We present a purely relativistic effect according to which asymmetric oscillations of a quasirigid body slow down or accelerate its fall in a gravitational background.

We study the decays ${\tilde{t}}_2\to {\tilde{t}}_{1}HH$, ${\tilde{t}}_2\to {\tilde{t}}_{1}ZZ$, ${\tilde{t}}_2\to {\tilde{t}}_1{W}^{+}{W}^{-}$, and ${\tilde{t}}_2\to {\tilde{t}}_{1}ZH$, with an eye towards measuring the $CP$-violating supersymmetric parameters contained in these processes. We find that ${\tilde{t}}_2\to {\tilde{t}}_{1}HH$ tends to have the largest $CP$ asymmetry and width, and is perhaps the most favorable experimentally. These decays are sensitive primarily to ${\varphi }_{A_t}$, the phase of the trilinear coupling $A_t$.

We determine baryon-baryon bound states in $3+1$ dimensional SU(3) lattice QCD with two flavors, $4\times 4$ spin matrices, and in an imaginary-time functional integral formulation. For small hopping parameter, $\kappa >0$, and large glueball mass (strong coupling regime), we show the existence of three-quark isospin $1/2$ particles (proton and neutron) and isospin $3/2$ baryons (delta particles), with asymptotic masses $-3\ln \kappa$ and isolated dispersion curves. We only consider the existence of bound states of total isospin $I=0,3$. Using a ladder approximation to a lattice Bethe-Salpeter equation, baryon-baryon bound states are found in these two sectors, with asymptotic masses $-6\ln \kappa$ and binding energies of order ${\kappa }^2$. The dominant baryon-baryon interaction is an energy-independent spatial range-one potential with an $\mathcal{O}({\kappa }^2)$ strength. There is also attraction arising from gauge field correlations associated with six overlapping bonds, but it is counterbalanced by Pauli repulsion to give a vanishing zero-range potential. The overall range-one potential results from a quark, antiquark exchange with no meson-exchange interpretation; the repulsive or attractive nature of the interaction does depend on the isospin and spin of the two-baryon state.

We analyze the uncertainties induced by different definitions of the momentum fraction $z$ in the application of gluon to heavy quarkonium color-singlet fragmentation functions. We numerically calculate the initial $g\to J/\psi$ fragmentation functions at leading order (LO) by using the noncovariant definitions of $z$ with finite gluon momentum and find that these fragmentation functions have strong dependence on the gluon momentum $\overrightarrow{k}$. As $|\overrightarrow{k}|\to \infty$, these fragmentation functions approach the fragmentation function in the light cone definition. Our numerical results show that large uncertainties remain while the noncovariant definitions of $z$ are employed in the application of the fragmentation functions. We present for the first time the polarized gluon to $J/\psi$ color-singlet fragmentation functions at the leading nontrivial order in ${\alpha }_s$ and relativistic expansion.

In order to clarify the puzzling problems in double-charm production, relativistic corrections at order $v^2$ to the processes $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ and $e^{+}{e}^{-}\to J/\psi +c\overline{c}$ at $B$ factories are studied in nonrelativistic quantum chromodynamics. The short-distance parts of production cross sections are calculated perturbatively, while the long-distance matrix elements are estimated from $J/\psi$ and ${\eta }_c$ decays up to errors of order $v^4$. Our results show that the relativistic correction to the exclusive process $e^{+}{e}^{-}\to J/\psi +{\eta }_c$ is significant, which, when combined together with the next-to-leading-order ${\alpha }_s$ corrections, could resolve the large discrepancy between theory and experiment; whereas for the inclusive process $e^{+}{e}^{-}\to J/\psi +c\overline{c}$ the relativistic correction is tiny and negligible. The physical reason for the above difference between exclusive and inclusive processes largely lies in the fact that in the exclusive process the relative momentum between quarks in charmonium substantially reduces the virtuality of the gluon that converts into a charm quark pair, but this is not the case for the inclusive process, in which the charm quark fragmentation $c\to J/\psi +c$ is significant, and QCD radiative corrections can be more essential.

We examine the exclusive rare decays of $B\to K_0^{*}(1430)\ell \overline{\ell }$ with $K_0^{*}(1430)$ being the $p$-wave scalar meson and $\ell =\nu$, $e$, $\mu$, $\tau$ in the standard model. The form factors for the $B\to K_0^{*}$ transition matrix elements are evaluated in the light-front quark model. For the decays of $B\to K_0^{*}\ell \overline{\ell }$, the branching ratios are found to be $(11.6,1.63,1.62,0.029)\times {10}^{-7}$ with $\ell =(\nu ,e,\mu ,\tau )$ and the integrated longitudinal lepton polarization asymmetries $(-0.97,-0.95,-0.03)$ with $\ell =(e,\mu ,\tau )$, respectively.

