Little Higgs theories often rely on an internal parity (“$T$-parity”) to suppress nonstandard electroweak effects or to provide a dark matter candidate. We show that such a symmetry is generally broken by anomalies, as described by the Wess-Zumino-Witten term. We study a simple $SU(3)\times SU(3)/SU(3)$ Little Higgs scheme where we obtain a minimal form for the topological interactions of a single Higgs field. The results apply to more general models, including $[SU(3)\times SU(3)/SU(3){]}^4$, $SU(5)/SO(5)$, and $SU(6)/Sp(6)$.

The analytical expressions and the numerical values of the renormalization constants of $\mathcal{O}(a)$ improved static-light currents are given at one-loop order of perturbation theory in the framework of heavy quark effective theory: the static quark is described by the HYP action and the light quark is described either with the Clover or the Neuberger action. These factors are relevant to extract from a lattice computation the decay constants $f_B$, $f_{B_S}$ and the set of bag parameters $B_i$ associated with $B-\overline{B}$ mixing phenomenology in the standard model and beyond.

The distribution of gluon fields in a baryon is of fundamental interest in QCD. We have observed the formation of gluon flux-tubes within baryons using lattice QCD techniques. In particular we use a high-statistics approach, based on the translational and rotational symmetries of the four-dimensional lattice, which enables us to observe correlations between the vacuum action density and the quark positions in a completely gauge independent manner. This contrasts with earlier studies which needed to use gauge-dependent smoothing techniques. We use 200 $\mathcal{O}(a^2)$-improved quenched QCD gauge-field configurations on a ${16}^3\times 32$ lattice with a lattice spacing of 0.123 fm. Vacuum field fluctuations are observed to be suppressed in the presence of static quarks such that flux tubes represent the suppression of gluon-field fluctuations. We considered numerous different link paths in the creation of the static quark sources in order to investigate the dependence of the flux tubes on the source shape. We have analyzed 11 L-shapes and 8 T- and Y-shapes of varying sizes in order to explore a variety of flux-tube topologies, including the ground state. At large separations, Y-shape flux-tube formation is observed. T-shaped paths are observed to relax towards a Y-shaped topology, whereas L-shaped paths give rise to a large potential energy. We do not find any evidence for the formation of a $\Delta$-shaped flux-tube (empty triangle) distribution. However, at small quark separations, we do observe an expulsion of gluon-field fluctuations in the shape of a filled triangle with maximal expulsion at the center of the triangle. Having identified the precise geometry of the flux distribution, we are able to perform a quantitative comparison between the length of the flux-tube and the associated static quark potential. For every source configuration considered we find a universal string tension, and conclude that, for large quark separations, the ground state potential is that which minimizes the length of the flux tube. The characteristic flux tube radius of the baryonic ground state potential is found to be $0.38\pm 0.03\mathrm{fm}$, with vacuum fluctuations suppressed by $7.2\pm 0.6\%$. The node connecting the flux tubes is 25% larger at $0.47\pm 0.02\mathrm{fm}$ with a larger suppression of the vacuum by $8.1\pm 0.7\%$

Based on the nonrelativistic QCD (NRQCD) factorization formalism, we calculate the inclusive charm production rate in ${\rm Y}(nS)$ decay at leading order in the strong coupling constant ${\alpha }_s$ and the relative velocity $v$ of the $b$ quark in the quarkonium rest frame. The branching fractions for ${\rm Y}(nS)$ to charm for $n=1$, 2, and 3 are all around 7%–9%. About 60% of the branching fraction into charm is from annihilation of the color-singlet $b\overline{b}$ pair into ${\gamma }^{*}\to c\overline{c}$. Most of the remaining branching fraction is from annihilation of the color-singlet $b\overline{b}$ pair decaying into $c\overline{c}gg$. We also compute the momentum distributions of the charm quark and charmed hadrons in the decays. The virtual-photon contribution to the charm-quark momentum distribution is concentrated at the end point while the $c\overline{c}gg$ contribution is broad. The momentum distributions for charmed hadrons are obtained by convolving the charm-quark momentum distribution with charm fragmentation functions. This makes the momentum distributions for charmed hadrons softer than that for the charm quark. This effect is particularly significant in the virtual-photon contribution.

