We analyze a scalar field nonminimally coupled to gravity in the context of a Universe described by the flat Friedmann-Robertson-Walker metric. The adopted model comprises a Universe filled by the scalar field and standard matter (dark and baryonic). The corresponding field equations are obtained through the Palatini formalism. From the action of the model in the flat Friedmann-Robertson-Walker space-time, a pointlike Lagrangian of first order is obtained and the Noether symmetry approach is applied to restrict the forms of the a priori undefined coupling and potential of the scalar field. We show that the massive scalar field is associated with a Noether symmetry of the model. Analytical cosmological solutions for this case are found and their respective importance for the description of the dark energy are discussed.

Topological phenomena in gauge theories have long been recognized as the driving force for chiral symmetry breaking and confinement. These phenomena can be conveniently investigated in the semiclassical picture, in which the topological charge is entirely carried by (anti-)self-dual gauge configurations. In such an approach, it has been shown that near the critical temperature, the nonzero expectation value of the Polyakov loop (holonomy) triggers the “Higgsing” of the color group, generating the splitting of instantons into $N_c$ self-dual dyons. A number of lattice simulations have provided some evidence for such dyons, and traced their relation with specific observables, such as the Dirac eigenvalue spectrum. In this work, we formulate a model, based on one-loop partition function and including Coulomb interaction, screening and fermion zero modes. We then perform the first numerical Monte Carlo simulations of a statistical ensemble of self-dual dyons, as a function of their density, quark mass and the number of flavors. We study different dyonic two-point correlation functions and we compute the Dirac spectrum, as a function of the ensemble diluteness and the number of quark flavors.

The decays of the $Z_b(10610)$ and the $Z_b(10650)$ to ${\rm Y}(nS)\pi$, $h_b(mP)\pi$ and ${\chi }_{bJ}(mP)\gamma$ ($n=1$, 2, 3, $m=1$, 2 and $J=0$, 1, 2) are investigated within a nonrelativistic effective field theory. It is argued that, while the decays to ${\rm Y}(nS)\pi$ suffer from potentially large higher order corrections, the $P$-wave transitions of the $Z_b$ states are dominated by a single one-loop diagram and therefore offer the best possibility to confirm the nature of the $Z_b$ states as molecular states and to further study their properties. We give nontrivial and parameter-free predictions for the ratios of various partial widths of the $Z_b$ and $Z_b^{\prime }$ into final states with $h_b(mP)\pi$ and ${\chi }_{bJ}(mP)\gamma$. While such relations appear naturally in the molecular picture for the mentioned transitions, they are not expected to hold for any other scenario. In addition, the branching fractions for the neutral $Z_b$ states to ${\chi }_{bJ}\gamma$ are predicted to be of order ${10}^{-4}–{10}^{-3}$. This provides a fine test of the molecular nature in future high-luminosity experiments.

We perform a search for the rare decay $B_s^0\to {\mu }^{+}{\mu }^{-}$ using data collected by the D0 experiment at the Fermilab Tevatron Collider. This result is based on the full D0 Run II data set corresponding to $10.4{\mathrm{fb}}^{-1}$ of $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$. We use a multivariate analysis to increase the sensitivity of the search. In the absence of an observed number of events above the expected background, we set an upper limit on the decay branching fraction of $\mathcal{B}(B_s^0\to {\mu }^{+}{\mu }^{-})<15\times {10}^{-9}(12\times {10}^{-9})$ at the 95% (90%) C.L.

Recently there have been differing viewpoints on how to evaluate the curvature power spectrum generated during inflation. Since the primordial curvature power spectrum is the seed for structure formation and provides a link between observations and inflationary parameters, it is important to resolve any disagreements over the expression for the power spectrum. In this article, we discuss these differing viewpoints and indicate issues that are relevant to both approaches. We then argue why the standard expression is valid.

A phenomenological attempt at alleviating the so-called coincidence problem is to allow the dark matter and dark energy to interact. By assuming a specific class of coupled quintessence models, characterized by a constant interaction parameter $ϵ$, we investigate the precision in the measurements of the expansion rate $H(z)$ required by future experiments in order to detect a possible deviation from the standard $\Lambda \mathrm{CDM}$ model ($ϵ=0$). We perform our analysis at two levels, namely, through Monte Carlo simulations based on $ϵ\mathrm{CDM}$ models, in which $H(z)$ samples with different accuracies are generated and through an analytic method that calculates the error propagation of $ϵ$ as a function of the error in $H(z)$. We show that our analytical approach traces simulations accurately and find that to detect an interaction using $H(z)$ data only, these must reach an accuracy better than 1%.

