We perform a complete calculation at the one-loop level for the $Zggg$ and $Z^{\prime }ggg$ couplings in the context of the minimal 331 model, which predicts the existence of a new $Z^{\prime }$ gauge boson and new exotic quarks. Bose symmetry is exploited to write a compact and manifest $S{U}_C(3)$-invariant vertex function for the $Vggg$ ($V=Z$, $Z^{\prime }$) coupling. Previous results on the $Z\to ggg$ decay in the standard model are reproduced. It is found that this decay is insensitive to the effects of the new exotic quarks. This in contrast with the $Z^{\prime }\to ggg$ decay, which is sensitive to both the standard model and exotic quarks, whose branching ratio is larger than that of the $Z\to ggg$ transition by about a factor of 4.

One-dimensional motion of a quantum point particle is usually described by its wave function $\psi (x)$, where the argument $x\in \mathbb{R}$ represents a (measurable) coordinate and where the integrated probability density is normalized to one, $\int {\psi }^{*}(x)\psi (x)=1$. The direct observability of $x$ may be lost in $\mathcal{P}\mathcal{T}$-symmetric quantum mechanics where a “smeared” metric kernel ${\Theta }_{(x,x^{\prime })}\ne \delta (x-x^{\prime })$ may enter the double-integral normalization $\iint {\psi }^{*}(x){\Theta }_{(x,x^{\prime })}\psi (x^{\prime })=1$. We argue that such a formalism proves particularly suitable for the introduction of a nonvanishing fundamental length $\theta >0$, which would characterize the “smearing width” of the kernel ${\Theta }_{(x,x^{\prime })}$. The technical feasibility of such a project is illustrated via a toy family of Hamiltonians $H^{(N)}(\lambda )$ taken from Ref. [11]. For each element of this family the complete set of all the eligible metric kernels ${\Theta }_{(x,x^{\prime })}^{(N)}(\lambda )$ is constructed in closed form. We show that at any preselected non-negative fundamental length these metrics can be made to vanish unless $|x-x^{\prime }|\le \theta$. The strictly local inner product of Ref. [11] recurs at $\theta =0$, while the popular $\mathcal{C}\mathcal{P}\mathcal{T}$-symmetric option requires $\theta =\infty$ in this language.

We reconsider the possibility of violating the generalized second law of thermodynamics in theories with spontaneous Lorentz violation. It has been proposed that this may be accomplished in particular with a black hole immersed in a ghost condensate background, which may be taken to break Lorentz invariance without appreciably distorting the space-time geometry. In this paper we show that there in fact exist solutions explicitly describing the flow of negative energy into these black holes, allowing for violation of the second law in a very simple way. This second law violation is independent of any additional assumptions such as couplings of the ghost condensate to secondary fields, and suggests that violation of the null energy condition may be the true source of pathology in these theories.

We consider the possibility that Lorentz violation can generate differences between the limiting velocities of light and charged matter. Such effects would lead to efficient vacuum Cherenkov radiation or rapid photon decay. The absence of such effects for 104.5 GeV electrons at the Large Electron Positron collider and for 300 GeV photons at the Tevatron therefore constrains this type of Lorentz breakdown. Within the context of the standard-model extension, these ideas imply an experimental bound at the level of $-5.8\times {10}^{-12}\le {\tilde{\kappa }}_{\mathrm{tr}}-(4/3)c_e^{00}\le 1.2\times {10}^{-11}$ tightening existing laboratory measurements by 3–4 orders of magnitude. Prospects for further improvements with terrestrial and astrophysical methods are discussed.

We investigate the bounds on the mass of the lightest neutralino from rare meson decays within the minimal supersymmetric standard model (MSSM) with and without minimal flavor violation. We present explicit formulas for the two-body decays of mesons into light neutralinos and perform the first complete calculation of the loop-induced decays of kaons to pions and light neutralinos and $B$ mesons to kaons and light neutralinos. We find that the supersymmetric branching ratios are strongly suppressed within the MSSM with minimal flavor violation, and that no bounds on the neutralino mass can be inferred from experimental data, i.e., a massless neutralino is allowed. The branching ratios for kaon and $B$ meson decays into light neutralinos may, however, be enhanced when one allows for nonminimal flavor violation. We find new constraints on the MSSM parameter space for such scenarios and discuss prospects for future kaon and $B$ meson experiments. Finally, we comment on the search for light neutralinos in monojet signatures at the Tevatron and at the LHC.

