The inclusive decay $\overline{B}\to X_u\ell \overline{\nu }$ is of much interest because of its potential to constrain the CKM element $|V_{ub}|$. Experimental cuts required to suppress charm background restrict measurements of this decay to the shape-function region, where the hadronic final state carries a large energy but only a moderate invariant mass. In this kinematic region, the differential decay distributions satisfy a factorization formula of the form $H·J\otimes S$, where $S$ is the nonperturbative shape function, and the object $H·J$ is a perturbatively calculable hard-scattering kernel. In this paper, we present the calculation of the hard function $H$ at next-to-next-to-leading order (NNLO) in perturbation theory. Combined with the known NNLO result for the jet function $J$, this completes the perturbative part of the NNLO calculation for this process.

We calculate the invariant-mass distribution for the $c\overline{c}$ pair produced in the inclusive ${\rm Y}(1S)$ decay based on the color-singlet mechanism of the nonrelativistic quantum chromodynamics factorization approach at leading order in the bottom-quark velocity $v_b$ in the meson rest frame. As the short-distance processes, we consider $b\overline{b}\to g^{*}gg$ followed by $g^{*}\to c\overline{c}$ and $b\overline{b}\to {\gamma }^{*}\to c\overline{c}$ at leading order in the strong coupling. The invariant-mass distribution of the $b\overline{b}\to c\overline{c}gg$ contribution has a sharp peak just above the threshold and that of the $b\overline{b}\to {\gamma }^{*}\to c\overline{c}$ channel is concentrated at the maximally allowed kinematic end point. We predict that $\Gamma [{\rm Y}(1S)\to c\overline{c}+X]/\Gamma [{\rm Y}(1S)\to \mathrm{\text{light hadrons}}]=(0.065\pm 0.048){\alpha }_s$, which is in agreement with a previous result within errors.

This paper reports the tenth-order QED contribution to the $g-2$ of electron and muon from two gauge-invariant sets: Set $\mathrm{I}(g)$ and Set $\mathrm{I}(h)$. In the case of electron $g-2$, Set $\mathrm{I}(g)$ consists of nine Feynman diagrams which have a fourth-order vacuum-polarization loop containing another fourth-order vacuum-polarization loop. Set $\mathrm{I}(h)$ consists of 30 Feynman diagrams which have a proper sixth-order vacuum-polarization loop containing a second-order vacuum-polarization loop. The results of numerical integration, including mass-dependent terms containing one closed loop of muon, are $0.028597(4)(\alpha /\pi {)}^5$ for Set $\mathrm{I}(g)$ and $0.001685(13)(\alpha /\pi {)}^5$ for Set $\mathrm{I}(h)$, respectively. We also report the contributions of Set $\mathrm{I}(g)$ and Set $\mathrm{I}(h)$ to the muon anomaly. Diagrams included are those containing electron, muon, and tau-lepton loops. Their sums are $2.6409(4)(\alpha /\pi {)}^5$ and $-0.5648(11)(\alpha /\pi {)}^5$, respectively. The sum of contributions of Sets $\mathrm{I}(g)$ and $\mathrm{I}(h)$ containing only electron loops are in fair agreement with the recently obtained asymptotic analytic results.

We extend earlier treatments of holographic superconductors by studying cases where operators of different dimension condense in both $2+1$ and $3+1$ superconductors. We also compute a correlation length. We find surprising regularities in quantities such as ${\omega }_g/T_c$ where ${\omega }_g$ is the gap in the frequency dependent conductivity. In special cases, new bound states arise corresponding to vector normal modes of the dual near-extremal black holes.

We investigate the propagation of electromagnetic waves in resistive ${\mathrm{e}}^{\pm }$ pair plasmas using a one-fluid theory derived from the relativistic two-fluid equations. When the resistivity normalized by the electron/positron inertia variable exceeds a critical value, the dispersion relation for electromagnetic waves shows that the group velocity is larger than the light speed in vacuum. However, in such a case, it also is found that the plasma parameter is less than unity: that is, the electron–positron pair medium no longer can be treated as plasma. Thus, the simple two-fluid approximation is invalid. This confirms that superluminal propagation of electromagnetic wave is forbidden in a plasma—a conclusion consistent with the relativistic principle of causality. As an alternative, we propose a new set of equations for “causal relativistic magnetohydrodynamics,” which both have nonzero resistivity and yet are consistent with the causality principle.

We study the dynamics of quantum entanglement between two Unruh-DeWitt detectors, one stationary (Alice), and another uniformly accelerating (Rob), with no direct interaction but coupled to a common quantum field in $(3+1)\mathrm{D}$ Minkowski space. We find that for all cases studied the initial entanglement between the detectors disappears in a finite time (“sudden death”). After the moment of total disentanglement the correlations between the two detectors remain nonzero until late times. The relation between the disentanglement time and Rob’s proper acceleration is observer dependent. The larger the acceleration is, the longer the disentanglement time in Alice’s coordinate, but the shorter in Rob’s coordinate.