Parton showers are widely used to generate fully exclusive final states needed to compare theoretical models to experimental observations. While, in general, parton showers give a good description of the experimental data, the precise functional form of the probability distribution underlying the event generation is generally not known. The reason is that realistic parton showers are required to conserve four-momentum at each vertex. In this paper we investigate in detail how four-momentum conservation is enforced in a standard parton shower and why this destroys the analytic control of the probability distribution. We show how to modify a parton shower algorithm such that it conserves four-momentum at each vertex, but for which the full analytic form of the probability distribution is known. We then comment how this analytic control can be used to match matrix element calculations with parton showers, and to estimate effects of power corrections and other uncertainties in parton showers.

We present a showcase for deriving bounds on the neutrino masses from laboratory experiments and cosmological observations. We compare the frequentist and Bayesian bounds on the effective electron neutrino mass $m_{\beta }$ which the KATRIN neutrino mass experiment is expected to obtain, using both an analytical likelihood function and Monte Carlo simulations of KATRIN. Assuming a uniform prior in $m_{\beta }$, we find that a null result yields an upper bound of about 0.17 eV at 90% confidence in the Bayesian analysis, to be compared with the frequentist KATRIN reference value of 0.20 eV. This is a significant difference when judged relative to the systematic and statistical uncertainties of the experiment. On the other hand, an input $m_{\beta }=0.35\mathrm{eV}$, which is the KATRIN $5\sigma$ detection threshold, would be detected at virtually the same level. Finally, we combine the simulated KATRIN results with cosmological data in the form of present (post-WMAP) and future (simulated Planck) observations. If an input of $m_{\beta }=0.2\mathrm{eV}$ is assumed in our simulations, KATRIN alone excludes a zero neutrino mass at $2.2\sigma$. Adding Planck data increases the probability of detection to a median $2.7\sigma$. The analysis highlights the importance of combining cosmological and laboratory data on an equal footing.

We reconsider the Feynman-Kislinger-Ravndal model applied to neutrino-excitation of baryon resonances. The effects of lepton mass are included, using the formalism of Kuzmin, Lyubushkin, and Naumov. In addition we take account of the pion-pole contribution to the hadronic axial vector current. Application of this new formalism to the reaction ${\nu }_{\mu }+p\to {\mu }^{-}+{\Delta }^{++}$ at $E_{\nu }\sim 1\mathrm{GeV}$ gives a suppressed cross section at small angles, in agreement with the screening correction in Adler’s forward-scattering theorem. Application to the process ${\nu }_{\tau }+p\to {\tau }^{-}+{\Delta }^{++}$ at $E_{\nu }\sim 7\mathrm{GeV}$ leads to the prediction of right-handed ${\tau }^{-}$ polarization for forward-going leptons, in line with a calculation based on an isobar model. Our formalism represents an improved version of the Rein-Sehgal model, incorporating lepton mass effects in a manner consistent with partially conserved axial-vector current.

We present a search for anomalous triple gauge couplings (ATGC) in $WW$ and $WZ$ boson production. The boson pairs are produced in $p\overline{p}$ collisions at $\sqrt{s}=1.96\mathrm{TeV}$, and the data sample corresponds to $350{\mathrm{pb}}^{-1}$ of integrated luminosity collected with the CDF II detector at the Fermilab Tevatron. In this search one $W$ decays to leptons, and the other boson ($W$ or $Z$) decays hadronically. Combining with a previously published CDF measurement of $W\gamma$ boson production yields ATGC limits of $-0.18<\lambda <0.17$ and $-0.46<\Delta \kappa <0.39$ at the 95% confidence level, using a cutoff scale $\Lambda =1.5\mathrm{TeV}$.

We investigate the effects of a mixing of active and sterile neutrinos on the ratios of supernova electron neutrino flux ($F_e$) and antineutrino flux ($F_{\overline{e}}$) to the total flux of the other neutrino and antineutrino flavors ($F_a$). We assume that the heaviest (in the normal hierarchy) standard model neutrino ${\nu }_3$ mixes with a sterile neutrino resulting in a pair of mass eigenstates with a small mass gap. Using the density matrix formalism we solve numerically the evolution of neutrino states in the envelope of a supernova and determine the flux ratios $F_e/F_a$ and $F_{\overline{e}}/F_a$ as a function of the active-sterile mixing angle and for the experimentally allowed range of the standard active-active mixing angle ${\theta }_{13}$.

