It is generally believed that the inhomogeneous Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase appears in a color superconductor when the pairing between different quark flavors is under the circumstances of mismatched Fermi surfaces. However, the real crystal structure of the LOFF phase is still unclear because an exact treatment of three-dimensional crystal structures is rather difficult. In this work we present a solid-state-like calculation of the ground-state energy of the body-centered cubic (BCC) structure for two-flavor pairing by diagonalizing the Hamiltonian matrix in the Bloch space without assuming a small amplitude of the order parameter. We develop a computational scheme to overcome the difficulties in diagonalizing huge matrices. Our results show that the BCC structure is energetically more favorable than the one-dimensional modulation in a narrow window around the conventional LOFF-normal phase transition point, which indicates the significance of the higher-order terms in the Ginzburg-Landau approach.

Surface-charge algebra associated with Bondi-Metzner-Sachs (${\mathrm{BMS}}_4$) symmetry on the null infinity of asymptotically flat spacetime is studied via a Hamiltonian framework. A coordinate system, where boundaries of constant-time hypersurfaces cross the null infinity, is adopted. The equation itself, which determines the variation of the surface charges, turns out the same as that previously obtained via the covariant framework by Barnich and Troessaert and is nonintegrable for general radiation field $C_{AB}$. However, if $C_{AB}$ is independent of retarded time $u$, the variation equation is integrable, and the conserved surface charges generate ${\mathrm{BMS}}_4$ algebra without central extension.

We present an $N=1$ supersymmetric generalization of the maximal Abelian gauge in its superfield and component-field formulations, and discuss its Faddeev-Popov quantization, the associated Becchi-Rouet-Stora-Tyutin symmetry and the corresponding Slavnov-Taylor identity in the superspace approach.

A Fubini instanton is a bounce solution which describes the decay of a vacuum state located at the top of the tachyonic potential via the tunneling without a barrier. We investigate various types of Fubini instantons of a self-gravitating scalar field under a tachyonic quartic potential. With gravity taken into account, we show there exist various types of unexpected solutions including oscillating bounce solutions. We present numerically oscillating Fubini bounce solutions in anti–de Sitter and de Sitter spaces. We construct the parametric phase diagrams of the solutions, which is the extension of our previous work. Of particular significance is that there always exist solutions in all parameter spaces in anti–de Sitter space. The regions are divided depending on the number of oscillations. On the other hand, de Sitter space allows solutions with codimension-one in parameter spaces. We numerically evaluate semiclassical exponents which give the finite tunneling probabilities.

We show that the so-called flat-space rotational Killing vector method for measuring the Cartesian components of a black hole spin can be derived from the surface integral of Weinberg’s pseudotensor over the apparent horizon surface when using Gaussian normal coordinates in the integration. Moreover, the integration of the pseudotensor in this gauge yields the Komar angular momentum integral in a foliation adapted to the axisymmetry of the spacetime. As a result, the method does not explicitly depend on the evolved lapse $\alpha$ and shift ${\beta }^i$ on the respective time slice, as they are fixed to Gaussian normal coordinates while leaving the coordinate labels of the spatial metric ${\gamma }_{ij}$ and the extrinsic curvature $K_{ij}$ unchanged. Such gauge fixing endows the method with coordinate invariance, which is not present in integral expressions using Weinberg’s pseudotensor, as they normally rely on the explicit use of Cartesian coordinates.

Searches for gravitational waves (GWs) from binary black holes using interferometric GW detectors require the construction of template banks for performing matched filtering while analyzing the data. Placement of templates over the parameter space of binaries, as well as coincidence tests of GW triggers from multiple detectors make use of the definition of a metric over the space of gravitational waveforms. Although recent searches have employed waveform templates coherently describing the inspiral, merger and ringdown (IMR) of the coalescence, the metric used in the template banks and coincidence tests was derived from post-Newtonian inspiral waveforms. In this paper, we compute (semianalytically) the template-space metric of the IMR waveform family IMRPhenomB over the parameter space of masses and the effective spin parameter. We also propose a coordinate system, which is a modified version of post-Newtonian chirp time coordinates, in which the metric is slowly varying over the parameter space. The match function semianalytically computed using the metric has excellent agreement with the “exact” match function computed numerically. We show that the metric is able to provide a reasonable approximation to the match function of other IMR waveform families, such that the effective-one-body model calibrated to numerical relativity (EOBNRv2). The availability of this metric can contribute to improving the sensitivity of searches for GWs from binary black holes in the advanced detector era.

