We perform a QCD sum rule calculation to determine the mass and the parity of the lowest lying pentaquark state. We include operators up to dimension $d=13$ in the operator product expansion and the direct instanton contributions. We find evidence for a positive parity state. The contribution from operators of dimension $d>5$ is instrumental in determining the parity of the state and achieving the convergence of the sum rule.

We extend the noncommutative standard model based on the minimal $\mathrm{SU}(3)\times \mathrm{SU}(2)\times \mathrm{U}(1)$ gauge group to include the interaction of photon with neutrinos. We show that, in the gauge invariant manner, only the right-handed neutrino can directly couple to the photon. Consequently, we obtain the Feynman rule for the $\gamma \nu \overline{\nu }$-vertex which does not exist in the minimal extension of the noncommutative standard model (mNCSM). We calculate the amplitude for $\gamma \nu \to \gamma \nu$ in both the nonminimal noncommutative standard model (nmNCSM) and the extended version of mNCSM. The obtained cross section grows in the center of mass frame, respectively, as $({\theta }_{\mathrm{NC}}{)}^2{M}_Z^{-4}{E}^6$ and $({\theta }_{\mathrm{NC}}{)}^4{E}^6$ which can exceed the cross section for $\gamma \nu \to \gamma \gamma \nu$ and $\gamma \nu \to \gamma \nu$ in the high energy limit in the commutative space.

We describe a search for $\psi (3770)$ decay to two-body non-$D\overline{D}$ final states in $e^{+}{e}^{-}$ data produced by the CESR collider and analyzed with the CLEO-c detector. Vector-pseudoscalar production ${\rho }^0{\pi }^0$, ${\rho }^{+}{\pi }^{-}$, $\omega {\pi }^0$, $\varphi {\pi }^0$, $\rho \eta$, $\omega \eta$, $\varphi \eta$, $\rho {\eta }^{\prime }$, $\omega {\eta }^{\prime }$, $\varphi {\eta }^{\prime }$, $K^{*0}\overline{K^0}$, and $K^{*+}{K}^{-}$ is studied along with that of $b_1\pi$ ($b_1^0{\pi }^0$ and $b_1^{+}{\pi }^{-}$) and ${\pi }^{+}{\pi }^{-}{\pi }^0$. The largest amount of disagreement between the expected rate for $e^{+}{e}^{-}\to {\gamma }^{*}\to X$ and that for $e^{+}{e}^{-}\to X$ at $\sqrt{s}=3.773\mathrm{GeV}$ is found for $X=\varphi \eta$, at an excess cross section of $(2.4\pm 0.6)\mathrm{pb}$ [${\Gamma }_{\varphi \eta }^{\psi (3770)}=(7.4\pm 1.6)\mathrm{keV}$], and a suggestive suppression is seen for ${\pi }^{+}{\pi }^{-}{\pi }^0$ and $\rho \pi$. We conclude with form factor determinations for $\omega {\pi }^0$, $\rho \eta$, and $\rho {\eta }^{\prime }$.

Radiative corrections in systems near imperfectly reflecting boundaries are investigated. As an example, the self-energy of an unbound electron close to a single surface is calculated at one-loop level. The surface is modeled by a nondispersive dielectric half-space of a constant refractive index $n$. In contrast to previous, perfectly reflecting models, the evanescent modes in the optically thinner medium are taken into account and are found to play a physically very important role. The Feynman propagator of the photon field is determined and given in two alternative representations, which include the evanescent modes either as a separate contribution or through analytic continuation and deformation of the integration path for the normal component of the complex wave vector $\mathbf{k}$. The evaluation of the self-energy diagram encounters a number of problems that are specific to the boundary dependence and to the imperfect reflection at the boundary. These problems and methods for their resolution are discussed in depth.

The quantum deformation of the Poisson bracket is the Moyal bracket. We construct quantum deformation of the Dirac bracket for systems which admit global symplectic basis for constraint functions. Equivalently, it can be considered as an extension of the Moyal bracket to second-class constraints systems and to gauge-invariant systems which become second class when gauge-fixing conditions are imposed.

The decoherent histories approach to quantum theory is applied to a class of reparametrization-invariant models whose state is an energy eigenstate. A key step in this approach is the construction of class operators characterizing the questions of physical interest, such as the probability of the system entering a given region of configuration space without regard to time. In nonrelativistic quantum mechanics these class operators are given by time-ordered products of projection operators. But in reparametrization-invariant models, where there is no time, the construction of the class operators is more complicated, the main difficulty being to find operators which commute with the Hamiltonian constraint (and so respect the invariance of the theory). Here, inspired by classical considerations, we put forward a proposal for the construction of such class operators for a class of reparametrization-invariant systems. They consist of continuous infinite temporal products of Heisenberg picture projection operators. We investigate the consequences of this proposal in a number of simple models and also compare with the evolving constants method. The formalism developed here is ultimately aimed at cosmological models described by a Wheeler-DeWitt equation, but the specific features of such models are left to future papers.

