Using the Brans-Dicke theory of gravitation we put under investigation a hypothetical universe filled with a fermionic field (with a self-interaction potential) and a matter constituent ruled by a barotropic equation of state. It is shown that the fermionic field [in combination with the Brans-Dicke scalar field $\phi (t)$] could be responsible for a final accelerated era, after an initial matter dominated period.

Semiclassical spinning string states in ${\mathrm{AdS}}_5$ are, in general, characterized by the three $SO(2,4)$ conserved charges: the energy $E$ and the two spins $S_1$ and $S_2$. We discuss several examples of explicit classical solutions for rigid closed strings of (bended) circular shape with two nonzero spins. In particular, we identify a solution that should represent a state that has minimal energy for large values of the two equal spins. Similarly to the spiky string in ${\mathrm{AdS}}_3$, in the large-spin limit this string develops long “arcs” that stretch towards the boundary of ${\mathrm{AdS}}_5$. This allows the string to increase the spin while having the energy growing only logarithmically with $S=S_1+S_2$. The large-spin asymptotics of such solutions is effectively controlled by their near-boundary parts which, as in the spiky string case, happen to be $SO(2,4)$ equivalent to segments of the straight folded spinning string. As a result, the coefficient of the $\log S$ term in the string energy should be given, up to an overall $3/2$ coefficient, by the same universal scaling function (cusp anomaly) as in the folded string case, to all orders in the inverse string tension or strong-coupling expansion.

We have obtained two classes of ($n+1$)-dimensional wormhole solutions using a traceless energy-momentum tensor in the Brans-Dicke theory of gravity. The first class contains wormhole solutions in an open geometry, while the second contains wormhole solutions in both open and closed universes. In addition to wormhole geometries, naked singularities and maximally symmetric space-time also appear among the solutions as special cases. We have also considered the traversability of the wormhole solutions and have shown that they are indeed traversable. Finally, we have discussed the energy-momentum tensor which supports this geometry and have checked for the energy conditions. We have found that wormhole solutions in the first class of solutions violate the weak energy condition (WEC). In the second class, the wormhole geometries in a closed universe do violate the WEC, but in an open universe with a suitable choice of constants the supporting matter energy-momentum tensor can satisfy the WEC. However, even in this case the full effective energy-momentum tensor including the scalar field and the matter energy-momentum tensor still violates the WEC.

We study the $d$-dimensional Fisher solution which represents a static, spherically symmetric, asymptotically flat spacetime with a massless scalar field. The solution has two parameters, the mass $M$ and the “scalar charge” $\Sigma$. The Fisher solution has a naked curvature singularity which divides the spacetime manifold into two disconnected parts. The part which is asymptotically flat we call the Fisher spacetime, and another part we call the Fisher universe. The $d$-dimensional Schwarzschild-Tangherlini solution and the Fisher solution belong to the same theory and are dual to each other. The duality transformation acting in the parameter space $(M,\Sigma )$ maps the exterior region of the Schwarzschild-Tangherlini black hole into the Fisher spacetime which has a naked timelike singularity, and interior region of the black hole into the Fisher universe, which is an anisotropic expanding-contracting universe and which has two spacelike singularities representing its “big bang” and “big crunch.” The big bang singularity and the singularity of the Fisher spacetime are radially weak in the sense that a 1-dimensional object moving along a timelike radial geodesic can arrive to the singularities intact. At the vicinity of the singularity the Fisher spacetime of nonzero mass has a region where its Misner-Sharp energy is negative. The Fisher universe has a marginally trapped surface corresponding to the state of its maximal expansion in the angular directions. These results and derived relations between geometric quantities of the Fisher spacetime, the Fisher universe, and the Schwarzschild-Tangherlini black hole may suggest that the massless scalar field transforms the black hole event horizon into the naked radially weak disjoint singularities of the Fisher spacetime and the Fisher universe which are “dual to the horizon.”