We propose a mechanism to obtain the generation of matter in the standard model. We start from the analysis of the $T^2/Z_N$ shifted orbifold with magnetic flux, which imposes a $Z_N$ symmetry on torus. We also consider several orbifolds such as $(T^2\times T^2)/Z_N$, $(T^2\times T^2\times T^2)/(Z_N\times Z_{N^{\prime }})$ and $(T^2\times T^2\times T^2)/(Z_N\times Z_{N^{\prime }}\times Z_{N^{\prime \prime }})$. On such orbifolds, we study the behavior of fermions in two different means—the operator formalism and the explicit analysis of wave functions. For an interesting result, it is found that the number of zero-mode fermions is related to $N$ of the $Z_N$ symmetry. In other words, the generation of matter relates to the type of orbifolds. Moreover, we find that shifted orbifold models are severely restricted from realizing three generations. For example, the three-generation model on the type of $M^4\times (T^2\times T^2)/Z_N$ is unique. One can also construct other types of three-generation orbifold models with rich flavor structure. Those results may bring us a realistic model with desired Yukawa structure.

A kinetic theory can be modified to incorporate triangle anomalies and the chiral magnetic effect by taking into account the Berry curvature flux through the Fermi surface. We show how such a kinetic theory can be derived from underlying quantum field theories. Using the new kinetic theory, we also compute the parity-odd correlation function that is found to be identical to the result in the perturbation theory in the next-to-leading order hard dense loop approximation.

We show how to define and compute in a nonperturbative way the potential between $q$ and $\overline{q}$ color sources in the singlet and octet (adjoint) representations of the color group.

We revisit the classical instability of closed strings in the Abelian Higgs model. The instability is expressed by a vanishing energy as the torus-like configuration shrinks to zero size. We treat the radius of the torus as a collective coordinate and demonstrate that a quantum-mechanical treatment of this coordinate leads to a stabilization of the closed string at small radii.

We study the $O(N)$ scalar field theory with quartic self-coupling in de Sitter space. When the field is light in units of the expansion rate, perturbative methods break down at very low momenta due to large infrared logarithmic terms. Using the nonperturbative large-$N$ limit, we compute the four-point vertex function in the deep infrared regime. The resummation of an infinite series of perturbative (bubble) diagrams leads to a modified power law which is analogous to the generation of an anomalous dimension in critical phenomena. We discuss in detail the role of high momentum (subhorizon) modes, including the issue of renormalization, and show that they influence the dynamics of infrared (superhorizon) modes only through a constant renormalization factor. This provides an explicit example of effective decoupling between high and low energy physics in an expanding space-time.

The Kerr spacetime in the Kaluza-Klein theory describes a rotating black hole in four dimensions from the Kaluza-Klein point of view and involves the signature of an extra dimension that shows up through the appearance of the electric and dilaton charges. In this paper, we study the separability properties of the Hamilton-Jacobi equation for geodesics and the associated hidden symmetries in the spacetime of the Kerr-Kaluza-Klein black hole. We show that the complete separation of variables occurs only for massless geodesics, implying the existence of hidden symmetries generated by a second rank conformal Killing tensor. Employing a simple procedure built up on an “effective” metric, which is conformally related to the original spacetime metric and admits a complete separability structure, we construct the explicit expression for the conformal Killing tensor. Next, we study the properties of the geodesic motion in the equatorial plane, focusing on the cases of static and rotating Kaluza-Klein black holes separately. In both cases, we obtain the defining equations for the boundaries of the regions of existence, boundedness and stability of the circular orbits as well as the analytical formulas for the orbital frequency, the radial and vertical epicyclic frequencies of the geodesic motion. Performing a detailed numerical analysis of these equations and frequencies, we show that the physical effect of the extra dimension amounts to the significant enlarging of the regions of existence, boundedness and stability towards the event horizon, regardless of the classes of orbits.

The mathematical structure of higher-dimensional physical phase spaces of the nondiagonal Bianchi IX model is analyzed in the neighborhood of the cosmological singularity by using dynamical system methods. Critical points of the Hamiltonian equations appear at infinities and are of a nonhyperbolic type, which is a generic feature of the considered singular dynamics. The reduction of the kinematical symplectic 2-form to the constraint surface enables the determination of the physical Hamiltonian. This procedure lowers the dimensionality of the dynamics arena. The presented analysis of the phase space is based on canonical transformations. We test our method for the specific subspace of the physical phase space. The obtained results encourage further examination of the dynamics within our approach.

We consider a Hořava theory that has a consistent structure of constraints and propagates two physical degrees of freedom. The Lagrangian includes the terms of Blas, Pujolàs, and Sibiryakov. The theory can be obtained from the general Horava’s formulation by setting $\lambda =1/3$. This value of $\lambda$ is protected in the quantum formulation of the theory by the presence of a constraint. The theory has two second-class constraints that are absent for other values of $\lambda$. They remove the extra scalar mode. There is no strong-coupling problem in this theory since there is no extra mode. We perform explicit computations on a model that put together a $z=1$ term and the IR effective action. We also show that the lowest-order perturbative version of the IR effective theory has dynamics identical to the one of linearized general relativity. Therefore, this theory is smoothly recovered at the deepest IR without discontinuities in the physical degrees of freedom.

