We analyze nonleptonic $B_s$ decays to a charmonium state and a light meson, induced by the $b\to c\overline{c}s$ transition, which are useful to access the $B_s\mathrm{\text{−}}{\overline{B}}_s$ mixing phase ${\beta }_s$. We use generalized factorization and $SU(3{)}_F$ symmetry to relate such modes to correspondent $B$ decay channels. We discuss the feasibility of the measurements in the various channels, stressing the importance of comparing different determinations of ${\beta }_s$ in view of the hints of new physics effects recently emerged in the $B_s$ sector. Finally, adopting a general parametrization of new physics contributions to the decay amplitudes, we discuss how to experimentally constrain new physics parameters.

A new and exact derivation of the Bogoliubov coefficients is obtained for the simplest case of a spinless, neutral, massive field in a uniformly accelerated frame with a constant acceleration. The method can be suitably generalized in a straightforward manner to any field with spin and charges.

We study modular properties of the ${\mathrm{AdS}}_3$ Wess-Zumino-Novikov-Witten model. Although the Euclidean partition function is modular invariant, the characters on the Euclidean torus diverge and the regularization proposed in the literature removes information on the spectrum and the usual one to one map between characters and representations of rational models is lost. Reconsidering the characters defined on the Lorentzian torus and focusing on their structure as distributions, we obtain expressions that recover those properties. We study their modular transformations and find a generalized $S$ matrix, depending on the sign of the real modular parameters, which has two diagonal blocks and one off-diagonal block, mixing discrete and continuous representations, that we fully determine. We then explore the relations among the modular transformations, the fusion algebra and the boundary states. We explicitly construct Ishibashi states for the maximally symmetric $D$-branes and show that the generalized $S$ matrix defines the one-point functions associated to pointlike and ${\mathrm{H}}_2$-branes as well as the fusion rules of the degenerate representations of $sl(2,\mathbb{R}$) appearing in the open string spectrum of the pointlike $D$-branes, through a generalized Verlinde theorem.

We reconsider Casimir free energy and internal energy at nonzero temperature in the static Einstein and closed Friedmann universe. It is shown that the Casimir free energy is given by the difference between the free energy of a topologically nontrivial manifold and a tangential Minkowski space-time. We derive exact expressions for the Casimir free energy, internal energy and pressure in Einstein and Friedmann universes in terms of single sums. The Casimir entropy is shown to satisfy the Nernst heat theorem. Exact expressions for corresponding total quantities in the Einstein universe are obtained from the Casimir ones by adding a contribution of the black-body radiation. The asymptotic expressions for the Casimir free energy and internal energy at both high and low temperature are shown to be in direct analogy with those for two ideal-metal plates and an ideal-metal spherical shell. Specifically, at high temperature the classical limit holds.

The puncture method for dealing with black holes in the numerical simulation of vacuum spacetimes is remarkably successful when combined with the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of the Einstein equations. We examine a generalized class of formulations modeled along the lines of the Laguna-Shoemaker system and including BSSN as a special case. The formulation is a two parameter generalization of the choice of variables used in standard BSSN evolutions. Numerical stability of the standard finite difference methods is proven for the formulation in the linear regime around flat space, a special case of which is the numerical stability of BSSN. Numerical evolutions are presented and compared with a standard BSSN implementation. Surprisingly, a significant portion of the parameter space yields (long-term) stable simulations, including the standard BSSN formulation as a special case. Furthermore, nonstandard parameter choices typically result in smoother behavior of the evolution variables close to the puncture.

We study twist and shear aspects of the stingy geodesic surface congruence. Under some natural conditions we derive the equations of the twist and shear in terms of the expansion of the Universe. We observe in this higher dimensional cosmology that, as the early universe evolves with expansion rate, the twist of the stringy congruence decreases exponentially and the initial twist value should be large enough to sustain the rotations of the ensuing universe, while the effects of the shear are negligible to produce the isotropic and homogeneous universe. We also investigate the twist and shear of the geodesic surface congruence of the null strings.

