Tseytlin has recently proposed that an action functional exists whose gradient generates to all orders in perturbation theory the renormalization group (RG) flow of the target space metric in the worldsheet sigma model. The gradient is defined with respect to a metric on the space of coupling constants which is explicitly known only to leading order in perturbation theory, but at that order is positive semidefinite, as follows from Perelman’s work on the Ricci flow. This gives rise to a monotonicity formula for the flow which is expected to fail only if the beta function perturbation series fails to converge, which can happen if curvatures or their derivatives grow large. We test the validity of the monotonicity formula at next-to-leading order in perturbation theory by explicitly computing the second-order terms in the metric on the space of coupling constants. At this order, this metric is found not to be positive semidefinite. In situations where this might spoil monotonicity, derivatives of curvature become large enough for higher-order perturbative corrections to be significant.

A computation of the inflationary observables $n_s$ and $r$ is made for logamediate inflation where the cosmological scale factor expands as $a=\exp (A(\ln t{)}^{\lambda })$, and is compared to their predicted values in the intermediate inflationary theory, where $a=\exp (B{t}^f)$. Both versions prove to be consistent with observational measurements of the cosmic background radiation. It is shown that the dynamics of a single inflaton field can be mimicked by a system of several fields in an analogous manner to that created by the joint evolution of the fields in assisted power-law inflation.

We derive a general ansatz for optimizing pseudo-$C_{\ell }$ estimators used to measure cosmic microwave background anisotropy power spectra, and apply it to the recently proposed pure pseudo-$C_{\ell }$ formalism, to obtain an estimator which achieves near-optimal $B$-mode power spectrum errors for any specified noise distribution while minimizing leakage from ambiguous modes. Our technique should be relevant for upcoming cosmic microwave background polarization experiments searching for $B$-mode polarization. We compare our technique both to the theoretical limits based on a full Fisher matrix calculation and to the standard pseudo-$C_{\ell }$ technique. We demonstrate it by applying it to a fiducial survey with realistic inhomogeneous noise, complex boundaries, point source masking, and a noise level comparable to what is expected for next-generation experiments ($\sim 5.75\mu \mathrm{K}\mathrm{\text{−}}\mathrm{arcmin}$). For such an experiment our technique could improve the constraints on the amplitude of a gravity wave background by over a factor of 10 compared to what could be obtained using ordinary pseudo-$C_{\ell }$, coming quite close to saturating the theoretical limit. Constraints on the amplitude of the lensing $B$-modes are improved by about a factor of 3.

Performing highly precise Monte-Carlo simulations of SU(2) gluodynamics, we observe for the first time Abelian dominance in the confining part of the static potential in local unitary gauges such as the F12 gauge. We also study the flux-tube profile between the quark and antiquark in these local unitary gauges, and we find a clear signal of the dual Meissner effect. The Abelian electric field is found to be squeezed into a flux tube by the monopole supercurrent. This feature is the same as that observed in the nonlocal maximally Abelian gauge. These results suggest that the Abelian confinement scenario is gauge independent. Observing the important role of spacelike monopoles in the Polyakov gauge also indicates that the monopoles defined on the lattice do not necessarily correspond to those proposed by ’t Hooft in the context of Abelian projection.

We compare Path Integral Monte Carlo calculations by Militzer and Pollock [Phys. Rev. B 71, 134303 (2005)] of Coulomb tunneling in nuclear reactions in dense matter to semiclassical calculations assuming WKB Coulomb barrier penetration through the radial mean-field potential. We find very good agreement of the two approaches at temperatures higher than $\sim \frac{1}{5}$ of the ion plasma temperature. We obtain a simple parametrization of the mean-field potential and of the respective reaction rates. We analyze Gamow-peak energies of reacting ions in various reaction regimes and discuss theoretical uncertainties of nuclear reaction rates taking carbon burning in dense stellar matter as an example.

In this paper we construct spherical thin-shell wormholes supported by a Chaplygin gas. For a rather general class of geometries we introduce a new approach for the stability analysis of static solutions under perturbations preserving the symmetry. We apply this to wormholes constructed from Schwarzschild, Schwarzschild–de Sitter, Schwarzschild–anti-de Sitter, and Reissner-Nordström metrics. In the last two cases, we find that there are values of the parameters for which stable static solutions exist.

We study both analytically and numerically the gravitational fields of stars in $f(R)$ gravity theories. We derive the generalized Tolman-Oppenheimer-Volkov equations for these theories and show that in metric $f(R)$ models the parametrized post-Newtonian parameter ${\gamma }_{\mathrm{PPN}}=1/2$ is a robust outcome for a large class of boundary conditions set at the center of the star. This result is also unchanged by the introduction of dark matter in the solar system. We find also a class of solutions with ${\gamma }_{\mathrm{PPN}}\approx 1$ in the metric $f(R)=R-{\mu }^4/R$ model, but these solutions turn out to be unstable and decay in time. On the other hand, the Palatini version of the theory is found to satisfy the solar system constraints. We also consider compact stars in the Palatini formalism, and show that these models are not inconsistent with polytropic equations of state. Finally, we comment on the equivalence between $f(R)$ gravity and scalar-tensor theories and show that many interesting Palatini $f(R)$ gravity models cannot be understood as a limiting case of a Jordan-Brans-Dicke theory with $\omega \to -3/2$.

