The renormalized Dyson-Schwinger equation for the quark propagator is studied, in the Landau gauge, in a novel truncation which preserves multiplicative renormalizability. The renormalization constants are formally eliminated from the integral equations, and the running coupling explicitly enters the kernels of the new equations. To construct a truncation which preserves multiplicative renormalizability and reproduces the correct leading order perturbative behavior, nontrivial cancellations involving the full quark-gluon vertex are assumed in the quark self-energy loop. A model for the running coupling is introduced with an infrared fixed point in agreement with previous Dyson-Schwinger studies of the gauge sector, and with the correct logarithmic tail. Dynamical chiral symmetry breaking is investigated, and the generated quark mass is of the order of the extension of the infrared plateau of the coupling, and about three times larger than in the Abelian approximation, which violates multiplicative renormalizability. The generated scale is of the right size for hadronic phenomenology, without requiring an infrared enhancement of the running coupling.

We present a fast one dimensional hybrid method to efficiently simulate extensive air showers up to the highest observed energies. Based on precalculated pion showers and a bootstrap technique, our method predicts the average shower profile, the number of muons at detector level above several energy thresholds as well as the fluctuations of the electromagnetic and hadronic components of the shower. We study the main characteristics of proton-induced air showers up to ultra high energy, comparing the predictions of three different hadronic interaction models: SIBYLL 1.7, SIBYLL 2.1 and QGSJET98. The influence of the hadronic interaction models on the shower evolution, in particular the elongation rate, is discussed and the applicability of analytical approximations is investigated.

A search for $B_s^0-\overline{B_s^0}$ oscillations is performed using a sample of 400 000 hadronic $Z^0$ decays collected by the SLAC Large Detector experiment. The $B_s^0$ candidates are reconstructed in the $B_s^0\to D_s^{-}X$ channel with $D_s^{-}\to \phi {\pi }^{-},$ $K^{*0}{K}^{-}.$ The $B_s^0$ production flavor is determined using the large forward-backward asymmetry of polarized $Z^0\to b\overline{b}$ decays and charge information in the hemisphere opposite that of the $B_s^0$ candidate. The decay flavor is tagged by the charge of the $D_s^{\pm }.$ From a sample of 361 candidates with an average $B_s^0$ purity of 40%, we exclude the following values of the oscillation frequency: $\Delta m_s<1.4\mathrm{}{\mathrm{ps}}^{-1}$ and $2.4<\mathrm{}\Delta m_s<5.3\mathrm{}{\mathrm{ps}}^{-1}$ at the 95% confidence level.

Based on 85 ${\mathrm{pb}}^{\mathrm{-}1}$ data of $p\overline{p}$ collisions at $\sqrt{s}=1.8\mathrm{}\mathrm{TeV}$ collected using the DØ detector at Fermilab during the 1994–1995 run of the Tevatron, we present a direct measurement of the total decay width of the W boson ${\Gamma }_W.$ The width is determined from the transverse mass spectrum in the $\overrightarrow{W}e+{\nu }_e$ decay channel and found to be ${\Gamma }_W{=2.23\mathrm{}}_{-0.14}^{+0.15\mathrm{}}\left(\mathrm{stat}\right)\pm 0.10\left(\mathrm{syst}\right)\mathrm{GeV},$ consistent with the expectation from the standard model.