We explicitly construct the metric of a Kerr black hole that is tidally perturbed by the external universe in the slow-motion approximation. This approximation assumes that the external universe changes slowly relative to the rotation rate of the hole, thus allowing the parameterization of the Newman-Penrose scalar ${\psi }_0$ by time-dependent electric and magnetic tidal tensors. This approximation, however, does not constrain how big the spin of the background hole can be and, in principle, the perturbed metric can model rapidly spinning holes. We first generate a potential by acting with a differential operator on ${\psi }_0$. From this potential we arrive at the metric perturbation by use of the Chrzanowski procedure in the ingoing radiation gauge. We provide explicit analytic formulas for this metric perturbation in Kerr coordinates, where the perturbation is finite at the horizon. This perturbation is parametrized by the mass and Kerr spin parameter of the background hole together with the electric and magnetic tidal tensors that describe the time evolution of the perturbation produced by the external universe. In order to make the metric accurate far away from the hole, these tidal tensors should be determined by asymptotically matching this metric to another one valid far from the hole. The tidally perturbed metric constructed here could be useful in initial data constructions to describe the metric near the horizons of a binary system of spinning holes. This perturbed metric could also be used to construct waveforms and study the absorption of mass and angular momentum by a Kerr black hole when external processes generate gravitational radiation.

The influence of higher-order terms in the Kähler potential of the supergravity $D$-term inflation model on the density perturbation is studied. We show that these terms can make the inflaton potential flatter, which lowers the energy scale of inflation under the COBE/WMAP normalization. As a result, the mass per unit length of cosmic strings, which are produced at the end of inflation, can be reduced to a harmless but detectable level without introducing a tiny Yukawa coupling. Our scenario can naturally be implemented in models with a low cutoff as in Type I or Type IIB orientifold models.

We consider supergravity models in which the lightest supersymmetric particle (LSP) is a stable gravitino. The next-to-lightest supersymmetric particle (NLSP) freezes out with its thermal relic density and then decays after $({10}^5–{10}^{10})\sec $, injecting high-energy photons into the cosmic plasma. These photons heat up the electron plasma which then thermalizes with the cosmic microwave background (CMB) via Compton scattering, bremsstrahlung and double-Compton scattering. Contrary to previous studies which assume instantaneous energy injection, we solve the full kinetic equation for the photon number density with a source term describing the decay of the NLSP. This source term is based on the requirement that the injected energy be almost instantaneously redistributed by Compton scattering, hence leading to a time-dependent chemical potential. We investigate the case of a stau NLSP and determine the constraints on the gravitino and stau masses from observations of the CMB spectrum by assuming that all gravitino LSPs come from stau NLSP decays. Unlike the analytical approximations, we find that there may be a stau mass below which the constraint from the CMB spectrum vanishes.

We consider a model with soft $CP$ violation which accommodates the $CP$ violation in the neutral kaons even if we assume that the Cabibbo-Kobayashi-Maskawa mixing matrix is real and the sources of $CP$ violation are three complex vacuum expectation values and a trilinear coupling in the scalar potential. We show that for some reasonable values of the masses and other parameters the model allows us to explain all the observed $CP$ violation processes in the $K^0$-${\overline{K}}^0$ system.

Models where supersymmetry (SUSY) is manifest only in a sector of the low-energy spectrum have been recently proposed as an alternative to the MSSM. In these models the electroweak scale is explained by a fine-tuning between different Higgs mass contributions (split-SUSY models), or by the localization of the Higgs sector in a point of an extra dimension where all the mass parameters are suppressed by the metric (partly-SUSY models). Therefore, the presence of a good dark matter candidate becomes the main motivation for (partial) low-energy SUSY. We study this issue in minimal frameworks where the higgsinos are the only light supersymmetric particles. Whereas in split-SUSY models the higgsino should have a mass around $1$ TeV, we show that in partly-SUSY models the lightest higgsino could also be found below $M_W$.

Lattice data on QCD thermodynamics, especially recent study of high order susceptibilities by UK-Bielefeld Collaboration, have provided valuable information about matter properties around and above the critical temperature $T_c$. In this work we tried to understand what physical picture would explain these numerical data. We found two scenarios which will do it: (i) a quark quasiparticle gas, with the effective mass which is strongly decreasing near the phase boundary into the quark-gluon plasma (QGP) phase; or (ii) a picture including baryons at $T>T_c$, with the mass rapidly increasing across the phase boundary toward QGP. We further provide several arguments in favor of the latter scenario, one of which is a natural continuity with the baryon gas picture at $T<T_c$.

