In supersymmetric $E_6$ the masses of the third family quarks and charged lepton, $t-b-\tau$, as well as the masses of the vectorlike quarks and leptons, $D-\overline{D}$ and $L-\overline{L}$, may arise from the coupling $27_3\times 27_3\times 27_H$, where $27_3$ and $27_H$ denote the third family matter and Higgs multiplets, respectively. We assume that the SO(10) singlet component in $27_H$ acquires a TeV-scale vacuum expectation value that spontaneously breaks $U(1{)}_{\psi }$ and provides masses to the vectorlike particles in $27_3$, while the Minimal Supersymmetric Standard Model doublets in $27_H$ provide masses to $t$, $b$, and $\tau$. Imposing Yukawa coupling unification $h_t=h_b=h_{\tau }=h_D=h_L$ at $M_{\mathrm{GUT}}$ and employing the ATLAS and CMS constraints on the $Z_{\psi }^{\prime }$ boson mass, we estimate the lower bounds on the third family vectorlike particles $D-\overline{D}$ and $L-\overline{L}$ masses to be around 5.85 TeV and 2.9 TeV, respectively. These bounds apply in the supersymmetric limit.

We give explicit analytical expressions for the partition function of $U(N{)}_k\times U(N+M{)}_{-k}$ ABJ theory at weak coupling ($k\to \infty$) for finite and arbitrary values of $N$ and $M$ (including the ABJM case and its mass-deformed generalization). We obtain the expressions by identifying the one-matrix model formulation with a Meixner-Pollaczek ensemble and using the corresponding orthogonal polynomials, which are also eigenfunctions of a $su(1,1)$ quantum oscillator. Wilson loops in mass-deformed ABJM are also studied in the same limit and interpreted in terms of $su(1,1)$ coherent states.

An auxiliary metric (reference metric) is inevitable in massive gravity theory. In the scenario of the gauge/gravity duality, massive gravity with a singular reference metric is used to study momentum dissipation, which describes the electric and heat conductivity for normal conductors. We demonstrate in detail that the de Rham-Gabadadze-Tolley (dRGT) massive gravity with a singular reference metric is ghost free.

We present an analytic computation of Detweiler’s redshift invariant for a point mass in a circular orbit around a Kerr black hole, giving results up to 8.5 post-Newtonian order while making no assumptions on the magnitude of the spin of the black hole. Our calculation is based on the functional series method of Mano, Suzuki and Takasugi, and employs a rigorous mode-sum regularization prescription based on the Detweiler-Whiting singular-regular decomposition. The approximations used in our approach are minimal; we use the standard self-force expansion to linear order in the mass ratio, and the standard post-Newtonian expansion in the separation of the binary. A key advantage of this approach is that it produces expressions that include contributions at all orders in the spin of the Kerr black hole. While this work applies the method to the specific case of Detweiler’s redshift invariant, it can be readily extended to other gauge-invariant quantities and to higher post-Newtonian orders.

We study the envelope approximation and its applicability to first-order phase transitions in the early Universe. We demonstrate that the power laws seen in previous studies exist independently of the nucleation rate. We also compare the envelope approximation prediction to results from large-scale phase transition simulations. For phase transitions where the contribution to gravitational waves from scalar fields dominates over that from the coupled plasma of light particles, the envelope approximation is in agreement, giving a power spectrum of the same form and order of magnitude. In all other cases the form and amplitude of the gravitational wave power spectrum is markedly different and new techniques are required.

When testing gravity in a model-independent way, one of the crucial tests is measuring the propagation speed of a gravitational wave (GW). In general relativity, a GW propagates with the speed of light, while in the alternative theories of gravity, the propagation speed could deviate from the speed of light due to the modification of gravity or spacetime structure at a quantum level. Previously, we proposed a method to measure the GW speed by directly comparing the arrival times between a GW and a photon from the binary merger of neutron stars or a neutron star and black hole, assuming that it is associated with a short gamma-ray burst. The sensitivity is limited by the intrinsic time delay between a GW and a photon at the source. In this paper, we extend the method to distinguish the intrinsic time delay from the true signal caused by anomalous GW speed with multiple events at cosmological distances, considering the redshift distribution of GW sources, redshift-dependent GW propagation speed, and the statistics of intrinsic time delays. We show that an advanced GW detector such as the Einstein Telescope will be able to robustly constrain the GW propagation speed at a precision of $\sim {10}^{-16}$. We also discuss the optimal statistic to measure the GW speed by performing numerical simulations.

