A consistent evolution of the strong coupling constant ${\alpha }_s$ from $M_Z$ to the grand unified theory (GUT) scale is presented, involving three-loop running and two-loop decoupling. The two-loop transition from the $\overline{\mathrm{MS}}$- to the $\overline{\mathrm{DR}}$-scheme is properly taken into account. In the second part of the paper, the bottom quark mass in the $\overline{\mathrm{DR}}$-scheme at the electroweak/supersymmetry (SUSY) scale is evaluated with four-loop accuracy. We find that the three-loop effects are comparable to the experimental uncertainty both for ${\alpha }_s$ and $m_b$.

We propose a gravitational dual of “single-sector” models of supersymmetry breaking which contain no messenger sector and naturally explain the scale of supersymmetry breaking and the fermion mass hierarchy. In five dimensions these models can be given a simple interpretation. Inspired by flux-background solutions of type IIB supergravity, a metric background that deviates from ${\mathrm{AdS}}_5$ in the IR breaks supersymmetry, while the fermion mass hierarchy results from the wave function overlap of bulk fermions with a UV-confined Higgs field. The first and second generation squarks and sleptons, which are localized near the IR brane, directly feel the supersymmetry breaking and obtain masses of order 10 TeV. These are interpreted as composite states of the dual 4D theory. The gauginos and third generation squarks and sleptons are elementary states that obtain soft masses of order 1 TeV at the loop level via direct gauge mediation. This particle spectrum leads to distinctive signatures at the LHC, similar to the usual gauge mediation with a neutralino NLSP that decays promptly to a gravitino LSP, but with lower event rates. Nevertheless we show that with $1–10{\mathrm{fb}}^{-1}$ of LHC data “single-sector” models can easily be detected above background and distinguished from conventional gravity and gauge mediation.

We calculate the inclusive decay rate of the spin-triplet bottomonium states ${\chi }_{bJ}$ into charm hadrons, including the leading-order color-singlet and color-octet $b\overline{b}$ annihilation mechanisms. We also calculate the momentum distribution of the charm quark from the decay of ${\chi }_{bJ}$. The infrared divergences from the color-singlet process $b\overline{b}\to c\overline{c}g$ are factored into the probability density at the origin for a $b\overline{b}$ pair in a color-octet state. That probability density can be determined phenomenologically from the fraction of decays of ${\chi }_{bJ}$ that include charm hadrons. It can then be used to predict the partial widths into light hadrons for all four states in the $P$-wave bottomonium multiplet.

We derive four-dimensional effective theories of the gauge-Higgs unification models in the warped spacetime. The effective action can be expressed in a simple form by neglecting subleading corrections to the wave functions. We have shown in our previous works that some Higgs couplings to the other fields are suppressed by factors that depend on ${\overline{\theta }}_{\mathrm{H}}$ from the values in the standard model. Here ${\overline{\theta }}_{\mathrm{H}}$ is the Wilson line phase along the fifth dimension, which characterizes the electroweak symmetry breaking. The effective action derived here explicitly shows a nonlinear structure of the Higgs sector, which clarifies the origins of those suppression factors.

In recent years, a number of alternative theories of gravity have been proposed as possible resolutions of certain cosmological problems or as toy models for possible but heretofore unobserved effects. However, the implications of such theories for the stability of structures such as stars have not been fully investigated. We use our “generalized variational principle,” described in a previous work [M. D. Seifert and R. M. Wald, Phys. Rev. D 75, 084029 (2007)], to analyze the stability of static spherically symmetric solutions to spherically symmetric perturbations in three such alternative theories: Carroll et al.’s $f(R)$ gravity, Jacobson and Mattingly’s “Einstein-æther theory,” and Bekenstein’s TeVeS theory. We find that in the presence of matter, $f(R)$ gravity is highly unstable; that the stability conditions for spherically symmetric curved vacuum Einstein-æther backgrounds are the same as those for linearized stability about flat spacetime, with one exceptional case; and that the “kinetic terms” of vacuum TeVeS theory are indefinite in a curved background, leading to an instability.

Linear perturbations of Friedmann-Robertson-Walker universes with any curvature and cosmological constant are studied in a general gauge without decomposition into harmonics. Desirable gauges are selected as those which embody best Mach’s principle: in these gauges local inertial frames can be determined instantaneously via the perturbed Einstein field equations from the distributions of energy and momentum in the universe. The inertial frames are identified by their “accelerations and rotations” with respect to the cosmological frames associated with the “Machian gauges.” In closed spherical universes, integral gauge conditions are imposed to eliminate motions generated by the conformal Killing vectors. The meaning of Traschen’s integral-constraint vectors is thus elucidated. For all three types of Friedmann-Robertson-Walker universes the Machian gauges admit much less residual freedom than the synchronous or generalized harmonic gauge. Mach’s principle is best exhibited in the Machian gauges in closed spherical universes. Independent of any Machian motivation, the general perturbation equations and discussion of gauges are useful for cosmological perturbation theory.

