The $B_c\to B_q^{(*)}P$, $B_{q}V$ decays are studied with the QCD factorization approach (where $P$ and $V$ denote pseudoscalar and vector mesons, respectively; $q=u$, $d$, and $s$). Considering the contributions of both current-current and penguin operators, the amplitudes of branching ratios are estimated at the leading approximation. We find that the contributions of the penguin operators are very small due to the serious suppression by the Cabibbo-Kobayashi-Maskawa elements. The most promising decay modes are $B_c\to B_s^{(*)}\pi$, $B_s\rho$, which might be easily detected at hadron colliders.

We extend a recent analysis of the pion electromagnetic form factor constrained by the conformal symmetry to explore the timelike region. We show explicitly that the timelike form factor obtained by the analytic continuation of the spacelike form factor correctly satisfies the dispersion relation. Our results indicate that the quark spin and dynamical mass effects are crucial to yield the realistic features of the vector meson dominance phenomena.

If future neutrino oscillation experiments show that the neutrino mass spectrum is with normal ordering, $m_1<m_2<m_3$, and the searches for neutrinoless double beta [$(\beta \beta {)}_{0\nu }$] decay with sensitivity to values of the effective Majorana mass $|⟨m⟩|\gtrsim {10}^{-2}\mathrm{eV}$ give negative results, the next frontier in the quest for $(\beta \beta {)}_{0\nu }$-decay will correspond to $|⟨m⟩|\sim {10}^{-3}\mathrm{eV}$. By assuming that massive neutrinos are Majorana particles and their exchange is the dominant mechanism generating $(\beta \beta {)}_{0\nu }$-decay, we analyze the conditions under which $|⟨m⟩|$, in the case of three-neutrino mixing and a neutrino mass spectrum with normal ordering, would satisfy $|⟨m⟩|\ge 0.001\mathrm{eV}$. We consider the specific cases of (i) a normal hierarchical neutrino mass spectrum, (ii) a relatively small value of the CHOOZ angle ${\theta }_{13}$, as well as (iii) the general case of a spectrum with normal ordering, a partial hierarchy, and a value of ${\theta }_{13}$ close to the existing upper limit. We study the ranges of the lightest neutrino mass $m_1$ and/or of ${sin}^2{\theta }_{13}$ for which $|⟨m⟩|\ge 0.001\mathrm{eV}$ and discuss the phenomenological implications of such scenarios. We provide also an estimate of $|⟨m⟩|$ when the three-neutrino masses and the neutrino mixing originate from a neutrino mass term of the Majorana type for the (left-handed) flavor neutrinos and $\sum _j^3{m}_j{U}_{ej}^2=0$, but there does not exist a symmetry which forbids the $(\beta \beta {)}_{0\nu }$-decay.

Domain walls in $U(N)$ gauge theories, coupled to Higgs scalar fields with degenerate masses, are shown to possess normalizable non-Abelian Nambu-Goldstone (NG) modes, which we call non-Abelian clouds. We construct the moduli space metric and its Kähler potential of the effective field theory on the domain walls by focusing on two models: a $U(1)$ gauge theory with several charged Higgs fields, and a $U(N)$ gauge theory with $2N$ Higgs fields in the fundamental representation. We find that non-Abelian clouds spread between two domain walls and that their rotation induces a long-range repulsive force, in contrast to a $U(1)$ mode in models with fully nondegenerate masses which gives a short-range force. We also construct a bound state of dyonic domain walls by introducing the imaginary part of the Higgs masses. In the latter model we find that when all walls coincide, $SU(N{)}_{\mathrm{L}}\times SU(N{)}_{\mathrm{R}}\times U(1)$ symmetry is broken down to $SU(N{)}_{\mathrm{V}}$, and $U(N{)}_{\mathrm{A}}$ NG modes and the same number of quasi-NG modes are localized on the wall. When $n$ walls separate, off-diagonal elements of $U(n)$ NG modes have wave functions spreading between two separated walls (non-Abelian clouds), whereas some quasi-NG modes turn to NG bosons as a result of further symmetry breaking $U(n{)}_{\mathrm{V}}\to U(1{)}_{\mathrm{V}}^n$. In the case of $4+1$-dimensional bulk, we can dualize the effective theory to the supersymmetric Freedman-Townsend model of non-Abelian 2-form fields.