Scalar-tensor theories of gravity are extensions of general relativity (GR) including an extra, nonminimally coupled scalar degree of freedom. A wide class of these theories, albeit indistinguishable from GR in the weak field regime, predicts a radically different phenomenology for neutron stars, due to a nonperturbative, strong-field effect referred to as spontaneous scalarization. This effect is known to occur in theories where the effective linear coupling ${\beta }_0$ between the scalar and matter fields is sufficiently negative, i.e. ${\beta }_0\lesssim -4.35$, and has been strongly constrained by pulsar timing observations. In the test-field approximation, spontaneous scalarization manifests itself as a tachyonic-like instability. Recently, it was argued that, in theories where ${\beta }_0>0$, a similar instability would be triggered by sufficiently compact neutron stars obeying realistic equations of state. In this work we investigate the end state of this instability for some representative coupling functions with ${\beta }_0>0$. This is done both through an energy balance analysis of the existing equilibrium configurations, and by numerically determining the nonlinear Cauchy development of unstable initial data. We find that, contrary to the ${\beta }_0<0$ case, the final state of the instability is highly sensitive to the details of the coupling function, varying from gravitational collapse to spontaneous scalarization. In particular, we show, for the first time, that spontaneous scalarization can happen in theories with ${\beta }_0>0$, which could give rise to novel astrophysical tests of the theory of gravity.

We present the solution space for the case of a minimally coupled scalar field with arbitrary potential in a Friedmann-Lemaître-Robertson-Walker metric. This is made possible due to the existence of a nonlocal integral of motion corresponding to the conformal Killing field of the two-dimensional minisuperspace metric. Both the spatially flat and nonflat cases are studied first in the presence of only the scalar field and subsequently with the addition of noninteracting perfect fluids. It is verified that this addition does not change the general form of the solution, but only the particular expressions of the scalar field and the potential. The results are applied in the case of parametric dark energy models where we derive the scalar field equivalence solution for some proposed models in the literature.

The quintom formalism is studied by considering the nonminimal coupling of the quintessence and the phantom field, respectively, with the scalar curvature of space-time. The dynamical aspects of the evolution of the system are evaluated by considering numerical solutions of the system of equations from the matter-dominated era. It is observed that the cosmic expansion is accelerated, the Universe is evolving toward the big rip, while the coupling coefficient $\xi$ is affecting mainly the dark energy equation of state. For significant values of the coupling coefficient, the dark energy equation of state presents an oscillatory behavior around the phantom divide line and the frequency of the oscillations is increasing with the strength of the coupling. At late times the Universe is dark-energy dominated, and dark energy evolves asymptotically to the cosmological constant.

If leptons do not couple directly to the one Higgs doublet of the standard model of particle interactions, they must still do so somehow indirectly to acquire mass, as proposed recently in several models where it happens in one loop through dark matter. We analyze the important consequences of this scenario in a specific model, including Higgs decay, muon anomalous magnetic moment, $\mu \to e\gamma$, $\mu \to eee$, and the proposed dark sector.

The chiral phase transition of the strongly interacting matter is investigated at nonzero temperature and baryon chemical potential (${\mu }_B$) within an extended ($2+1$) flavor Polyakov constituent quark-meson model that incorporates the effect of the vector and axial vector mesons. The effect of the fermionic vacuum and thermal fluctuations computed from the grand potential of the model is taken into account in the curvature masses of the scalar and pseudoscalar mesons. The parameters of the model are determined by comparing masses and tree-level decay widths with experimental values in a ${\chi }^2$-minimization procedure that selects between various possible assignments of scalar nonet states to physical particles. We examine the restoration of the chiral symmetry by monitoring the temperature evolution of condensates and the chiral partners’ masses and of the mixing angles for the pseudoscalar $\eta -{\eta }^{\prime }$ and the corresponding scalar complex. We calculate the pressure and various thermodynamical observables derived from it and compare them to the continuum extrapolated lattice results of the Wuppertal-Budapest collaboration. We study the $T-{\mu }_B$ phase diagram of the model and find that a critical endpoint exists for parameters of the model, which give acceptable values of ${\chi }^2$.

The decay of neutrino mass eigenstates leads to a change of the conversion and survival probability of neutrino flavor eigenstates. Exploiting the recent results released by the long-baseline OPERA experiment we perform the statistical investigation of the neutrino invisible decay hypothesis in the ${\nu }_{\mu }\to {\nu }_{\tau }$ appearance channel. We find that the neutrino decay provides an enhancement of the expected tau appearance signal with respect to the standard oscillation scenario for the long-baseline OPERA experiment. The increase of the ${\nu }_{\mu }\to {\nu }_{\tau }$ conversion probability by the decay of one of the mass eigenstates is due to a reduction of the “destructive interference” among the different massive neutrino components. Despite data showing a very mild preference for invisible decays with respect to the oscillations only hypothesis, we provide an upper limit for the neutrino decay lifetime in this channel of ${\tau }_3/m_3\gtrsim 1.3\times {10}^{-13}\mathrm{s}/\mathrm{eV}$ at the 90% confidence level.