We study observational constraints on the assisted k-inflation models in which multiple scalar fields join an attractor characterized by an effective single field $\varphi$. This effective single-field system is described by the Lagrangian $P=Xg(Y)$, where $X$ is the kinetic energy of $\varphi$, $\lambda$ is a constant, and $g$ is an arbitrary function in terms of $Y=X{e}^{\lambda \varphi }$. Our analysis covers a wide variety of k-inflation models such as dilatonic ghost condensate, Dirac-Born-Infeld field, and tachyon, as well as the canonical field with an exponential potential. We place observational bounds on the parameters of each model from the WMAP 7yr data combined with baryon acoustic oscillations and the Hubble constant measurement. Using the observational constraints of the equilateral non-Gaussianity parameter $f_{\mathrm{NL}}^{\mathrm{equil}}$, we further restrict the allowed parameter space of dilatonic ghost condensate and Dirac-Born-Infeld models. We extend the analysis to more general models with several different choices of $g(Y)$ and show that the models such as $g(Y)=c_0+c_p{Y}^p$ ($p\ge 3$) are excluded by the joint data analysis of the scalar/tensor spectra and primordial non-Gaussianities.

Prior to recombination photons, electrons, and atomic nuclei rapidly scattered and behaved, almost, like a single tightly-coupled photon-baryon plasma. We investigate here the accuracy of the tight-coupling approximation commonly used to numerically evolve the baryon and photon perturbation equations at early times. By solving the exact perturbations equations with a stiff solver starting deep in the radiation-dominated epoch, we find the level of inaccuracy introduced by resorting to the standard first-order tight-coupling approximation. We develop a new second-order approximation in the inverse Thomson opacity expansion and show that it closely tracks the full solution, at essentially no extra numerical cost. We find the bias on estimates of cosmological parameters introduced by the first-order approximation is, for most parameters, negligible. Finally, we show that our second-order approximation can be used to reduce the time needed to compute cosmic microwave background angular spectra by as much as $\sim 17\%$.

The technique of 21 cm tomography promises to be a powerful tool for estimating cosmological parameters, constraining the epoch of reionization, and probing the so-called dark ages. However, realizing this promise will require the extraction of a cosmological power spectrum from beneath overwhelmingly large sources of foreground contamination. In this paper, we develop a unified matrix-based framework for foreground subtraction and power spectrum estimation, which allows us to quantify the errors and biases that arise in the power spectrum as a result of foreground subtraction. We find that existing line-of-sight foreground subtraction proposals can lead to substantial mode mixing as well as residual noise and foreground biases, whereas our proposed inverse-variance foreground subtraction eliminates noise and foreground biases, gives smaller error bars, and produces less correlated measurements of the power spectrum. We also numerically confirm the intuitive belief in the literature that 21 cm foreground subtraction is best done using frequency rather than angular information.

Cosmic magnetic fields may be generated during early cosmic phase transition, such as the QCD or electroweak transitions. The magnitude of the remainder of such fields at the present epoch crucially depends on the exponent $n$ of their (initially super-Hubble) large-scale tail, i.e., $B_{\lambda }\sim {\lambda }^{-n}$. It has been claimed that causality requires $n=5/2$, contrary to much earlier claims of $n=3/2$. Here we analyze this question in detail. First, we note that contrary to current belief, the large-scale magnetic field tail is not established at the phase transition itself, but rather continuously evolves up to the present epoch. Neglecting turbulent flows we find $n=7/2$, i.e., very strongly suppressed large-scale fields. However, in the inevitable presence of turbulent flows we find that the large-scale magnetic field tail has sufficient time to evolve to that of the fluid turbulence. For white noise fluid turbulence this yields $n=3/2$ up to a certain scale and $n=5/2$ beyond for the magnetic field spectrum. This picture is also not changed when primordial viscosity and fluid flow dissipation is taken into account. Appreciable primordial magnetic fields originating from cosmic phase transitions thus seem possible.

We calculate the quark spin contribution to the total angular momentum of flavor octet and flavor decuplet ground state baryons using a spin-flavor symmetry based parametrization method of quantum chromodynamics. We find that third order SU(6) symmetry breaking three-quark operators are necessary to explain the experimental result ${\Sigma }_1=0.29(09)$. For spin $3/2$ decuplet baryons, we predict that the quark spin contribution is ${\Sigma }_3=3.93(22)$, i.e. considerably larger than their total angular momentum.

We investigate the nonlinear dynamics of hybrid inflation models, which are characterized by two real scalar fields interacting quadratically. We start by solving numerically the coupled Klein-Gordon equations in static Minkowski spacetime, searching for possible coherent structures. We find long-lived, localized configurations, which we identify as a new kind of oscillon. We demonstrate that these two-field oscillons allow for “excited” states with much longer lifetimes than those found in previous studies of single-field oscillons. We then solve the coupled field equations in an expanding Friedmann-Robertson-Walker spacetime, finding that as the field responsible for inflating the Universe rolls down to oscillate about its minimum, it triggers the formation of long-lived two-field oscillons, which can contribute up to 20% of the total energy density of the Universe. We show that these oscillons emerge for a wide range of parameters consistent with WMAP 7-year data. These objects contain total energy of about $25\times {10}^{20}\mathrm{GeV}$, localized in a region of approximate radius $6\times {10}^{-26}\mathrm{cm}$. We argue that these structures could have played a key role during the reheating of the Universe.

