We calculate the statistical entropy of a scalar field on the background of $(2+1)$-dimensional de Sitter space without an artificial cutoff considering corrections to all orders in the Planck length from a generalized uncertainty principle on the quantum state density. The desired entropy proportional to the horizon perimeter is obtained.

We study the phase structure of a 4D complex scalar field theory with a potential $V(\Phi )=|\frac{{\Lambda }^3}{\Phi }-\Lambda \Phi {|}^2$ at zero and at finite temperature. The model is analyzed by mean-field and Monte Carlo methods. At zero temperature the theory falls in the universality class of the 4D Ising model when varying $\Lambda$. The situation is less clear cut for variations with respect to $\Lambda$ at large temperatures and variations with respect to temperature at a given value of $\Lambda$. We observe temperature independence of the mass of the first excitation.

Sterile neutrino with mass of several keV can be the cosmological dark matter, can explain the observed velocities of pulsars, and can play an important role in the formation of the first stars. We describe the production of sterile neutrinos in a model with an extended Higgs sector, in which the Majorana mass term is generated by the vacuum expectation value of a gauge-singlet Higgs boson. In this model the relic abundance of sterile neutrinos does not necessarily depend on their mixing angles, the free-streaming length can be much smaller than in the case of warm dark matter produced by neutrino oscillations, and, therefore, some of the previously quoted bounds do not apply. The presence of the gauge singlet in the Higgs sector has important implications for the electroweak phase transition, baryogenesis, and the upcoming experiments at the Large Hadron Collider and a Linear Collider.

The energy losses of a small black hole passing through the Earth are examined. In particular, we investigate the excitations in the frequency range accessible to modern acoustic detectors. The main contribution to the effect is given by the coherent sound radiation of the Cherenkov type.

The Hamiltonian structure of general relativity provides a natural canonical measure on the space of all classical universes, i.e., the multiverse. We review this construction and show how one can visualize the measure in terms of a “magnetic flux” of solutions through phase space. Previous studies identified a divergence in the measure, which we observe to be due to the dilatation invariance of flat Friedmann-Lemaitre-Robertson-Walker universes. We show that the divergence is removed if we identify universes which are so flat they cannot be observationally distinguished. The resulting measure is independent of time and of the choice of coordinates on the space of fields. We further show that, for some quantities of interest, the measure is very insensitive to the details of how the identification is made. One such quantity is the probability of inflation in simple scalar field models. We find that, according to our implementation of the canonical measure, the probability for $N$ e-folds of inflation in single-field, slow-roll models is suppressed by of order $\exp (-3N)$ and we discuss the implications of this result.

Large-scale magnetic fields affect the scalar modes of the geometry whose ultimate effect is to determine the anisotropies of the cosmic microwave background (CMB in what follows). For the first time, a consistent numerical approach to the magnetized CMB anisotropies is pursued with the aim of assessing the angular power spectra of temperature and polarization when the scalar modes of the geometry and a stochastic background of inhomogeneous magnetic fields are simultaneously present in the plasma. The effects related to the magnetized nature of the plasma are taken into account both at the level of the dynamical equations and at the level of the initial conditions of the Einstein-Boltzmann hierarchy. The temperature and polarization observables are exploited to infer the peculiar signatures of a pre-equality magnetic field. Using the extrapolated best fit to the three-year WMAP (Wilkinson Microwave Anisotropy Probe) data the increase and distortions of the first seven peaks in the temperature autocorrelations are monitored for different values of the regularized magnetic field intensity and for the physical range of spectral indices. Similar analyses are also conducted for the first few anticorrelation (and corrrelation) peaks of the temperature-polarization power spectra. Possible interesting degeneracies and stimulating perspectives are pointed out and explored.

The calculational precision of $e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-}$ and $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$ production cross sections in electron-positron annihilations at $\sqrt{s}=10.58\mathrm{GeV}$ is studied for the $\mathtt{K}\mathtt{K}\mathtt{M}\mathtt{C}$ Monte Carlo simulation program, modified to include contributions from recent implementation of the hadronic part of vacuum polarization. We determine $\sigma (e^{+}{e}^{-}\to {\tau }^{+}{\tau }^{-})=(0.919\pm 0.003)\mathrm{nb}$ and $\sigma (e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-})=(1.147\pm 0.005)\mathrm{nb}$, where the error represents the precision of the calculation.