Developing a noncompact version of the supersymmetric Hopf map, we formulate the quantum Hall effect on a superhyperboloid. Based on $OSp(1|2)$ group theoretical methods, we first analyze the one-particle Landau problem, and successively explore the many-body problem where the Laughlin wave function, hard-core pseudopotential Hamiltonian, and topological excitations are derived. It is also shown that the fuzzy superhyperboloid emerges at the lowest Landau level.

In the present work, we study different aspects of Lorentz and CPT symmetry violation in extended massless QED. By following the observation that the $2+1$-dimensional Maxwell-Chern-Simons theory can be originated from the $3+1$-dimensional Chern-Simons-like action, we also focus on the fermion sector to relate the $3+1$ dimensional extended massless QED to $2+1$-dimensional massive QED. We take advantage of this to state that the Chern-Simons-like action in extended massless QED can be induced with its coefficient being well defined and finite just as its $2+1$ counterpart. We make use of three different regularization schemes by inducting the Chern-Simons-like term in $3+1$ dimensions to support the conjecture.

We investigate the Dirichlet-scalar equivalent of Casimir-Polder forces between an atom and a surface with arbitrary uniaxial corrugations. The complexity of the problem can be reduced to a one-dimensional Green’s function equation along the corrugation which can be solved numerically. Our technique is fully nonperturbative in the height profile of the corrugation. We present explicit results for experimentally relevant sinusoidal and sawtooth corrugations. Parameterizing the deviations from the planar limit in terms of an anomalous dimension which measures the power-law deviation from the planar case, we observe up to order-one anomalous dimensions at small and intermediate scales and a universal regime at larger distances. This large-distance universality can be understood from the fact that the relevant fluctuations average over corrugation structures smaller than the atom-wall distance.

The mapping between bulk supergravity fields in anti–de Sitter space and operators in the dual boundary conformal field theory usually relies heavily on the available global symmetries. In the present work, we study a generalization of this mapping to time dependent situations, for the simple case of collapsing shock waves in two spacetime dimensions. The construction makes use of analyticity of the conformal field theory and the properties of the asymptotic bulk geometry to reconstruct the nonanalytic bulk observables. Many of the features of this construction are expected to apply to higher dimensional asymptotically anti–de Sitter spacetimes and their conformal field theory duals.

We examine hilltop quintessence models, in which the scalar field is rolling near a local maximum in the potential, and $w\approx -1$. We first derive a general equation for the evolution of $\varphi$ in the limit where $w\approx -1$. We solve this equation for the case of hilltop quintessence to derive $w$ as a function of the scale factor; these solutions depend on the curvature of the potential near its maximum. Our general result is in excellent agreement ($\delta w\lesssim 0.5\%$) with all of the particular cases examined. It works particularly well ($\delta w\lesssim 0.1\%$) for the pseudo-Nambu-Goldstone boson potential. Our expression for $w(a)$ reduces to the previously-derived slow-roll result of Sen and Scherrer in the limit where the curvature goes to zero. Except for this limiting case, $w(a)$ is poorly fit by linear evolution in $a$.

The static spherically symmetric quark star structure is calculated by using an equation of state which takes into account the superconducting color-flavor locked phase of the strange quark matter. Some fundamental aspects of QCD (asymptotic freedom and confinement) are considered by means of a phenomenological description of the deconfined quark phase, namely, the density-dependent quark mass model. The effects from the strong interaction described by these models can affect the equation of state of the quark matter substantially. In this work we discuss the influence of these effects on the conventional mass-radius relationship of quark stars. Massive quark stars are found due to the stiffness of the equation of state at low densities, when reasonable values of the superconducting gap, taken as a free parameter, are used.

We propose two distinct atom interferometer gravitational wave detectors, one terrestrial and another satellite based, utilizing the core technology of the Stanford 10 m atom interferometer presently under construction. Each configuration compares two widely separated atom interferometers run using common lasers. The signal scales with the distance between the interferometers, which can be large since only the light travels over this distance, not the atoms. The terrestrial experiment with two $\sim 10\mathrm{m}$ atom interferometers separated by a $\sim 1\mathrm{km}$ baseline can operate with strain sensitivity $\sim \frac{{10}^{-19}}{\sqrt{\mathrm{Hz}}}$ in the 1 Hz–10 Hz band, inaccessible to LIGO, and can detect gravitational waves from solar mass binaries out to megaparsec distances. The satellite experiment with two atom interferometers separated by a $\sim 1000\mathrm{km}$ baseline can probe the same frequency spectrum as LISA with comparable strain sensitivity $\sim \frac{{10}^{-20}}{\sqrt{\mathrm{Hz}}}$. The use of ballistic atoms (instead of mirrors) as inertial test masses improves systematics coming from vibrations and acceleration noise, and significantly reduces spacecraft control requirements. We analyze the backgrounds in this configuration and discuss methods for controlling them to the required levels.

