We have measured the $\alpha$ parameter of the ${\Omega }^{-}\to \Lambda K^{-}$ decay using data collected with the HyperCP spectrometer during the 1997 fixed-target run at Fermilab. Analyzing a sample of $0.96\times {10}^6$ ${\Omega }^{-}\to \Lambda K^{-}$, $\Lambda \to p{\pi }^{-}$ decays, we obtain ${\alpha }_{\Omega }{\alpha }_{\Lambda }=[1.33\pm 0.33(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.52(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})]\times {10}^{-2}$. With the accepted value of ${\alpha }_{\Lambda }$, ${\alpha }_{\Omega }$ is found to be $[2.07\pm 0.51(\mathrm{s}\mathrm{t}\mathrm{a}\mathrm{t})\pm 0.81(\mathrm{s}\mathrm{y}\mathrm{s}\mathrm{t})]\times {10}^{-2}$.

Five-dimensional field theories compactified on an $S^1/{\mathbb{Z}}_2$ orbifold naturally include local brane kinetic terms at the orbifold fixed points at the tree as well as the quantum level. We study the quantization of these theories before the Kaluza-Klein reduction and derive the relevant Ward and Slavnov-Taylor identities that result from the underlying gauge and Becchi-Rouet-Stora symmetries of the theory. With the help of these identities, we obtain a generalization of the equivalence theorem, where the known high-energy equivalence relation between the longitudinal Kaluza-Klein gauge modes and their respective would-be Goldstone bosons is extended to consistently include the energetically suppressed terms in the high-energy scatterings. Demanding perturbative unitarity, we compute upper limits on the number of the Kaluza-Klein modes. We find that these limits weakly depend on the size of the brane kinetic terms.

We present a symbolic method for organizing the representation theory of one-dimensional superalgebras. This relies on special objects, which we have called adinkra symbols, which supply tangible geometric forms to the still-emerging mathematical basis underlying supersymmetry.

It is shown how grand unification can occur in models which are partly supersymmetric. The particle states which are composite do not contribute to the running of gauge couplings above the compositeness scale, while the elementary states contribute the usual large logarithms. This introduces a new differential running contribution to the gauge couplings from partly composite SU(5) matter multiplets. In particular, for partly supersymmetric models, the incomplete SU(5) elementary matter multiplets restore gauge coupling unification even though the usual elementary gaugino and Higgsino contributions need not be present.

We present a scenario where brane inflation arises more generically. We start with D3 and anti-D3-branes at the infrared ends of two different throats. This setup is a natural consequence of the assumption that in the beginning we have a multithroat string compactification with many wandering anti-D3-branes. A long period of inflation is triggered when D3-branes slowly exit the highly warped infrared region, under a potential generically arising from the moduli stabilization. In this scenario, the usual slow-roll conditions are not required, and a large warping is allowed to incorporate the Randall-Sundrum model.

We analyze the role of final state interactions (FSI) in decay of the lightest exotic meson, with $J^{PC}=1^{-+}{\pi }_1$. We use the relativistic Lippmann-Schwinger equation for two coupled $\pi b_1$ and $\pi \rho$ channels. The first one is the predicted dominant decay mode of the ${\pi }_1$, whereas in the other a narrow ${\pi }_1(1600)$ exotic signal has been reported by the E852 collaboration. The FSI potential is constructed, based on the $\omega$ meson exchange between the two channels. We find that this process introduces corrections to the ${\pi }_1$ widths of the order of only a few MeV. Therefore, we conclude that a substantial $\pi \rho$ mode cannot be generated through level mixing.

We consider a $(2+1)$-dimensional $\mathrm{S}\mathrm{U}(N)$ lattice gauge theory in an axial gauge with the link field $U_1$ set equal to one. The term in the Hamiltonian containing the square of the electric field in the $1$-direction is nonlocal. Despite this nonlocality, we show that weak-coupling perturbation theory in this term gives a finite vacuum-energy density to second order, and suggest that this property holds to all orders. Heavy quarks are confined, the spectrum is gapped, and the spacelike Wilson loop has area decay.

Inspired by the exotic measurements on the $CP$ asymmetry in $B\to \varphi K_s$, we study a new diagram in supersymmetric models which can make the difference $\sin 2{\varphi }_1^{\mathrm{e}\mathrm{f}\mathrm{f}}(J/\Psi K_s)-\sin 2{\varphi }_1^{\mathrm{e}\mathrm{f}\mathrm{f}}(\varphi K_s)$ to be $20-50\%$ after satisfying the constraint from $b\to s\gamma$. We also find that the direct $CP$ asymmetry of $b\to s\gamma$ could be $\sim 10\%$ and testable at $B$ factories.

Within Ginzburg-Landau theory, we study the structure of a magnetic vortex in color-flavor locked quark matter. This vortex is characterized by winding of the $SU(3)$ phase in color-flavor space, as well as by the presence of a color-flavor unlocked condensate in the core. We estimate the upper and lower critical fields and the critical Ginzburg-Landau parameter that distinguishes between type I and type II superconductors.