We extract the Boer-Mulders functions of valence and sea quarks in the proton from unpolarized $p+D$ Drell-Yan data measured by the FNAL E866 Collaboration. Using these Boer-Mulders functions, we calculate the $\cos 2\varphi$ asymmetries in unpolarized $pp$ Drell-Yan processes, both for the FNAL E866/NuSea and the BNL Relativistic Heavy Ion Collider experiments. We also estimate the $\cos 2\varphi$ asymmetries in the unpolarized $p\overline{p}$ Drell-Yan processes at GSI.

The analysis of tagged $B_s\to J/\psi \varphi$ decays determines the $CP$ phase ${\varphi }_s$ in $B_s-{\overline{B}}_s$ mixing with a twofold ambiguity. The solutions differ in the sign of $\cos {\varphi }_s$ which equals the sign of the width difference $\Delta {\Gamma }_s$ among the two $B_s$ mass eigenstates. We point out that this ambiguity can be removed with the help of $B_s\to D_{s}K$ decays. We compare untagged and tagged strategies and find the tagged analysis more promising. The removal of the sign ambiguity in $\Delta {\Gamma }_s$ can be done with relatively low statistics and could therefore be a target for the early stage of $B_s\to D_{s}K$ studies.

We study the zero-temperature crystalline structure of baby Skyrmions by applying a full-field numerical minimization algorithm to baby Skyrmions placed inside different parallelogramic unit cells and imposing periodic boundary conditions. We find that within this setup, the minimal energy is obtained for the hexagonal lattice, and that in the resulting configuration the Skyrmion splits into quarter Skyrmions. In particular, we find that the energy in the hexagonal case is lower than the one obtained on the well-studied rectangular lattice, in which splitting into half Skyrmions is observed.

The observed pattern of neutrino mass splittings and mixing angles indicates that their family structure is significantly different from that of the charged fermions. We investigate the implications of these data for the fermion mass matrices in grand-unified theories with a type-I seesaw mechanism. We show that, with simple assumptions, naturalness leads to a strongly hierarchical Majorana mass matrix for heavy right-handed neutrinos and a partially cascade form for the Dirac neutrino matrix. We consider various model building scenarios which could alter this conclusion, and discuss their consequences for the construction of a natural model. We find that including partially lopsided matrices can aid us in generating a satisfying model.

Experiment E949 at Brookhaven National Laboratory studied the rare decay $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ and other processes with an exposure of $1.77\times {10}^{12}$ $K^{+}$’s. The data were analyzed using a blind analysis technique yielding one candidate event with an estimated background of $0.30\pm 0.03$ events. Combining this result with the observation of two candidate events by the predecessor experiment E787 gave the branching ratio $\mathcal{B}(K^{+}\to {\pi }^{+}\nu \overline{\nu })=({1.47}_{-0.89}^{+1.30})\times {10}^{-10}$, consistent with the standard model prediction of $(0.74\pm 0.20)\times {10}^{-10}$. This is a more detailed report of results previously published [V. V. Anisimovsky et al., Phys. Rev. Lett. 93, 031801 (2004)].

We calculate the Lüscher term for recently suggested non-Abelian flux tubes (strings). The main feature of the non-Abelian strings is the presence of orientational zero modes associated with rotation of their color flux inside a non-Abelian subgroup. The Lüscher term is determined by the number of light degrees of freedom on the string world sheet. Unlike the standard $\pi /12$ we get $N\pi /12$ for non-Abelian strings in the $\mathrm{U}(N)$ gauge theories. Thus, the Lüscher coefficient acquires a dependence on the rank of the gauge group. In the models with non-Abelian strings discussed in the literature there are two distinct scales: the string tension $\xi$ (the string thickness $\sim {\xi }^{-1/2}$) and the dynamical scale of strong interactions $\Lambda$. At weak coupling $\xi \gg {\Lambda }^2$. The Lüscher term for non-Abelian strings experiences a jump: at ${\xi }^{-1/2}\ll L\ll {\Lambda }^{-1}$ it is $N\pi /12$ while at $L\gg {\Lambda }^{-1}$ the orientational moduli are frozen out and the Lüscher coefficient approaches its “Lüscher” value $\pi /12$. We raise the question of possible extra (i.e. nontranslational) light moduli on the world sheet of QCD strings at large $N$.