In a recent publication, we have demonstrated that differentially rotating stars admit new channels of black hole formation via fragmentation instabilities. Since a higher order instability of this kind could potentially transform a differentially rotating supermassive star into a multiple black hole system embedded in a massive accretion disk, we investigate the dependence of the instability on parameters of the equilibrium model. We find that many of the models constructed exhibit nonaxisymmetric instabilities with corotation points, even for low values of $T/|W|$, which lead to a fission of the stars into one, two, or three fragments, depending on the initial perturbation. At least in the models selected here, an $m=1$ mode becomes unstable at lower values of $T/|W|$, which would seem to favor a scenario where one black hole with a massive accretion disk forms. In this case, we have gained evidence that low values of compactness of the initial model can lead to a stabilization of the resulting fragment, thus preventing black hole formation in this scenario.

We study gravitational waves from a particle moving around a system of a point mass with a disk in Newtonian gravitational theory. A particle motion in this system can be chaotic when the gravitational contribution from a surface density of a disk is comparable with that from a point mass. In such an orbit, we sometimes find that there appears a phase in which particle motion becomes nearly regular (so-called “stagnant motion” or stickiness) for a finite time interval between more strongly chaotic phases. To study how these different chaotic behaviors affect observation of gravitational waves, we investigate a correlation of the particle motion and the waves. We find that such a difference in chaotic motions reflects on the wave forms and energy spectra. The character of the waves in the stagnant motion is quite different from that either in a regular motion or in a more strongly chaotic motion. This suggests that we may make a distinction between different chaotic behaviors of the orbit via the gravitational waves.

We study the impact of astrophysical processes on the gamma-ray background produced by the annihilation of dark matter particles in cosmological halos, with particular attention to the consequences of the formation of supermassive black holes. In scenarios where these objects form adiabatically from the accretion of matter on small seeds, dark matter is first compressed into very dense “spikes,” then its density progressively decreases due to annihilations and scattering off of stellar cusps. With respect to previous analyses, based on nonevolving halos, the predicted annihilation signal is higher and significantly distorted at low energies, reflecting the large contribution to the total flux from unevolved spikes at high redshifts. The peculiar spectral feature arising from the specific redshift distribution of the signal, would discriminate the proposed scenario from more conventional astrophysical explanations. We discuss how this affects the prospects for detection and demonstrate that the gamma-ray background from dark matter (DM) annihilations might be detectable even in the absence of a signal from the Galactic center.

We show how leptogenesis can occur at the TeV scale with neutrinos that possess almost purely Dirac masses and negligible Majorana mass contributions as a consequence of the small wave-function overlap in a warped fifth dimension. Lepton-number violation at the Planck scale is introduced via a Majorana mass term on the Planck brane. Such a Majorana mass operator leads to the small mass splitting of otherwise degenerate Kaluza-Klein excited states on the TeV brane. This tiny mass splitting can compensate for the small Yukawa couplings to give a $CP$ asymmetry large enough to produce the sufficient baryon asymmetry from the decay of the nearly degenerate neutrino Kaluza-Klein states. In this way the standard baryogenesis via leptogenesis scenario can naturally occur at the TeV scale without the need for a high mass scale.

We disclose a deep connection between thermodynamics and gravity in a general braneworld model with curvature correction terms on the brane and in the bulk, respectively. We show that the Friedmann equations on the 3-brane embedded in the 5D spacetime with curvature correction terms can be written directly in the form of the first law of thermodynamics on the apparent horizon. Using the first law, we extract the entropy expression of the apparent horizon on the brane, which is useful in studying the thermodynamical properties of the black hole horizon on the brane in Gauss-Bonnet gravity.

We discuss the general framework for a perfect continuum medium in cosmology and show that an interesting generalization of the fluids normally used is for the medium to have rigidity and, hence, be analogous to an elastic solid. Such models can provide perfect, adiabatic fluids which are stable even when the pressure is negative, if the rigidity is sufficiently large, making them natural candidates to describe the dark energy. In fact, if the medium is adiabatic and isotropic, they provide the most general description of linearized perturbations. We derive the equations of motion and wave propagation speeds in the isotropic case. We point out that anisotropic models can also be incorporated within the same formalism and that they are classified by the standard Bravais lattices. We identify the adiabatic and isocurvature modes allowed in both the scalar and vector sectors and discuss the predictions they make for cosmic microwave background and matter power spectra. We comment on the relationship between these models and other fluid-based approaches to dark energy, and discuss a possible microphysical manifestation of this class of models as a continuum description of defect-dominated scenarios.