We investigate the (partial) chiral restoration at finite temperature $(T)$ under the strong external magnetic field $\mathit{B}=B_0\widehat{z}$ of the SU(2) light-flavor QCD matter. To this end, we employ the instanton-liquid QCD vacuum configuration accompanied with the linear Schwinger method for inducing the magnetic field. The Harrington-Shepard caloron solution is used to modify the instanton parameters, i.e. the average instanton size $(\overline{\rho })$ and interinstanton distance $(\overline{R})$, as functions of $T$. In addition, we include the meson-loop corrections as the large-$N_c$ corrections because they are critical for reproducing the universal chiral-restoration pattern. We present the numerical results for the constituent-quark mass as well as chiral condensate, which signal the spontaneous breakdown of chiral-symmetry ($\mathrm{SB}\chi \mathrm{S}$), as functions of $T$ and $B_0$. From our results we observe that the strengths of those chiral order parameters are enhanced with respect to $B_0$ due to the magnetic-catalysis effect. We also find that there appears a region where the $u$ and $d$-quark constituent masses coincide with each other at $e{B}_0\approx (7–9)m_{\pi }^2$, even in the presence of the explicit isospin breaking ($m_u\ne m_d$). The critical $T$ for the chiral restoration $T_c$ tends to shift to the higher temperature in the presence of the $B_0$ for the chiral limit but keeps almost stationary for the physical quark mass case. The strength of the isospin breaking between the quark condensates is also explored in detail by defining the ratio $\mathcal{R}\equiv (⟨i{u}^{†}u⟩-⟨i{d}^{†}d⟩)/(⟨i{u}^{†}u⟩+⟨i{d}^{†}d⟩)$, which indicates the competition between the explicitly isospin-breaking effect and magnetic-catalysis effect. We also compute the pion weak-decay constant $F_{\pi }$ and pion mass $m_{\pi }$ below $T_c$, varying the strength of the magnetic field, showing correct partial chiral-restoration behaviors. Besides we find that the changes for the $F_{\pi }$ and $m_{\pi }$ due to the magnetic field is relatively small, in comparison to those caused by the finite $T$ effect.

We extend the renormalization group transformation based on the two-lattice matching to the complex inverse temperature plane for Dyson’s hierarchical Ising model. We consider values of the dimensional parameter above, below, and exactly at the critical value where the ordered low temperature phase becomes impossible for a real positive temperature. We show numerically that, as the volume increases, the Fisher’s zeros appear to accumulate along lines that separate the flows ending on different fixed points. We justify these findings in terms of finite size scaling. We argue that the location of the Fisher’s zeros at large volume determine the phase diagram in the complex plane. We discuss the implications for nontrivial infrared fixed points in lattice gauge theory.

We perform a nonperturbative lattice calculation of the $P$-wave pion-pion scattering phase in the $\rho$-meson decay channel using two flavors of maximally twisted mass fermions at pion masses ranging from 480 to 290 MeV. Making use of finite-size methods, we evaluate the pion-pion scattering phase in the center-of-mass frame and two moving frames. Applying an effective range formula, we find a good description of our results for the scattering phase as a function of the energy covering the resonance region. This allows us to extract the $\rho$-meson mass and decay width and to study their quark mass dependence.

The recent Belle and BABAR measurements of the branching ratio of $B^{+}\to {\tau }^{+}{\nu }_{\tau }$ indicate a significant deviation from the standard model prediction. We demonstrate that this measurement has a serious impact on models with minimal flavor violation involving a charged Higgs boson, ruling out a large portion of the currently allowed parameter space. In the constrained minimal supersymmetric standard model, this creates a tension between the measurements of $B^{+}\to {\tau }^{+}{\nu }_{\tau }$ and the anomalous magnetic moment of the muon, unless $\tan \beta$ is small, $\mu >0$, and $A_0$ takes a large negative value. In fact, a very small region of the parameter space of this model, with small values of $m_0$ and $m_{1/2}$, survives all the constraints at 95% C.L. It is remarkable that this specific region is still consistent with the lightest supersymmetric particle as the dark matter. Moreover, it predicts observable supersymmetric signals in the early runs of the LHC, even perhaps at 7 TeV. We also show that a consistent explanation for the deviation of the $B^{+}\to {\tau }^{+}{\nu }_{\tau }$ branching ratio from the standard model can be achieved in a nonuniversal Higgs-mass model, which could also predict early signals of supersymmetry at the LHC.