We report on a study of inclusive $B^{-}$ and ${\overline{B}}^0$ meson decays to $D^{0}X$, ${\overline{D}}^{0}X$, $D^{+}X$, $D^{-}X$, $D_s^{+}X$, $D_s^{-}X$, ${\mathit{\Lambda }}_c^{+}X$, ${\overline{\mathit{\Lambda }}}_c^{-}X$, based on a sample of $231\times {10}^6$ $B\overline{B}$ events recorded with the BABAR detector at the $\mathit{{\rm Y}}(4S)$ resonance. Events are selected by completely reconstructing one $B$ and searching for a reconstructed charm particle in the rest of the event. From the measured branching fractions of these decays, we infer the number of charm and anticharm particles per $\overline{B}$ decay, separately for charged and neutral parents. We derive the total charm yield per $B^{-}$ decay, $n_c^{-}=1.208\pm 0.023\pm {0.040}_{-0.029}^{+0.035}$, and per ${\overline{B}}^0$ decay, $n_c^0=1.203\pm 0.030\pm {0.034}_{-0.035}^{+0.044}$ where the first uncertainty is statistical, the second is systematic, and the third reflects the charm branching-fraction uncertainties. We also present the charm momentum distributions measured in the $\overline{B}$ rest frame.

The fermion propagator is studied in the whole Minkowski space with the help of the Schwinger-Dyson equations. Various integral representations are employed to get solutions for the dynamical breaking of chiral symmetry in different regimes of the coupling constant. In particular, in the case of massive boson, we extend the singularity structure of the fermion propagator to the two real pole Ansätze.

In theories with multiple vacua, reheating to a temperature greater than the height of a barrier can stimulate transitions from a desirable metastable vacuum to a lower energy state. We discuss the constraints this places on various theories and demonstrate that in a class of supersymmetric models this transition does not occur even for arbitrarily high reheating temperature.

Five tensor equations are obtained for a thin shell in Gauss-Bonnet gravity. There is the well-known junction condition for the singular part of the stress tensor intrinsic to the shell, which we also prove to be well defined. There are also equations relating the geometry of the shell (jump and average of the extrinsic curvature as well as the intrinsic curvature) to the nonsingular components of the bulk stress tensor on the sides of the thin shell. The equations are applied to spherically symmetric thin shells in the vacuum. The shells are part of the vacuum; they carry no energy tensor. We classify these solutions of “thin shells of nothingness” in the pure Gauss-Bonnet theory. There are three types of solutions, with one, zero, or two asymptotic regions, respectively. The third kind of solutions are wormholes. Although vacuum solutions, they have the appearance of mass in the asymptotic regions. It is striking that in this theory, exotic matter is not needed in order for wormholes to exist—they can exist even with no matter.

We perform a quasinormal mode analysis of black-hole configurations in Bose-Einstein condensates (BECs). In this analysis we use the full Bogoliubov dispersion relation, not just the hydrodynamic or geometric approximation. We restrict our attention to one-dimensional flows in BECs with steplike discontinuities. For this case we show that in the hydrodynamic approximation quasinormal modes do not exist. The full dispersion relation, however, allows the existence of quasinormal modes. Remarkably, the spectrum of these modes is not discrete but continuous.

Loop quantum cosmology (LQC) predicts a nonsingular evolution of the universne through a bounce in the high energy region. We show that this is always true in tachyon matter LQC. Differing from the classical Friedman-Robertson-Walker (FRW) cosmology, the super inflation can appear in the tachyon matter LQC; furthermore, the inflation can be extended to the region where classical inflation stops. Using the numerical method, we give an evolution picture of the tachyon field with an exponential potential in the context of LQC. It indicates that the quantum dynamical solutions have the same attractive behavior as the classical solutions do. The whole evolution of the tachyon field is that in the distant past, the tachyon field—being in the contracting cosmology—accelerates to climb up the potential hill with a negative velocity; then at the boundary the tachyon field is bounced into an expanding universe with positive velocity rolling down to the bottom of the potential. In the slow roll limit, we compare the quantum inflation with the classical case in both an analytic and a numerical way.

We reformulate the problem of the cancellation of the ultraviolet divergencies of the vacuum energy, particularly important at the cosmological level, in terms of a saturation of spectral function sum rules which leads to a set of conditions on the spectrum of the fundamental theory. We specialize the approach to both Minkowski and de Sitter space-times and investigate some examples.