We study the problem of selecting between different mechanisms of supersymmetry breaking in the minimal supersymmetric standard model using current data. We evaluate the Bayesian evidence of four supersymmetry breaking scenarios: mSUGRA, mGMSB, mAMSB, and moduli mediation. The results show a strong dependence on the dark matter assumption. Using the inferred cosmological relic density as an upper bound, minimal anomaly mediation is at least moderately favored over the CMSSM. Our fits also indicate that evidence for a positive sign of the $\mu$ parameter is moderate at best. We present constraints on the anomaly and gauge mediated parameter spaces and some previously unexplored aspects of the dark matter phenomenology of the moduli mediation scenario. We use sparticle searches, indirect observables and dark matter observables in the global fit and quantify robustness with respect to prior choice. We quantify how much information is contained within each constraint.

Comparisons of lattice-QCD calculations of semileptonic form factors with experimental measurements often display two sets of points, one each for lattice QCD and experiment. Here we propose to display the output of a lattice-QCD analysis as a curve and error band. This is justified, because lattice-QCD results rely in part on fitting, both for the chiral extrapolation and to extend lattice-QCD data over the full physically allowed kinematic domain. To display an error band, correlations in the fit parameters must be taken into account. For the statistical error, the correlation comes from the fit. To illustrate how to address correlations in the systematic errors, we use the Bećirević-Kaidalov parametrization of the $D\to \pi l\nu$ and $D\to Kl\nu$ form factors, and an analyticity-based fit for the $B\to \pi l\nu$ form factor $f_{+}$.

We study the semileptonic decays of double-heavy baryons using a manifestly Lorentz covariant constituent three-quark model. We present complete results on transition form factors between double-heavy baryons for finite values of the heavy quark/baryon masses and in the heavy quark symmetry limit, which is valid at and close to zero recoil. Decay rates are calculated and compared to each other in the full theory, keeping masses finite, and also in the heavy quark limit.

Using the entire CLEO-c $\psi (3770)\to D\overline{D}$ event sample, corresponding to an integrated luminosity of $818{\mathrm{pb}}^{-1}$ and approximately $5.4\times {10}^6$ $D\overline{D}$ events, we present a study of the decays $D^0\to {\pi }^{-}{e}^{+}{\nu }_e$, $D^0\to K^{-}{e}^{+}{\nu }_e$, $D^{+}\to {\pi }^0{e}^{+}{\nu }_e$, and $D^{+}\to {\overline{K}}^0{e}^{+}{\nu }_e$. Via a tagged analysis technique, in which one $D$ is fully reconstructed in a hadronic mode, partial rates for semileptonic decays by the other $D$ are measured in several $q^2$ bins. We fit these rates using several form factor parametrizations and report the results, including form factor shape parameters and the branching fractions $\mathcal{B}(D^0\to {\pi }^{-}{e}^{+}{\nu }_e)=(0.288\pm 0.008\pm 0.003)\%$, $\mathcal{B}(D^0\to K^{-}{e}^{+}{\nu }_e)=(3.50\pm 0.03\pm 0.04)\%$, $\mathcal{B}(D^{+}\to {\pi }^0{e}^{+}{\nu }_e)=(0.405\pm 0.016\pm 0.009)\%$, and $\mathcal{B}(D^{+}\to {\overline{K}}^0{e}^{+}{\nu }_e)=(8.83\pm 0.10\pm 0.20)\%$, where the first uncertainties are statistical and the second are systematic. Taking input from lattice quantum chromodynamics, we also find $|V_{cd}|=0.234\pm 0.007\pm 0.002\pm 0.025$ and $|V_{cs}|=0.985\pm 0.009\pm 0.006\pm 0.103$, where the third uncertainties are from lattice quantum chromodynamics.

Semi-inclusive ${\pi }^{+}$ electroproduction on protons has been measured with the CLAS detector at Jefferson Lab. The measurement was performed on a liquid-hydrogen target using a 5.75 GeV electron beam. The complete five-fold differential cross sections were measured over a wide kinematic range including the complete range of azimuthal angles between hadronic and leptonic planes, $\varphi$, enabling us to separate the $\varphi$-dependent terms. Our measurements of the $\varphi$-independent term of the cross section at low Bjorken $x$ were found to be in fairly good agreement with pQCD calculations. Indeed, the conventional current fragmentation calculation can account for almost all of the observed cross section, even at small ${\pi }^{+}$ momentum. The measured center-of-momentum spectra are in qualitative agreement with high-energy data, which suggests a surprising numerical similarity between the spectator diquark fragmentation in the present reaction and the antiquark fragmentation measured in $e^{+}{e}^{-}$ collisions. We have observed that the two $\varphi$-dependent terms of the cross section are small. Within our precision the $\cos 2\varphi$ term is compatible with zero, except for the low-$z$ region, and the measured $\cos \varphi$ term is much smaller in magnitude than the sum of the Cahn and Berger effects.

