The random-phase approximation is applied to coupled cluster expansions for $\mathrm{}(2+1)\mathrm{}$-dimensional SU(3) lattice gauge theory. The $0^{++}$ glueball mass is calculated up to the fourth order. The result agrees with the recent Monte Carlo result.

QCD sum rules are used to calculate the $\hat{\rho }{(1\mathrm{}}^{-+})\to \pi \eta ,\hspace{0.5em}\pi {\eta }^{\prime }$ decay widths of the exotic hybrid in two different $\eta -{\eta }^{\prime }$ mixing schemes. In the conventional flavor octet-singlet mixing scheme, the decay widths are both found to be small, while in the recently proposed quark mixing scheme, the decay width ${\Gamma }_{\hat{\rho }\to \eta \pi }\approx 250\hspace{0.5em}\mathrm{MeV}$ is large compared with the decay width ${\Gamma }_{\hat{\rho }\to {\eta }^{\prime }\pi }\approx 20\hspace{0.5em}\mathrm{MeV}.$ These results provide some insight into $\eta -{\eta }^{\prime }$ mixing and hybrid decay features.

The small-$x$ behavior of the singlet contributions to the polarized structure function $g_2{(x,Q}^2)$ is calculated in the double-logarithmic approximation of perturbative QCD. The dominant contribution is due to the gluons which, in contrast with the unpolarized case, mix with the fermions also in the small-$x$ domain. We find a powerlike growth in $1/x$ in the odd-signature parts of the amplitude with the same power as in the singlet function $g_1{(x,Q}^2)$ at $x\ll 1.$

We report on QCD radiative corrections to the processes $p\overline{p}\to W+2\mathrm{}\hspace{0.5em}\mathrm{jets}$ and $p\overline{p}\to Z+2\mathrm{}\hspace{0.5em}\mathrm{jets}$ at the Fermilab Tevatron. These processes are included in the Monte Carlo program MCFM, which allows the calculation of any infrared finite variable at next-to-leading order. Because of a better theoretical description of jets at next-to-leading order, some distributions exhibit significant corrections. As expected, the unphysical dependence of theoretical predictions upon the renormalization and factorization scales is greatly reduced compared to leading order. As an example of the predictions that may now be made with MCFM, we present a next-to-leading order estimate of the heavy flavor content of jets produced in association with vector bosons.

Both the static and homogeneous metrics describing the spherically symmetric gravitational field of a crossflow of incoming and outgoing null dust streams are generalized for the case of the two-component ghost radiation. Static solutions represent either naked singularities or the wormholes recently found by Hayward. The critical value of the parameter separating the two possibilities is given. The wormhole is allowed to have a positive mass. The homogeneous solutions are open universes.

Orientifolds with three-form flux provide some of the simplest string examples of warped compactification. In this paper we show that some models of this type have the unusual feature of $D=4,$ $\mathcal{N}=3\mathrm{}$ spacetime supersymmetry. We discuss their construction and low energy physics. Although the local form of the moduli space is fully determined by supersymmetry, to find its global form requires a careful study of the Bogomol’nyi-Prasad-Sommerfield spectrum.

In this work we discuss the effect of the quartic fermion self-interaction of Thirring type in QED in $D=2\mathrm{}$ and $D=3\mathrm{}$ dimensions. This is done through the computation of the effective action up to quadratic terms in the photon field. We analyze the corresponding nonlocal photon propagators nonperturbatively in $k/m,$ where k is the photon momentum and m the fermion mass. The poles of the propagators were determined numerically by using the MATHEMATICA software. In $D=2\mathrm{}$ there is always a massless pole whereas for strong enough Thirring coupling a massive pole may appear. For $D=3\mathrm{}$ there are three regions in parameter space. We may have one or two massive poles or even no pole at all. The interquark static potential is computed analytically in $D=2.\mathrm{}$ We notice that the Thirring interaction contributes with a screening term to the confining linear potential of massive two-dimensional QED $\left({\mathrm{QED}}_2\right).\mathrm{}$ In $D=3\mathrm{}$ the static potential must be calculated numerically. The screening nature of the massive ${\mathrm{QED}}_3$ prevails at any distance, indicating that this is a universal feature of $D=3\mathrm{}$ electromagnetic interaction. Our results become exact for an infinite number of fermion flavors.

