The Jülich model for $\pi \pi$ scattering, based on an effective meson-meson Lagrangian, is applied to the analysis of the S-wave production amplitudes derived from the BNL E852 experiment ${\pi }^{-}\overrightarrow{p}{\pi }^0{\pi }^{0}n$ for a pion momentum of 18.3 GeV and the GAMS experiments performed at 38 GeV and 100 GeV. The unexpected strong dependence of the S-wave partial wave amplitude on the momentum transfer between the proton and neutron in the vicinity of the $f_0\mathrm{}\left(980\right)\mathrm{}$ resonance is explained in our analysis as an interference effect between the resonance and the nonresonant background.

We systematically study the minimal supersymmetric Pati-Salam theory, paying special attention to the unification constraints. We find that the $\mathrm{SU}{\mathrm{}\left(4\right)\mathrm{}}_c$ scale $M_c$ and the left-right scale $M_R$ lie in the range ${10}^{10}\mathrm{GeV}<M_c<{10}^{14}\mathrm{GeV},$ ${10}^3\mathrm{GeV}<M_R<{10}^{10}\mathrm{GeV}$ (with single-step breaking at ${10}^{10}\mathrm{GeV}),$ giving a potentially accessible scale of parity breaking. The theory includes the possibility of having doubly charged supermultiplets at the supersymmetry breaking scale, color octet states with a mass $\sim M_R^2{/M}_c,$ magnetic monopoles of intermediate mass that do not conflict with cosmology, and a “clean” (type I) form for the seesaw mechanism of the neutrino mass.

When the free energy density of QCD is expanded in a Taylor series in the chemical potential $\mu ,$ the coefficients are the nonlinear quark number susceptibilities. We show that these depend on the prescription for putting the chemical potential on the lattice, making all extrapolations in the chemical potential prescription dependent at finite lattice spacing. To put bounds on the prescription dependence, we investigate the magnitude of the nonlinear susceptibilities over a range of temperature, T, in QCD with two degenerate flavors of light dynamical quarks at lattice spacing $1/4T.$ The prescription dependence is removed in quenched QCD through a continuum extrapolation, and the dependence of the pressure P on $\mu$ is obtained.

Calculation of the moments of generalized parton distributions in lattice QCD requires more powerful techniques than those previously used to calculate the moments of structure functions. Hence, we present a novel approach that exploits the full information content from a given lattice configuration by measuring an overdetermined set of lattice observables to provide maximal statistical constraints on the generalized form factors at a given virtuality t. In an exploratory investigation using unquenched QCD configurations at intermediate sea quark masses, we demonstrate that our new technique is superior to conventional methods and leads to reliable numerical signals for the $n=2\mathrm{}$ flavor singlet generalized form factors up to $3{\mathrm{GeV}}^2.$ The contribution from connected diagrams in the flavor singlet sector to the total quark angular momentum is measured to an accuracy of the order of 1%.

We analyze neutrinoless double $\beta$ decay $(0\mathrm{}\nu \beta \beta$ decay) mediated by heavy particles from the standpoint of effective field theory. We show how symmetries of the $0\nu \beta \beta$-decay quark operators arising in a given particle physics model determine the form of the corresponding effective, hadronic operators. We classify the latter according to their symmetry transformation properties as well as the order at which they appear in a derivative expansion. We apply this framework to several particle physics models, including R-parity violating supersymmetry (RPV SUSY) and the left-right symmetric model (LRSM) with mixing and a right-handed Majorana neutrino. We show that, in general, the pion exchange contributions to $0\nu \beta \beta$ decay dominate over the short-range four-nucleon operators. This confirms previously published RPV SUSY results and allows us to derive new constraints on the masses in the LRSM. In particular, we show how a nonzero mixing angle $\zeta$ in the left-right symmetry model produces a new potentially dominant contribution to $0\nu \beta \beta$ decay that substantially modifies previous limits on the masses of the right-handed neutrino and boson stemming from constraints from $0\nu \beta \beta$ decay and vacuum stability requirements.

