are at least two nondegenerate charged Higgs scalars and an imaginary phase in the coupling constants. For the masses of the charged scalar bosons we consider values above 300 GeV and find that the form factors can reach the following orders of magnitude: $|h_1^Z|\sim {10}^{-5}-{10}^{-4}$, $|h_2^Z|\sim {10}^{-7}-{10}^{-6}$, $|f_4^{\gamma }|\sim {10}^{-5}-{10}^{-3}$, and $|f_4^Z|\sim {10}^{-6}-{10}^{-5}$, although there could be an additional suppression factor arising from the coupling constants. We also find that the form factors decouple at high energies and are not very sensitive to a change in the masses of the charged scalar bosons. Apart from a proportionality factor, our results for the $f_4^Z$ form factor, associated with the $ZZ{Z}^{*}$ vertex, are of the same order of magnitude as that induced via nondiagonal neutral scalar boson couplings in the framework of a two-Higgs doublet model.

We study the analytic continuation used by Lewkowycz and Maldacena to prove the Ryu-Takayanagi formula for entanglement entropy, which is the holographic dual of the trace of the $\beta$-power of the Euclidean time evolution operator when $\beta \in \mathbb{R}$. This will be done perturbatively using a weakly time dependent Hamiltonian, corresponding to a small shift of the dual static background. The perturbation will be set to either satisfy the Lewkowycz-Maldacena proposal or a different analytic continuation, depending on its periodicity conditions. The two choices will be tested by computing the associated entropies and compared to the Ryu-Takayanagi formula. To our surprise we discover that, at first order, they both correctly reproduce the associated entanglement entropy. Furthermore in both cases we find unexpected divergent contributions that we have to discard in order to fit the minimal area computation, and an additional requirement on the $\beta$ dependence on the metric.

This paper presents the Hilbert series technique to a wider audience in the context of constructing group-invariant Lagrangians. This technique provides a fast way to calculate the number of operators of a specified mass dimension for a given field content and is a useful cross-check on more well-known group theoretical methods. In addition, at least when restricted to invariants without derivatives, the Hilbert series technique supplies a robust way of counting invariants in scenarios which, due to the large number of fields involved or to high-dimensional group representations, are intractable by traditional methods. We work out several practical examples.

A class of self-dual and geodesically complete spacetimes with maximally superintegrable geodesic flows is constructed by applying the Eisenhart lift to mechanics in pseudo-Euclidean spacetime of signature (1,1). It is characterized by the presence of a second-rank Killing tensor. Spacetimes of the ultrahyperbolic signature $(2,q)$ with $q>2$, which admit a second-rank Killing tensor and possess superintegrable geodesic flows, are built.

Bimetric gravity theories allow for many different types of cosmological solutions, but not all of them are theoretically allowed. In this work we discuss the conditions to satisfy the Higuchi bound and to avoid gradient instabilities in the scalar sector at the linear level. We find that in expanding universes the ratio of the scale factors of the reference and observable metric has to increase at all times. This automatically implies a ghost-free helicity-2 and helicity-0 sector and enforces a phantom dark energy. Furthermore, the condition for the absence of gradient instabilities in the scalar sector will be analyzed. Finally, we discuss whether cosmological solutions can exist, including exotic evolutions like bouncing cosmologies, in which both the Higuchi ghost and scalar instabilities are absent at all times.