We study the response of the QCD vacuum to an external magnetic field, in the presence of strong $CP$ violation. Using chiral perturbation theory and large $N_c$ expansion, we show that the external field would polarize quantum fluctuations and induce an electric dipole moment of the vacuum along the direction of the magnetic field. We estimate the magnitude of this effect in different physical scenarios. In particular, we find that the polarization induced by the magnetic field of a magnetar could accelerate electric charges up to energies of the order $\sim \theta {10}^3\mathrm{TeV}$. We also suggest a connection with the possible existence of “hot-spots” on the surface of neutron stars.

Comparing the theoretically predicted and measured values of the mass difference of the $B_s^0$ system, we estimate the lower bound on the mass of the $Z^{\prime }$ boson of models based on the $SU(3{)}_c\otimes SU(3{)}_L\otimes U(1{)}_X$ gauge group. By assuming zero-texture approaches of the quark mass matrices, we find the ratio of the measured value to the theoretical prediction from the standard model and the $Z^{\prime }$ contribution from the 331 models of the mass difference of the $B_s^0$ system. We find lower bounds on the $Z^{\prime }$ mass ranging between 1 TeV and 30 TeV for the two most popular 331 models, and four different zero-textures ansätze. The above results are expressed as a function of the weak angle associated to the $b-s-Z^{\prime }$ couplings.

We consider the consequences of the absence of Birkhoff’s theorem in theories of modified gravity. As an example, we calculate the gravitational force on a test particle due to a spherical mass shell in the Dvali-Gabadadze-Porrati model. We show that unlike in general relativity, the force depends on the mass distribution. In particular, the gravitational force within a spherical mass shell depends on the geometric structure of the bulk, and is likely nonzero.

We revisit the paradigm of unified dark energy discussing in detail the averaging problem in this type of scenario, highlighting the need for a full nonlinear treatment. We also address the question of if and how models with one or several dark fluids can be observationally distinguished. Simpler and physically clearer derivations of some key results, most notably on the relation between the generalized Chaplygin gas and the standard ($\Lambda \mathrm{CDM}$) “concordance” model and on a Jeans-type small-scale instability of some coupled dark energy/dark matter models are presented.

The generation of dark matter in late decays of quasistable massive particles has been proposed as a viable framework to address the excess of power found in numerical $N$-body simulations for cold dark matter cosmologies. We identify a convenient set of variables to illustrate which requirements need to be satisfied in any generic particle-physics model to address the small-scale problems and to fulfill other astrophysical constraints. As a result of this model-independent analysis, we point out that meeting these requirements in a completely natural way is inherently difficult. In particular, we reexamine the role of gravitinos and Kaluza-Klein gravitons in this context and find them disfavored as a solution to the small-scale problems in case they are dark matter candidates generated in the decay of thermally produced weakly interacting massive particles. We propose right-handed sneutrinos and right-handed Kaluza-Klein neutrinos as alternatives. We find that they are viable dark matter candidates, but that they can contribute to a solution of the small-scale problems only in case the associated Dirac neutrino mass term appears as a subdominant contribution in the neutrino mass matrix.

We investigate the nonlinear behavior of the dynamically unstable rotating star for the bar mode by three-dimensional hydrodynamics in Newtonian gravity. We find that an oscillation along the rotation axis is induced throughout the growth of the unstable bar mode, and that its characteristic frequency is twice that of the bar mode, which oscillates mainly along the equatorial plane. A possibility to observe Faraday resonance in gravitational waves is demonstrated and discussed.

We present a measurement of the branching fraction and photon-energy spectrum for the decay $B\to X_s\gamma$ using data from the BABAR experiment. The data sample corresponds to an integrated luminosity of $210{\mathrm{fb}}^{-1}$, from which approximately 680 000 $B\overline{B}$ events are tagged by a fully reconstructed hadronic decay of one of the $B$ mesons. In the decay of the second $B$ meson, an isolated high-energy photon is identified. We measure $\mathcal{B}(B\to X_s\gamma )=(3.66\pm {0.85}_{\mathrm{stat}}\pm {0.60}_{\mathrm{syst}})\times {10}^{-4}$ for photon energies $E_{\gamma }$ above 1.9 GeV in the $B$ rest frame. From the measured spectrum we calculate the first and second moments for different minimum photon energies, which are used to extract the heavy-quark parameters $m_{\mathrm{b}}$ and ${\mu }_{\pi }^2$. In addition, measurements of the direct $CP$ asymmetry and isospin asymmetry are presented.