We study the accuracy of the post-Newtonian (PN) approximation and its formal region of validity, by investigating its optimal asymptotic expansion for the quasicircular, adiabatic inspiral of a point particle into a Schwarzschild black hole. By comparing the PN expansion of the energy flux to numerical calculations in the perturbative Teukolsky formalism, we show that (i) the inclusion of higher multipoles is necessary to establish the accuracy of high-order PN terms, and (ii) the region of validity of PN theory is largest at relative $\mathcal{O}(1/c^6)$ (3PN order). The latter result suggests that the series diverges beyond 3PN order, at least in the extreme-mass-ratio limit, probably due to the appearance of logarithmic terms in the energy flux. The study presented here is a first formal attempt to determine the region of validity of the PN approximation using asymptotic analysis. Therefore, it should serve as a template to perform similar studies on other systems, such as comparable-mass quasicircular inspirals computed by high-accuracy numerical relativistic simulations.

We have studied the charged scalar perturbation around a dilaton black hole in $2+1$ dimensions. The wave equations of a massless charged scalar field are shown to be exactly solvable in terms of hypergeometric functions. The quasinormal frequencies are computed exactly. The relation between the quasinormal frequencies and the charge of the black hole, charge of the scalar, and the temperature of the black hole are analyzed. The asymptotic form of the real part of the quasinormal frequencies is evaluated exactly.

We investigate the so-called superWIMP scenario with the gravitino as the lightest supersymmetric particle (LSP) in the context of nonstandard cosmology, in particular, brane world cosmology. As a candidate of the next-to-LSP (NLSP), we examine the slepton and the sneutrino. Brane world cosmological effects dramatically enhance the relic density of the slepton or sneutrino NLSP, so that the NLSP with mass of order 100 GeV can provide the correct abundance of gravitino dark matter through its decay. We find that with an appropriate five-dimensional Planck mass, this scenario can be realized consistently with the constraints from big bang nucleosynthesis for both NLSP candidates of the slepton and the sneutrino. The big bang nucleosynthesis constraints for the slepton NLSP are more stringent than that for the sneutrino; as the result, the gravitino must be rather warm in the slepton NLSP case. The energy density of the gravitino produced by thermal scattering is highly suppressed and negligible due to the brane world cosmological effects.

We consider top quarks produced at large energy in $e^{+}{e}^{-}$ collisions, and address the question of what top mass can be measured from reconstruction. The production process is characterized by well-separated scales: the center-of-mass energy $Q$, the top mass $m$, the top decay width ${\Gamma }_t$, and also ${\Lambda }_{\mathrm{QCD}}$; scales which can be disentangled with effective theory methods. In particular we show how the mass measurement depends on the way in which soft radiation is treated, and that this can shift the mass peak by an amount of order $Q{\Lambda }_{\mathrm{QCD}}/m$. We sum large logs for $Q\gg m\gg {\Gamma }_t>{\Lambda }_{\mathrm{QCD}}$ and demonstrate that the renormalization group ties together the jet and soft interactions below the scale $m$. Necessary conditions for the invariant mass spectrum to be protected from large logs are formulated. Results for the cross section are presented at next-to-leading order with next-to-leading-log (NLL) resummation, for invariant masses in the peak region and the tail region. Using our results we also predict the thrust distribution for massive quark jets at NLL order for large thrust. We demonstrate that soft radiation can be precisely controlled using data on massless jet production, and that in principle, a short-distance mass parameter can be measured using jets with precision better than ${\Lambda }_{\mathrm{QCD}}$.

Neutrinos and antineutrinos emitted from a core collapse supernova interact among themselves, giving rise to collective flavor conversion effects that are significant near the neutrinosphere. We develop a formalism to analyze these collective effects in the complete three-flavor framework. It naturally generalizes the spin-precession analogy to three flavors and is capable of analytically describing phenomena like vacuum/Mikheyev-Smirnov-Wolfenstein (MSW) oscillations, synchronized oscillations, bipolar oscillations, and spectral split. Using the formalism, we demonstrate that the flavor conversions may be “factorized” into two-flavor oscillations with hierarchical frequencies. We explicitly show how the three-flavor solution may be constructed by combining two-flavor solutions. For a typical supernova density profile, we identify an approximate separation of regions where distinctly different flavor conversion mechanisms operate, and demonstrate the interplay between collective and MSW effects. We pictorialize our results in terms of the “${\mathbf{e}}_3\mathrm{\text{−}}{\mathbf{e}}_8$ triangle” diagram, which is a tool that can be used to visualize three-neutrino flavor conversions in general, and offers insights into the analysis of the collective effects in particular.