We study the semileptonic decays of the lowest-lying $bc$ baryons to the lowest-lying $cc$ baryons (${\Xi }_{bc}^{(\prime *)}\to {\Xi }_{cc}^{(*)}$ and ${\Omega }_{bc}^{(\prime *)}\to {\Omega }_{cc}^{(*)}$), in the limit $m_b,m_c\gg {\Lambda }_{\mathrm{QCD}}$ and close to the zero-recoil point. The separate heavy quark spin symmetries make it possible to describe all these decays using a single form factor. We recover results derived previously by White and Savage in a manner which we think is more straightforward and parallels the method applied later to study $B_c$ semileptonic decays. We further discuss the resemblance between the $bc$ baryon decays and those of $B_c$ mesons to ${\eta }_c$ and $J/\psi$ mesons and comment on the relation between the slopes of the single functions describing each set of decays. Our results can straightforwardly be applied to the decays of $bb$ baryons to $bc$ baryons.

We have searched for $D^0-{\overline{D}}^0$ mixing in $D^{*+}\to {\pi }^{+}{D}^0$ decays with $D^0\to K^{(*)}e\nu$ in a sample of $e^{+}{e}^{-}\to c\overline{c}$ events produced near 10.58 GeV. The charge of the slow pion from charged $D^{*}$ decay tags the charm flavor at production, and it is required to be consistent with the flavor of a fully reconstructed second charm decay in the same event. We observe 3 mixed candidates compared to 2.85 background events expected from simulation. We ascribe a 50% systematic uncertainty to this expected background rate. We find a central value for the mixing rate of $0.4\times {10}^{-4}$. Using a frequentist method, we set corresponding 68% and 90% confidence intervals at $(-5.6,7.4)\times {10}^{-4}$ and $(-13,12)\times {10}^{-4}$, respectively.

We show that the absence of spin-orbit inversions in heavy-light mesons can be explained by the chiral radiative corrections in potential model. A new potential model estimate is given of the masses for P-wave bottom mesons.

We point out that in the minimal supersymmetric standard model terms from the mixing of Higgs and Goldstone bosons which are connected to the renormalization of $\tan \beta$ via Slavnov-Taylor identities give rise to corrections that do not vanish in the limit where the supersymmetric particles are much heavier than the Higgs bosons. These additional contributions have important phenomenological implications as they can lead to potentially large supersymmetric effects in $\Delta M_d$ and to a significant increase of $\Delta M_s$ relative to the standard model prediction for a light pseudoscalar Higgs $A^0$. We calculate all the missing one-loop pieces and combine them with the known effective nonholomorphic terms to obtain improved predictions for the $B_{d,s}-{\overline{B}}_{d,s}$ mass differences $\Delta M_{d,s}$ and the branching ratios of $B_{d,s}\to {\mu }^{+}{\mu }^{-}$ in the large $\tan \beta$ regime of the minimal supersymmetric standard model with minimal flavor violation.

Motivated by a recent paper that compares the results of the analysis of the CKM angle $\alpha$ in the frequentist and in the Bayesian approaches, we have reconsidered the information on the hadronic amplitudes, which helps in constraining the value of $\alpha$ in the standard model. We find that the Bayesian method gives consistent results irrespective of the parametrization of the hadronic amplitudes and that the results of the frequentist and Bayesian approaches are equivalent when comparing meaningful probability ranges or confidence levels. We also find that from $B\to \pi \pi$ decays alone the 95% probability region for $\alpha$ is the interval [80°, 170°], well consistent with recent analyses of the unitarity triangle where, by using all the available experimental and theoretical information, one gets $\alpha =(93\pm 4)°$. Last but not least, by using simple arguments on the hadronic matrix elements, we show that the unphysical region $\alpha \sim 0$, present in several experimental analyses, can be eliminated.

We compare the dependences on the number of colors of the leading $\pi \pi$ scattering amplitudes using the single index quark field and two index quark fields. These are seen to have different relationships to the scattering amplitudes suggested by chiral dynamics which can explain the long puzzling pion pion $s$ wave scattering up to about 1 GeV. This may be interesting for getting a better understanding of the large $N_c$ approach as well as for application to recently proposed technicolor models.

The light-cone method provides a convenient nonperturbative tool to study the heavy-to-light form factors. We construct a light-cone quark model utilizing the soft collinear effective theory. In the leading order of effective theory, the form factors for $B$-to-light pseudoscalar and vector mesons are reduced to three universal form factors which can be calculated as overlaps of hadron light-cone wave functions. The numerical results show that the leading contribution is close to the results from other approaches. The $q^2$ dependence of the heavy-to-light form factors is also presented.