This article is devoted to $B_c\to B_s^{(*)}+n\pi$ decays with $n=1$, 2, 3, 4. In the framework of factorization theorem the branching fractions of these processes can be written as a convolution of the hard part, describing $B_c\to B_s^{(*)}W$ vertices, and spectral functions, that correspond to the transition of the virtual $W$-boson into a final $\pi$-meson system. These functions were obtained from the fit of experimental data on $\tau$-lepton decay and electron-positron annihilation. Using different sets of $B_c\to B_s^{(*)}W$ decay form-factors we present branching fractions and distributions over the invariant mass of the final $\pi$-meson system.

We study the leading long-distance attractive force between two holes in a plate arising from a scalar field with Dirichlet boundary conditions on the plate. We use a formalism in which the interaction is governed by a nonlocal field theory which lives on the two holes. The interaction energy is proportional to $Q_1{Q}_2/r^7$ at large separation $r$, where $Q_1$ and $Q_2$ are certain charges associated with the holes. We compute these charges for round and rectangular holes. We show that the $1/r^7$ behavior is universal for separations large compared to the linear dimensions of the holes, irrespective of the spin or interactions of the bosonic field. We also study the interaction between two long thin slits, for which the energy falls off as $1/r^6$.

We construct a scalar field theory on the Snyder noncommutative space-time. The symmetry underlying the Snyder geometry is deformed at the co-algebraic level only, while its Poincaré algebra is undeformed. The Lorentz sector is undeformed at both the algebraic and co-algebraic level, but the coproduct for momenta (defining the star product) is non-coassociative. The Snyder-deformed Poincaré group is described by a non-coassociative Hopf algebra. The definition of the interacting theory in terms of a nonassociative star product is thus questionable. We avoid the nonassociativity by the use of a space-time picture based on the concept of the realization of a noncommutative geometry. The two main results we obtain are (i) the generic (namely, for any realization) construction of the co-algebraic sector underlying the Snyder geometry and (ii) the definition of a nonambiguous self-interacting scalar field theory on this space-time. The first-order correction terms of the corresponding Lagrangian are explicitly computed. The possibility to derive Noether charges for the Snyder space-time is also discussed.

Just as big bang nucleosynthesis allows us to probe the expansion rate when the temperature of the Universe was around 1 MeV, the measurement of gravity waves from electroweak scale first order phase transitions may allow us to probe the expansion rate when the temperature of the Universe was at the electroweak scale. We compute the simple transformation rule for the gravity wave spectrum under the scaling transformation of the Hubble expansion rate. We then apply this directly to the scenario of quintessence kination domination and show how gravity wave spectra would shift relative to Laser Interferometer Space Antenna and Big Bang Observer projected sensitivities.

The Markovian diffusion theory in the phase space is generalized within the framework of the general theory of relativity. The introduction of moving orthonormal frame vectors both for the position as well the velocity space avoids difficulties in the general relativistic stochastic calculus. The general relativistic Kramers equation in the phase space is derived both in the parametrization of phase-space proper time and the coordinate time. The transformation of the obtained diffusion equation under hypersurface-preserving coordinate transformations is analyzed and diffusion in the expanding universe is studied. It is shown that the validity of the fluctuation-dissipation theorem ensures that in the quasisteady state regime, the result of the derived diffusion equation is consistent with the kinetic theory in thermodynamic equilibrium.

Several different explicit reconstructions of $f(R)$ gravity are obtained from the background Friedmann-Laîmatre-Robertson-Walker expansion history. It is shown that the only theory whose Lagrangian is a simple function of the Ricci scalar $R$, that admits an exact $\Lambda \mathrm{CDM}$ expansion history, is standard general relativity with a positive cosmological constant and the only way to obtain this behavior of the scale factor for more general functions of $R$ is to add additional degrees of freedom to the matter sector.