We discuss the stabilization of the conformal factor by higher derivative terms in a conformally reduced $R+R^2$ Euclidean gravity theory. The flat spacetime is unstable towards the condensation of modes with nonzero momentum, and they “condense” in a modulated phase above a critical value of the coupling $\beta$ of the $R^2$ term. By employing a combination of variational, numerical and lattice methods, we show that in the semiclassical limit the corresponding functional integral is dominated by a single nonlinear plane wave of frequency $\approx 1/\sqrt{\beta }{\ell }_{\mathrm{Pl}}$. We argue that the ground state of the theory is characterized by a spontaneous breaking of translational invariance at Planckian scales.

Inflationary theory predicts that the observable Universe should be very close to flat, with a spatial-curvature parameter $|{\Omega }_K|\lesssim {10}^{-4}$. The WMAP satellite currently constrains $|{\Omega }_K|\lesssim 0.01$, and the Planck satellite will be sensitive to values near ${10}^{-3}$. Suppose that Planck were to find ${\Omega }_K\ne 0$ at this level. Would this necessarily be a serious problem for inflation? We argue that an apparent departure from flatness could be due either to a local (wavelength comparable to the observable horizon) inhomogeneity, or a truly superhorizon departure from flatness. If there is a local inhomogeneity, then secondary cosmic microwave background (CMB) anisotropies distort the CMB frequency spectrum at a level potentially detectable by a next-generation experiment. We discuss how these spectral distortions would complement constraints on the Grishchuk-Zel’dovich effect from the low-$\ell$ CMB power spectrum in discovering the source of the departure from flatness.

Recently, the large $CP$ asymmetries in $B^{\pm }\to {\pi }^{\pm }{\pi }^{+}{\pi }^{-}$ decays were found by the LHCb Collaboration to localize in the region $m_{{\pi }^{+}{\pi }^{-}}^2<0.4{\mathrm{GeV}}^2$. We find such large localized $CP$ asymmetries may be due to the interference between a light scalar and ${\rho }^0(770)$ intermediate resonances. Consequently, we argue that the distribution of $CP$ asymmetries in the Dalitz plots of three-body $B$ decays could be very helpful for identifying the presence of the scalar resonance.

We propose an effective field theory incorporating light SU(3)-flavor and heavy quark spin symmetry to describe charmed meson-antimeson bound states. At lowest order the effective field theory entails a remarkable simplification: it only involves contact range interactions among the heavy meson and antimeson fields. We show that the isospin violating decays of the $X(3872)$ can be used to constrain the interaction between the $D$ and a ${\overline{D}}^{*}$ mesons in the isovector channel. As a consequence, we can rule out the existence of an isovector partner of the $X(3872)$. If we additionally assume that the $X(3915)$ and $Y(4140)$ are $D^{*}{\overline{D}}^{*}$ and $D_s^{*}{\overline{D}}_s^{*}$ molecular states, we can determine the full spectrum of molecular states with isospin $I=0$, $\frac{1}{2}$ and 1.

We study the Higgs sector of the $U(1{)}^{\prime }$-extended minimal supersymmetric standard model with $CP$ violation. This is an extension of the minimal supersymmetric standard model Higgs sector by one singlet field, introduced to generate the $\mu$ term dynamically. We are particularly interested in nonstandard decays of Higgs particles, especially of the lightest one, in the presence of $CP$ violating phases for ${\mu }_{\mathrm{eff}}$ and the soft parameters. We present analytical expressions for neutral and charged Higgs boson masses at tree and one-loop levels, including contributions from top and bottom scalar quark sectors. We then study the production and decay channels of the neutral Higgs for a set of benchmark points consistent with low energy data and relic density constraints. Numerical simulations show that a Higgs boson lighter than $2m_W$ can decay in a quite distinctive manner, including invisible modes into two neutralinos ($h\to {\tilde{\chi }}^0{\tilde{\chi }}^0$) up to $\sim 50\%$ of the time, when kinematically allowed. The branching ratio into $h\to \overline{b}b$, the dominant decay in the standard model, is reduced in some $U(1{)}^{\prime }$ models and enhanced in others, while the branching ratios for the decays $h\to {\tau }^{+}{\tau }^{-}$, $h\to W{W}^{*}$, and $h\to Z{Z}^{*}\to 4\ell$ are always reduced with respect to their standard model expectations. This possibility has important implications for testing the $U(1{)}^{\prime }$ model both at the LHC and later at the ILC.

We compute matrix elements of the chromomagnetic operator, often denoted by ${\mathcal{O}}_8$, between $B/D$ states and light mesons plus an off-shell photon by employing the method of light-cone sum rules at leading twist-2. These matrix elements are relevant for processes such as $B\to K^{*}{l}^{+}{l}^{-}$ and they can be seen as the analogues of the well-known penguin form factors $T_{1,2,3}$ and $f_T$. We find a large $CP$-even phase for which we give a long-distance interpretation. We compare our results to QCD factorization for which the spectator photon emission is end-point divergent. The analytic structure of the correlation function used in our method admits a complex anomalous threshold on the physical sheet. The meaning and handling within the sum rule approach of the anomalous threshold is discussed.