If electroweak symmetry is broken by a new strongly interacting sector, new physics will probably manifest itself in gauge boson scattering at the CERN LHC. The relevant dynamics is well described in terms of an effective Lagrangian. We discuss the probable size of the coefficients of the relevant operators under a combination of model-independent constraints and reasonable assumptions based on two models of the strongly interacting sector. We compare these values with the LHC sensitivity and argue that they will be too small to be seen. Therefore, the presence of vector and scalar resonances required by unitarity will be the only characteristic signature. We analyze the most likely masses and widths of these resonances.

We construct the integration measure over the moduli space of an arbitrary number of $N$ kinds of dyons of the pure $SU(N)$ gauge theory at finite temperatures. The ensemble of dyons governed by the measure is mathematically described by a (supersymmetric) quantum field theory that is exactly solvable and is remarkable for a number of striking features: (i) The free energy has the minimum corresponding to the zero average Polyakov line, as expected in the confining phase; (ii) the correlation function of two Polyakov lines exhibits a linear potential between static quarks in any $N$-ality nonzero representation, with a calculable string tension roughly independent of temperature; (iii) the average spatial Wilson loop falls off exponentially with its area and the same string tension; (iv) at a critical temperature, the ensemble of dyons rearranges and deconfines; and (v) the estimated ratio of the critical temperature to the square root of the string tension is in excellent agreement with the lattice data.

It is known that the kinetic mixing of a photon and another $\mathrm{U}(1{)}_{\mathrm{ex}}$ gauge boson can introduce millicharged particles. Millicharged particles $f$ of mass 0.1 eV can explain the PVLAS experiment. I suggest a temperature dependent gauge symmetry breaking of $\mathrm{U}(1{)}_{\mathrm{ex}}$ for this idea to be consistent with astrophysical and cosmological constraints.

Recently [J. Haro and E. Elizalde, Phys. Rev. Lett. 97, 130401 (2006)], a Hamiltonian formulation has been introduced in order to address some long-standing severe problems associated with the physical description of the dynamical Casimir effect at all times while the mirrors are moving. Here we present the complete calculation providing precise details, in particular, of the regularization procedure, which is decisive for the correct derivation of physically meaningful quantities. A basic difference when comparing with the results previously obtained by other authors is the fact that the motion force derived in our approach contains a reactive term—proportional to the mirrors’ acceleration. This is of the essence in order to obtain particles with a positive energy at all times during the oscillation of the mirrors—while always satisfying the energy conservation law. A careful analysis of the interrelations among the different results previously obtained in the literature is then carried out. For simplicity, the specific case of a neutral scalar field in one dimension, with one or two partially transmitting mirrors (a fundamental proviso for the regularization issue), is considered in more detail, but our general method is shown to be generalizable, without essential problems (Sec. II of this paper), to fields of any kind in two and higher dimensions.

The averaged null energy condition (ANEC) requires that the integral over a complete null geodesic of the stress-energy tensor projected onto the geodesic tangent vector is never negative. This condition is sufficient to prove many important theorems in general relativity, but it is violated by quantum fields in curved spacetime. However there is a weaker condition, which is free of known violations, requiring only that there is no self-consistent spacetime in semiclassical gravity in which ANEC is violated on a complete, achronal null geodesic. We indicate why such a condition might be expected to hold and show that it is sufficient to rule out closed timelike curves and wormholes connecting different asymptotically flat regions.

A Bohr-Sommerfeld equation is derived for the highly damped quasinormal mode frequencies $\omega (n\gg 1)$ of rotating black holes. It may be written as $2{\int }_C(p_r+i{p}_0)dr=(n+1/2)h$, where $p_r$ is the canonical momentum conjugate to the radial coordinate $r$ along a null geodesic of energy $\hslash \omega$ and angular momentum $\hslash m$, $p_0=O({\omega }^0)$, and the contour $C$ connects two complex turning points of $p_r$. The solutions are $\omega (n)=-m\widehat{\omega }-i(\widehat{\varphi }+n\widehat{\delta })$, where $\{\widehat{\omega },\widehat{\delta }\}>0$ are functions of the black-hole parameters alone. Some physical implications are discussed.