In magnetized plasmas gravitational and electromagnetic waves may interact coherently and exchange energy between themselves and with plasma flows. We derive the wave interaction equations for these processes in the case of waves propagating perpendicular or parallel to the plasma background magnetic field. In the latter case, the electromagnetic waves are taken to be circularly polarized waves of arbitrary amplitude. We allow for a background drift flow of the plasma components which increases the number of possible evolution scenarios. The interaction equations are solved analytically, and the characteristic time scales for conversion between gravitational and electromagnetic waves are found. In particular, it is shown that in the presence of a drift flow there are explosive instabilities resulting in the generation of gravitational and electromagnetic waves. Conversely, we show that energetic waves can interact to accelerate particles and thereby produce a drift flow. The relevance of these results for astrophysical and cosmological plasmas is discussed.

A regular bouncing universe is obtained in the context of a dilaton-gravity brane world scenario. The scale factor starts in a contracting inflationary phase both in the Einstein and in the string frame; it then undergoes a bounce (due to interaction with the bulk Weyl tensor), and subsequently enters into a decelerated expanding era. This graceful exit is obtained at low curvature and low coupling, and without violating the null energy condition.

We study theoretical and experimental constraints on electroweak theories including a new color-singlet and electrically neutral gauge boson. We first note that the electric charges of the observed fermions imply that any such $Z^{\prime }$ boson may be described by a gauge theory in which the Abelian gauge groups are the usual hypercharge along with another $U\left(1\right)\mathrm{}$ component in a kinetic-diagonal basis. Assuming that the observed quarks and leptons have generation-independent $U\left(1\right)\mathrm{}$ charges, and that no new fermions couple to the standard model gauge bosons, we find that their $U\left(1\right)\mathrm{}$ charges form a two-parameter family consistent with anomaly cancellation and viable fermion masses, provided there are at least three right-handed neutrinos. We then derive bounds on the $Z^{\prime }$ mass and couplings imposed by direct production and Z-pole measurements. For generic charge assignments and a gauge coupling of electromagnetic strength, the strongest lower bound on the $Z^{\prime }$ mass comes from Z-pole measurements, and is of the order of 1 TeV. If the new $U\left(1\right)\mathrm{}$ charges are proportional to $B-L,$ however, there is no tree-level mixing between the Z and $Z^{\prime },$ and the best bounds come from the absence of direct production at CERN LEP II and the Fermilab Tevatron. If the $U\left(1\right)\mathrm{}$ gauge coupling is one or two orders of magnitude below the electromagnetic one, these bounds are satisfied for most values of the $Z^{\prime }$ mass.

Path integral Monte Carlo simulations have been performed for U(1) lattice gauge theory in 2+1 dimensions on anisotropic lattices. We extract the static quark potential, the string tension and the low-lying “glueball” spectrum. The Euclidean string tension and mass gap decrease exponentially at weak coupling in excellent agreement with the predictions of Polyakov and Göpfert and Mack, but their magnitudes are five times bigger than predicted. Extrapolations are made to the extreme anisotropic or Hamiltonian limit, and comparisons are made with previous estimates obtained in the Hamiltonian formulation.

Inclusive and exclusive B decays into the ${\eta }^{\prime }$ meson plus others are investigated in a model based on the QCD anomaly. The invariant mass distribution is discussed. A constraint on the effective coupling is obtained from data on the exclusive decay modes. The branching ratio of $J/\overrightarrow{\psi }{\eta }^{\prime }\eta \gamma$ is predicted to be as large as $5.4\times {10}^{-5},$ which can be tested in the forthcoming CLEO c experiments.

The first law of black hole mechanics is derived from the Einstein-Maxwell Lagrangian by comparing two infinitesimally nearby stationary black holes. With similar arguments, the first law of black hole mechanics in Einstein-Yang-Mills theory is also derived.