Networks or webs of domain walls are admitted in Abelian or non-Abelian gauge theory coupled to fundamental Higgs fields with complex masses. We examine the dynamics of the domain wall loops by using the moduli approximation and find a phase rotation induces a repulsive force which can be understood as a Noether charge of $Q$-solitons. Non-Abelian gauge theory allows different types of loops which can be deformed to each other by changing a modulus. This admits the moduli geometry like a sandglass made by gluing the tips of the two cigar-(cone-)like metrics of a single triangle loop. We conclude that the sizes of all loops tend to grow for a late time in general models with complex Higgs masses, while the sizes are stabilized at some values once triplet masses are introduced for the Higgs fields. We also show that the stationary motion on the moduli space of the domain wall webs represents $1/4$ Bogomol’nyi-Prasad-Sommerfield $Q$-webs of walls.

We present a new computational framework (LEO) that enables us to carry out the very first large-scale, high-resolution computations in the context of the characteristic approach in numerical relativity. At the analytic level, our approach is based on a new implementation of the eth formalism, using a nonstandard representation of the spin-raising and spin-lowering angular operators in terms of nonconformal coordinates on the sphere; we couple this formalism to a partially first-order reduction (in the angular variables) of the Einstein equations. The numerical implementation of our approach supplies the basic building blocks for a highly parallel, easily extensible numerical code. We demonstrate the adaptability and excellent scaling of our numerical code by solving, within our numerical framework, for a scalar field minimally coupled to gravity (the Einstein-Klein-Gordon problem) in 3 dimensions. The nonlinear code is globally second-order convergent, and has been extensively tested using as a reference a calibrated code with the same initial and boundary data and radial marching algorithm. In this context, we show how accurately we can follow quasinormal mode ringing. In the linear regime, we show energy conservation for a number of initial data sets with varying angular structure. A striking result that arises in this context is the saturation of the flow of energy through the Schwarzschild radius. As a final calibration check, we perform a large simulation with resolution never achieved before.

In this paper I study the detectability of $\gamma$ rays from dark matter annihilation in the subhalos of the Milky Way by the satellite-based experiments EGRET and GLAST. I work in the frame of supersymmetric extension of the standard model and assume the lightest neutralino being the dark matter particles. Based on the N-body simulation of the evolution of dark matter subhalos I first calculate the average intensity distribution of this new class of $\gamma$-ray sources by neutralino annihilation. It is possible to detect these $\gamma$-ray sources by EGRET and GLAST. Conversely, if these sources are not detected the nature of the dark matter particles will be constrained by these experiments, depending, however, on the uncertainties of the subhalo profile.

We have recently given a construction of the overlap Dirac operator at nonzero quark chemical potential. Here, we introduce a quark chemical potential in the domain-wall fermion formalism and show that our earlier result is reproduced if the extent of the fifth dimension is taken to infinity and its lattice spacing is taken to zero. We also extend this result to include a bare quark mass, consider its continuum limit, and prove a number of properties of the overlap operator at nonzero quark chemical potential. In particular, we show that the relation between the anomaly and the index of the overlap operator remains valid.

We present an updated measurement of the $CP$-odd fraction and the time-dependent $CP$ asymmetries in the decay $B^0\to D^{*+}{D}^{*-}$ using $(383\pm 4)\times {10}^{6}B\overline{B}$ pairs collected with the BABAR detector. We determine the $CP$-odd fraction to be $0.143\pm 0.034(\mathrm{stat})\pm 0.008(\mathrm{syst})$. The time-dependent $CP$ asymmetry parameters are determined to be $C_{+}=-0.05\pm 0.14(\mathrm{stat})\pm 0.02(\mathrm{syst})$ and $S_{+}=-0.72\pm 0.19(\mathrm{stat})\pm 0.05(\mathrm{syst})$. The nonzero value of the measured $S_{+}$ indicates the evidence of $CP$ violation at the $3.7\sigma$ confidence level.