We describe a measurement of the $W$ boson mass $m_W$ using $200{\mathrm{pb}}^{-1}$ of $\sqrt{s}=1.96\mathrm{TeV}$ $p\overline{p}$ collision data taken with the CDF II detector. With a sample of 63 964 $W\to e\nu$ candidates and 51 128 $W\to \mu \nu$ candidates, we measure $m_W=[80.413\pm 0.034(\mathrm{stat})\pm 0.034(\mathrm{sys})=80.413\pm 0.048]\mathrm{GeV}/c^2$. This is the single most precise $m_W$ measurement to date. When combined with other measured electroweak parameters, this result further constrains the properties of new unobserved particles coupling to $W$ and $Z$ bosons.

We construct supergravity solutions describing a stack of D3-branes localized at a point on a blown-up cycle of a resolved $L^{a,b,c}$ cone. The geometry flows from ${\mathrm{AdS}}_5\times L^{a,b,c}$ to ${\mathrm{AdS}}_5\times S^5/{\mathbb{Z}}_k$. The corresponding quiver gauge theory undergoes a renormalization group flow between two superconformal fixed points, which leads to semi-infinite chains of flows between the various $L^{a,b,c}$ fixed points. The general system is described by a triplet of Heun equations, which can each be solved by an expansion with a three-term recursion relation, though there are closed-form solutions for certain cases. This enables us to read off the operators that acquire nonzero vacuum expectation values as the quiver gauge theory flows away from a fixed point.

Vector theories with spontaneous Lorentz violation, known as bumblebee models, are examined in flat spacetime using a Hamiltonian constraint analysis. In some of these models, Nambu-Goldstone modes appear with properties similar to photons in electromagnetism. However, depending on the form of the theory, additional modes and constraints can appear that have no counterparts in electromagnetism. An examination of these constraints and additional degrees of freedom, including their nonlinear effects, is made for a variety of models with different kinetic and potential terms, and the results are compared with electromagnetism. The Hamiltonian constraint analysis also permits an investigation of the stability of these models. For certain bumblebee theories with a timelike vector, suitable restrictions of the initial-value solutions are identified that yield ghost-free models with a positive Hamiltonian. In each case, the restricted phase space is found to match that of electromagnetism in a nonlinear gauge.

In the previous article, we proposed two new regulators for quantum field theories in spacetimes with compactified extra dimensions. Unlike most other regulators that have been used in the extra-dimension literature, these regulators are specifically designed to respect the original higher-dimensional Lorentz and gauge symmetries that exist prior to compactification, and not merely the four-dimensional symmetries which remain afterward. In this paper, we use these regulators in order to develop a method for extracting ultraviolet-finite results from one-loop calculations. This method also allows us to derive Wilsonian effective field theories for Kaluza-Klein modes at different energy scales. Our method operates by ensuring that divergent corrections to parameters describing the physics of the excited Kaluza-Klein modes are absorbed into the corresponding parameters for zero modes, thereby eliminating the need to introduce independent counterterms for parameters characterizing different Kaluza-Klein modes. Our effective field theories can therefore simplify calculations involving Kaluza-Klein modes, and be compared directly to potential experimental results emerging from collider data.

In this paper, we propose two new regulators for quantum field theories in spacetimes with compactified extra dimensions. We refer to these regulators as the “extended hard cutoff” and “extended dimensional regularization.” Although based on traditional four-dimensional regulators, the key new feature of these higher-dimensional regulators is that they are specifically designed to handle mixed spacetimes in which some dimensions are infinitely large and others are compactified. Moreover, unlike most other regulators which have been used in the extra-dimension literature, these regulators are designed to respect the original higher-dimensional Lorentz and gauge symmetries that exist prior to compactification, and not merely the four-dimensional symmetries which remain afterward. This distinction is particularly relevant for calculations of the physics of the excited Kaluza-Klein modes themselves, and not merely their radiative effects on zero modes. By respecting the full higher-dimensional symmetries, our regulators avoid the introduction of spurious terms which would not have been easy to disentangle from the physical effects of compactification. As part of our work, we also derive a number of ancillary results. For example, we demonstrate that in a gauge-invariant theory, analogues of the Ward-Takahashi identity hold not only for the usual zero-mode (four-dimensional) photons, but for all excited Kaluza-Klein photons as well.