We study equal- and unequal-mass neutron star mergers by means of new numerical relativity simulations in which the general relativistic hydrodynamics solver employs an algorithm that guarantees mass conservation across the refinement levels of the computational mesh. We consider eight binary configurations with total mass $M=2.7M_{\odot }$, mass ratios $q=1$ and $q=1.16$, four different equations of state (EOSs) and one configuration with a stiff EOS, $M=2.5M_{\odot }$ and $q=1.5$, which is one of the largest mass ratios simulated in numerical relativity to date. We focus on the postmerger dynamics and study the merger remnant, the dynamical ejecta, and the postmerger gravitational wave spectrum. Although most of the merger remnants are a hypermassive neutron star collapsing to a black $\text{hole}+\text{disk}$ system on dynamical time scales, stiff EOSs can eventually produce a stable massive neutron star. During the merger process and on very short time scales, about $\sim {10}^{-3}–{10}^{-2}{M}_{\odot }$ of material become unbound with kinetic energies $\sim {10}^{50}\mathrm{erg}$. Ejecta are mostly emitted around the orbital plane and favored by large mass ratios and softer EOS. The postmerger wave spectrum is mainly characterized by the nonaxisymmetric oscillations of the remnant neutron star. The stiff EOS configuration consisting of a $1.5M_{\odot }$ and a $1.0M_{\odot }$ neutron star, simulated here for the first time, shows a rather peculiar dynamics. During merger the companion star is very deformed; about $\sim 0.03M_{\odot }$ of the rest mass becomes unbound from the tidal tail due to the torque generated by the two-core inner structure. The merger remnant is a stable neutron star surrounded by a massive accretion disk of rest mass $\sim 0.3M_{\odot }$. This and similar configurations might be particularly interesting for electromagnetic counterparts. Comparing results obtained with and without the conservative mesh refinement algorithm, we find that postmerger simulations can be affected by systematic errors if mass conservation is not enforced in the mesh refinement strategy. However, mass conservation also depends on grid details and on the artificial atmosphere setup; the latter are particularly significant in the computation of the dynamical ejecta.

We present numerical evidence that fictitious diffusing particles in the causal dynamical triangulation (CDT) approach to quantum gravity exceed the speed of light on small distance scales. We argue this superluminal behavior is responsible for the appearance of dimensional reduction in the spectral dimension. By axiomatically enforcing a scale invariant speed of light we show that time must dilate as a function of relative scale, just as it does as a function of relative velocity. By calculating the Hausdorff dimension of CDT diffusion paths we present a seemingly equivalent dual description in terms of a scale dependent Wick rotation of the metric. Such a modification to the nature of time may also have relevance for other approaches to quantum gravity.

In this paper, we study classical general relativistic static wormhole configurations with pseudospherical symmetry. We show that, in addition to the hyperbolic wormhole solutions discussed by Lobo and Mimoso in [Phys. Rev. D 82, 044034 (2010)], there exists another wormhole class, which is a truly pseudospherical counterpart of spherical Morris–Thorne wormhole (contrary to the Lobo–Mimoso wormhole class), since all constraints originally defined by Morris and Thorne for spherically symmetric wormholes are satisfied. We show that, for both classes of hyperbolic wormholes, the energy density, at the throat, is always negative, while the radial pressure is positive, contrary to the spherically symmetric Morris–Thorne wormhole. Specific hyperbolic wormholes are constructed and discussed by imposing different conditions for the radial and lateral pressures, or by considering restricted choices for the redshift and the shape functions. In particular, we show that a hyperbolic wormhole cannot be sustained at the throat by phantom energy and that there are pseudospherically symmetric wormholes supported by matter with isotropic pressure and characterized by space sections with an angle deficit (or excess).