We determine the relative branching fractions of semileptonic $B$ decays to charmed final states. The measurement is performed on the recoil from a fully reconstructed $B$ meson in a sample of $362\times {10}^6$ $B\overline{B}$ pairs collected at the ${\rm Y}(4S)$ resonance with the BABAR detector. A simultaneous fit to a set of discriminating variables is performed on a sample of $\overline{B}\to DX{\ell }^{-}{\overline{\nu }}_{\ell }$ decays to determine the contributions from the different channels. We measure $\Gamma (B^{-}\to D{\ell }^{-}{\overline{\nu }}_{\ell })/\Gamma (B^{-}\to DX{\ell }^{-}{\overline{\nu }}_{\ell })=0.227\pm 0.014\pm 0.016$, $\Gamma (B^{-}\to D^{*}{\ell }^{-}{\overline{\nu }}_{\ell })/\Gamma (B^{-}\to DX{\ell }^{-}{\overline{\nu }}_{\ell })=0.582\pm 0.018\pm 0.030$, and $\Gamma (B^{-}\to D^{**}{\ell }^{-}{\overline{\nu }}_{\ell })/\Gamma (B^{-}\to DX{\ell }^{-}{\overline{\nu }}_{\ell })=0.191\pm 0.013\pm 0.019$ for the charged $B$ sample, and $\Gamma (\overline{B^0}\to D{\ell }^{-}{\overline{\nu }}_{\ell })/\Gamma (\overline{B^0}\to DX{\ell }^{-}{\overline{\nu }}_{\ell })=0.215\pm 0.016\pm 0.013$, $\Gamma (\overline{B^0}\to D^{*}{\ell }^{-}{\overline{\nu }}_{\ell })/\Gamma (\overline{B^0}\to DX{\ell }^{-}{\overline{\nu }}_{\ell })=0.537\pm 0.031\pm 0.036$, and $\Gamma (\overline{B^0}\to D^{**}{\ell }^{-}{\overline{\nu }}_{\ell })/\Gamma (\overline{B^0}\to DX{\ell }^{-}{\overline{\nu }}_{\ell })=0.248\pm 0.032\pm 0.030$ for the neutral $B$ sample, where uncertainties are statistical and systematic, respectively.

We study the behavior of an initially spherical bunch of particles accelerated along trajectories parallel to the symmetry axis of a rotating black hole. We find that, under suitable conditions, curvature and inertial strains compete to generate jetlike structures. This is a purely kinematical effect which does not account by itself for physical processes underlying the formation of jets. In our analysis a crucial role is played by the property of the electric and magnetic part of the Weyl tensor to be Lorentz invariant along the axis of symmetry in Kerr spacetime.

A complete thermodynamical analysis of the $2+1$ dimensional massless Gross-Neveu model is performed using the optimized perturbation theory. This is a nonperturbative method that allows us to go beyond the known large-$N$ results already at lowest order. Our results, for a finite number of fermion species, $N$, show the existence of a tricritical point in the temperature and chemical potential phase diagram for a discrete chiral phase transition allowing us precisely to locate it. By studying the phase diagram in the pressure and inverse density plane, we also show the existence of a liquid-gas phase, which, so far, was unknown to exist in this model. Finally, we also derive $N$ dependent analytical expressions for the order parameter, critical temperature, and critical chemical potential.

In this article we calculate the electrical conductivity in QED using the two-particle-irreducible (2PI) effective action. We use a resummed version of the usual 2PI effective action which is defined with respect to self-consistent solutions of the 2-point functions. We show that the Green functions obtained from this 2PI resummed effective action satisfy Ward identities and that the conductivity obtained from the Kubo relation is gauge-invariant. We work to 3-loop order in the 2PI resummed effective action and show explicitly that the resulting expression for the conductivity contains the square of the amplitude that corresponds to all binary collision and production processes.

The Lorentz covariant classical and quantum statistical mechanics and thermodynamics of an ideal relativistic gas of bradyons (particles slower than light), luxons (particles moving with the speed of light), and tachyons (hypothetical particles faster than light) is discussed. The Lorentz covariant formulation is based on the preferred frame approach which among others enables a consistent, free of paradoxes description of tachyons. The thermodynamic functions within the covariant approach are obtained both in the classical and quantum case.

We compute the precise elementary/composite field content of mass eigenstates in holographic duals of warped models in a slice of $\mathrm{Ad}{\mathrm{S}}_5$. This is accomplished by decomposing the bulk fields not in the usual Kaluza-Klein basis, but rather into a holographic basis of 4D fields, corresponding to purely elementary source or conformal field theory (CFT) composite fields. Generically, this decomposition yields kinetic and mass mixing between the elementary and composite sectors of the holographic theory. Depending on where the bulk zero mode is localized, the elementary/composite content may differ radically, which we show explicitly for several examples including the bulk Randall-Sundrum graviton, bulk gauge boson, and Higgs boson.

General hypersurface layers are considered in order to describe braneworlds and shell cosmologies. No restriction is placed on the causal character of the hypersurface which may thus have internal changes of signature. Strengthening the results in our previous paper [M. Mars, J. M. M. Senovilla, and R. Vera, Phys. Rev. Lett. 86, 4219 (2001).], we confirm that a good, regular, and consistent description of signature change is achieved in these brane/shells scenarios, while keeping the hypersurface and the bulk completely regular. Our formalism allows for a unified description of the traditional timelike branes/shells together with the signature changing, or pure null, ones. This allows for a detailed comparison of the results in both situations. An application to the case of hypersurface layers in static bulks is presented, leading to the general Robertson-Walker geometry on the layer—with a possible signature change. Explicit examples on anti-de Sitter bulks are then studied. The permitted behaviors in different settings ($Z_2$-mirror branes, asymmetric shells, signature changing branes) are analyzed in detail. We show, in particular, that (i) in asymmetric shells there is an upper bound for the energy density, and (ii) that the energy density within the brane vanishes when approaching a change of signature. The description of a signature change as a “singularity” seen from within the brane is considered. We also find new relations between the fundamental constants in the brane/shell, its tension, and the cosmological and gravitational constants of the bulk, independently of the existence or not of a change of signature.