We present a polymer quantization of spherically symmetric Einstein gravity in which the polymerized variable is the area of the Einstein-Rosen wormhole throat. In the classical polymer theory, the singularity is replaced by a bounce at a radius that depends on the polymerization scale. In the polymer quantum theory, we show numerically that the area spectrum is evenly spaced and in agreement with a Bohr-Sommerfeld semiclassical estimate, and this spectrum is not qualitatively sensitive to issues of factor ordering or boundary conditions except in the lowest few eigenvalues. In the limit of small polymerization scale we recover, within the numerical accuracy, the area spectrum obtained from a Schrödinger quantization of the wormhole throat dynamics. The prospects of recovering from the polymer throat theory a full quantum-corrected spacetime are discussed.

We prove that the only four-dimensional, stationary, rotating, asymptotically flat (analytic) vacuum black hole with a single degenerate horizon is given by the extremal Kerr solution. We also prove a similar uniqueness theorem for the extremal Kerr-Newman solution. This closes a long-standing gap in the black hole uniqueness theorems.

In this paper we study the effects of the generalized uncertainty principle (GUP) on canonical quantum gravity of black holes. Through the use of modified partition function that involves the effects of the GUP, we obtain the thermodynamical properties of the Schwarzschild black hole. We also calculate the Hawking temperature and entropy for the modification of the Schwarzschild black hole in the presence of the GUP.

We consider the stochastic background of gravitational waves produced during the radiation-dominated hot big bang as a constraint on the primordial density perturbation on comoving length scales much smaller than those directly probed by the cosmic microwave background or large-scale structure. We place weak upper bounds on the primordial density perturbation from current data. Future detectors such as BBO and DECIGO will place much stronger constraints on the primordial density perturbation on small scales.

We calculate the redshift space correlation function and the power spectrum of density peaks of a Gaussian random field. Our derivation, which is valid on linear scales $k\lesssim 0.1h{\mathrm{Mpc}}^{-1}$, is based on the peak biasing relation given by Desjacques [Phys. Rev. D, 78, 103503 (2008)]. In linear theory, the redshift space power spectrum is $P_{\mathrm{pk}}^s(k,\mu )=\exp (-f^2{\sigma }_{\mathrm{vel}}^2{k}^2{\mu }^2)[b_{\mathrm{pk}}(k)+b_{\mathrm{vel}}(k)f{\mu }^2{]}^2{P}_{\delta }(k)$, where $\mu$ is the angle with respect to the line of sight, ${\sigma }_{\mathrm{vel}}$ is the one-dimensional velocity dispersion, $f$ is the growth rate, and $b_{\mathrm{pk}}(k)$ and $b_{\mathrm{vel}}(k)$ are $k$-dependent linear spatial and velocity bias factors. For peaks, the value of ${\sigma }_{\mathrm{vel}}$ depends upon the functional form of $b_{\mathrm{vel}}$. When the $k$ dependence is absent from the square brackets and $b_{\mathrm{vel}}$ is set to unity, the resulting expression is assumed to describe models where the bias is linear and deterministic, but the velocities are unbiased. The peak model is remarkable because it has unbiased velocities in this same sense—peak motions are driven by dark matter flows—but, in order to achieve this, $b_{\mathrm{vel}}$ must be $k$ dependent. We speculate that this is true in general: $k$ dependence of the spatial bias will lead to $k$ dependence of $b_{\mathrm{vel}}$ even if the biased tracers flow with the dark matter. Because of the $k$ dependence of the linear bias parameters, standard manipulations applied to the peak model will lead to $k$-dependent estimates of the growth factor that could erroneously be interpreted as a signature of modified dark energy or gravity. We use the Fisher formalism to show that the constraint on the growth rate $f$ is degraded by a factor of 2 if one allows for a $k$-dependent velocity bias of the peak type. Our analysis also demonstrates that the Gaussian smoothing term is part and parcel of linear theory. We discuss a simple estimate of nonlinear evolution and illustrate the effect of the peak bias on the redshift space multipoles. For $k\lesssim 0.1h{\mathrm{Mpc}}^{-1}$, the peak bias is deterministic but $k$ dependent, so the configuration-space bias is stochastic and scale dependent, both in real and redshift space. We provide expressions for this stochasticity and its evolution.

