We study the mixing of neutral particles in quantum field theory: the neutral boson field and Majorana field are treated in the case of mixing among two generations. We derive the orthogonality of flavor and mass representations and show how to consistently calculate oscillation formulas, which agree with previous results for charged fields and exhibit corrections with respect to the usual quantum mechanical expressions.

We apply to the ${\mathrm{CP}}^9$ model two recently proposed numerical techniques for the simulation of systems with a $\theta$ term. The algorithms, successfully tested in the strong coupling limit, are applied to the weak coupling region. The results agree and errors have been evaluated and are at the % level. The results scale well with the renormalization group equation and show that, for ${\mathrm{CP}}^9$ in the presence of a $\theta$ term, CP symmetry is spontaneously broken at $\theta =\pi$ in the continuum limit.

We study the phenomenology of a 5D ${\mathrm{SU}\left(3\right)\mathrm{}}_W$ model on an $S_1{/(Z}_2\times Z_2^{\prime })$ orbifold in which the minimal scalar sector plays the essential role of radiatively generating neutrino Majorana masses without the benefit of right-handed singlets. We carefully examine how the exotic scalars affect the renormalization group equations for the gauge couplings and the 5D ${\mathrm{SU}\left(3\right)\mathrm{}}_W$ unification. We find that the compactification scale of the extra dimension is in the range of $1/R\sim 1.5–5\mathrm{TeV}.$ The possibility of the existence of relatively low mass Kaluza-Klein excitations makes the phenomenology of the near term of interest. Some possible bilepton signatures can be searched for in future colliders and in neutrino scattering experiments with intense neutrino beams. The low energy constraints from muon physics and the lepton number violating decay process induced by the bilepton are also discussed. These constraints can provide new information about the structure of Yukawa couplings which might be useful for future model building.

We present an extension of the standard model to the local gauge group ${\mathrm{SU}\left(3\right)\mathrm{}}_c\otimes {\mathrm{SU}\left(4\right)\mathrm{}}_L\otimes {U\left(1\right)\mathrm{}}_X$ with a family nonuniversal treatment and anomalies canceled among the three families in a nontrivial fashion. The mass scales, the gauge boson masses, and the masses for the spin 1/2 particles in the model are analyzed. The neutral currents coupled to all neutral vector bosons in the model are studied, and particular values of the parameters are used in order to simplify the mixing between the three neutral currents present in the theory, mixing which is further constrained by experimental results from the CERN LEP, SLAC Linear Collider, and atomic parity violation.

We consider extra dimensional gauge theories on an interval. We first review the derivation of the consistent boundary conditions (BC’s) from the action principle. These BC’s include choices that give rise to the breaking of the gauge symmetries. The boundary conditions could be chosen to coincide with those commonly applied in orbifold theories, but there are many more possibilities. To investigate the nature of gauge symmetry breaking via BC’s we calculate the elastic scattering amplitudes for longitudinal gauge bosons. We find that using a consistent set of BC’s the terms in these amplitudes that explicitly grow with energy always cancel without having to introduce any additional scalar degree of freedom, but rather by the exchange of Kaluza-Klein (KK) gauge bosons. This suggests that perhaps the standard model Higgs boson could be completely eliminated in favor of some KK towers of gauge fields. We show that from the low-energy effective theory perspective this seems to be indeed possible. We display an extra dimensional toy model, where BC’s introduce a symmetry breaking pattern and mass spectrum that resembles that in the standard model.

We point out that the chiral Lagrangian describing pseudo Goldstone bosons in partially quenched QCD has one more four-derivative operator than that for unquenched QCD with three flavors. The new operator can be chosen to vanish in the unquenched sector of the partially quenched theory. Its contributions begin at next-to-leading order in the chiral expansion. At this order it contributes only to unphysical scattering processes, and we work out some examples. Its contributions to pseudo Goldstone properties begin at next-to-next-to-leading order, and we determine their form. We also determine all the zero and two derivative operators in the ${O(p}^6)$ partially quenched chiral Lagrangian, finding three more than in unquenched QCD, and use these to give the general form of the analytic next-to-next-to-leading order contributions to the pseudo Goldstone mass and decay constant. We discuss the general implications of such additional operators for the utility of partially quenched simulations.

