We show that the literature on pion exchange between charm and bottom mesons is inconsistent. We derive the formalism explicitly, expose differences between papers in the literature, and clarify the implications. We show that the $X(3872)$ can be a bound state but that results are very sensitive to a poorly constrained parameter. We confirm that bound states in the $B\overline{B}$ sector are possible. The circumstances whereby exotic combinations can bind with $cc$ or $bb$ quantum numbers are explored.

We compute the leading-log QED, the next-to-leading-log QED-QCD, and the electroweak corrections to the charm quark contribution relevant for the rare decay $K^{+}\to {\pi }^{+}\nu \overline{\nu }$. The corresponding parameter $P_c(X)$ is increased by up to 2% with respect to the pure QCD estimate to $P_c(X)=0.372\pm 0.015$ for $m_c(m_c)=(1.286\pm 0.013)\mathrm{GeV}$, ${\alpha }_s(M_Z)=0.1176\pm 0.0020$, and $|V_{us}|=0.2255$. For the branching ratio we find $B(K^{+}\to {\pi }^{+}\nu \overline{\nu })=(8.5\pm 0.7)\times {10}^{-11}$, where the quoted uncertainty is dominated by the Cabibbo-Kobayashi-Maskawa elements.

In this paper we study two kinds of $\tau$ decays: (a) ${\tau }^{-}\to ({\rho }^0{\pi }^{-},\omega {\pi }^{-},\varphi {\pi }^{-},K^{*0}{K}^{-}){\nu }_{\tau }$, which belong to $\Delta S=0$ processes and (b) $\Delta S=1$ processes, such as ${\tau }^{-}\to ({\rho }^0{K}^{-},\omega K^{-},\varphi K^{-},{\overline{K}}^{*0}{\pi }^{-}){\nu }_{\tau }$, in the framework of resonance chiral theory ($\mathrm{R}\chi \mathrm{T}$). We fit the ${\tau }^{-}\to \omega {\pi }^{-}{\nu }_{\tau }$ spectral function and the invariant mass distribution of $\omega K$ in the process of ${\tau }^{-}\to \omega K^{-}{\nu }_{\tau }$ to get the values of unknown resonance couplings. Then we make a prediction for branching ratios of all channels.

In models of maximal flavor violation (MxFV) suggested in [S. Bar-Shalom and A. Rajaraman, Phys. Rev. D 77, 095011 (2008).] there is at least one new scalar ${\Phi }_{\mathrm{FV}}$ which couples to the quarks via ${\Phi }_{\mathrm{FV}}{q}_i{q}_j\propto {\xi }_{ij}$ where ${\xi }_{i3},{\xi }_{3i}\sim V_{tb}$ for $i=1$, 2 and ${\xi }_{33}\sim V_{td}$ and $V$ is the CKM matrix. In this article, we explore the potential phenomenological implications of MxFV for collider experiments. We study MxFV signals of same-sign leptons from same-sign top-quark pair production at the Tevatron and at the LHC. We show that the current Tevatron data set has strong sensitivity to this signature, for which there are no current limits. For example, if $m_{{\Phi }_{\mathrm{FV}}}\sim 200\mathrm{GeV}$ and the MxFV coupling $\xi$ has a natural value of $\sim 1$, we expect $\sim 12$ MxFV events to survive a selection requiring a pair of same-sign leptons, a tagged $b$-jet and missing transverse energy, over a background of approximately 4–5 events.

The multiplicative conservation of both lepton and baryon numbers, i.e. $(-{)}^L$ and $(-{)}^{3B}$, is connected to an axionic solution of the strong $CP$ problem in a supersymmetric, unifiable model of quark and lepton interactions. New particles are predicted at the TeV scale, with verifiable consequences at the Large Hadron Collider.

We show that there exist five-dimensional multi-black hole solutions which have analytic event horizons when the space-time has nontrivial asymptotic structure, unlike the case of five-dimensional multi-black hole solutions in asymptotically flat space-time.

We present a study of the worldsheets that describe the classical limit of various string scattering processes. Our main focus is on string scattering in AdS spacetime because of its relation via the AdS/CFT (anti–de Sitter/conformal field theory) correspondence to gluon scattering in $\mathcal{N}=4$ supersymmetric Yang-Mills theory. But we also consider analogous processes in flat Minkowski spacetime which we compare to the AdS case. In addition to scattering of string by string we also find and study worldsheets describing the scattering of a string by external sources.