This article describes an observation of mixing-induced $\mathrm{CP}$ violation and a measurement of the $\mathrm{CP}$ violation parameter, $\sin 2{\phi }_1,$ with the Belle detector at the KEKB asymmetric $e^{+}{e}^{-}$ collider. Using a data sample of $29.1\hspace{0.5em}{\mathrm{fb}}^{-1}$ recorded on the ${\rm Y}\mathrm{}\left(4S\right)\mathrm{}$ resonance that contains 31.3 million $B\overline{B}$ pairs, we reconstruct decays of neutral B mesons to the following $\mathrm{CP}$ eigenstates: $J/\psi K_S^0,$ $\psi {\mathrm{}\left(2S\right)K}_S^0,$ ${\chi }_{c1\mathrm{}}{K}_S^0,$ ${\eta }_c{K}_S^0,$ $J/\psi K_L^0$ and $J/\psi K^{*0}.$ The flavor of the accompanying B meson is identified by combining information from primary and secondary leptons, $K^{\pm }$ mesons, $\Lambda$ baryons, slow and fast pions. The proper-time interval between the two B meson decays is determined from the distance between the two decay vertices measured with a silicon vertex detector. The result $\sin 2{\phi }_1=0.99\mathrm{}\pm 0.14\left(\mathrm{stat}\right)\pm 0.06\left(\mathrm{syst}\right)$ is obtained by applying a maximum likelihood fit to the 1137 candidate events. We conclude that there is large $\mathrm{CP}$ violation in the neutral B meson system. A zero value for $\sin 2{\phi }_1$ is ruled out by more than six standard deviations.

We explore a version of the cosmological dilaton-fixing and decoupling mechanism in which the dilaton dependence of the low-energy effective action is extremized for infinitely large values of the bare string coupling $g_s^2{=e}^{\phi }.$ We study the efficiency with which the dilaton $\phi$ runs away toward its “fixed point” at infinity during a primordial inflationary stage, and thereby approximately decouples from matter. The residual dilaton couplings are found to be related to the amplitude of the density fluctuations generated during inflation. For the simplest inflationary potential $V\left(\chi \right)=\frac{1}{2}{m}_{\chi }^2\left(\phi \right){\chi }^2,$ the residual dilaton couplings are shown to predict violations of the universality of gravitational acceleration near the $\Delta a/a\sim {10}^{-12}$ level. This suggests that a modest improvement in the precision of equivalence principle tests might be able to detect the effect of such a runaway dilaton. Under some assumptions about the coupling of the dilaton to dark matter and/or dark energy, the expected time variation of natural “constants” (in particular of the fine-structure constant) might also be large enough to be within reach of improved experimental or observational data.

Numerical simulations of the chiral phase transition in the (3+1)-dimensional $O\left(4\right)\mathrm{}$ model are presented. The evolutions of the chiral field follow purely dissipative dynamics, starting from random chirally symmetric initial configurations down to the true vacuum with spontaneously broken symmetry. The model stabilizes topological textures which are formed together with domains of a disoriented chiral condensate (DCC) during the roll-down phase. The classically evolving field acts as a source for the emission of pions and $\sigma$ mesons. The exponents of power laws for the growth of angular correlations and for emission rates are extracted. Fluctuations in the abundance ratios for neutral and charged pions are compared with those for uncorrelated sources as a potential signature for the chiral phase transition after heavy-ion collisions. It is found that the presence of stabilizing textures (baryons and antibaryons) prevents the sufficiently rapid growth of the DCC domain size, so observability of anomalous tails in the abundance ratios is unlikely. However, the transient formation of growing DCC domains causes sizable broadening of the distributions as compared to the statistical widths of generic sources.

Covariant quantization of the Nambu-Goto spinning particle in 2+1 dimensions is studied. The model is relevant in the context of recent activities in noncommutative space-time. From a technical point of view also covariant quantization of the model poses an interesting problem: the set of second class constraints (in the Dirac classification scheme) is reducible. The reducibility problem is analyzed from two contrasting approaches: (i) the auxiliary variable method and (ii) the projection operator method. Finally in the former scheme, a Batalin-Tyutin quantization has been done. This induces a mapping between the non-commutative and the ordinary space-time. The Becchi-Rouet-Stora-Tyutin (BRST) quantization program in the latter scheme has also been discussed.