The cryogenic sapphire oscillator at the Paris Observatory has been continuously compared to various hydrogen masers since 2001. The early data sets were used to test local Lorentz invariance in the Robertson-Mansouri-Sexl (RMS) framework by searching for sidereal modulations with respect to the cosmic microwave background, and represent the best Kennedy-Thorndike experiment to date. In this work, we present continuous operation over a period of greater than six years from September 2002 to December 2008 and present a more precise way to analyze the data by searching the time derivative of the comparison frequency. Because of the long-term operation we are able to search both sidereal and annual modulations. The results give $P_{\mathrm{KT}}={\beta }_{\mathrm{RMS}}-{\alpha }_{\mathrm{RMS}}-1=-1.7(4.0)\times {10}^{-8}$ for the sidereal and $-23(10)\times {10}^{-8}$ for the annual term, with a weighted mean of $-4.8(3.7)\times {10}^{-8}$, a factor of 8 better than previous. Also, we analyze the data with respect to a change in gravitational potential for both diurnal and annual variations. The result gives ${\beta }_{H\mathrm{\text{−}}\mathrm{Maser}}-{\beta }_{\mathrm{CSO}}=-2.7(1.4)\times {10}^{-4}$ for the annual and $-6.9(4.0)\times {10}^{-4}$ for the diurnal terms, with a weighted mean of $-3.2(1.3)\times {10}^{-4}$. This result is 2 orders of magnitude better than other tests that use electromagnetic resonators. With respect to fundamental constants a limit can be provided on the variation with ambient gravitational potential and boost of a combination of the fine structure constant ($\alpha$), the normalized quark mass ($m_q$), and the electron to proton mass ratio ($m_e/m_p$), setting the first limit on boost dependence of order ${10}^{-10}$.

We present a minimally parametric reconstruction of the primordial power spectrum using the most recent cosmic microwave background and large-scale structure data sets. Our goal is to constrain the shape of the power spectrum while simultaneously avoiding strong theoretical priors and over-fitting of the data. We find no evidence for any departure from a power-law spectral index. We also find that an exact scale-invariant power spectrum is disfavored by the data, but this conclusion is weaker than the corresponding result assuming a theoretically-motivated power-law spectral index prior. The reconstruction shows that better data are crucial to justify the adoption of such a strong theoretical prior observationally. These results can be used to determine the robustness of our present knowledge when compared with forthcoming precision data from Planck.

We propose a simple method for incorporating correlations into the impact parameter space description of multiple (semi)hard partonic collisions in high energy hadron-hadron scattering. The perturbative QCD input is the standard factorization theorem for inclusive dijet production with a lower cutoff on transverse momentum. The width of the transverse distribution of hard partons is fixed by parametrizations of the two-gluon form factor. We then reconstruct the hard contribution to the total inelastic profile function and obtain corrections due to correlations to the more commonly used eikonal description. Estimates of the size of double correlation corrections are based on the rate of double collisions measured at the Tevatron. We find that, if typical values for the lower transverse momentum cutoff are used in the calculation of the inclusive hard dijet cross section, then the correlation corrections are necessary for maintaining consistency with expectations for the total inelastic proton-proton cross section at LHC energies.

The structure of the $D_1^0(2420[2430])$, ($J^P=1^{+}$) mesons via analyzing the semileptonic $B_c\to D_1^{0}l\nu$ transition is considered in the framework of the three-point QCD sum rules. In this work, we consider the $D_1^0(2420[2430])$ axial vectors as conventional $c\overline{u}$ mesons. Taking into account the gluon condensate contributions, the relevant form factors are obtained. The obtained results for the form factors are used to evaluate the decay rate and the branching ratio.

