We report on a search for the lepton-flavor-violating processes $e^{+}{e}^{-}\to {\mu }^{+}{\tau }^{-}$ and $e^{+}{e}^{-}\to e^{+}{\tau }^{-}$. The data sample corresponds to an integrated luminosity of $211{\mathrm{fb}}^{-1}$ recorded by the BABAR experiment at the SLAC PEP-II asymmetric-energy $B$ Factory at a center-of-mass energy of $\sqrt{s}=10.58\mathrm{GeV}$. We find no evidence for a signal and set the 90% confidence level upper limits on the cross sections to be ${\sigma }_{\mu \tau }<3.8\mathrm{fb}$ and ${\sigma }_{e\tau }<9.2\mathrm{fb}$. The ratio of the cross sections with respect to the dimuon cross section are measured to be ${\sigma }_{\mu \tau }/{\sigma }_{\mu \mu }<3.4\times {10}^{-6}$ and ${\sigma }_{e\tau }/{\sigma }_{\mu \mu }<8.2\times {10}^{-6}$.

Diquark excitations of dense quark matter are considered in the framework of the Nambu–Jona-Lasinio model with three types of massless quarks in the presence of a quark number chemical potential $\mu$. We investigate the effective action of meson and diquark fields at sufficiently high values of $\mu$, where the color-flavor locked (CFL) phase is realized, and prove the existence of NG bosons in the sector of pseudoscalar diquarks. In the sector of scalar diquarks an additional NG boson is found, corresponding to the spontaneous breaking of the $\mathrm{U}(1{)}_B$ baryon symmetry in the CFL phase. Finally, the existence of massive scalar and pseudoscalar diquark excitations is demonstrated.

It has been believed since the paper by Fischler, Kogut, and Susskind that in ${\mathrm{QED}}_2$ at finite charge density the chiral condensate exhibits a spatially inhomogeneous, oscillating behavior. In this paper we demonstrate that this inhomogeneity is due to the explicit breaking of the translational invariance by a uniform background charge density. Moreover, we investigate in the context of a simple statistical model what happens if the neutralizing background is composed instead of heavy, but dynamical, particles. We find that in contrast to the standard picture of Fischler et al., the chiral condensate will not exhibit coherent oscillations on large distance scales, unless the heavy neutralizing particles themselves form a crystal and the density is high.

We apply a recently suggested technique of the Neumann-Dirichlet reduction to a toy model of brane-induced gravity for the calculation of its quantum one-loop effective action. This model is represented by a massive scalar field in the $(d+1)$-dimensional flat bulk supplied with the $d$-dimensional kinetic term localized on a flat brane and mimicking the brane Einstein term of the Dvali-Gabadadze-Porrati (DGP) model. We obtain the inverse mass expansion of the effective action and its ultraviolet divergences which turn out to be nonvanishing for both even and odd spacetime dimensionality $d$. For the massless case, which corresponds to a limit of the toy DGP model, we obtain the Coleman-Weinberg type effective potential of the system. We also obtain the proper-time expansion of the heat kernel in this model associated with the generalized Neumann boundary conditions containing second-order tangential derivatives. We show that in addition to the usual integer and half-integer powers of the proper time this expansion exhibits, depending on the dimension $d$, either logarithmic terms or powers multiple of one quarter. This property is considered in the context of strong ellipticity of the boundary value problem, which can be violated when the Euclidean action of the theory is not positive definite.

We study the appearance of multiple solutions to certain decompositions of Einstein’s constraint equations. Pfeiffer and York recently reported the existence of two branches of solutions for a particular family of background data in the extended conformal thin-sandwich decomposition. We show that the Hamiltonian constraint alone, when expressed in a certain way, admits two branches of solutions with properties very similar to those found by Pfeiffer and York. We construct these two branches analytically for a constant-density star in spherical symmetry, but argue that this behavior is more general. In the case of the Hamiltonian constraint this nonuniqueness is well known to be related to the sign of one particular term, and we argue that the extended conformal thin-sandwich equations contain a similar term that causes the breakdown of uniqueness.

We study the bending of light for static spherically symmetric (SSS) space-times which include a dark energy contribution. Geometric dark energy models generically predict a correction to the Einstein angle written in terms of the distance to the closest approach, whereas a cosmological constant $\Lambda$ does not. While dark energy is associated with a repulsive force in cosmological context, its effect on null geodesics in SSS space-times can be attractive as for the Newtonian term. This dark energy contribution may not be negligible with respect to the Einstein prediction in lensing involving clusters of galaxies. Strong lensing may therefore be useful to distinguish $\Lambda$ from other dark energy models.