By demanding a compact spectrum for the right-handed neutrinos and an approximate quark-lepton symmetry inspired from $SO(10)$ gauge unification (assuming a Dirac neutrino mass matrix close to the up quark mass matrix), we construct a fine-tuning scenario for baryogenesis via leptogenesis. We find two solutions with a normal hierarchy, with the lightest neutrino mass $m_1$ different from zero, providing an absolute scale for the spectrum. In the approximations of the model, there are three independent $CP$ phases: ${\delta }_L$ (that we take of the order of the quark Kobayashi-Maskawa phase) and the two light neutrino Majorana phases $\alpha$ and $\beta$. A main conclusion is that, although this general scheme is rather flexible, in some regions of parameter space we find that the necessary baryogenesis with its sign is given in terms of the ${\delta }_L$ phase alone. The light Majorana phases can also be computed, and they turn out to be close to $\pi /2$ or very small. Moreover, $SO(10)$ breaks down to the Pati-Salam group $SU(4)\times SU(2)\times SU(2)$ at the expected natural intermediate scale of about ${10}^{10}–{10}^{11}\mathrm{GeV}$. A prediction is made for the effective mass in $(\beta \beta {)}_{0\nu }$ decay, the ${\nu }_e$ mass, and the sum of all light neutrino masses.

In the note, we extend the discussion of the new agegraphic dark energy (NADE) model to include the inflation stage. Usually, in the inflation models, for convenience the conformal time $\eta$ is set to be zero at the end of inflation. This is incompatible with the NADE model since $\eta =0$ indicates the divergence of NADE. To avoid the difficulty, we can redefine the conformal time as $\eta +\delta$. However, we find that the positive constant $\delta$ must be so large that NADE cannot become dominated at present time.

We consider the Casimir effect of the electromagnetic field in a higher-dimensional spacetime of the form $M\times \mathcal{N}$, where $M$ is the four-dimensional Minkowski spacetime and $\mathcal{N}$ is an $n$-dimensional compact manifold. The Casimir force acting on a planar piston that can move freely inside a closed cylinder is investigated. Different combinations of perfectly conducting boundary conditions and infinitely permeable boundary conditions are imposed on the cylinder and the piston. It is verified that if the piston and the cylinder have the same boundary conditions, the piston is always going to be pulled towards the closer end of the cylinder. However, if the piston and the cylinder have different boundary conditions, the piston is always going to be pushed to the middle of the cylinder. By taking the limit where one end of the cylinder tends to infinity, one obtains the Casimir force acting between two parallel plates inside an infinitely long cylinder. The asymptotic behavior of this Casimir force in the high temperature regime and the low temperature regime are investigated for the case where the cross section of the cylinder in $M$ is large. It is found that if the separation between the plates is much smaller than the size of $\mathcal{N}$, the leading term of the Casimir force is the same as the Casimir force on a pair of large parallel plates in the ($4+n$)-dimensional Minkowski spacetime. However, if the size of $\mathcal{N}$ is much smaller than the separation between the plates, the leading term of the Casimir force is $1+h/2$ times the Casimir force on a pair of large parallel plates in the four-dimensional Minkowski spacetime, where $h$ is the first Betti number of $\mathcal{N}$. In the limit the manifold $\mathcal{N}$ vanishes, one does not obtain the Casimir force in the four-dimensional Minkowski spacetime if $h$ is nonzero. Therefore the data obtained from Casimir experiments suggest that the first Betti number of the extra dimensions should be zero.

We calculate quarkonium binding energies using a realistic complex-valued potential for both an isotropic and anisotropic quark-gluon plasma. We determine the disassociation temperatures of the ground and first excited states considering both the real and imaginary parts of the binding energy. We show that the effect of momentum-space anisotropy is smaller on the imaginary part of the binding energy than on the real part of the binding energy. In the case that one assumes an isotropic plasma, we find disassociation temperatures for the $J/\psi$, ${\rm Y}$, and ${\chi }_b$ of $2.3T_c$, $2.9T_c$, and $1.8T_c$, respectively. We find that a finite oblate momentum-space anisotropy increases the disassociation temperature for all states considered and results in a splitting of the $p$-wave states associated with the ${\chi }_b$ first excited state of bottomonium.