We numerically solve the massless test scalar field equation on the space-time background of boson stars and black holes. In order to do so, we use a numerical domain that contains future null infinity. We achieve this construction using a scri-fixing conformal compactification technique based on hyperboloidal constant mean curvature foliations of the space-time and solve the conformally invariant wave equation. We present two results: the scalar field shows oscillations of the quasinormal mode type found for black holes only for boson star configurations that are compact; and no signs of tail decay are found in the parameter space we explored. Even though our results do not correspond to the master equation of perturbations of boson star solutions, they indicate that the parameter space of boson stars as black hole mimickers is restricted to compact configurations.

We give a prescription to define in loop quantum gravity the electric field operator related to the scale factor of a homogeneous and isotropic cosmological space-time. This procedure allows us to link the fundamental theory with its cosmological implementation. In view of the conjugate relation existing between holonomies and fluxes, the edge length and the area of surfaces in the fiducial metric satisfy a duality condition. As a consequence, the area operator has a discrete spectrum also in loop quantum cosmology. This feature makes the super-Hamiltonian regularization an open issue of the whole formulation.

The energies of the excited states of the nucleon, $\Delta$, and $\Omega$ are computed in lattice QCD, using two light quarks and one strange quark on anisotropic lattices. The calculation is performed at three values of the light quark mass, corresponding to pion masses $m_{\pi }=392(4)$, 438(3), and 521(3) MeV. We employ the variational method with a large basis of interpolating operators enabling six energies in each irreducible representation of the lattice to be distinguished clearly. We compare our calculation with the low-lying experimental spectrum, with which we find reasonable agreement in the pattern of states. The need to include operators that couple to the expected multihadron states in the spectrum is clearly identified.

Strongly coupled gauge systems with many fermions are important in many phenomenological models. I use the 2-lattice matching Monte Carlo renormalization group method to study the fixed point structure and critical indexes of $SU(3)$ gauge models with 8 and 12 flavors of fundamental fermions. With an improved renormalization group block transformation I am able to connect the perturbative and confining regimes of the $N_f=8$ flavor system, thus verifying its QCD-like nature. With $N_f=12$ flavors the data favor the existence of an infrared fixed point and conformal phase, though the results are also consistent with very slow walking. I measure the anomalous mass dimension in both systems at several gauge couplings and find that they are barely different from the free-field value.

$S$- and $P$-wave $D\overline{D}$ scatterings are studied in a meson exchange model with the coupling constants obtained in the heavy quark effective theory. With the extracted $P$-wave phase shifts and the separable potential approximation, we include the $D\overline{D}$ rescattering effect and investigate the production process $e^{+}{e}^{-}\to D\overline{D}$. We find that it is difficult to explain the anomalous line shape observed by the BES Collaboration with this mechanism. Combining our model calculation and the experimental measurement, we estimate the upper limit of the nearly universal cutoff parameter to be around 2 GeV. With this number, the upper limits of the binding energies of the $S$-wave $D\overline{D}$ and $B\overline{B}$ bound states are obtained. Assuming that the $S$-wave and $P$-wave interactions rely on the same cutoff, our study provides a way of extracting the information about $S$-wave molecular bound states from the $P$-wave meson pair production.

We study a higher derivative (HD) field theory with an arbitrary order of derivative for a real scalar field. The degree of freedom for the HD field can be converted to multiple fields with canonical kinetic terms up to the overall sign. The Lagrangian describing the dynamics of the multiple fields is known as the Lee-Wick (LW) form. The first step to obtain the LW form for a given HD Lagrangian is to find an auxiliary field (AF) Lagrangian which is equivalent to the original HD Lagrangian up to the quantum level. Until now, the AF Lagrangian has been studied only for $N=2$ and 3 cases, where $N$ is the number of poles of the two-point function of the HD scalar field. We construct the AF Lagrangian for arbitrary $N$. By the linear combinations of AF fields, we also obtain the corresponding LW form. We find the explicit mapping matrices among the HD fields, the AF fields, and the LW fields. As an exercise of our construction, we calculate the relations among parameters and mapping matrices for $N=2$, 3, and 4 cases.