We systematically study the question of identification and consistent inclusion of the radion, within the Lagrangian approach, in a two-brane Randall-Sundrum model. Exploiting the symmetry properties of the theory, we show how the radion can be identified unambiguously and give the action to all orders in the radion field and the metric. Using the background field method, we expand the theory to quadratic orders in the fields. We show that the most general classical solutions, for the induced metric on the branes in the case of a constant radion and a factorizable four-dimensional metric, correspond to Einstein spaces. We discuss extensively the diagonalization of the quadratic action. Furthermore, we obtain the four-dimensional effective theory from this and study the question of the spectrum as well as the couplings in these theories.

We consider radion stabilization in hyperbolic brane-world scenarios. We demonstrate that in the context of Einstein gravity, matter fields which stabilize the extra dimensions must violate the null energy condition. This result is shown to hold even allowing for Friedmann-Robertson-Walker-like expansion on the brane. In particular, we explicitly demonstrate how one putative source of stabilizing matter fails to work, and how others violate the above condition. We speculate on a number of ways in which we may bypass this result, including the effect of Casimir energy in these spaces. A brief discussion of supersymmetry in these backgrounds is also given.

We investigate O(4) textures in a background with a positive cosmological constant. We find static solutions which comove with the expanding background. There exists a solution in which the scalar field is regular at the horizon. This solution has a noninteger winding number smaller than 1. There also exist solutions in which scalar-field derivatives are singular at the horizon. Such solutions can complete one winding within the horizon. If the winding number is larger than some critical value, static solutions including the regular one are unstable under perturbations.

We study a classical reparametrization-invariant system, in which “time” is not a priori defined. It consists of a nonrelativistic particle moving in five dimensions, two of which are compactified to form a torus. There, assuming a suitable potential, the internal motion is ergodic or more strongly irregular. We consider quasilocal observables which measure the system’s “change” in a coarse-grained way. Based on this, we construct a statistical timelike parameter, particularly with the help of maximum entropy method and Fisher-Rao information metric. The emergent reparametrization-invariant “time” does not run smoothly but is simply related to the proper time on the average. For sufficiently low energy, the external motion is then described by a unitary quantum mechanical evolution in accordance with the Schrödinger equation.

It is demonstrated that gravity waves of a flowing fluid in a shallow basin can be used to simulate phenomena around black holes in the laboratory. Since the speed of the gravity waves as well as their high-wave-number dispersion (subluminal vs superluminal) can be adjusted easily by varying the height of the fluid (and its surface tension) this scenario has certain advantages over the sonic and dielectric black hole analogs, for example, although its use in testing quantum effects is dubious. It can be used to investigate the various classical instabilities associated with black (and white) holes experimentally, including positive and negative norm mode mixing at horizons.

Runaway solutions can be avoided in fourth order gravity by doubling the matter operator algebra with a symmetry constraint with respect to the exchange of observable and hidden degrees of freedom together with a change in sign of the ghost and the dilaton fields. The theory is classically equivalent to Einstein gravity, while its nonunitary Newtonian limit is shown to lead to a sharp transition, around ${10}^{11}$ proton masses, from the wavelike properties of microscopic particles to the classical behavior of macroscopic bodies, as well as to a trans-Planckian regularization of collapse singularities. A unified reading of ordinary and black hole entropy emerges as entanglement entropy with hidden degrees of freedom. The emergent picture gives substantial agreement with Bekenstein-Hawking entropy and the Hawking temperature.

In most models of dark energy the structure formation stops after the accelerated expansion begins. In contrast, we show that the coupling of dark energy to dark matter may induce the growth of perturbations even in the accelerated regime. In particular, we show that this occurs in the models proposed to solve the cosmic coincidence problem, in which the ratio of dark energy to dark matter is constant. Depending on the parameters, the growth may be much faster than in a standard matter-dominated era. Moreover, if the dark energy couples only to dark matter and not to baryons, as requested by the constraints imposed by local gravity measurements, the baryon fluctuations develop a constant, scale-independent, large-scale bias which is in principle directly observable. We find that a lower limit to the baryon bias $b>\mathrm{}0.5\mathrm{}$ requires the total effective parameter of state $w_e=1+p/\rho$ to be larger than $0.6$ while a limit $b>\mathrm{}0.73\mathrm{}$ would rule out the model.