Neutrino scattering on nucleons in the regime of deeply virtual kinematics is studied both in the charged and the neutral electroweak sectors using a formalism developed by Blümlein, Robaschik, Geyer, and collaborators for the analysis of the virtual Compton amplitude in the generalized Bjorken region. We discuss the structure of the leading twist amplitudes of the process.

This paper gives a new, simple and concise derivation of brane actions and brane dynamics in general relativity and in Einstein-Gauss-Bonnet gravity. We present a unified treatment, applicable to timelike surface layers and spacelike transition layers, and including consideration of the more difficult lightlike case.

Studying the Yang-Mills field and the gravitational field in class A Bianchi spacetimes, we find that chaotic behavior appears in the late phase (the asymptotic future). In this phase, the Yang-Mills field behaves as that in Minkowski spacetime, in which we can understand it by a potential picture, except for types VIII and IX. At the same time, in the initial phase (near the initial singularity), we numerically find that the behavior seems to approach the Kasner solution. However, we show that the Kasner circle is unstable and the Kasner solution is not an attractor. From an analysis of stability and numerical simulation, we find a Mixmaster-like behavior in Bianchi I spacetime. Although this result may provide a counterexample to the Belinskii, Khalatnikov, and Lifshitz (BKL) conjecture, we show that the BKL conjecture is still valid in Bianchi IX spacetime. We also analyze a multiplicative effect of two types of chaos, that is, chaos with the Yang-Mills field and that in vacuum Bianchi IX spacetime. Two types of chaos seem to coexist in the initial phase. However, the effect due to the Yang-Mills field is much smaller than that of the curvature term.

In this paper we analyze the ground state of the heavy-quark $qqqG$ system using standard principles of quark confinement and massive constituent gluons as established in the center-vortex picture. The known string tension $K_F$ and approximately-known gluon mass $M$ lead to a precise specification of the long-range nonrelativistic part of the potential binding the gluon to the quarks with no undetermined phenomenological parameters, in the limit of large interquark separation $R$. Our major tool (also used earlier by Simonov) is the use of proper-time methods to describe gluon propagation within the quark system, along with some elementary group theory describing the gluon Wilson-line as a composite of colocated $q$ and $\overline{q}$ lines. We show that (aside from color-Coulomb and similar terms) the gluon potential energy in the presence of quarks is accurately described (for small gluon fluctuations) via attaching these three strings to the gluon, which in equilibrium sits at the Steiner point of the Y-shaped string network joining the three quarks. The gluon undergoes small harmonic fluctuations that slightly stretch these strings and quasiconfine the gluon to the neighborhood of the Steiner point. To describe nonrelativistic ground-state gluonic fluctuations at large $R$ we use the Schrödinger equation, ignoring mixing with $l=2$ states. Available lattice data and real-world hybrids require consideration of $R$ values small enough for significant relativistic corrections, which we apply using a variational principle for the relativistic harmonic-oscillator. We also consider the role of color-Coulomb contributions. In terms of interquark separations $R$, we find leading nonrelativistic large-$R$ terms in the gluon excitation energy of the form $\epsilon (R)\to M+\xi [K_F/(MR){]}^{1/2}-\zeta {\alpha }_c/R$ where $\xi ,\zeta$ are calculable numerical coefficients and ${\alpha }_c\simeq$ 0.15 is the color-Coulomb $q\overline{q}$ coupling. When the gluon is relativistic, $\epsilon \sim (K_F/R{)}^{1/3}$. We get an acceptable fit to lattice data with $M=500$ MeV. Although we do not consider it in full detail, we show that in the $q\overline{q}G$ hybrid the gluon is a bead that can slide without friction on a string joining the $q$ and $\overline{q}$. We comment briefly on the significance of our findings to fluctuations of the minimal surface, a subject difficult to understand from the point of view of center vortices.

We compare the lattice results on QCD phase diagram for two and three flavors with the hadron resonance gas model (HRGM) calculations. Lines of constant energy density $ϵ$ have been determined at different baryo-chemical potentials ${\mu }_B$. For the strangeness chemical potentials ${\mu }_S$, we use two models. In one model, we explicitly set ${\mu }_S=0$ for all temperatures and baryo-chemical potentials. This assignment is used in lattice calculations. In the other model, ${\mu }_S$ is calculated in dependence on $T$ and ${\mu }_B$ according to the condition of vanishing strangeness. We also derive an analytical expression for the dependence of $T_c$ on ${\mu }_B/T$ by applying Taylor expansion of $ϵ$. In both cases, we compare HRGM results on $T_c-{\mu }_B$ diagram with the lattice calculations. The agreement is excellent, especially when the trigonometric function of $ϵ$ is truncated up to the same order as done in lattice simulations. For studying the efficiency of the truncated Taylor expansion, we calculate the radius of convergence. For zero- and second-order radii, the agreement with lattice is convincing. Furthermore, we make predictions for QCD phase diagram for nontruncated expressions and physical masses. These predictions are to be confirmed by heavy-ion experiments and future lattice calculations with very small lattice spacing and physical quark masses.