The photoproduction of $\omega$ mesons off protons has been studied at the Bonn ELSA accelerator from threshold to $E_{\gamma }=1700\mathrm{MeV}$. Linearly polarized beams were produced via coherent bremsstrahlung. Large photon asymmetries in excess of 50% were obtained. For the first time the pion asymmetries associated with the $\omega \to {\pi }^0\gamma$ decay were measured and found close to zero. The asymmetries indicate $s$-channel resonance formation on top of $t$-channel exchange processes.

In general, the kernel of QCD’s gap equation possesses a domain of analyticity upon which the equation’s solution at nonzero chemical potential is simply obtained from the in-vacuum result through analytic continuation. On this domain the single-quark number- and scalar-density distribution functions are $\mu$ independent. This is illustrated via two models for the gap equation’s kernel. The models are alike in concentrating support in the infrared. They differ in the form of the vertex, but qualitatively the results are largely insensitive to the Ansatz. In vacuum both models realize chiral symmetry in the Nambu-Goldstone mode, and in the chiral limit, with increasing chemical potential, they exhibit a first-order chiral symmetry restoring transition at $\mu \approx M(0)$, where $M(p^2)$ is the dressed-quark mass function.

We consider the production and scattering amplitudes of heavy mesons in a situation, where there are two closely spaced narrow resonances, whose structure we refer to as a diresonance. Assuming strong overlapping of the resonances coupled to common channels, it is found, using the unitarity and analyticity constraints, that the production amplitudes by a weak source should have similar behavior with energy in different channels. In particular, the ratio of the coefficients for each pole contribution to the production amplitude is fixed at $-1$.

When the mass difference between the lightest slepton, the next to lightest supersymmetric particle, and the lightest neutralino, the lightest supersymmetric particle, is smaller than the tau mass, the lifetime of the lightest slepton increases in many orders of magnitude with respect to typical lifetimes of other supersymmetric particles. These small mass differences are possible in the minimal supersymmetric standard model (MSSM) and, for instance, they correspond to the coannihilation region of the constrained MSSM for $M_{1/2}\gtrsim 700\mathrm{GeV}$. In a general gravity-mediated MSSM, where the lightest supersymmetric particle is the neutralino, the lifetime of the lightest slepton is inversely proportional to the square of the intergenerational mixing in the slepton mass matrices. Such a long-lived slepton would produce a distinctive signature at LHC and a measurement of its lifetime would be relatively simple. Therefore, the long-lived slepton scenario offers an excellent opportunity to study lepton flavor violation at ATLAS and CMS detectors in the LHC and an improvement of the leptonic mass insertion bounds by more than 5 orders of magnitude would be possible.

Viable neutrino and charged lepton masses and mixings are obtained by imposing a $S_3\times Z_4\times Z_3$ flavor symmetry in a model with a few additional Higgs. We use two $SU(2{)}_L$ triplet Higgs which are arranged as a doublet of $S_3$, and standard model singlet Higgs which are also put as doublets of $S_3$. We break the $S_3$ symmetry in this minimal model by giving vacuum expectation values (VEV) to the additional Higgs fields. Dictated by the minimum condition for the scalar potential, we obtain certain VEV alignments which allow us to maintain $\mu –\tau$ symmetry in the neutrino sector, while breaking it maximally for the charged leptons. This helps us to simultaneously explain the hierarchical charged lepton masses, and the neutrino masses and mixings. In particular, we obtain maximal ${\theta }_{23}$ and zero ${\theta }_{13}$. We allow for a mild breaking of the $\mu –\tau$ symmetry for the neutrinos and study the phenomenology. We give predictions for ${\theta }_{13}$ and the $CP$ violating Jarlskog invariant $J_{CP}$, as a function of the $\mu –\tau$ symmetry breaking parameter. We also discuss possible collider signatures and phenomenology associated with lepton flavor violating processes.

We analytically derive a decomposition of the lattice fermion determinant for Wilson’s Dirac operator with chemical potential into winding sectors, i.e., factors with a fixed number of quarks. Dividing the lattice into four domains, the determinant is factorized into terms which can be classified with respect to the winding number of the closed loops they consist of. The individual factors are expressed in terms of subdeterminants and propagators on the domains of the lattice. We numerically analyze properties of the factorization formula and discuss two applications for the determination of canonical partition functions with a fixed quark number: a speedup for the Fourier transformation technique through a dimensional reduction, and a power series expansion.

Using flavor twisted boundary conditions, we study nucleon matrix elements of the vector current. We twist only the active quarks that couple to the current. Finite volume corrections due to twisted boundary conditions are determined using partially twisted, partially quenched, heavy baryon chiral perturbation theory, which we develop for the graded group $SU(7|5)$. Asymptotically these corrections are exponentially small in the volume, but can become pronounced for small twist angles. Utilizing the Breit frame does not mitigate volume corrections to nucleon vector current matrix elements. The derived expressions will allow for better controlled extractions of the isovector magnetic moment and the electromagnetic radii from simulations at zero lattice momentum. Our formalism, moreover, can be applied to any nucleon matrix elements.