We extend the argument presented by Benincasa, Boucher-Veronneau, and Cachazo to show that graviton tree amplitudes are well behaved under large complex deformations of the momenta of a pair of like-helicity gravitons. This shows that Britto-Cachazo-Feng-Witten recursion relations for gravity amplitudes can be constructed using such shifts, providing an alternative proof to the recent one by Arkani-Hamed and Kaplan. By using auxiliary recursion relations the cancellations which are hidden when using covariant Feynman diagrams become manifest.

We construct an explicit model of the gravity trapping domain-wall potential, where for the first time we can study explicitly the graviton wave function fluctuations for any thickness of domain wall. A concrete form of the potential depends on one parameter $0\le x\le \frac{\pi }{2}$, which effectively parameterizes the thickness of the domain wall with specific limits $x\to 0$ and $x\to \frac{\pi }{2}$ corresponding to the thin and the thick wall, respectively. The analysis of continuum Kaluza-Klein fluctuations yields explicit expressions for both small and large Kaluza-Klein energy. We also derive specific explicit conditions in the regime $x>1$, for which the fluctuation modes exhibit a resonance behavior, and which could sizably affect the modifications of the four-dimensional Newton’s law at distances that typically are by 4 orders of magnitude larger than those relevant for Newton’s law modifications of thin walls.

In a quantum gravity theory the entropy of entanglement $S$ between the fundamental degrees of freedom spatially divided by a surface is discussed. Classical gravity is considered as an emergent phenomenon and arguments are presented that (1) $S$ is a macroscopical quantity which can be determined without knowing a real microscopical content of the fundamental theory; (2) $S$ is given by the Bekenstein-Hawking formula in terms of the area of a codimension 2 hypesurface $\mathcal{B}$; (3) in static space-times $\mathcal{B}$ can be defined as a minimal hypersurface of a least volume separating the system in a constant-time slice. It is shown that properties of $S$ are in agreement with basic properties of the von Neumann entropy. Explicit variational formulae for $S$ in different physical examples are considered.

Interacting dark energy and the holographic principle offer a possible way of addressing the cosmic coincidence problem as well as accounting for the size of the dark energy component. The equilibrium points of the Friedmann equations which govern the evolution behavior of dark energy, matter, and curvature components can determine the qualitative behavior of the cosmological models. These possible equilibria and their behavior are examined in a general framework, and some illustrative examples are presented.

We present a possible explanation of the recently observed 511 keV $\gamma$-ray anomaly with a new “millicharged” fermion. The new fermion is light [$\mathcal{O}(\mathrm{MeV})$] but has never been observed by any collider experiments mainly because of its tiny electromagnetic charge $\epsilon e$. We show that constraints from its relic density in the Universe and collider experiments allow a parameter range such that the 511 keV cosmic $\gamma$-ray emission from the galactic bulge may be due to positron production from this millicharged fermion.

In a previous paper [Phys. Rev. D 68, 034017 (2003)], we investigated the inclusive production of prompt $J/\psi$ mesons in polarized hadron-hadron, photon-hadron, and photon-photon collisions in the factorization formalism of nonrelativistic quantum chromodynamics providing compact analytic results for the double longitudinal-spin asymmetry ${\mathcal{A}}_{LL}$. For convenience, we adopted a simplified expression for the tensor product of the gluon polarization four-vector with its charge conjugate, at the expense of allowing for ghosts and antighosts to appear as external particles. While such ghost contributions cancel in the cross section asymmetry ${\mathcal{A}}_{LL}$ and thus were not listed in our previous paper, they do contribute to the absolute cross sections. Evaluating the latter from those formulas thus leads to erroneous results. For completeness and the reader’s convenience, they are provided in this addendum. This fully reconciles our results with those obtained by M. M. Meijer, J. Smith, and W. L. van Neerven [Phys. Rev. D 77, 034014 (2008)].