Cartan’s structure equations in the Riemann-Cartan framework and some topological invariants of gravity are reanalyzed from the perspective of $BF$ theories. This is related to a variational approach to Chern-Simons terms and Bianchi identities employing Lagrange multipliers. Here, it is pointed out that the $BF$ scheme has some limitations to the effect that a coupling to matter would leave the minimal coupling prescription of gauge theories. In the case of gravity, the field equations would, generically, become higher order with a coupling to the relocalized Belinfante-Rosenfeld energy-momentum current.

In this article we present results for tensor graviton modes (in seven dimensions and greater, $n\ge 3$) for gray-body factors of Kerr–de Sitter black holes and for Hawking radiation from simply rotating ($n+4$)-dimensional Kerr black holes. Although there is some subtlety with defining the Hawking temperature of a Kerr–de Sitter black hole, we present some preliminary results for emissions assuming the standard Hawking normalization and a Bousso-Hawking-like normalization.

We examine a few simple extremal black hole configurations of $\mathcal{N}=8$, $d=4$ supergravity. We first elucidate the relation between the BPS Reissner-Nördstrom black hole and the non-BPS Kaluza-Klein dyonic black hole. Their classical entropy, given by the Bekenstein-Hawking formula, can be reproduced via the attractor mechanism by suitable choices of symplectic frame. Then, we display the embedding of the axion-dilaton black hole into $\mathcal{N}=8$ supergravity.

We perform an $su(2)$ Hamiltonian reduction of the general $su(2)$-invariant action for a self-coupled (4, 4, 0) supermultiplet. As a result, we elegantly recover the $\mathcal{N}=4$ supersymmetric mechanics with spin degrees of freedom which was recently constructed in [S. Fedoruk, E. Ivanov, and O. Lechtenfeld, Phys. Rev. D 79, 105015 (2009)]. This observation underscores the exceptional role played by the root supermultiplet in $\mathcal{N}=4$ supersymmetric mechanics.

We study what might be called fractional vortices, vortex configurations with the minimum winding from the viewpoint of their topological stability, but which are characterized by various notable substructures in the transverse energy distribution. The fractional vortices occur in diverse Abelian or non-Abelian generalizations of the Higgs model. The global and local features characterizing these are studied, and we identify the two crucial ingredients for their occurrence—the vacuum degeneracy leading to nontrivial vacuum moduli $\mathcal{M}$, and the BPS nature of the vortices. Fractional vortices are further classified into two kinds. The first type of such vortices appear when $\mathcal{M}$ has orbifold ${\mathbb{Z}}_n$ singularities; the second type occurs in systems in which the vacuum moduli space $\mathcal{M}$ possesses either a deformed geometry or some singularity. These general features are illustrated with several concrete models.

We show that it is possible to equate the intensity reduction of a light wave caused by weak absorption with a geometrical reduction in intensity caused by a “transverse” conformal transformation of the spacetime metric in which the wave travels. We are consequently able to modify Gordon’s optical metric to account for electromagnetic properties of ponderable material whose properties include both refraction and absorption. Unlike refraction alone, however, including absorption requires a modification of the optical metric that depends on the eikonal of the wave itself. We derive the distance-redshift relation from the modified optical metric for Friedman-Lemaître-Robertson-Walker spacetimes whose cosmic fluid has associated refraction and absorption coefficients. We then fit the current supernovae data and provide an alternate explanation (other than dark energy) of the apparent acceleration of the Universe.

We apply a type of background independent “polymer” quantization to a free scalar field in a flat spacetime. Using semiclassical states, we find an effective wave equation that is both nonlinear and Lorentz invariance violating. We solve this equation perturbatively for several cases of physical interest, and show that polymer corrections to solutions of the Klein-Gordon equation depend on the amplitude of the field. This leads to an effective dispersion relation that depends on the amplitude, frequency, and shape of the wave packet, and is hence distinct from other modified dispersion relations found in the literature. We also demonstrate that polymer effects tend to accumulate with time for plane-symmetric waveforms. We conclude by discussing the possibility of measuring deviations from the Klein-Gordon equation in particle accelerators or astrophysical observations.

In this note we derive the slow-roll and rapid-roll conditions for the minimally and nonminimally coupled spacelike vector fields. The function $f(B^2)$ represents the nonminimal coupling effect between vector fields and gravity, the $f=0$ case is the minimal coupling case. For a clear comparison with the scalar field, we define a new function $F=\pm B^2/12+f(B^2)$, where $B^2=A_{\mu }{A}^{\mu }$, $A_{\mu }$ is the “comoving” vector field. With reference to the slow-roll and rapid-roll conditions, we find the small-field model is more suitable than the large-field model in the minimally coupled vector field case. As a nonminimal coupling example, the $F=0$ case just has the same slow-roll conditions as the scalar fields.