We investigate the effect of equilateral-type primordial trispectrum on the halo/galaxy bispectrum. We consider three types of equilateral primordial trispectra which are generated by quartic operators naturally appearing in the effective field theory of inflation and can be characterized by three nonlinearity parameters, $g_{\mathrm{NL}}^{{\dot{\sigma }}^4}$, $g_{\mathrm{NL}}^{{\dot{\sigma }}^2(\partial \sigma {)}^2}$, and $g_{\mathrm{NL}}^{(\partial \sigma {)}^4}$. Recently, constraints on these parameters have been investigated from Cosmic Microwave Background (CMB) observations by using WMAP9 data. In order to consider the halo/galaxy bispectrum with the equilateral-type primordial trispectra, we adopt the integrated perturbation theory in which the effects of primordial non-Gaussianity are wholly encapsulated in the linear primordial polyspectrum for the evaluation of the biased polyspectrum. We show the shapes of the halo/galaxy bispectrum with the equilateral-type primordial trispectra and find that the primordial trispectrum characterized by $g_{\mathrm{NL}}^{{\dot{\sigma }}^4}$ provides the same scale dependence as the gravity-induced halo/galaxy bispectrum. Hence, it would be difficult to obtain the constraint on $g_{\mathrm{NL}}^{{\dot{\sigma }}^4}$ from the observations of the halo/galaxy bispectrum. On the other hand, the primordial trispectra characterized by $g_{\mathrm{NL}}^{{\dot{\sigma }}^2(\partial \sigma {)}^2}$ and $g_{\mathrm{NL}}^{(\partial \sigma {)}^4}$ provide the common scale dependence which is different from that of the gravity-induced halo/galaxy bispectrum on large scales. Hence, future observations of the halo/galaxy bispectrum would give constraints on the nonlinearity parameters, $g_{\mathrm{NL}}^{{\dot{\sigma }}^2(\partial \sigma {)}^2}$ and $g_{\mathrm{NL}}^{(\partial \sigma {)}^4}$ independently from CMB observations.

The nonlinear hydrodynamic equations for axion/scalar field dark matter (DM) in the nonrelativistic Madelung-Shcrödinger form are derived in a simple manner, including the effects of universal expansion and Hubble drag. The hydrodynamic equations are used to investigate the relative velocity between axion DM and baryons, and the moving-background perturbation theory (MBPT) derived. Axions massive enough to be all of the DM do not affect the coherence length of the relative velocity, but the MBPT equations are modified by the inclusion of the axion effective sound speed. These MBPT equations are necessary for accurately modeling the effects of axion DM on the formation of the first cosmic structures, and suggest that the 21-cm power spectrum could improve constraints on axion mass by up to 4 orders of magnitude with respect to the current best constraints. A further application of these results uses the “quantum force” analogy to model scalar field gradient energy in a smoothed-particle hydrodynamics model of axion DM. Such a model can treat axion DM in the nonlinear regime and could be incorporated into existing N-body codes.

The $\mathrm{\Lambda }$ cold dark matter ($\mathrm{\Lambda }\mathrm{CDM}$) model is currently known as the simplest cosmology model that best describes observations with a minimal number of parameters. Here we introduce a cosmology model that is preferred over the conventional $\mathrm{\Lambda }\mathrm{CDM}$ one by constructing dark energy as the sum of the cosmological constant $\mathrm{\Lambda }$ and an additional fluid that is designed to have an extremely short transient spike in energy density during the radiation-matter equality era and an early scaling behavior with radiation and matter densities. The density parameter of the additional fluid is defined as a Gaussian function plus a constant in logarithmic scale-factor space. Searching for the best-fit cosmological parameters in the presence of such a dark energy spike gives a far smaller chi-square value by about 5 times the number of additional parameters introduced and narrower constraints on the matter density and Hubble constant compared with the best-fit $\mathrm{\Lambda }\mathrm{CDM}$ model. The significant improvement in reducing the chi square mainly comes from the better fitting of the Planck temperature power spectrum around the third ($\ell \approx 800$) and sixth ($\ell \approx 1800$) acoustic peaks. The likelihood ratio test and the Akaike information criterion suggest that the model of a dark energy spike is strongly favored by the current cosmological observations over the conventional $\mathrm{\Lambda }\mathrm{CDM}$ model. However, based on the Bayesian information criterion which penalizes models with more parameters, the strong evidence supporting the presence of a dark energy spike disappears. Our result emphasizes that the alternative cosmological parameter estimation with even better fitting of the same observational data is allowed in Einstein’s gravity.

Non-Gaussianity in the distribution of inflationary perturbations, measurable in statistics of the cosmic microwave background (CMB) and large scale structure fluctuations, can be used to probe nontrivial initial quantum states for these perturbations. The bispectrum shapes predicted for generic non-Bunch-Davies initial states are nonfactorizable (“nonseparable”) and are highly oscillatory functions of the three constituent wave numbers. This can make the computation of CMB bispectra, in particular, computationally intractable. To efficiently compare with CMB data one needs to construct a separable template that has a significant similarity with the actual shape in momentum space. In this paper we consider a variety of inflationary scenarios, with different nonstandard initial conditions, and how best to construct viable template matches. In addition to implementing commonly used separable polynomial and Fourier bases, we introduce a basis of localized piecewise spline functions. The spline basis is naturally nearly orthogonal, making it easy to implement and to extend to many modes. We show that, in comparison to existing techniques, the spline basis can provide better fits to the true bispectrum, as measured by the cosine between shapes, for sectors of the theory space of general initial states. As such, it offers a useful approach to investigate nontrivial features generated by fundamental properties of the inflationary Universe.