Using data recorded by the CLEO III detector at the Cornell electron storage ring (CESR), we have made measurements of some properties of the ${\Sigma }_c^{*++}$ and ${\Sigma }_c^{*0}$ charmed baryons. In particular: $\Gamma ({\Sigma }_c^{*++})={14.4}_{-1.5}^{+1.6}\pm 1.4\mathrm{M}\mathrm{e}\mathrm{V}$, $M({\Sigma }_c^{*++})-M({\Lambda }_c^{+})=231.5\pm 0.4\pm 0.3\mathrm{M}\mathrm{e}\mathrm{V}$, $\Gamma ({\Sigma }_c^{*0})={16.6}_{-1.7}^{+1.9}\pm 1.4\mathrm{M}\mathrm{e}\mathrm{V}$,$M({\Sigma }_c^{*0})-M({\Lambda }_c^{+})=231.4\pm 0.5\pm 0.3\mathrm{M}\mathrm{e}\mathrm{V}$.

We discuss how the propagation of electromagnetic fields described by a general two-parameter Lagrangian, which contains the Euler-Heisenberg effective Lagrangian and the Born-Infeld Lagrangian as particular cases, is affected by a pair of parallel plates that impose boundary conditions in the quantized field. We consider three differents setups, namely: (i) two perfectly conducting plates; (ii) two infinitely permeable plates and (iii) a pair of plates in which one of them is a perfect conductor and the other has an infinite magnetic permeability.

We propose and study a specific gauge theory dual of the smooth, nonsupersymmetric (and apparently stable) Janus solution of Type IIB supergravity found in Bak et al. [J. High Energy Phys. 05 (2003) 072]. The dual field theory is $\mathcal{N}=4$ SYM theory on two half-spaces separated by a planar interface with different coupling constants in each half-space. We assume that the position dependent coupling multiplies the operator ${\mathcal{L}}^{\prime }$ which is the fourth descendent of the primary $\mathrm{T}\mathrm{r}{X}^{\{I}{X}^{J\}}$ and closely related to the $\mathcal{N}=4$ Lagrangian density. At the classical level supersymmetry is broken explicitly, but $SO(3,2)$ conformal symmetry is preserved. We use conformal perturbation theory to study various correlation functions to first and second order in the discontinuity of $g_{YM}^2$, confirming quantum level conformal symmetry. Certain quantities such as the vacuum expectation value $⟨{\mathcal{L}}^{\prime }⟩$ are protected to all orders in $g_{YM}^{2}N$, and we find perfect agreement between the weak coupling value in the gauge theory and the strong coupling gravity result. $SO(3,2)$ symmetry requires vanishing vacuum energy, $⟨T_{\mu \nu }⟩=0$, and this is confirmed in first order in the discontinuity.

For bouncing cosmologies such as the ekpyrotic/cyclic scenarios we show that it is possible to make predictions for density perturbations which are independent of the details of the bouncing phase. This can be achieved, as in inflationary cosmology, thanks to the existence of a dynamical attractor, which makes local observables equal to the unperturbed solution up to exponentially small terms. Assuming that the physics of the bounce is not extremely sensitive to these corrections, perturbations can be evolved even at the nonlinear level. The resulting spectrum is not scale invariant and thus incompatible with experimental data. This can be explicitly shown in synchronous gauge where, contrary to what happens in the commonly used Newtonian gauge, all perturbations remain small going towards the bounce and the existence of the attractor is manifest.

In the standard model, energy release in dense stars is severely restricted by the Pauli exclusion principle. However, if, in regions of space of high fermion degeneracy, there is a phase transition to a state of exact supersymmetry (SUSY), fermion to sfermion pair conversion followed by radiative transitions to the Bose ground state could lead to a highly collimated gamma ray burst. We calculate the cross section for $ee\to \tilde{e}\tilde{e}$ in a SUSY bubble and construct a monte carlo for the resulting sfermion amplification by stimulated emission.

We investigate the nature of the near-threshold enhancement in the $p\overline{p}$ invariant-mass spectrum of the reaction $J/\Psi \to \gamma p\overline{p}$ reported recently by the BES Collaboration. Using the Jülich $N\overline{N}$ model we show that the mass dependence of the $p\overline{p}$ spectrum close to the threshold can be reproduced by the $S$-wave $p\overline{p}$ final state interaction in the isospin $I=1$ state within the Watson-Migdal approach. However, because of our poor knowledge of the $N\overline{N}$ interaction near-threshold and of the $J/\Psi \to \gamma p\overline{p}$ reaction mechanism and in view of the controversal situation in the decay $J/\Psi \to {\pi }^{0}p\overline{p}$, where no obvious signs of a $p\overline{p}$ final state interaction are seen, explanations other than final state interactions cannot be ruled out at the present stage.