In a six-dimensional brane world model with multiple $S_1/Z_2$ warping, two of the 4-branes at the boundaries have coordinate-dependent brane tensions in order to implement the orbifolded boundary conditions consistently. Such brane tension is shown to be equivalent to a scalar field distribution on the brane [D. Choudhury and S. SenGupta, Phys. Rev. D 76, 064030 (2007).]. We show that in such a scenario a massless left chiral fermion on the 4-brane localizes naturally on the standard model 3-brane located at one edge of the compact manifold while the massless right chiral fermion wave function, as well as the wave functions for the massive fermion modes, peak away from this brane. This offers a mechanism of obtaining a massless chiral fermion with only one of its chiral components present in our brane.

We construct a class of supersymmetric $SU(5)$ grand unified theory (GUT) models that produce nearly tribimaximal lepton mixing, the observed quark mixing matrix, and the quark and lepton masses, from discrete non-Abelian flavor symmetries. The $SU(5)$ GUTs are formulated on five-dimensional throats in the flat limit and the neutrino masses become small due to the type-I seesaw mechanism. The discrete non-Abelian flavor symmetries are given by semidirect products of cyclic groups that are broken at the infrared branes at the tip of the throats. As a result, we obtain $SU(5)$ GUTs that provide a combined description of non-Abelian flavor symmetries and quark-lepton complementarity.

We propose an extension of general relativity with two different metrics. To each metric we define a Levi-Cevità connection and a curvature tensor. We then consider two types of fields, each of which moves according to one of the metrics and its connection. To obtain the field equations for the second metric we impose an exchange symmetry on the action. As a consequence of this ansatz, additional source terms for Einstein’s field equations are generated. We discuss the properties of these additional fields, and consider the examples of the Schwarzschild solution, and the Friedmann-Robertson-Walker metric.

Different aspects of particle dynamics on ${\mathrm{AdS}}_2\times S^2$ background with two-form flux are discussed. These include solution of equations of motion, a canonical transformation to conformal mechanics, and an $N=4$ supersymmetric extension.

Using effective field theory techniques we compute the next to leading order Spin(1)Spin(1) terms in the potential of spinning compact objects at third post-Newtonian (PN) order, including subleading self-induced finite size effects. This result represents the last ingredient to complete the relevant spin potentials to 3PN order from which the equations of motion follow via a canonical formalism. As an example we include the precession equation.

We use effective field theory techniques to compute the potentials due to spin-spin and spin-orbit effects, from which the $\mathcal{O}({\mathbf{S}}_1{\mathbf{S}}_2)$ contribution to the motion of spinning compact binaries to third Post-Newtonian (PN) order follow. We use a formalism which allows us to impose the spin supplementary condition (SSC) in a canonical framework to all orders in the PN expansion. We explicitly show the equivalence with our previous results, obtained using the Newton-Wigner SSC at the level of the action for spin-spin and spin-orbit potentials reported in arXiv:gr-qc/0604099 and arXiv:0712.2032 , respectively.

We investigate whether or not an Einstein static universe is a solution to the cosmological equations in $f(R)$ gravity. It is found that only one class of $f(R)$ theories admits an Einstein static model, and that this class is neutrally stable with respect to vector and tensor perturbations for all equations of state on all scales. Scalar perturbations are only stable on all scales if the matter fluid equation of state satisfies $c_{\mathrm{s}}^2>\frac{\sqrt{5}-1}{6}\approx 0.21$. This result is remarkably similar to the general relativity case, where it was found that the Einstein static model is stable for $c_s^2>\frac{1}{5}$.

The action for a class of three-dimensional dilaton-gravity theories with a negative cosmological constant can be recast in a Brans-Dicke type action, with its free $\omega$ parameter. These theories have static spherically symmetric black holes. Those with well formulated asymptotics are studied through a Hamiltonian formalism, and their thermodynamical properties are found out. The theories studied are general relativity ($\omega \to \infty$), a dimensionally reduced cylindrical four-dimensional general relativity theory ($\omega =0$), and a theory representing a class of theories ($\omega =-3$). The Hamiltonian formalism is set up in three dimensions through foliations on the right region of the Carter-Penrose diagram, with the bifurcation 1-sphere as the left boundary, and anti–de Sitter infinity as the right boundary. The metric functions on the foliated hypersurfaces are the canonical coordinates. The Hamiltonian action is written, the Hamiltonian being a sum of constraints. One finds a new action which yields an unconstrained theory with one pair of canonical coordinates $\{M,P_M\}$, $M$ being the mass parameter and $P_M$ its conjugate momenta The resulting Hamiltonian is a sum of boundary terms only. A quantization of the theory is performed. The Schrödinger evolution operator is constructed, the trace is taken, and the partition function of the canonical ensemble is obtained. The black hole entropies differ, in general, from the usual quarter of the horizon area due to the dilaton.