In this work we consider Randall-Sundrum brane-world type scenarios, in which the spacetime is described by a five-dimensional manifold with matter fields confined in a domain wall or three-brane. We present the results of a systematic analysis, using dynamical systems techniques, of the qualitative behavior of Friedmann-Lemaître-Robertson-Walker type models, whose matter is described by a scalar field with an exponential potential. We construct the state spaces for these models and discuss how their structure changes with respect to the general-relativistic case, and in particular, what new critical points appear and their nature and the occurrence of bifurcation.

There is no doubt that the ${}^1{P}_1$ charmonium $h_c$ exists in the mass range between $J/\psi$ and ${\psi }^{\prime }.$ While experiment produced a candidate in the past, it still requires a confirmation. Given the recent progress in the exclusive B decay into charmonia, we now have an opportunity to detect $h_c$ by measuring the final state $\gamma {\eta }_c$ of the cascade decay $\overrightarrow{B}{h}_c{K/K}^{*}\to \gamma {\eta }_c{K/K}^{*}.$ Confirmation of $h_c$ may turn out to be much easier in the B decay than at charm factories, although one may have to work a little harder to attain a high precision in the mass determination.

We show that perturbation theory provides two distinct mechanisms for the powerlike growth of hadronic cross sections at high energy. One, the leading Balitskiĭ-Fadin-Kuraev-Lipatov (BFKL) effect, is due to the growth of the parton density, and is characterized by the leading BFKL exponent $\omega .$ The other mechanism is due to the infrared diffusion, or the long range nature of the Coulomb field of perturbatively massless gluons. When perturbative saturation effects are taken into account, the first mechanism is rendered ineffective but the second one persists. We suggest that these two distinct mechanisms are responsible for the appearance of two Pomerons. The density growth effects are responsible for the hard Pomeron and manifest themselves in small systems (e.g. ${\gamma }^{*}$ or small size fluctuations in the proton wave function) where saturation effects are not important. The soft Pomeron is the manifestation of the exponential growth of the black saturated regions which appear in typical hadronic systems. We point out that the nonlinear generalization of the BFKL equation which takes into account wave function saturation effects (“Pomeron loops”) provides a well defined perturbative framework for the calculation of the soft Pomeron intercept. The conjecture of a perturbative soft Pomeron is consistent with picturing the proton as a loosely bound system of several small black regions corresponding e.g. to constituent quarks of size about 0.3 fm. Phenomenological implications of this picture are compatible with the main qualitative features of data on $p-p$ scattering.

We evaluate the masses of baryons composed of two heavy quarks and a strange quark, taking into account spin-dependent splittings in the framework of the potential model with the ${\mathrm{K}}^2\mathrm{O}$ potential [V. V. Kiselev, A. E. Kovalsky, and A. I. Onishchenko, Phys. Rev. D 64, 054009 (2001)] motivated by QCD with a three-loop $\beta$ function for the effective charge consistent with both the perturbative limit at short distances and a linear confinement term at long distances between the quarks. The factorization of dynamics is assumed and explored in the nonrelativistic Schrödinger equation for motion in a system of two heavy quarks constituting the doubly heavy diquark and the strange quark interaction with the diquark. The limits of the approach, its justification, and uncertainties are discussed. Excited quasistable states are classified by the quantum numbers of a heavy diquark composed of heavy quarks of the same flavor.

We analyze the diffractive (Pomeron) contribution to the $\mathrm{pp}$ spin-flip amplitude and discuss the possible scenarios for energies available at the Relativistic Heavy-Ion Collider (RHIC). In particular, we show that RHIC data will be instrumental in assessing the real contribution of diffraction to spin amplitudes.