We study the behavior of the two- and three-point thermal Green functions to one-loop order in the noncommutative $\mathrm{U}\mathrm{}\left(N\right)\mathrm{}$ Yang-Mills theory at temperatures T, much higher than the external momenta p. We evaluate the amplitudes for small and large values of the variable $\theta \mathrm{pT}$ $(\theta$ is the noncommutative parameter) and exactly compute the static gluon self-energy for all values of $\theta \mathrm{pT}.\mathrm{}$ We show that these gluon functions, which have a leading $T^2$ behavior, are gauge independent and obey simple Ward identities. We argue that these properties, together with the results for the lowest order amplitudes, may be sufficient to fix uniquely the hard thermal loop effective action of the noncommutative theory.

We investigate the effect of the minimal length uncertainty relation, motivated by perturbative string theory, on the density of states in momentum space. The relation is implemented through the modified commutation relation $[x_i,p_j]=iħ\left[\right(1+\beta p^2){\delta }_{\mathrm{ij}}+{\beta }^{\prime }{p}_i{p}_j].$ We point out that this relation, which is an example of a UV/IR relation, implies the finiteness of the cosmological constant. While our result does not solve the cosmological constant problem, it does shed new light on the relation between this outstanding problem and UV/IR correspondence. We also point out that the blackbody radiation spectrum will be modified at higher frequencies, but the effect is too small to be observed in the cosmic microwave background spectrum.

We determine the energy eigenvalues and eigenfunctions of the harmonic oscillator where the coordinates and momenta are assumed to obey the modified commutation relations $[x_i,p_j]=iħ\left[\right(1+\beta p^2){\delta }_{\mathrm{ij}}+{\beta }^{\prime }{p}_i{p}_j].$ These commutation relations are motivated by the fact that they lead to the minimal length uncertainty relations which appear in perturbative string theory. Our solutions illustrate how certain features of string theory may manifest themselves in simple quantum mechanical systems through the modification of the canonical commutation relations. We discuss whether such effects are observable in precision measurements on electrons trapped in strong magnetic fields.

The structure of the history phase space $\mathcal{G}$ of a covariant field system and its history group (in the sense of Isham and Linden) is analyzed on an example of a bosonic string. The history space $\mathcal{G}$ includes the time map $T$ from the spacetime manifold (the two-sheet) $\mathcal{Y}$ to a one-dimensional time manifold $\mathcal{T}$ as one of its configuration variables. A canonical history action is posited on $\mathcal{G}$ such that its restriction to the configuration history space yields the familiar Polyakov action. The standard Dirac-ADM action is shown to be identical with the canonical history action, the only difference being that the underlying action is expressed in two different coordinate charts on $\mathcal{G}.$ The canonical history action encompasses all individual Dirac-ADM actions corresponding to different choices $T$ of foliating $\mathcal{Y}.$ The history Poisson brackets of spacetime fields on $\mathcal{G}$ induce the ordinary Poisson brackets of spatial fields in the instantaneous phase space ${\mathcal{G}}_0$ of the Dirac-ADM formalism. The canonical history action is manifestly invariant both under spacetime diffeomorphisms $\mathrm{Diff}\mathcal{Y}$ and temporal diffeomorphisms $\mathrm{Diff}\mathcal{T}.$ Both of these diffeomorphisms are explicitly represented by symplectomorphisms on the history phase space $\mathcal{G}.$ The resulting classical history phase space formalism is offered as a starting point for projection operator quantization and consistent histories interpretation of the bosonic string model.