A simple extension of the standard model (SM) providing transient magnetic moments to right-handed neutrinos is presented. In this model, the decay of the next-to-lightest right-handed heavy neutrino to the lightest one and a photon ($N_2\to N_1+\gamma$) can explain the $\sim 3.5\mathrm{keV}$ x-ray line signal observed by the XMM-Newton X-ray observatory. Beside the SM particles and heavy right-handed Majorana neutrinos, the model contains a singly charged scalar ($H^{\pm }$) and an extra Higgs doublet ($\mathrm{\Sigma }$). Within this minimal set of extra fields the sub-eV masses of left-handed neutrinos are also explained. Moreover, we show that the spin-independent dark matter–nucleon cross section is compatible with the latest LUX data.

We find bounds on scalar masses resulting from a criterion of naturalness, in a broad class of two Higgs doublet models. Specifically, we assume the cancellation of quadratic divergences in what are called the type I, type II, lepton-specific, and flipped two Higgs doublet models, with an additional U(1) symmetry. This results in a set of relations among masses of the physical scalars and coupling constants, a generalization of the Veltman conditions of the standard model. Assuming that the lighter $CP$-even neutral Higgs particle is the observed scalar particle of mass $\sim 125\mathrm{GeV}$, and imposing further the constraints from the electroweak T-parameter, stability, and perturbative unitarity, we calculate the range of the mass of each of the remaining physical scalars.

Neutral $B$ meson mixing matrix elements and $B$ meson decay constants are calculated. The static approximation is used for the $b$ quark and the domain-wall fermion formalism is employed for light quarks. The calculations are carried out on $2+1$-flavor dynamical ensembles generated by the RBC and UKQCD collaborations with lattice spacings of 0.086 fm ($a^{-1}\sim 2.3\mathrm{GeV}$) and 0.11 fm (1.7 GeV), and a fixed physical spatial volume of about $(2.7\mathrm{fm}{)}^3$. In the static quark action, link smearings are used to improve the signal-to-noise ratio. We employ two kinds of link smearings, HYP1 and HYP2, and their results are combined when taking the continuum limit. For the matching between the lattice and the continuum theory, one-loop perturbative $O(a)$ improvements are made to reduce discretization errors. As the most important quantity of this work, we obtain the SU(3) breaking ratio $\xi =1.208(60)$, where the error includes both the statistical and systematic errors. (The uncertainty from an infinite $b$-quark mass is not included.) We also find other neutral $B$ meson mixing quantities, $f_B\sqrt{{\widehat{B}}_B}=240(22)\mathrm{MeV}$, $f_{B_s}\sqrt{{\widehat{B}}_{B_s}}=290(22)\mathrm{MeV}$, ${\widehat{B}}_B=1.17(22)$, ${\widehat{B}}_{B_s}=1.22(13)$, and $B_{B_s}/B_B=1.028(74)$, and the $B$ meson decay constants $f_B=219(17)\mathrm{MeV}$, $f_{B_s}=264(19)\mathrm{MeV}$, and $f_{B_s}/f_B=1.193(41)$ in the static limit of the $b$ quark, which do not include an infinite $b$-quark mass uncertainty.

The Abelian decomposition of QCD which decomposes the gluons to the color neutral binding gluons and the colored valence gluons shows that QCD can be viewed as the restricted QCD (RCD) made of the binding gluons which has the valence gluons as colored source, and simplifies the QCD dynamics greatly. In particular, it tells that the gauge covariant valence gluons can be treated as the constituents of hadrons, and generalizes the quark model to the quark and valence gluon model. So it provides a comprehensive picture of glueballs and their mixing with quarkoniums, and predicts new hybrid hadrons made of quarks and valence gluons. We discuss how these predictions could be confirmed experimentally. In particular we present a systematic search for the ground state glueballs and their mixing with quarkoniums below 2 GeV in $0^{++}$, $2^{++}$, and $0^{-+}$ channels within the framework of QCD, and predict the relative branching ratios of the radiative decay of $\psi$ to the physical states.