Radiative corrections to high-energy scattering processes were given previously in terms of universal soft and collinear functions. This paper gives the collinear functions for all standard model particles, the general form of the soft function, and explicit expressions for the soft functions for fermion-fermion scattering, longitudinal and transverse gauge boson production, single $W/Z$ production, and associated Higgs production. An interesting subtlety in the use of the Goldstone boson equivalence theorem for longitudinal $W^{+}$ production is discussed.

In the standard model the two-body charmless hadronic $B_c$ meson decays can occur via annihilation diagrams only. In this work, we studied the $B_c\to PP$, $PV/VP$, $VV$ decays by employing the perturbative QCD (pQCD) factorization approach. From our calculations, we find that (a) the pQCD predictions for the branching ratios of the considered $B_c$ decays are in the range of ${10}^{-6}$ to ${10}^{-8}$; (b) for $B_c\to PV/VP$, $VV$ decays, the branching ratios of $\Delta S=0$ decays are much larger than those of $\Delta S=1$ because the different Cabibbo-Kobayashi-Maskawa (CKM) factors are involved; (c) analogous to $B\to K{\eta }^{(\prime )}$ decays, we find $\mathrm{Br}(B_c\to K^{+}{\eta }^{\prime })\sim 10\times \mathrm{Br}(B_c\to K^{+}\eta )$, which can be understood by the destructive and constructive interference between the ${\eta }_q$ and ${\eta }_s$ contribution to the $B_c\to K^{+}\eta$ and $B_c\to K^{+}{\eta }^{\prime }$ decay; (d) the longitudinal polarization fractions of $B_c\to VV$ decays are in the range of 86%–95% and play the dominant role; and (e) there is no $CP$-violating asymmetries for the considered $B_c$ decays because only one type tree operator is involved.

The strong decays of the $D_{s1}(2710)$ and $D_{sJ}(2860)$ are investigated in the framework of the ${}^{3}P_0$ model. Its decay properties newly reported by the BABAR Collaboration can be reasonably accounted for in the presence of the $D_{s1}(2710)$ being a mixture of the $D_s(2{}^{3}S_1)$ and $D_s(1{}^{3}D_1)$. The orthogonal partner of the $D_{s1}(2710)$ is expected to have a mass of about $2.66\sim 2.9\mathrm{GeV}$ in quark models and a width of about $40\sim 60\mathrm{MeV}$ in the ${}^{3}P_0$ model. The predicted decay properties turn out to be consistent with BABAR’s new data in both the orthogonal partner of the $D_{s1}(2710)$ and the $D_s(1{}^{3}D_3)$ interpretations for the $D_{sJ}(2860)$. The available experimental information is not enough to distinguish these two possibilities. The $E1$ radiative transitions of the $D_{s1}(2710)$ and $D_{sJ}(2860)$ are also studied. We tend to conclude that the $D_{s1}(2710)$ can be identified as a mixture of the $D_s(2{}^{3}S_1)$ and $D_s(1{}^{3}D_1)$, and the $D_{sJ}(2860)$ could be either the orthogonal partner of the $D_{s1}(2710)$ or the $D_s(1{}^{3}D_3)$. Further experimental information on the $D_{sJ}(2860)$ in the $D_s\eta$, $D_s^{*}\eta$, and $D{K}^{*}$ channels is needed.