We present a measurement of the average multiplicity of φ mesons in $B^0,$ $B^0,$ and $B^{\pm }$ meson decays. Using 17.6 ${\mathrm{fb}}^{\mathrm{-}1}$ of data taken at the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ resonance by the BABAR detector at the PEP-II $e^{+}{e}^{-}$ storage ring at the Stanford Linear Accelerator Center, we reconstruct φ mesons in the $K^{+}{K}^{-}$ decay mode and measure $\mathcal{B}\left(\overrightarrow{B}\phi X\right)=(3.41\mathrm{}\pm 0.06\pm 0.12)\%.$ This is significantly more precise than any previous measurement.

A superfield formulation is presented of the central charge anomaly in quantum corrections to solitons in two-dimensional theories with $N=1\mathrm{}$ supersymmetry. Extensive use is made of the superfield supercurrent that places the supercurrent $J_{\alpha }^{\mu },$ energy-momentum tensor ${\Theta }^{\mu \nu },$ and topological current ${\zeta }^{\mu }$ in a supermultiplet to study the structure of supersymmetry and related superconformal symmetry in the presence of solitons. It is shown that the supermultiplet structure of ${(J}_{\alpha }^{\mu },{\Theta }^{\mu \nu },{\zeta }^{\mu })$ is kept exact while the topological current ${\zeta }^{\mu }$ acquires a quantum modification through the superconformal anomaly. In addition, the one-loop superfield effective action is explicitly constructed to verify the BPS saturation of the soliton spectrum as well as the effect of the anomaly.

Motivated by phenomenological models of hidden local symmetries and the ideas of dimensional deconstruction and gauge/gravity duality, we consider the model of an “open moose.” Such a model has a large number K of hidden gauge groups as well as a global chiral symmetry. In the continuum limit $\overrightarrow{K}\infty$ the model becomes a 4+1 dimensional theory of a gauge field propagating in a dilaton background and an external space-time metric with two boundaries. We show that the model reproduces several well known phenomenological and theoretical aspects of low-energy hadron dynamics, such as vector meson dominance. We derive the general formulas for the mass spectrum, the decay constants of the pion and vector mesons, and the couplings between mesons. We then consider two simple realizations, one with a flat metric and another with a “cosh” metric interpolating between two anti–de Sitter (AdS) boundaries. For the pion form factor, the single pole ρ-meson dominance is exact in the latter case and approximate in the former case. We discover that an AdS/conformal field theory-like prescription emerges in the computation of current-current correlators. We speculate on the role of the model in the theory dual to QCD.

We discuss the evolution of cosmological tensor perturbations in the Randall-Sundrum model with one brane. In Gaussian normal coordinates the wave equation is nonseparable, so we use the near-brane limit to perform the separation and study the evolution of perturbations. Massive excitations, which may also mix, decay outside the horizon, which could lead to some novel cosmological signatures.

An analytic method is given for deriving the part of the retarded Green’s function ${v(x,x}^{\prime })$ that contributes to the tail term in the radiation reaction force felt by a particle coupled to a massless minimally coupled scalar field. The method gives an expansion of ${v(x,x}^{\prime })$ for small separations of the points ${x,x}^{\prime }$ valid for an arbitrary static spherically symmetric spacetime. It is obtained by using a WKB approximation for the Euclidean Green’s function for the massless minimally coupled scalar field and is equivalent to the DeWitt-Schwinger expansion for ${v(x,x}^{\prime }).\mathrm{}$ The first few terms in this expansion are displayed here for the case of Schwarzschild spacetime.

We explore the possibility that the dark energy is due to a potential of a scalar field and that the magnitude and the slope of this potential in our part of the Universe are largely determined by anthropic selection effects. We find that, in some models, the most probable values of the slope are very small, implying that the dark energy density stays constant to very high accuracy throughout cosmological evolution. In other models, however, the most probable values of the slope are such that the slow roll condition is only marginally satisfied, leading to a recollapse of the local universe on a time scale comparable to the lifetime of the Sun. In the latter case, the effective equation of state varies appreciably with the redshift, leading to a number of testable predictions.