Recent cosmic ray, gamma ray, and microwave signals observed by Fermi, PAMELA, and WMAP indicate an unexpected primary source of $e^{+}{e}^{-}$ at 10–1000 GeV. We fit these data to “standard backgrounds” plus a new source, assumed to be a separable function of position and energy. For the spatial part, we consider three cases: annihilating dark matter, decaying dark matter, and pulsars. In each case, we use GALPROP to inject energy in log-spaced energy bins and compute the expected cosmic ray and photon signals for each bin. We then fit a linear combination of energy bins, plus backgrounds, to the data. We use a nonparametric fit, with no prior constraints on the spectrum except smoothness and non-negativity. In addition, we consider arbitrary modifications to the energy spectrum of the ordinary primary source function, fixing its spatial part, finding this alone to be inadequate to explain the PAMELA or WMAP signals. We explore variations in the fits due to choice of magnetic field, primary electron injection index, spatial profiles, propagation parameters, and fit regularization method. Dark matter annihilation fits well, where our fit finds a mass of $\sim 1\mathrm{TeV}$ and a boost factor times energy fraction of $\sim 70$. While it is possible for dark matter decay and pulsars to fit the data, unconventionally high magnetic fields and radiation densities are required near the Galactic center to counter the relative shallowness of the assumed spatial profiles. We also fit to linear combinations of these three scenarios, though the fit is much less constrained.

In this manuscript we study the vector-vector interaction within the hidden-gauge formalism in a coupled channel unitary approach. In the sector $C=1$, $S=1$, $J=2$ we get a pole in the $T$ matrix around 2572 MeV that we identify with the $D_{s2}^{*}(2573)$, coupling strongly to the $D^{*}{K}^{*}(D_s^{*}\varphi (\omega ))$ channels. In addition we obtain resonances in other exotic sectors which have not been studied before such as $C=1$, $S=-1$, $C=2$, $S=0$ and $C=2$, $S=1$. These “flavor-exotic” states are interpreted as $D^{*}{\overline{K}}^{*}$, $D^{*}{D}^{*}$, and $D_s^{*}{D}^{*}$ molecular states but have not been observed yet. In total we obtain nine states with different spin, isospin, charm, and strangeness of non-$C=0$, $S=0$ and $C=1$, $S=0$ character, which have been reported before.

There are two observations of galaxies that can offer some insight into the nature of dark matter (DM), namely, the rotation curves and the gravitational lensing. While the first one can be studied using the Newtonian limit, the second one is completely relativistic. Each one separately cannot determine the nature of DM, but both together give us key information about this open problem. In this work we use a static and spherically symmetric metric to model the DM halo in a galaxy or in a galaxy cluster. The metric contains two free functions, one associated with the distribution of mass and the other one with the gravitational potential. We use galactic, typical rotation curves to uniquely determine the kinematics of the halos. We compute separately the mass functions for a perfect fluid and a scalar field, and demonstrate that both models can be fitted to the observations, though with different masses. We then employ lensing to discriminate between these models. This procedure represents a test of models using two measurements: rotation curves and lensing.

Recent studies have shown that the primordial non-Gaussianity affects the clustering of dark matter halos through a scale-dependent bias, and various constraints on the non-Gaussianity through this scale-dependent bias have been placed. Here, we introduce the cross correlation between the CMB lensing potential and the galaxy angular distribution to effectively extract information about the bias from the galaxy distribution. Then, we estimate the error of the nonlinear parameter, $f_{\mathrm{NL}}$, for the ongoing CMB experiments and galaxy surveys, such as Planck and Hyper Suprime-Cam. We found that for the constraint on $f_{\mathrm{NL}}$ with Planck and Hyper Suprime-Cam, the wide field galaxy survey is preferable to the deep one, and the expected error on $f_{\mathrm{NL}}$ can be as small as $\Delta f_{\mathrm{NL}}\sim 80$ for $b_0=2$ and $\Delta f_{\mathrm{NL}}\sim 30$ for $b_0=4$, where $b_0$ is the linear bias parameter. It is also found that a future wide field galaxy survey could achieve $\Delta f_{\mathrm{NL}}\sim 5$ with cosmic microwave background prior to Planck, if one could observe highly biased objects at higher redshift ($z\sim 2$).