Starting from a self-dual formulation of gravity, we obtain a noncommutative theory of pure Einstein theory in four dimensions. In order to do that, we use the Seiberg-Witten map. A procedure is outlined that allows one to find the solution of the noncommutative torsion constraint through the vanishing of the commutative one. Finally, the noncommutative corrections to the action are computed up to second order.

In models with large extra dimensions, particle collisions with a center-of-mass energy larger than the fundamental gravitational scale can generate nonperturbative gravitational objects. Since cosmic rays have been observed with energies above ${10}^8\mathrm{TeV},$ gravitational effects in the TeV energy range can, in principle, be observed by ultrahigh energy cosmic ray detectors. We consider the interaction of ultrahigh energy neutrinos in the atmosphere and compare extensive air showers from TeV black hole formation and fragmentation with standard model processes. Departures from the standard model predictions arise in the interaction cross sections and in the multiplicity of secondary particles. Large theoretical uncertainties in the black hole cross section weaken attempts to constrain TeV gravity based solely on differences between predicted and observed event rates. The large multiplicity of secondaries in black hole fragmentation enhances the detectability of TeV gravity effects. We simulate TeV black hole air showers using PYTHIA and AIRES, and find that black-hole–induced air showers are quite distinct from standard model air showers. However, the limited amount of information registered by realistic detectors together with large air shower fluctuations limit in practice the ability to distinguish TeV gravity events from standard model events in a shower by shower case. We discuss possible strategies to optimize the detectability of black hole events and propose a few unique signatures that may allow future high statistics detectors to separate black hole from standard model events.

We propose a new means for a quick and efficient acceleration of protons and/or electrons in relativistic bulk flows. The maximum attainable particle energies are limited either by radiative losses or by the condition of confinement in the magnetic field. The new mechanism takes advantage of a conversion of particles from the charged state (protons, electrons or positrons) into a neutral state (neutrons or photons) and back. In most cases, the conversion is photon induced and requires the presence of intense radiation fields, but under special circumstances the converter acceleration mechanism may operate via other charge-changing reactions, for example, inelastic nucleon-nucleon collisions. As in the traditional, “stochastic” (or diffusive) acceleration models, the acceleration cycle in the proposed scenario consists of the escape of particles from the relativistic flow followed by their return back after deflection from the ambient magnetic field. The difference is that the charge-changing reactions, which occur during the cycle, allow accelerated particles to increase their energies in each cycle by a factor much larger than 2 and usually roughly equal to the bulk Lorentz factor squared. The emerging spectra of accelerated particles can be very hard and their maximum energy in some cases is larger than in the standard mechanism. This significantly reduces the required energy budget of the sources of the highest-energy particles observed in cosmic rays. The proposed acceleration mechanism has a distinctive feature—it unavoidably creates neutral beams, consisting of photons, neutrinos, or neutrons, whose beam pattern may be much broader than the inverse Lorentz factor of the relativistic flow. Also, the new mechanism may serve as an efficient means of transferring the energy of bulk motion to gamma radiation and, if the accelerated particles are nucleons, inevitably produces high-energy neutrinos at a relative efficiency approaching $\gtrsim 50\%.$

We theoretically analyze the quantum noise of signal-recycled laser interferometric gravitational-wave detectors with additional input and output optics, namely, frequency-dependent squeezing of the vacuum state of light entering the dark port and frequency-dependent homodyne detection. We combine the work of Buonanno and Chen on the quantum noise of signal-recycled interferometers with ordinary input and output optics, and the work of Kimble et al. on frequency-dependent input and output optics with conventional interferometers. Analytical formulas for the optimal input and output frequency dependencies are obtained. It is shown that injecting squeezed light with the optimal frequency-dependent squeezing angle into the dark port yields an improvement in the noise spectral density by a factor of $e^{-2r}$ (in power) over the entire squeezing bandwidth, where r is the squeezing parameter. It is further shown that a frequency-dependent (variational) homodyne readout leads to an additional increase in sensitivity which is significant in the wings of the doubly resonant structure. The optimal variational input squeezing in the case of an ordinary output homodyne detection is shown to be realizable by applying two optical filters on a frequency-independent squeezed vacuum. Throughout this paper, we take as an example the signal-recycled topology currently being completed at the GEO 600 site. However, theoretical results obtained here are also applicable to the proposed topology of the Advanced LIGO.

Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein’s equations in harmonic coordinates to show that it is well posed for homogeneous boundary data and for boundary data that is small in a linearized sense. The method is implemented as a nonlinear evolution code, which satisfies convergence tests in the nonlinear regime and is stable in the weak field regime. A linearized version has been stably matched to a characteristic code to compute the gravitational wave form radiated to infinity.

We study the nonequilibrium dynamics of the $\mathrm{O}\mathrm{}\left(N\right)\mathrm{}$ model in classical and quantum field theory in 1+1 dimensions, for $N>\mathrm{}1.\mathrm{}$ We compare numerical results obtained using the Hartree approximation and two next to leading order approximations: the bare vertex approximation and the two-particle irreducible $1/N$ expansion. The latter approximations differ through terms of order $g^2,$ where g is the scaled coupling constant, $g=\lambda /N.\mathrm{}$ In this paper we investigate the statement regarding the convergence with respect to g. The differences between these two approximation schemes are computed and found to be already small for relatively small values of N, when $\lambda$ is fixed.

We analyze the chargino contribution to the recently measured $\mathrm{CP}$ asymmetry in the $\overrightarrow{B}\phi K_s$ decay. Using the mass insertion approximation in the context of a left-right supersymmetric model, we give complete analytical expressions for the contributions to the direct and mixing $\mathrm{CP}$ asymmetry. A numerical analysis indicates that the flavor and $\mathrm{CP}$ violations in the up squark mass matrix can consistently explain the direct and mixing $\mathrm{CP}$ asymmetry over a large region of the parameter space.

We show how to compute chiral logarithms that take into account both the $\mathcal{O}{(a}^2)$ taste-symmetry breaking of staggered fermions and the fourth-root trick that produces one taste per flavor. The calculation starts from the Lee-Sharpe Lagrangian generalized to multiple flavors. An error in a previous treatment by one of us is explained and corrected. The one loop chiral logarithm corrections to the pion and kaon masses in the full (unquenched), partially quenched, and quenched cases are computed as examples.

We consider rare radiative B decays such as $\overline{B}\to K^{*}\gamma$ or $\overline{B}\to \rho \gamma$ in soft-collinear effective theory (SCET) and show that the decay amplitudes are factorized to all orders in ${\alpha }_s$ and at leading order in ${\Lambda }_{\mathrm{QCD}}{/m}_b.$ By employing two-step matching, we classify the operators for radiative B decays in powers of a small parameter $\lambda \left(\sim \sqrt{{\Lambda }_{\mathrm{QCD}}{/m}_b}\right)$ and obtain the relevant operators to order $\lambda$ in ${\mathrm{SCET}}_{\mathrm{I}}.$ These operators are constructed with or without spectator quarks including the four-quark operators contributing to annihilation and W-exchange channels. And we employ ${\mathrm{SCET}}_{\mathrm{II}}$ where the small parameter becomes of order ${\Lambda }_{\mathrm{QCD}}{/m}_b,$ and evolve the operators in order to compute the decay amplitudes for rare radiative decays in soft-collinear effective theory. We show explicitly that the contributions from the annihilation channels and the W-exchange channels vanish at leading order in SCET. We present the factorized result for the decay amplitudes in rare radiative B decays at leading order in SCET and at next-to-leading order in ${\alpha }_s.$