We have studied some possible four-quark and molecule configurations of the $X(3872)$ using double ratios of sum rules, which are more accurate than the usual simple ratios often used in the literature to obtain hadron masses. We found that the different structures ($\overline{3}-3$ and $\overline{6}-6$ tetraquarks and $D-D^{(*)}$ molecule) lead to the same prediction for the mass (within the accuracy of the method), indicating that the alone prediction of the $X$ mass may not be sufficient to reveal its nature. In doing these analyses, we also find that (within our approximation) the use of the $\overline{\mathrm{MS}}$ running ${\overline{m}}_c(m_c^2)$, rather than the on-shell mass, is more appropriate to obtain the $J/\psi$ and $X$ meson masses. Using vertex sum rules to roughly estimate the $X(3872)$ hadronic and radiative widths, we found that the available experimental data does not exclude a $\lambda -J/\psi$-like molecule current.

In this article, we study the strong decays of the newly observed charmed mesons $D(2550)$, $D(2600)$, $D(2750)$, and $D(2760)$ with the heavy quark effective theory in the leading order approximation, and tentatively identify the $(D(2550),D(2600))$ as the $2S$ doublet $(0^{-},1^{-})$ and the $(D(2750),D(2760))$ as the $1D$ doublet $(2^{-},3^{-})$, respectively. The identification of the $D(2750)$ and $D(2760)$ as the same particle with $J^P=3^{-}$ is disfavored.

We calculate the $B_{u,d,s}\to T$ form factors within the framework of the perturbative QCD approach, where $T$ denotes a light tensor meson with $J^P=2^{+}$. Because of the similarities between the wave functions of a vector and a tensor meson, the factorization formulas of $B\to T$ form factors can be obtained from the $B\to V$ transition through a replacement rule. As a consequence, we find that these two sets of form factors have the same signs and correlated $q^2$-dependence behaviors. At $q^2=0$ point, the $B\to T$ form factors are smaller than the $B\to V$ ones, in accordance with the experimental data of radiative $B$ decays. In addition, we use our results for the form factors to explore semilteptonic $B\to Tl{\overline{\nu }}_l$ decays and the branching fractions can reach the order ${10}^{-4}$.

In this paper, we investigate phenomenologically two-body weak decays of the bottom mesons emitting pseudoscalar/vector meson and a tensor meson. Form factors are obtained using the improved Isgur-Scora-Grinstein-Wise II model. Consequently, branching ratios for the Cabibbo-Kobayashi-Maskawa–favored and Cabibbo-Kobayashi-Maskawa–suppressed decays are calculated.

Within the framework of the QCD sum rules, we consider the three-point correlation function, work at the limit $q^2\to 0$ and $m_{\pi }\to 0$, and pick out the singular term $\sim \frac{1}{q^2}$ to extract the pionic coupling constants of the $1^{-+}$ hybrid meson. Then, we calculate the decay widths of different modes. The decay width of the $S$-wave modes $b_1\pi$, $f_1\pi$ increases quickly as the hybrid meson mass and decay momentum increase. But for the low mass hybrid meson around 1.6 GeV, the $P$-wave decay mode $\rho \pi$ is very important and its width is around 180 MeV, while the widths of $\eta \pi$ and ${\eta }^{\prime }\pi$ are strongly suppressed. We suggest the experimental search of ${\pi }_1(1600)$ through the decay chains at the Beijing Spectrometer: $J/\psi ({\psi }^{\prime })\to {\pi }_1+\gamma$ or $J/\psi ({\psi }^{\prime })\to {\pi }_1+\rho$, where the ${\pi }_1$ state can be reconstructed through the decay modes ${\pi }_1\to \rho \pi \to {\pi }^{+}{\pi }^{-}{\pi }^0$ or ${\pi }_1\to f_1(1285){\pi }^0$. It is also interesting to look for ${\pi }_1$ using the available BELLE/BABAR data through the process $e^{+}{e}^{-}\to {\gamma }^{*}\to \rho {\pi }_1$, $b_1{\pi }_1$, $\gamma {\pi }_1$, etc.

The heavy-quark QCD sum rules are applied to a model of charmonium based upon the gauge/gravity duality. We find that there is strong agreement between the moments of the polarization function calculated from the holographic model and the experimental data suggesting that the model is consistent with the heavy-quark QCD sum rules at zero temperature.

We consider a 4D model for photon production induced by a refractive index perturbation in a dielectric medium. We show that, in this model, we can infer the presence of a Hawking type effect. This prediction shows up both in the analogue Hawking framework, which is implemented in the pulse frame and relies on the peculiar properties of the effective geometry in which quantum fields propagate, as well as in the laboratory frame, through standard quantum field theory calculations. Effects of optical dispersion are also taken into account, and are shown to provide a limited energy bandwidth for the emission of Hawking radiation.