We calculate deep inelastic scattering (DIS) scheme splitting and coefficient functions for electromagnetic DIS with small $x$ resummations, as given by the next-to-leading-logarithmic Balitsky-Fadin-Kuraev-Lipatov (NLL BFKL) equation with running coupling and approximate NLL resummed impact factors. The resummations are combined with a next-to-leading order (NLO) fixed-order expansion, and the improved quantities thus obtained are stable at small $x$ and significantly suppressed with respect to leading logarithmic (LL) results. These results are implemented in a global fit to DIS and related data, and the results compared to a NLO fixed-order DIS scheme fit and with a previous LL resummed fit. The NLL resummed fit quality is excellent and constitutes a marked improvement over the purely fixed-order approach. The input gluon, at $Q_0^2=1{\mathrm{GeV}}^2$, obtained from the resummed fit is positive and slightly increasing as $x\to 0$, in contrast to the result obtained at fixed order. A resummed prediction for the longitudinal structure function $F_L$ is presented. It is positive definite and growing with energy at low $x$ and $Q^2$, where the fixed-order results show a significant perturbative instability.

We calculate the branching ratios for $B\to (b_1,h_1)\gamma$ at next-to-leading order (NLO) of ${\alpha }_s$ where $b_1$ and $h_1$ are the corresponding orbitally excited axial vector mesons of $\rho$ and $\omega$ respectively. Using the $SU(3)$ symmetry for the form factors, the branching ratio for $B\to (b_1,h_1)\gamma$ is expressed in terms of the branching ratio of the $B\to K_1\gamma$ and it is found to be $\mathcal{B}(B\to b_1\gamma )=0.53\times {10}^{-6}$ and $\mathcal{B}(B\to h_1\gamma )=0.51\times {10}^{-6}$. We also calculate direct $CP$-asymmetry for these decays and find that its typical values lies around 11% and is negative like $\rho$ and $\omega$ in the standard model. The predicted value of $CP$-asymmetry, in confirmity with the observations made in the literature, is scale dependent which has also been discussed in detail.

We construct static solutions to a $SU(2)$ Yang-Mills (YM) dilaton model in $4+1$ dimensions subject to bi-azimuthal symmetry. The YM sector of the model consists of the usual YM term and the next higher order term of the YM hierarchy, which is required by the scaling condition for the existence of finite energy solutions. The basic features of two different types of configurations are studied, corresponding to (multi)solitons with topological charge $n^2$, and soliton-antisoliton pairs with zero topological charge.

We study the renormalization of (softly) broken supersymmetric theories at the one loop level in detail. We perform this analysis in a superspace approach in which the supersymmetry breaking interactions are parametrized using spurion insertions. We comment on the uniqueness of this parametrization. We compute the one loop renormalization of such theories by calculating superspace vacuum graphs with multiple spurion insertions. To perform this computation efficiently we develop algebraic properties of spurion operators, that naturally arise because the spurions are often surrounded by superspace projection operators. Our results are general apart from the restrictions that higher super covariant derivative terms and some finite effects due to noncommutativity of superfield dependent mass matrices are ignored. One of the soft potentials induces renormalization of the Kähler potential.

We examine how nonperturbative effects in string theory are transformed under the $T$-duality in its nonperturbative framework by analyzing the $c=1/2$ noncritical string theory as a simplest example. We show that in the $T$-dual theory they also take the form of $\exp (-S_0/g_s)$ in the leading order and that the instanton actions $S_0$ of the dual Zamolodchikov-Zamolodchikov (ZZ)-branes are exactly the same as those in the original $c=1/2$ string theory. Furthermore we present formulas for coefficients of $\exp (-S_0/g_s)$ in the dual theory.

We consider Einstein-Gauss-Bonnet gravity in $n(\ge 6)$-dimensional Kaluza-Klein spacetime ${\mathcal{M}}^4\times {\mathcal{K}}^{n-4}$, where ${\mathcal{K}}^{n-4}$ is the Einstein space with negative curvature. In the case where ${\mathcal{K}}^{n-4}$ is the space of negative constant curvature, we have recently obtained a new static black-hole solution [Phys. Rev. D 74, 021501(R) (2006)] which is a pure gravitational creation including Maxwell field in four-dimensional vacuum spacetime. The solution has been generalized to make it radially radiate null radiation representing gravitational creation of charged null dust. The same class of solutions though exists in spacetime ${\mathcal{M}}^d\times {\mathcal{K}}^{n-d}$ for $d=3,4$, however the gravitational creation of the Maxwell field is achieved only for $d=4$. Also, the Gauss-Bonnet effect could be brought down to ${\mathcal{M}}^d$ only for $d=4$. Further some new exact solutions are obtained including its analogue in Taub-NUT spacetime on ${\mathcal{M}}^4$ for $d=4$.