Among the $O\left({\alpha }_s\tan \beta \right)$ contributions to the Wilson coefficients $C_7$ and $C_8,$ relevant for the decay $\overline{B}\to X_s\gamma ,$ those induced by two-loop diagrams with charged-Higgs-boson exchange and squark-gluino corrections are calculated in supersymmetric models at large $\tan \beta .$ The calculation of the corresponding Feynman integrals is exact, unlike in previous studies that are valid when the typical supersymmetric scale $M_{\mathrm{SUSY}}$ is sufficiently larger than the electroweak scale $m_{\mathrm{weak}}\left(\sim m_W{,m}_t\right)$ and the mass of the charged Higgs boson $m_{H^{\pm }}.$ Therefore, the results presented here can be used for any value of the various supersymmetric masses. These results are compared with those of an approximate calculation, already existing in the literature, that is at the zeroth order in the expansion parameter ${(m}_{\mathrm{weak}}^2{,m}_H^2{)/M}_{\mathrm{SUSY}}^2,$ and with the results of two new approximate calculations in which the first and second order in the same expansion parameter are retained, respectively. This comparison allows us to assess whether the results of these three approximate calculations can be extended beyond the range of validity for which they were derived, i.e., whether they can be used for $m_H\gtrsim M_{\mathrm{SUSY}}$ and/or $M_{\mathrm{SUSY}}\sim m_{\mathrm{weak}}.$ It is found that the zeroth-order approximation works well even for $m_H\gtrsim M_{\mathrm{SUSY}},$ provided $M_{\mathrm{SUSY}}^2\gg m_{\mathrm{weak}}^2.$ The inclusion of the higher-order terms improves the zeroth-order approximation for $m_H^2\ll M_{\mathrm{SUSY}}^2,$ but it worsens it for $m_H\gtrsim M_{\mathrm{SUSY}}.$

It is pointed out that the concepts and methods introduced by Bachelier and by Mandelbrot to finance and economics can be used to examine the fluctuations observed in high-energy hadron production processes. Theoretical arguments and experimental evidence are presented which show that the relative variations of hadron numbers between successive rapidity intervals are non-Gaussian stable random variables, which exhibit stationarity and scaling. The implications of the obtained results are discussed.

Using the CLEO III detector at CESR, we have measured the branching ratio of the decay ${\Xi }_c^0\to {\mathrm{pK}}^{-}{K}^{-}{\pi }^{+}$ relative to ${\Xi }_c^0\to {\Xi }^{-}{\pi }^{+}.$ We find $\mathcal{B}({\Xi }_c^0\to {\mathrm{pK}}^{-}{K}^{-}{\pi }^{+})/\mathcal{B}({\Xi }_c^0\to {\Xi }^{-}{\pi }^{+})=0.35\mathrm{}\pm 0.06\left(\mathrm{stat}\right)\pm 0.03\left(\mathrm{syst}\right).\mathrm{}$ In the resonant substructure of this mode, we find evidence for ${\Xi }_c^0$ decays to $p\overline{K^{*}}{\mathrm{}\left(892\right)\mathrm{}}^0{K}^{-},$ and measure $\mathcal{B}({\Xi }_c^0\to p\overline{K^{*}}{\mathrm{}\left(892\right)\mathrm{}}^0{K}^{-})\times \mathcal{B}(\overline{K^{*}}{\mathrm{}\left(892\right)\mathrm{}}^0\to K^{-}{\pi }^{+})/\mathcal{B}({\Xi }_c^0\to {\Xi }^{-}{\pi }^{+})=0.14\mathrm{}\pm 0.03\left(\mathrm{stat}\right)\pm 0.01\left(\mathrm{syst}\right)$ and $\mathcal{B}({\Xi }_c^0\to {\mathrm{pK}}^{-}{K}^{-}{\pi }^{+})/\mathcal{B}({\Xi }_c^0\to {\Xi }^{-}{\pi }^{+})=0.21\mathrm{}\pm 0.04\left(\mathrm{stat}\right)\pm 0.02\left(\mathrm{syst}\right)$ for the $\mathrm{n}\mathrm{o}\mathrm{n}-\overline{K^{*}}{\mathrm{}\left(892\right)\mathrm{}}^0{\Xi }_c^0\to {\mathrm{pK}}^{-}{K}^{-}{\pi }^{+}$ decays.