We introduce a model of scalar field dark energy, Cuscuton, which can be realized as the incompressible (or infinite speed of sound) limit of a scalar field theory with a noncanonical kinetic term (or $k$-essence). Even though perturbations of Cuscuton propagate superluminally, we show that they have a locally degenerate phase space volume (or zero entropy), implying that they cannot carry any microscopic information, and thus the theory is causal. Even coupling to ordinary scalar fields cannot lead to superluminal signal propagation. Furthermore, we show that the family of constant field hypersurfaces is the family of constant mean curvature hypersurfaces, which are the analogs of soap films (or soap bubbles) in Euclidian space. This enables us to find the most general solution in $1+1$ dimensions, whose properties motivate conjectures for global degeneracy of the phase space in higher dimensions. Finally, we show that the Cuscuton action can model the continuum limit of the evolution of a field with discrete degrees of freedom and argue why it is protected against quantum corrections at low energies. While this paper mainly focuses on interesting features of Cuscuton in a Minkowski space-time, a companion paper examines cosmology with Cuscuton dark energy.

In a recent paper, Liddle and Urena-Lopez suggested that to have a unified model of inflation and dark matter is imperative to have a proper reheating process where part of the inflaton field remains. In this paper I propose a model where this is possible. I found that incorporating the effect of plasma masses generated by the inflaton products enables us to stop the process. A numerical estimated model is presented.

It was commonly thought that the observation of low energy leptonic $CP$-violating phases would not automatically imply the existence of a baryon asymmetry in the leptogenesis scenario. This conclusion does not generically hold when the issue of flavor is relevant and properly taken into account in leptogenesis. We illustrate this point with various examples studying the correlation between the baryon asymmetry and the $CP$-violating asymmetry in neutrino oscillations and the effective Majorana mass in neutrinoless double beta decay.

We discuss the variation of cosmological upper bounds on $M_{\nu }$, the sum of the neutrino masses, with the choice of data sets included in the analysis, pointing out a few oddities not easily seen when all data sets are combined. For example, the effect of applying different priors varies significantly depending on whether we use the power spectrum from the 2dFGRS or SDSS galaxy survey. A conservative neutrino mass limit of $M_{\nu }<1.43\mathrm{eV}$ (95% C.L.) is obtained by combining the WMAP 3 yr data with the cluster mass function measured by weak gravitational lensing. This limit has the virtue of not making any assumptions about the bias of luminous matter with respect to the dark matter, and is in this sense (and this sense only) bias-free.

In a recent paper [J. Montano, F. Ramírez-Zavaleta, G. Tavares-Velasco, and J. J. Toscano, Phys. Rev. D 72, 055023 (2005).], we investigated the effects of the massive charged gauge bosons (bileptons) predicted by the minimal 331 model on the off-shell vertex $WW{V}^{*}$ ($V=\gamma$, $Z$) using a $S{U}_L(2)\times U_Y(1)$ covariant gauge-fixing term for the bileptons. We proceed along the same lines and calculate the effects of the gauge bosons predicted by the 331 model with right-handed neutrinos. It is found that the bilepton effects on the $WW{V}^{*}$ vertex are of the same order of magnitude as those arising from the standard model and several of its extensions, provided that the bilepton mass is of the order of a few hundred of GeVs. For heavier bileptons, their effects on the $WW{V}^{*}$ vertex are negligible. The behavior of the form factors at high energies is also discussed as it is a reflection of the gauge invariance and gauge independence of the $WW{V}^{*}$ Green function obtained via our quantization method.

We discuss the renormalization group (RG) evolution for the $\Delta S=1$ operators in unquenched QCD with $N_f=3$ ($m_u=m_d=m_s$) or, more generally, $N_f=2+1$ ($m_u=m_d\ne m_s$) flavors. In particular, we focus on the specific problem of how to treat the singularities which show up only for $N_f=3$ or $N_f=2+1$ in the original solution of Buras et al. for the RG evolution matrix at next-to-leading order. On top of the original treatment of Buras et al., we use a new method of analytic continuation to obtain the correct solution in this case. It is free of singularities and can therefore be used in numerical analysis of data sets calculated in lattice QCD.

The Schrödinger equation for the charmonium and bottomonium states at finite temperature is solved by employing an effective temperature-dependent potential given by a linear combination of the color-singlet free and internal energies obtained on the lattice from the Polyakov loop correlation functions. The melting temperatures and other properties of the quarkonium states are evaluated. The consistency of the potential model approach with the available lattice data on the quarkonium temporal correlators and spectral functions is explored.