We investigate neutral quark matter with homogeneous and inhomogeneous color condensates at finite temperature in the frame of an extended NJL model. By calculating the Meissner masses squared and gap susceptibility, the uniform color superconductor is stable only in a temperature window close to the critical temperature and becomes unstable against LOFF phase, mixed phase and gluonic phase at low temperatures. The introduction of the inhomogeneous phases leads to disappearance of the strange intermediate temperature 2SC/g2SC and changes the phase diagram of neutral dense quark matter significantly.

We consider the sign problem of the fermion determinant at finite density. It is unavoidable not only in Monte Carlo simulations on the lattice but in the mean-field approximation as well. A simple model deriving from quantum chromodynamics (QCD) in the double limit of large quark mass and large quark chemical potential exemplifies how the sign problem arises in the Polyakov loop dynamics at finite temperature and density. In the color SU(2) case our mean-field estimate is in excellent agreement with the lattice simulation. We combine the mean-field approximation with a simple phase reweighting technique to circumvent the complex action encountered in the color SU(3) case. We also investigate the mean-field free energy, from the saddle point of which we can estimate the expectation value of the Polyakov loop.

The Goldberger-Treiman relation for heavy-light systems is derived in the context of a quark model. As a paradigmatic example, the case of $\overline{D}\to {\overline{D}}^{\prime }\pi$ is studied in detail. The fundamental role played by the pion two-component wave function, in the context of the Salpeter equation, is emphasized.

We compute the total cross section and the transverse momentum distribution for single charged slepton and sneutrino production at hadronic colliders including NLO supersymmetric and nonsupersymmetric QCD corrections. The supersymmetric QCD corrections can be substantial. We also resum the gluon transverse momentum distribution and compare our results with two Monte Carlo generators. We compute branching ratios of the supersymmetric decays of the slepton and determine event rates for the like-sign dimuon final state at the Tevatron and at the LHC.

We calculate the chiral corrections to the s-wave pseudoscalar meson octet-baryon scattering lengths $a_{MB}$ to $\mathcal{O}(p^3)$ in the SU(3) heavy baryon chiral perturbation theory ($\mathrm{HB}\chi \mathrm{PT}$). Hopefully the obtained analytical expressions will be helpful in the chiral extrapolation of these scattering lengths in the future lattice simulation.

Within the framework of the standard model plus one heavy Higgs triplet, we derive a full set of one-loop renormalization group equations of the neutrino mass matrix and Higgs couplings in both full and effective theories. The explicit RGEs of neutrino masses, flavor mixing angles and $CP$-violating phases are also obtained, and their nontrivial running behaviors around the Higgs triplet mass threshold are numerically illustrated.

Using $65\times {10}^6$ $\mathit{{\rm Y}}(4S)\to B\overline{B}$ events collected with the BABAR detector at the PEP-II $e^{+}{e}^{-}$ storage ring at the Stanford Linear Accelerator Center, we measure the color-favored branching fractions $\mathcal{B}({\overline{B}}^0\to D^{+}{\pi }^{-})=(2.55\pm 0.05\pm 0.16)\times {10}^{-3}$, $\mathcal{B}({\overline{B}}^0\to D^{*+}{\pi }^{-})=(2.79\pm 0.08\pm 0.17)\times {10}^{-3}$, $\mathcal{B}(B^{-}\to D^0{\pi }^{-})=(4.90\pm 0.07\pm 0.22)\times {10}^{-3}$ and $\mathcal{B}(B^{-}\to D^{*0}{\pi }^{-})=(5.52\pm 0.17\pm 0.42)\times {10}^{-3}$, where the first error is statistical and the second is systematic. With these results and the current world average for the branching fraction for the color-suppressed decay ${\overline{B}}^0\to D^{(*)0}{\pi }^0$, the cosines of the strong phase difference $\delta$ between the $I=1/2$ and $I=3/2$ isospin amplitudes are determined to be $\cos \delta ={0.872}_{-0.007-0.029}^{+0.008+0.031}$ for the $\overline{B}\to D\pi$ process and $\cos \delta ={0.924}_{-0.017-0.054}^{+0.019+0.063}$ for the $\overline{B}\to D^{*}\pi$ process. Under the isospin symmetry, the results for $\cos \delta$ suggest the presence of final-state interactions in the $D\pi$ system.