We offer a physicist’s proof that center-vortex theory requires the area in the (quenched) Wilson-loop area law to involve an extremal area. This means that, unlike in string-theory-inspired models of confining flux tubes, area-law dynamics is determined by integrating over Wilson loops only, not over surface fluctuations for a fixed loop. Fluctuations leading to perimeter-law corrections come from loop fluctuations as well as integration over finite-thickness center-vortex collective coordinates. In $d=3\mathrm{}$ (or $d=2+1)$ we exploit a contour form of the extremal area in isothermal (conformally flat metric on the surface) coordinates which is similar to $d=2\mathrm{}$ (or $d=1+1)$ QCD in many respects, except that there are both quartic and quadratic terms in the action. One major result is that at large angular momentum $\mathcal{l}$ in $d=3+1\mathrm{}$ the center-vortex extremal-area picture yields a linear Regge trajectory with a Regge slope–string tension product ${\alpha }^{\prime }{\mathrm{}\left(0\right)K}_F$ of $1/\left(2\pi \right),$ which is the canonical Veneziano or string value. In a curious effect traceable to retardation, the quark kinetic terms in the action vanish relative to area-law terms in the large-$\mathcal{l}$ limit, in which light-quark masses $\sim K_F^{1/2}$ are negligible. This corresponds to string-theoretic expectations, even though we emphasize that the extremal-area law is not a string theory quantum mechanically. We show how some quantum trajectory fluctuations as well as nonleading classical terms for finite mass yield corrections scaling with ${\mathcal{l}}^{-1/2}.$ We compare to old semiclassical calculations of relativistic (massless) $q\overline{q}$ bound states at large $\mathcal{l},$ which also yield asymptotically linear Regge trajectories, finding agreement with a naive string picture (classically, not quantum mechanically) and disagreement with an effective-propagator model. We show that contour forms of the area law can be expressed in terms of Abelian gauge potentials, and we relate this to old work of Comtet.

We develop a new approach to the Lagrangian description of the bubble wall dynamics in the nonlinear Klein-Gordon equation with a two-vacuum potential of general form having a small vacuum energy difference. The approach is based on an ordinary differential equation governing the motion of an arbitrary point of the wall in the second approximation in the vacuum energy difference and inverse bubble radius. The equation is model independent: the concrete shape of the potential affects the constants involved only. We give a detailed derivation of this equation and present the full scheme of our method. As examples, we find some wall solutions for the ${\phi }^3-{\phi }^4$ and ${\phi }^4-{\phi }^6$ potentials and compare them with solutions obtained by the direct numerical integration of the nonlinear Klein-Gordon equation.

We analyze the question of $U_{\star }\mathrm{}\left(1\right)\mathrm{}$ gauge invariance in a flat noncommutative space where the parameter of noncommutativity, ${\theta }^{\mu \nu }\mathrm{}\left(x\right),$ is a local function satisfying the Jacobi identity (and thereby leading to an associative Kontsevich product). We show that in this case both gauge transformations as well as the definitions of covariant derivatives have to be modified so as to have a gauge invariant action. We work out the gauge invariant actions for the matter fields in the fundamental and the adjoint representations up to order ${\theta }^2$ while we discuss the gauge invariant Maxwell theory up to order $\theta .$ We show that, despite the modifications in the gauge transformations, the covariant derivative, and the field strength, the Seiberg-Witten map continues to hold for this theory. In this theory, translations do not form a subgroup of the gauge transformations (unlike in the case when ${\theta }^{\mu \nu }$ is a constant) which is reflected in the stress tensor not being conserved.

In a two-dimensional toy model, motivated from five-dimensional heterotic M theory, we study the collision of scalar field kinks with boundaries. By numerical simulation of the full two-dimensional theory, we find that the kink is always inelastically reflected with a model-independent fraction of its kinetic energy converted into radiation. We show that the reflection can be analytically understood as a fluctuation around the scalar field vacuum. This picture suggests the possibility of spontaneous emission of kinks from the boundary due to small perturbations in the bulk. We verify this picture numerically by showing that the radiation emitted from the collision of an initial single kink eventually leads to a bulk populated by many kinks. Consequently, processes changing the boundary charges are practically unavoidable in this system. We speculate that the system has a universal final state consisting of a stack of kinks, their number being determined by the initial energy.

Gravitational waves in isotropic cosmologies were recently studied using the gauge-invariant approach of Ellis and Bruni. We now construct the linearized metric perturbations of the background Robertson-Walker space-time which reproduce the results obtained in that study. The analysis carried out here also facilitates an easy comparison with Bardeen.