Recent research shows that Hawking radiation can be treated as a quantum tunneling process, and Hawking temperatures of Dirac particles across the horizon of a black hole can be correctly recovered via the fermion tunneling method. In this paper, motivated by the fermion tunneling method, we attempt to apply the analysis to derive Hawking radiation of Dirac particles via tunneling from black ring solutions of 5-dimensional Einstein-Maxwell-dilaton gravity theory. Finally, it is interesting to find that, as in the black hole case, fermion tunneling can also result in correct Hawking temperatures for the rotating neutral, dipole, and charged black rings.

We develop a technique to study relativistic perturbations in the generalized brane cosmological scenario, which is a generalization of the multifluid cosmological perturbations to brane cosmology. The novelty of the technique lies in the inclusion of a radiative bulk which is responsible for bulk-brane energy exchange, and in turn, modifies the standard perturbative analysis to a great extent. The analysis involves a geometric fluid—called the Weyl fluid—whose nature and role have been studied extensively both for the empty bulk and the radiative bulk scenario. Subsequently, we find that this Weyl fluid can be a possible geometric candidate for dark matter in this generalized brane cosmological framework.

We study the cosmological evolution of the fine structure constant $\alpha$ and the proton-to-electron mass ratio $\mu =m_p/m_e$ in the context of a generic class of models, where the gauge kinetic function is a linear function of a quintessence-type real scalar field $\varphi$ described by a Lagrangian with a standard kinetic term and a scalar field potential $V(\varphi )$. We further assume that the scalar field potential is a monotonic function of $\varphi$ and that the scalar field is always rolling down the potential. We show that, for this class of models, low-redshift constraints on the evolution of $\alpha$ and $\mu$ can provide very stringent limits on the corresponding variations at high redshift. We also demonstrate that these limits may be relaxed by considering more general models for the dynamics of $\alpha$ and $\mu$. However, in this case, the ability to reconstruct the evolution of the dark energy equation of state using varying couplings could be seriously compromised.

A red-tilted primordial power spectrum is preferred by WMAP five-year data and a large positive local-type non-Gaussianity $f_{NL}$ might be observed as well. In this short paper we find that a red-tilted and large non-Gaussian primordial power spectrum cannot be naturally obtained in the curvaton model, because $f_{NL}$ is related to the initial condition of inflation.

Cosmologists are exploring two possible sets of explanations for the remarkable observation of cosmic acceleration: dark energy fills space or general relativity fails on cosmological scales. We define a null test parameter $ϵ(k,a)\equiv {\Omega }_m^{-\gamma }d\ln D/d\ln a-1$, where $a$ is the scale factor, $D$ is the growth rate of structure, ${\Omega }_m(a)$ is the matter density parameter, and $\gamma$ is a simple function of redshift. We show that it can be expressed entirely in terms of the bias factor, $b(a)$, measured from cross correlations with cosmic microwave background (CMB) lensing, and the amplitude of redshift-space distortions, $\beta (k,a)$. Measurements of the CMB power spectrum determine ${\Omega }_{m0}{H}_0^2$. If dark energy within general relativity is the solution to the cosmic acceleration problem, then the logarithmic growth rate of structure $d\ln D/d\ln a={\Omega }_m^{\gamma }$. Thus, $ϵ(k,a)=0$ on linear scales to better than 1%. We show that in the class of modified gravity models known as $f(R)$, the growth rate has a different dependence on scale and redshift. By combining measurements of the amplitude of $\beta$ and of the bias, $b$, redshift surveys will be able to determine the logarithmic growth rate as a function of scale and redshift. We estimate the predicted sensitivity of the proposed SDSS III (BOSS) survey and the proposed ADEPT mission and find that they will test structure growth in general relativity to the percent level.