A well known result of a theorem due to Buchdahl, for a regular fluid sphere with a mass density which does not increase outwards, is that the ratio of its gravitational mass M to the coordinate radius R satisfies the inequality $GM/R<~\frac{4}{9}.$ This restriction arises from the condition that the isotropic pressure does not become infinity at the center of the sphere to prevent collapse. Buchdahl has also derived an inequality for the value of the central pressure of the sphere which we use to show that the minimum value for this pressure corresponds to a fluid of constant density. Then, using these results and the energy condition $\left(|p\right(r)\mathrm{}|<~\beta \rho \mathrm{}(r)/3),$ we find new bounds for the mass to radius ratio given by $2GM/R<~S\left(\xi \right),$ where $S\left(\xi \right)$ is a nondecreasing function of its argument $\xi =\beta {\rho }_c/3\mathrm{}\overline{\rho },$ where ${\rho }_c$ is the central density of the star and $\overline{\rho }$ its mean density. For a constant density star, and $\beta =3\mathrm{}$ (which corresponds to the dominant energy condition), we have $S\left(1\right)=3/4,$ which implies an upper limit for the gravitational redshift factor for light coming from the surface of the star given by $z<~1.$ We reobtain, for a general model and the values $\beta =3,$ ${\rho }_c\to \infty ,$ Buchdahl’s limit; however, a comparison of our results with a previous inequality found by Buchdahl shows that for any values of $\beta$ and the ratio ${\rho }_c/\overline{\rho }$ our bound of the mass to radius ratio is more strict.

If extra spacetime dimensions and low-scale gravity exist, black holes will be produced in observable collisions of elementary particles. For the next several years, ultrahigh-energy cosmic rays provide the most promising window on this phenomenon. In particular, cosmic neutrinos can produce black holes deep in the Earth’s atmosphere, leading to quasihorizontal giant air showers. We determine the sensitivity of cosmic ray detectors to black hole production and compare the results to other probes of extra dimensions. With $n>~4$ extra dimensions, current bounds on deeply penetrating showers from AGASA already provide the most stringent bound on low-scale gravity, requiring a fundamental Planck scale $M_D>1.3\mathrm{}–1.8\hspace{0.5em}\mathrm{TeV}.$ The Auger Observatory will probe $M_D$ as large as 4 TeV and may observe on the order of a hundred black holes in 5 years. We also consider the implications of angular momentum and possible exponentially suppressed parton cross sections; including these effects, large black hole rates are still possible. Finally, we demonstrate that even if only a few black hole events are observed, a standard model interpretation may be excluded by comparison with Earth-skimming neutrino rates.

Regular magnetic monopoles in the non-Abelian Born-Infeld-Higgs theory are known to exist in the region of the field strength parameter $\beta >{\beta }_{\mathrm{cr}},$ bounded from below. Beyond this region, only pointlike (embedded Abelian) monopoles exist, and we show that the transition from the regular to singular structure is reminiscent of gravitational collapse. Near the threshold behavior is characterized by the rapidly increasing negative pressure, which typically arises in the high density non-Abelian Born-Infeld (NBI) matter. Another feature, shared by both the NBI and gravitating monopoles, is the existence of excited states, which can be thought of as bound states of monopoles and sphalerons. These are labeled by the number N of nodes of the Yang-Mills function. Their masses are greater than the mass of the ground state monopole, and they are expected to be unstable. The sequence of masses $M_N$ rapidly converges to the mass of the embedded Abelian solution with a constant Higgs boson. The ratio of the sphaleron size to that of the monopole grows with decreasing $\beta ,$ and, at the same time, both fall down until the solutions cease to exist, again exhibiting a collapse to the point-like monopole. The results are presented and compared both for the ordinary and the symmetrized trace NBI actions.

Gravitational wave detectors will need optimal signal-processing algorithms to extract weak signals from the detector noise. Most algorithms designed to date are based on the unrealistic assumption that the detector noise may be modeled as a stationary Gaussian process. However most experiments exhibit a non-Gaussian “tail” in the probability distribution. This “excess” of large signals can be a troublesome source of false alarms. This article derives an optimal (in the Neyman-Pearson sense, for weak signals) signal processing strategy when the detector noise is non-Gaussian and exhibits tail terms. This strategy is robust, meaning that it is close to optimal for Gaussian noise but far less sensitive than conventional methods to the excess large events that form the tail of the distribution. The method is analyzed for two different signal analysis problems: (i) a known waveform (e.g., a binary inspiral chirp) and (ii) a stochastic background, which requires a multi-detector signal processing algorithm. The methods should be easy to implement: they amount to truncation or clipping of sample values which lie in the outlier part of the probability distribution.