The prospects of searching for the flavor changing neutral current effect in the decay of $t\to Hc$, $H\to \tau \tau$ are investigated with the simulated $p-p$ collision data for the ATLAS detector at the LHC, where the Higgs mass is assumed to be 125 GeV. A fit based on the constraints from the Higgs mass and the tau decay kinematics is performed for each event, which improves significantly the Higgs and top mass reconstruction and helps the signal-background separation. Boosted decision trees discriminants are developed to achieve an optimal sensitivity of searching for the flavor changing neutral current signal. An expected upper limit of the branching ratio $\mathcal{B}(t\to Hc)$ at 95% confidence level of 0.25% is obtained with a data set of $100{\mathrm{fb}}^{-1}$ at $\sqrt{s}=13\mathrm{TeV}$ during the LHC Run-2 period.

A search for the production of a heavy $B$ quark, having electric charge $-1/3$ and vector couplings to $W$, $Z$, and $H$ bosons, is carried out using proton-proton collision data recorded at the CERN LHC by the CMS experiment, corresponding to an integrated luminosity of $19.7{\mathrm{fb}}^{-1}$. The $B$ quark is assumed to be pair produced and to decay in one of three ways: to $tW$, $bZ$, or $bH$. The search is carried out in final states with one, two, and more than two charged leptons, as well as in fully hadronic final states. Each of the channels in the exclusive final-state topologies is designed to be sensitive to specific combinations of the $B$ quark-antiquark pair decays. The observed event yields are found to be consistent with the standard model expectations in all the final states studied. A statistical combination of these results is performed, and upper limits are set on the cross section of the strongly produced $B$ quark-antiquark pairs as a function of the $B$ quark mass. Lower limits on the $B$ quark mass between 740 and 900 GeV are set at a 95% confidence level, depending on the values of the branching fractions of the $B$ quark to $tW$, $bZ$, and $bH$. Overall, these limits are the most stringent to date.

The Auger Engineering Radio Array (AERA) is part of the Pierre Auger Observatory and is used to detect the radio emission of cosmic-ray air showers. These observations are compared to the data of the surface detector stations of the Observatory, which provide well-calibrated information on the cosmic-ray energies and arrival directions. The response of the radio stations in the 30–80 MHz regime has been thoroughly calibrated to enable the reconstruction of the incoming electric field. For the latter, the energy deposit per area is determined from the radio pulses at each observer position and is interpolated using a two-dimensional function that takes into account signal asymmetries due to interference between the geomagnetic and charge-excess emission components. The spatial integral over the signal distribution gives a direct measurement of the energy transferred from the primary cosmic ray into radio emission in the AERA frequency range. We measure 15.8 MeV of radiation energy for a 1 EeV air shower arriving perpendicularly to the geomagnetic field. This radiation energy—corrected for geometrical effects—is used as a cosmic-ray energy estimator. Performing an absolute energy calibration against the surface-detector information, we observe that this radio-energy estimator scales quadratically with the cosmic-ray energy as expected for coherent emission. We find an energy resolution of the radio reconstruction of 22% for the data set and 17% for a high-quality subset containing only events with at least five radio stations with signal.

We discuss detectability of the nonlinear growth of the large-scale structure in the cosmic microwave background (CMB) lensing. The lensing signals involved in the CMB fluctuations have been measured from multiple CMB experiments, such as Atacama Cosmology Telescope (ACT), Planck, POLARBEAR, and South Pole Telescope (SPT). The reconstructed CMB lensing signals are useful to constrain cosmology via their angular power spectrum, while detectability and cosmological application of their bispectrum induced by the nonlinear evolution are not well studied. Extending the analytic estimate of the galaxy lensing bispectrum presented by Takada and Jain (2004) to the CMB case, we show that even near term CMB experiments such as Advanced ACT, Simons Array and SPT3G could detect the CMB lensing bispectrum induced by the nonlinear growth of the large-scale structure. In the case of the CMB Stage-IV, we find that the lensing bispectrum is detectable at $\gtrsim 50\sigma$ statistical significance. This precisely measured lensing bispectrum has rich cosmological information, and could be used to constrain cosmology, e.g., the sum of the neutrino masses and the dark-energy properties.