We investigate the Glauber-gluon effect on the $B\to \pi \pi$ and $\rho \rho$ decays, which is introduced via a convolution of a universal Glauber phase factor with transverse-momentum-dependent meson wave functions in the $k_T$ factorization theorem. For an appropriate parametrization of the Glauber phase, it is observed that a transverse-momentum-dependent wave function for the pion ($\rho$ meson) with a weak (strong) falloff in parton transverse momentum $k_T$ leads to significant (moderate) modification of the $B^0\to {\pi }^0{\pi }^0$ ($B^0\to {\rho }^0{\rho }^0$) branching ratio: the former (latter) is enhanced (reduced) by about a factor of 2 (15%). This observation is consistent with the dual role of the pion as a massless Nambu-Goldstone boson and as a $q\overline{q}$ bound state, which requires a tighter spatial distribution of its leading Fock state relative to higher Fock states. The agreement between the theoretical predictions and the data for all the $B\to \pi \pi$ and ${\rho }^0{\rho }^0$ branching ratios is then improved simultaneously, and it is possible to resolve the $B\to \pi \pi$ puzzle.

We discuss the sensitivity of a 100 TeV $pp$ collider to heavy resonances produced in longitudinal vector-boson scattering and decaying to a pair of Higgs bosons. A Monte Carlo study has been performed using the $H\to \tau \tau$ decay channel for both Higgs bosons, comparing the kinematics of such a signal to the irreducible Standard Model backgrounds. The results are presented in the context of a phenomenological model of a resonance ($\eta$) coupling to Goldstone modes, $V_L{V}_L\to \eta \to HH$, as can arise in composite Higgs models. With a fractional width of 70% (20%), the $5\sigma$ discovery reach is 4.2 (2.9) TeV in resonance mass for $10{\mathrm{ab}}^{-1}$ of integrated luminosity. We also discuss the dependence of the mass reach on the collider energy and integrated luminosity.

We report measurement of the cross section of $e^{+}{e}^{-}\to {\pi }^{+}{\pi }^{-}\psi (2S)$ between 4.0 and 5.5 GeV, based on an analysis of initial state radiation events in a $980{\mathrm{fb}}^{-1}$ data sample recorded with the Belle detector. The properties of the $Y(4360)$ and $Y(4660)$ states are determined. Fitting the mass spectrum of ${\pi }^{+}{\pi }^{-}\psi (2S)$ with two coherent Breit-Wigner functions, we find two solutions with identical mass and width but different couplings to electron-positron pairs: $M_{Y(4360)}=(4347\pm 6\pm 3)\mathrm{MeV}/c^2$, ${\mathrm{\Gamma }}_{Y(4360)}=(103\pm 9\pm 5)\mathrm{MeV}$, $M_{Y(4660)}=(4652\pm 10\pm 8)\mathrm{MeV}/c^2$, ${\mathrm{\Gamma }}_{Y(4660)}=(68\pm 11\pm 1)\mathrm{MeV}$; and $\mathcal{B}[Y(4360)\to {\pi }^{+}{\pi }^{-}\psi (2S)]·{\mathrm{\Gamma }}_{Y(4360)}^{e^{+}{e}^{-}}=(10.9\pm 0.6\pm 0.7)\mathrm{eV}$ and $\mathcal{B}[Y(4660)\to {\pi }^{+}{\pi }^{-}\psi (2S)]·{\mathrm{\Gamma }}_{Y(4660)}^{e^{+}{e}^{-}}=(8.1\pm 1.1\pm 0.5)\mathrm{eV}$ for one solution; or $\mathcal{B}[Y(4360)\to {\pi }^{+}{\pi }^{-}\psi (2S)]·{\mathrm{\Gamma }}_{Y(4360)}^{e^{+}{e}^{-}}=(9.2\pm 0.6\pm 0.6)\mathrm{eV}$ and $\mathcal{B}[Y(4660)\to {\pi }^{+}{\pi }^{-}\psi (2S)]·{\mathrm{\Gamma }}_{Y(4660)}^{e^{+}{e}^{-}}=(2.0\pm 0.3\pm 0.2)\mathrm{eV}$ for the other. Here, the first errors are statistical and the second systematic. Evidence for a charged charmoniumlike structure at $4.05\mathrm{GeV}/c^2$ is observed in the ${\pi }^{\pm }\psi (2S)$ intermediate state in the $Y(4360)$ decays.