We demonstrate a method for calculating the neutral $B$-meson decay constants and mixing matrix elements in unquenched lattice QCD with domain-wall light quarks and static $b$-quarks. Our computation is performed on the “$2+1$” flavor gauge configurations generated by the RBC and UKQCD Collaborations with a lattice spacing of $a\approx 0.11\mathrm{fm}$ ($a^{-1}=1.729\mathrm{GeV}$) and a lattice spatial volume of approximately $(1.8\mathrm{fm}{)}^3$. We simulate at three different light sea quark masses with pion masses down to approximately 430 MeV, and extrapolate to the physical quark masses using a phenomenologically-motivated fit function based on next-to-leading order heavy-light meson SU(2) chiral perturbation theory. For the $b$-quarks, we use an improved formulation of the Eichten-Hill action with static link-smearing to increase the signal-to-noise ratio. We also improve the heavy-light axial current used to compute the $B$-meson decay constant to $\mathcal{O}({\alpha }_{s}pa)$ using one-loop lattice perturbation theory. We present initial results for the SU(3)-breaking ratios $f_{B_s}/f_{B_d}$ and $\xi =f_{B_s}\sqrt{B_{B_s}}/f_{B_d}\sqrt{B_{B_d}}$, thereby demonstrating the viability of the method. For the ratio of decay constants, we find $f_{B_s}/f_{B_d}=1.15(12)$ and for the ratio of mixing matrix elements, we find $\xi =1.13(12)$, where in both cases the errors reflect the combined statistical and systematic uncertainties, including an estimate of the size of neglected $\mathcal{O}(1/m_b)$ effects.

Reparametrization invariance relations are determined for the inclusive decay spectra of heavy hadrons. They connect the leading-order result to the ${\lambda }_1$ term, and the ${\lambda }_2$ and ${\rho }_2$ terms, and imply that the ${\lambda }_1$ and ${\rho }_2$ terms in the total rate occur in the combinations $1+{\lambda }_1/(2m_Q^2)$ and ${\lambda }_2-{\rho }_2/m_Q$. The relations are satisfied by the known results for the hadronic decay tensors for $\overline{B}\to X_{c,u}\ell \nu$, $\overline{B}\to X_s\gamma$ and $\overline{B}\to X_s{\ell }^{+}{\ell }^{-}$ decays. An interesting field-theory result, the connection between currents in full and effective theories and the change in currents under field redefinitions, is discussed, and is used to determine the effective theory operator whose hadron matrix element is unity to all order in $1/m_Q$. The hadron masses are given to order ${\Lambda }_{\mathrm{QCD}}^3/m_Q^2$ including radiative corrections, and provide an example illustrating the relation between renormalization and reparametrization invariance and $\mu$-independence of $1/m_Q^3$ corrections to physical quantities.

Perturbative QCD results in the $\overline{\mathrm{MS}}$ scheme can be dramatically improved by switching to a scheme that accounts for the dominant power law dependence on the factorization scale in the operator product expansion. We introduce the “MSR scheme” which achieves this in a Lorentz and gauge invariant way and has a very simple relation to $\overline{\mathrm{MS}}$. Results in MSR depend on a cutoff parameter $R$, in addition to the $\mu$ of $\overline{\mathrm{MS}}$. $R$ variations can be used to independently estimate (i.) the size of power corrections, and (ii.) higher-order perturbative corrections (much like $\mu$ in $\overline{\mathrm{MS}}$). We give two examples at three-loop order, the ratio of mass splittings in the $B^{*}\mathrm{\text{−}}B$ and $D^{*}\mathrm{\text{−}}D$ systems, and the Ellis-Jaffe sum rule as a function of momentum transfer $Q$ in deep inelastic scattering. Comparing to data, the perturbative MSR results work well even for $Q\sim 1\mathrm{GeV}$, and power corrections are reduced compared to $\overline{\mathrm{MS}}$.

We argue that there is a phase transition in the expectation value of the Polyakov loop operator in the large $N$ limit of the high temperature deconfined phase of $\mathcal{N}=4$ Yang-Mills theory on a spatial $S^3$. It occurs for the large completely symmetric representation of the $SU(N)$ symmetry group. We speculate that this transition is reflected in the $D$-branes which are the string theory duals of giant loops.