We study the diffusion of heavy quarks in the quark gluon plasma using the Langevin equations of motion and estimate the contribution of the transport peak to the Euclidean current-current correlator. We show that the Euclidean correlator is remarkably insensitive to the heavy quark diffusion coefficient and give a physical interpretation of this result using the free streaming Boltzmann equation. However if the diffusion coefficient is smaller than $\sim 1/(\pi T)$, as favored by RHIC phenomenology, the transport contribution should be visible in the Euclidean correlator. We outline a procedure to isolate this contribution.

We present a study of the pentaquark system in quenched lattice QCD using diquark-diquark and kaon-nucleon local and smeared interpolating fields. We examine the volume dependence of the spectral weights of local correlators on lattices of size ${16}^3\times 32$, ${24}^3\times 32$, and ${32}^3\times 64$ at $\beta =6.0$. We find that a reliable evaluation of the volume dependence of the spectral weights requires accurate determination of the correlators at large time separations. Our main result from the spectral weight analysis in the pentaquark system is that within our variational basis and statistics we cannot exclude a pentaquark resonance. However, our data also do not allow a clear identification of a pentaquark state since only the spectral weights of the lowest state can be determined to sufficient accuracy to test for volume dependence. In the negative parity channel, the mass extracted for this state is very close to the kaon-nucleon threshold, whereas in the positive parity channel it is about 60% above.

We provide the analytic predictions for the flavor nonsinglet scalar correlator, which will enable determination of the scalar meson mass from the lattice scalar correlator. We consider simulations with $2+1$ staggered sea quarks and staggered or chiral valence quarks. At small $u/d$ masses the correlator is dominated by the bubble contribution, which is the intermediate state with two pseudoscalar mesons. We determine the bubble contribution within staggered and mixed chiral perturbation theory. Its effective mass is smaller than the mass of $\pi \eta$, which is the lightest intermediate state in proper $2+1$ QCD. The unphysical effective mass is a consequence of the taste breaking that makes possible the intermediate state with mass $2M_{\pi }$. We find that the scalar correlator can be negative in the simulations with mixed quark actions if the sea- and valence-quark masses are tuned by matching the pion masses $M_{\mathrm{val},\mathrm{val}}=M_{{\pi }_5}$.

We present a QCD sum rule analysis for the anticharmed pentaquark state with and without strangeness. While the sum rules for most of the currents are either nonconvergent or dominated by the $DN$ continuum, the one for the nonstrange pentaquark current composed of two diquarks and an antiquark is convergent and has a structure consistent with a positive-parity pentaquark state after subtracting out the $DN$ continuum contribution. Arguments are presented on the similarity between the result of the present analysis and that based on the constituent quark models, which predict a more stable pentaquark state when the antiquark is heavy.

Top quark pair production at proton-antiproton colliders is known to exhibit a forward-backward asymmetry due to higher-order QCD effects. We explore how this asymmetry might be studied at the Fermilab Tevatron, including how the asymmetry depends on the kinematics of extra hard partons. We consider results for top quark pair events with one and two additional hard jets. We further note that a similar asymmetry, correlated with the presence of jets, arises in specific models for parton showers in Monte Carlo simulations. We conclude that the measurement of this asymmetry at the Tevatron will be challenging, but important both for our understanding of QCD and for our efforts to model it.

Pioneering atmospheric muon neutrino experiments have demonstrated the near-maximal magnitude of the flavor mixing angle ${\theta }_{23}$. But the precise value of the deviation $D\equiv 1/2-{sin}^2{\theta }_{23}$ from maximality (if nonzero) needs to be known, being of great interest—especially to builders of neutrino mass and mixing models. We quantitatively investigate in a three-generation framework the feasibility of determining $D$ in a statistically significant manner from studies of the atmospheric ${\nu }_{\mu },{\overline{\nu }}_{\mu }$ survival probability including both vacuum oscillations and matter effects. We show how this determination will be sharpened by considering the up-down ratios of observed ${\nu }_{\mu }$- and ${\overline{\nu }}_{\mu }$-induced events and the differences of these ratios in specified energy and zenith angle bins. We consider 1 Megaton year of exposure to a magnetized iron calorimeter such as the proposed India-based Neutrino Observatory detector ICAL, taking into account both energy and zenith angle resolution functions. The sensitivity of such an exposure and the dependence of the determination of $D$ on the concerned oscillation parameters are discussed in detail. The vital use of matter effects in fixing the octant of ${\theta }_{23}$ is highlighted.

We present a simple formalism for the evaluation of the Casimir energy for two spheres and a sphere and a plane, in case of a scalar fluctuating field, valid at any separations. We compare the exact results with various approximation schemes and establish when such schemes become useful. The formalism can be easily extended to any number of spheres and/or planes in three or arbitrary dimensions, with a variety of boundary conditions or nonoverlapping potentials/nonideal reflectors.