Phase diagram of the chiral random matrix model with $\mathrm{U}(1{)}_{\mathrm{A}}$ breaking term is studied with the quark chemical potentials varied independently at zero temperature by taking the chiral and meson condensates as the order parameters. Although, without the $\mathrm{U}(1{)}_{\mathrm{A}}$ breaking term, chiral transition of each flavor can happen separately responding to its chemical potential, the $\mathrm{U}(1{)}_{\mathrm{A}}$ breaking terms mix the chiral condensates and correlate the phase transitions. In the three-flavor case, we find that there are mixings between the meson and chiral condensates due to the $\mathrm{U}(1{)}_{\mathrm{A}}$ anomaly, which makes the meson condensed phase more stable. Increasing the hypercharge chemical potential (${\mu }_Y$) with the isospin and quark chemical potentials $({\mu }_I,{\mu }_q)$ kept small, we observe that the kaon-condensed phase becomes the ground state and at the larger ${\mu }_Y$ the pion-condensed phase appears unexpectedly, which is caused by the competition between the chiral restoration and the meson condensation. The similar happens when ${\mu }_Y$ and ${\mu }_I$ are exchanged, and the kaon-condensed phase becomes the ground state at larger ${\mu }_I$ below the full chiral restoration.

We calculate the thermal spectral function of strongly interacting Yang-Mills plasma with finite density using the holographic technique. The gravity dual of the finite temperature and density is taken as the Reissner-Nordström–anti-de Sitter black hole. In the presence of charge, linearized vector modes of gravitational and electromagnetic perturbation are coupled with each other. By introducing master variables for these modes, we solve the coupled system and calculate spectral function. The spectral function gets a new peak due to the density effect, which is most dramatic in the momentum plot with fixed frequency. We also calculate the photoemission rate of our gauge theory plasma from the spectral function for lightlike momentum. AC, dc conductivity, and their density dependence is also computed.

We derive a new functional renormalization group equation for Hamiltonian Yang-Mills theory in Coulomb gauge. The flow equations for the static gluon and ghost propagators are solved under the assumption of ghost dominance within different diagrammatic approximations. The results are compared to those obtained in the variational approach and the reliability of the approximations is discussed.

We calculate stellar oscillations, including the hadron-quark mixed phase, considering finite-size effects. We find that it is possible to distinguish whether the density discontinuity exists or not in the stars, even if one observes the gravitational waves of the fundamental mode. Additionally, the normalized eigenfrequencies of pressure modes depend strongly on the stellar mass and on the adopted equation of state. In particular, in spite of the fact that the radius of the neutron star with $1.4M_{\odot }$, which is the standard mass, is almost independent of the equation of state with quark matter, the frequencies of the pressure modes depend on the adopted equation of state. Thus, via observing the many kinds of gravitational waves, it will be possible to make a restriction on the equation of state.

Last moments of a mini black hole escaping from a brane are studied. It is argued that at the point of reconnection, where the piece of the brane attached to the black hole separates from the rest, the world sheet of the brane becomes isotropic (lightlike). The degenerate mode of evolution, with the world sheet isotropic everywhere, is investigated. In particular, it is shown that the brane approaches the reconnection point from below if it reconnects within a certain limit distance, and from above if it reconnects beyond that distance. The rate of relaxation to the degenerate mode is established. If the dimension of the brane is $p$, the nondegeneracy, measured by the determinant of the relevant part of the induced metric tensor, falls down as $(\mathrm{\text{latitudinal angle}}{)}^{2(p-1)}$.

We interpret the scalar $B_{s0}^{*}(5725)$ as an $S$-wave $B\overline{K}$ molecular bound state in the Bethe-Salpeter approach. In the ladder and instantaneous approximation, with the kernel induced by $\rho$ and $\omega$ exchanges, we establish the Bethe-Salpeter equation for $B_{s0}^{*}(5725)$. We find that the bound state of $B\overline{K}$ can exist. We also calculate the isospin-violating decay width of the process $B_{s0}^{*}(5725)\to B_s{\pi }^0$ through exchanging $K^{*}$ and $B^{*}$ mesons including the $\eta -{\pi }^0$ mixing effect. We hope that the obtained decay width is instructive for the forthcoming experiment.