Within the framework of the nonrelativistic QCD (NRQCD) factorization approach, we compute the polarization of prompt $J/\psi$ produced at the Brookhaven’s Relativistic Heavy-Ion Collider from proton-proton collisions at the center-of-momentum energy $\sqrt{s}=200\mathrm{GeV}$. The perturbative contributions are computed at leading order in the strong coupling constant. The prediction reveals that the color-singlet contribution severely underestimates the PHENIX preliminary data for the differential cross section integrated over the rapidity range $|y|<0.35$ and its contribution is strongly transversely polarized, which disagrees with the PHENIX preliminary data. After including the color-octet contributions, we find that the NRQCD predictions for both the cross section and polarization over the transverse-momentum range $1.5\mathrm{GeV}<p_T<5\mathrm{GeV}$ ($1.5\mathrm{GeV}<p_T<2\mathrm{GeV}$) integrated over the rapidity range $|y|<0.35$ ($1.2<|y|<2.2$) agree with the data within errors.

We analyze recent data from the BABAR and Belle Collaborations on the $X(3872)$ resonance in the $J/\psi {\pi }^{+}{\pi }^{-}$ and $D^0{\overline{D}}^0{\pi }^0$ decay channels, taking careful account of the universal features of an $S$-wave threshold resonance. Because the line shapes for such a resonance are not integrable functions of the energy, the resonance parameters depend on the prescriptions used to define them. In recent experimental analyses of the $D^0{\overline{D}}^0{\pi }^0$ channel, an event near the $D^{*0}{\overline{D}}^0$ threshold was assumed to come from $D^{*0}{\overline{D}}^0$ or $D^0{\overline{D}}^{*0}$ and was therefore assigned an energy above the threshold. Taking this effect into account, our analysis of the $D^0{\overline{D}}^0{\pi }^0$ data gives a mass for the $X(3872)$ that is below the $D^{*0}{\overline{D}}^0$ threshold. Our analyses in both the $J/\psi {\pi }^{+}{\pi }^{-}$ and $D^0{\overline{D}}^0{\pi }^0$ channels are consistent with the identification of the $X(3872)$ as an extremely weakly bound charm meson molecule.

In this paper we investigate the one-loop radiative corrections to the neutrino indices of refraction from supersymmetric models. We consider the next-to-minimal supersymmetric extension of the standard model which happens to be a better supersymmetric candidate than the minimal supersymmetric standard model for both theoretical and experimental reasons. We scan the relevant supersymmetry parameters and identify regions in the parameter space which yield interesting values for $V_{\mu \tau }$. If R-parity is broken there are significant differences between the minimal supersymmetric standard model and next-to-minimal supersymmetric extension of the standard model contributions contrary to the R-parity conserved case. Finally, for a nonzero $CP$-violating phase, we show analytically that the presence of $V_{\mu \tau }$ will explicitly imply $CP$-violation effects on the supernova electron (anti)neutrino fluxes.

We report measurements of $CP$ violation parameters in $B^0\to K^0{\pi }^0$ decays based on a data sample of $657\times {10}^{6}B\overline{B}$ pairs collected with the Belle detector at the KEKB $e^{+}{e}^{-}$ asymmetric-energy collider. We use $B^0\to K_S^0{\pi }^0$ decays for both mixing-induced and direct $CP$ violating asymmetry measurements and $B^0\to K_L^0{\pi }^0$ decays for the direct $CP$ violation measurement. The $CP$ violation parameters obtained are $\sin 2{\varphi }_1^{\mathrm{eff}}=+0.67\pm 0.31(\mathrm{stat})\pm 0.08(\mathrm{syst})$ and ${\mathcal{A}}_{K^0{\pi }^0}=+0.14\pm 0.13(\mathrm{stat})\pm 0.06(\mathrm{syst})$. The branching fraction of $B^0\to K^0{\pi }^0$ decay is measured to be $\mathcal{B}(B^0\to K^0{\pi }^0)=(8.7\pm 0.5(\mathrm{stat}.)\pm 0.6(\mathrm{syst}.))\times {10}^{-6}$. The observed ${\mathcal{A}}_{K^0{\pi }^0}$ value differs by 1.9 standard deviations from the value expected from an isospin sum rule.