We construct “flying saucer” solitons in supersymmetric $\mathcal{N}=2$ gauge theory, which is known to support Bogomol’nyi-Prasad-Sommerfield domain walls with a U(1) gauge field localized on its worldvolume. We demonstrate that this model supports exotic particlelike solitons with the shape of a torus. $Q$ tori, and also similar solitons of higher genera, are obtained by folding the domain wall into an appropriate surface. Nontrivial cycles on the domain wall worldvolume (handles) are stabilized by crossed electric and magnetic fields inside the folded domain wall. Three distinct frameworks are used to prove the existence of these flying saucer solitons and study their properties: the worldvolume description (including the Dirac-Born-Infeld action), the bulk-theory description in the sigma-model limit, and the bulk-theory description in the thin-edge approximation. In the sigma-model framework the $Q$ torus is shown to be related to the Hopf Skyrmion studied previously.

The effective action associated with the trace anomaly provides a general algorithm for approximating the expectation value of the stress tensor of conformal matter fields in arbitrary curved spacetimes. In static, spherically symmetric spacetimes, the algorithm involves solving a fourth order linear differential equation in the radial coordinate $r$ for the two scalar auxiliary fields appearing in the anomaly action, and its corresponding stress tensor. By appropriate choice of the homogeneous solutions of the auxiliary field equations, we show that it is possible to obtain finite stress tensors on all Reissner-Nordström event horizons, including the extreme $Q=M$ case. We compare these finite results to previous analytic approximation methods, which yield invariably an infinite stress energy on charged black hole horizons, as well as with detailed numerical calculations that indicate the contrary. The approximation scheme based on the auxiliary field effective action reproduces all physically allowed behaviors of the quantum stress tensor, in a variety of quantum states, for fields of any spin, in the vicinity of the entire family ($0\le Q\le M$) of RN horizons.

When a charge is held static near a constant density spherical star, it experiences a self-force $F_{\mathrm{self}}$, which is significantly different from the force $F_{\mathrm{self}}^{\mathrm{BH}}$ it would experience when placed near a black hole of the same mass. In this paper, an expression for the self-force (as measured by a locally inertial observer) is given for an insulating Schwarzschild star, and the result is explicitly computed for the extreme density case, which has a singularity at its center. The force is found to be repulsive. A similar calculation of the self-force is also performed for a conducting star. This calculation is valid for any static, spherically conducting star, since the result is independent of the interior metric. When the charge is placed very close to the conducting star, the force is found to be attractive but when the charge is placed beyond a certain distance (2.95 M for a conducting star of radius 2.25 M), the force is found to be repulsive. When the charge is placed very far from the star (be it conducting or insulating), the charge experiences the same repulsive force it would experience when placed in the space-time of a black hole with the same mass as the star.

The mirror relative motion of a suspended Fabry-Perot cavity is studied in the frequency range 3–100 Hz. The experimental measurements presented in this paper have been performed at the Low Frequency Facility, a high finesse optical cavity 1 cm long suspended to a mechanical seismic isolation system like the one of the VIRGO gravitational wave antenna. Because of the radiation pressure between the two mirrors of the cavity, the dynamic behavior of the system is characterized by the optical spring stiffness. In the frequency region above 3 Hz, where seismic noise contamination is negligible, the mirror displacement noise is stationary and its statistical distribution is Gaussian. Using a simplified mechanical model of the suspended system and applying the fluctuation dissipation theorem, we show that the measured power spectrum is reproduced in the frequency region 3–90 Hz. Since the contribution coming from different sources of the system to the total noise budget turns out to be negligible, we conclude that the relative displacement power spectrum of this opto-mechanical system is compatible with a system at thermal equilibrium within its environment. In the region 3–10 Hz this measurement gives so far the best upper limit for the thermal noise of the suspension for a gravitational wave interferometer.

We study the Higgs sector of the next-to-minimal supersymmetric standard model with explicit $CP$ violation at one-loop level, where the radiative corrections due to the quarks and squarks of the third generation are taken into account. We expect that, within a reasonable region of the parameter space of the present model, at least one of the five neutral Higgs bosons may be produced at the future $e^{+}{e}^{-}$ International Linear Collider with $\sqrt{s}=500\mathrm{GeV}$, with cross sections larger than 12 fb, 15 fb, and 1.5 fb, respectively, via the Higgs-strahlung process, the $WW$ fusion process, and the $ZZ$ fusion process. We find that the effect of the $CP$ phase in the present model yields significant influences upon the production cross sections of the five neutral Higgs bosons. We also study the decay modes of the five neutral Higgs bosons to find that their decay widths are similarly affected by the $CP$ phase. Some of the decay modes in the present model behave differently from those of the standard model.