The presence of substructures in dark matter haloes is an unavoidable consequence of the cold dark matter paradigm. Indirect signals from these objects have been extensively searched for with cosmic rays and $\gamma$ rays. At first sight, Cherenkov telescopes seem not very well suited for such searches, due to their small fields of view and the random nature of the possible dark matter substructure positions in the sky. However, with long enough exposure and an adequate observation strategy, the very good sensitivity of this experimental technique allows us to constrain particle dark matter models. We confront here the sensitivity map of the HESS experiment built out of their Galactic scan survey to the state-of-the-art cosmological $N$-body simulation Via Lactea II. We obtain competitive constraints on the annihilation cross section, at the level of ${10}^{-24}–{10}^{-23}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$. The results are extrapolated to the future Cherenkov Telescope Array, in the cases of a Galactic plane survey and of an even wider extragalactic survey. In the latter case, it is shown that the sensitivity of the Cherenkov Telescope Array will be sufficient to reach the most natural particle dark matter models.

We introduce two new eccentricity measures to analyze numerical simulations. Unlike earlier definitions these eccentricity measures do not involve any free parameters which makes them easy to use. We show how relatively inexpensive grid setups can be used to estimate the eccentricity during the early inspiral phase. Furthermore, we compare standard puncture data and post-Newtonian data in ADMTT gauge. We find that both use different coordinates. Thus low eccentricity initial momentum parameters for a certain separation measured in ADMTT coordinates are hard to use in puncture data, because it is not known how the separation in puncture coordinates is related to the separation in ADMTT coordinates. As a remedy we provide a simple approach which allows us to iterate the momentum parameters until our numerical simulations result in acceptably low eccentricities.

In addition to shear and vorticity a homogeneous background may also exhibit anisotropic curvature. Here a class of spacetimes is shown to exist where the anisotropy is solely of the latter type, and the shear-free condition is supported by a canonical, massless 2-form field. Such spacetimes possess a preferred direction in the sky and at the same time a CMB which is isotropic at the background level. A distortion of the luminosity distances is derived and used to test the model against the CMB and supernovae (using the Union catalog), and it is concluded that the latter exhibit a higher-than-expected dependence on angular position. It is shown that future surveys could detect a possible preferred direction by observing $\sim 20/(\Omega _{k0}{}^2)$ supernovae over the whole sky.

A design study is currently in progress for a third-generation gravitational-wave (GW) detector called the Einstein Telescope (ET). An important kind of source for ET will be the inspiral and merger of binary neutron stars up to $z\sim 2$. If binary neutron star mergers are the progenitors of short-hard $\gamma$-ray bursts, then some fraction of them will be seen both electromagnetically and through GW, so that the luminosity distance and the redshift of the source can be determined separately. An important property of these “standard sirens” is that they are self-calibrating: the luminosity distance can be inferred directly from the GW signal, with no need for a cosmic distance ladder. Thus, standard sirens will provide a powerful independent check of the $\Lambda \mathrm{CDM}$ model. In previous work, estimates were made of how well ET would be able to measure a subset of the cosmological parameters (such as the dark energy parameter $w_0$) it will have access to, assuming that the others had been determined to great accuracy by alternative means. Here we perform a more careful analysis by explicitly using the potential Planck cosmic microwave background data as prior information for these other parameters. We find that ET will be able to constrain $w_0$ and $w_a$ with accuracies $\Delta w_0=0.099$ and $\Delta w_a=0.302$, respectively. These results are compared with projected accuracies for the JDEM baryon acoustic oscillations project and the SNAP type Ia supernovae observations.

We present an unquenched $N_f=2$ lattice computation of the $B_K$ parameter which controls $K^0-{\overline{K}}^0$ oscillations. A partially quenched setup is employed with two maximally twisted dynamical (sea) light Wilson quarks, and valence quarks of both the maximally twisted and the Osterwalder-Seiler variety. Suitable combinations of these two kinds of valence quarks lead to a lattice definition of the $B_K$ parameter which is both multiplicatively renormalizable and $\mathrm{O}(a)$ improved. Employing the nonperturbative RI-MOM scheme, in the continuum limit and at the physical value of the pion mass we get $B_K^{\mathrm{RGI}}=0.729\pm 0.030$, a number well in line with the existing quenched and unquenched determinations.

We investigate the generalized parton distributions for $u$ and $d$ quarks in a proton in transverse and longitudinal position space using a recent phenomenological parametrization. We take nonzero skewness $\zeta$ and consider the region $x>\zeta$. The impact parameter space representation of the generalized parton distribution $E$ is found to depend sharply on the parameters used within the model, in particular, in the low $x$ region. In the longitudinal position space a diffraction pattern is observed, as seen before in several other models.

We examine some noncommutative spherically symmetric spaces in three space dimensions. A generalization of Snyder’s noncommutative (Euclidean) space allows the inclusion of the generator of dilations into the defining algebra of the coordinate and rotation operators. We then construct a spherically symmetric noncommutative Laplacian on this space having the correct limiting spectrum. This is presented via a creation and annihilation operator realization of the algebra, which may lend itself to a truncation of the Hilbert space.