We analyze forward Compton scattering, using real analytic amplitudes. By fitting the total $\gamma p$ scattering cross section data in the high energy region $5\hspace{0.5em}\mathrm{GeV}<~\sqrt{s}<~200\hspace{0.5em}\mathrm{GeV},$ using a cross section rising as ${\ln }^{2}s,$ we calculate ${\rho }_{\gamma p},$ the ratio of the real to the imaginary portion of the forward Compton scattering amplitude, and compare this to ${\rho }_{\mathrm{nn}},$ the ratio of the even portions of the $\mathrm{pp}$ and $\overline{p}p$ forward scattering amplitudes. We find that the two $\rho$ values are, within errors, the same in the c.m.s. energy region $5\hspace{0.5em}\mathrm{GeV}<~\sqrt{s}<~200\hspace{0.5em}\mathrm{GeV},$ as predicted by a factorization theorem of Block and Kaidalov.

We generalize the so-called “deflected anomaly mediation” scenario to the case where threshold corrections of heavy messengers to the sparticle squared masses are positive. A concrete model realizing this scenario is also presented. The tachyonic slepton problem can be fixed with only a pair of messengers. The resultant sparticle mass spectrum is quite different from that in the conventional deflected anomaly mediation scenario, but is similar to the one in the gauge mediation scenario. The lightest sparticle is mostly B-ino.

A survey of the literature dealing with the quark-model configurations of the scalar-isoscalar light mesons suggests that a theoretical model is needed to deal with these characterizations, since various researchers have come to widely different conclusions concerning the nature of the σ(500–600) or the $f_0\mathrm{}\left(980\right),$ basing their analysis on an attempt to fit experimental data with models for the wave functions of these states. In an earlier work we demonstrated that our generalized Nambu–Jona-Lasinio model may be used to provide a very good fit to the mixing angles and decay constants of the η(547) and ${\eta }^{\prime }\mathrm{}\left(958\right)\mathrm{}$ mesons. It was found that the η(547) was mainly a flavor octet state. On the other hand, when we use our model to describe the scalar-isoscalar $f_0\mathrm{}\left(980\right)\mathrm{}$ meson, we find that it is mainly a singlet state, in agreement with the recent suggestion of Ochs. We stress that these results for the properties of the pseudoscalar and scalar mesons arise from the different behavior of the ’t Hooft interaction in the two cases. In this work we demonstrate that the singlet-octet flavor representation largely brings the interaction matrix to diagonal form, with some residual singlet-octet mixing due, in part, to the ’t Hooft interaction and to the difference of the up (or down) and the strange quark constituent mass values. We find that, if we neglect the coupling to the two-meson continuum and use the same interaction that was used in our study of the η mesons, the $f_0\mathrm{}\left(980\right)\mathrm{}$ has a mass of 981 MeV and is the $q\overline{q}$ state of lowest energy. That result implies that the σ(500–600) is not a $q\overline{q}$ state, but is generated dynamically in ππ scattering, as well have discussed in an earlier work. We suggest that the proper treatment of the ’t Hooft interaction leads to a unified interpretation of the pseudoscalar and scalar meson characteristics.

$\mathcal{O}\left({\alpha }^2{\ln }^2{(m}_{\mu }{/m}_e\right))$ QED corrections to the electron spectrum and angular distribution in muon decay are evaluated. The impact on the determination of Michel parameters is estimated. The current theoretical uncertainty in the muon decay distributions is discussed.

The NuTeV Collaboration recently reported a value of ${\sin }^2{\theta }_W$ measured in neutrino-nucleon scattering that is 3 standard deviations above the standard model prediction. This result is derived assuming that (1) the strange sea is quark-antiquark symmetric, $s\left(x\right)=\overline{s}\mathrm{}\left(x\right),$ and (2) up and down quark distributions are symmetric under the simultaneous interchange of $u\leftrightarrow d$ and $p\leftrightarrow n.\mathrm{}$ We report the impact of violations of these symmetries on ${\sin }^2{\theta }_W$ and discuss the theoretical and experimental constraints on such asymmetries.