We reexamine constraints on the spatial size of closed toroidal models with cold dark matter and the cosmological constant from a cosmic microwave background. We carry out Bayesian analyses using the Cosmic Background Explorer (COBE) data properly taking into account the statistically anisotropic correlation, i.e., off-diagonal elements in the covariance. We find that the COBE constraint becomes more stringent in comparison with that using only the angular power spectrum, if the likelihood is marginalized over the orientation of the observer. For some limited choices of orientations, the fit to the COBE data is considerably better than that of the infinite counterpart. The best-fit matter normalization is increased because of large-angle suppression in the power and the global anisotropy of the temperature fluctuations. We also study several deformed closed toroidal models in which the fundamental cell is described by a rectangular box. In contrast with the cubic models, the large-angle power can be enhanced in comparison with the infinite counterparts if the cell is sufficiently squashed in a certain direction. It turns out that constraints on some slightly deformed models are less stringent. We comment on how these results affect our understanding of the global topology of our Universe.

We have analyzed 44.3M single muons collected by MACRO from 1991 through 2000 in 2145 live days of operation. We have searched for the solar diurnal, apparent sidereal, and pseudosidereal modulation of the underground muon rate by computing hourly deviations of the muon rate from 6 month averages. We find evidence for statistically significant modulations with the solar diurnal and the sidereal periods. The amplitudes of these modulations are $<0.1\%,$ and are at the limit of the detector statistics. The pseudosidereal modulation is not statistically significant. The solar diurnal modulation is due to the daily atmospheric temperature variations at 20 km, the altitude of primary cosmic ray interactions with the atmosphere; MACRO is the deepest experiment to report this result. The sidereal modulation is in addition to the expected Compton-Getting modulation due to solar system motion relative to the local standard of rest; it represents motion of the solar system with respect to the galactic cosmic rays toward the galactic plane.

It has been suggested that the observed value of the cosmological constant is related to the supersymmetry breaking scale $M_{\mathrm{susy}}$ through the formula $\Lambda \sim M_p^4{(M}_{\mathrm{susy}}{/M}_p{)}^8.$ We point out that a similar relation naturally arises in the codimension two solutions of warped spacetime varying compactifications of string theory, in which nonisotropic stringy moduli induce a small but positive cosmological constant.

We present a model independent analysis of $\Lambda$ baryon polarizations in the ${\Lambda }_b\to \Lambda {\mathcal{l}}^{+}{\mathcal{l}}^{-}$ decay. The sensitivity of the averaged $\Lambda$ polarizations to the new Wilson coefficients is studied. It is observed that there exist certain regions of the new Wilson coefficients where the branching ratio coincides with the standard model prediction, while the $\Lambda$ baryon polarizations deviate from the standard model results remarkably.

We study the lepton flavor violating (LFV) $H^{+}\to W^{+}{l}_i^{-}{l}_j^{+}$ and the lepton flavor conserving (LFC) $H^{+}\to W^{+}{l}_i^{-}{l}_i^{+}$ ${(l}_i=\tau {,l}_j=\mu )$ decays in the framework of the general two Higgs doublet model, the so-called model III. We estimate the decay width of LFV (LFC) decay at the order of magnitude of ${10}^{-11}–{10}^{-5}\mathrm{GeV}$ ${(10\mathrm{}}^{-9}–{10}^{-4}\mathrm{GeV}),$ for $200\mathrm{GeV}<~m_{H^{\pm }}<~400\mathrm{GeV},$ and intermediate values of the coupling ${\overline{\xi }}_{N,\tau \mu }^E\sim 5\mathrm{GeV}$ $\left({\overline{\xi }}_{N,\tau \tau }^E\sim 30\mathrm{GeV}\right).\mathrm{}$ We observe that experimental results for the process under consideration can give comprehensive information about physics beyond the standard model and the existing free parameters.

We study a neutral top-pion production process $\gamma \overrightarrow{\gamma }f\overline{f}{\Pi }_t^0\mathrm{}(f=t,b)\mathrm{}$ in the top-color-assisted technicolor (TC2) model. We find that the cross section of $\gamma \overrightarrow{\gamma }t\overline{t}{\Pi }_t^0$ is much larger than that of $\gamma \overrightarrow{\gamma }b\overline{b}{\Pi }_t^0.$ On the other hand, the cross section can be obviously enhanced with increasing the c.m. energy. With $\sqrt{s}=1600\mathrm{}\mathrm{GeV},$ the cross section of $t\overline{t}{\Pi }_t^0$ production can reach the level of a few fb. The results show that $\gamma \overrightarrow{\gamma }t\overline{t}{\Pi }_t^0\to t\overline{t}\left(t\overline{c}\right)$ is the most ideal channel to detect a neutral top-pion due to the clean standard model (SM) background. With such sufficient signals and clean background, a neutral top-pion could be detected at DESY TESLA with a high c.m. energy.

We analyze the zero modes of the Dirac operator in quenched SU(3) gauge configurations at a nonzero temperature and compare periodic and anti-periodic temporal boundary conditions for the fermions. It is demonstrated that for the different boundary conditions often the modes are localized at different space-time points and have different sizes. Our observations are consistent with patterns expected for Kraan–van Baal solutions of the classical Yang-Mills equations. These solutions consist of constituent monopoles and the zero modes are localized on different constituents for different boundary conditions. Our findings indicate that the excitations of the QCD vacuum are more structured than simple instantonlike lumps.

We examine the $\mathrm{CP}$ properties of chiral gauge theory defined by a formulation of the domain wall fermion, where the light field variables q and $\overline{q}$ together with Pauli-Villars fields Q and $\overline{Q}$ are utilized. It is shown that this domain wall representation in the infinite flavor limit $N=\infty$ is valid only in the topologically trivial sector, and that the conflict among lattice chiral symmetry, strict locality and $\mathrm{CP}$ symmetry still persists for finite lattice spacing a. The $\mathrm{CP}$ transformation generally sends one representation of lattice chiral gauge theory into another representation of lattice chiral gauge theory, resulting in the inevitable change of propagators. A modified form of lattice $\mathrm{CP}$ transformation motivated by the domain wall fermion, which keeps the chiral action in terms of the Ginsparg-Wilson fermion invariant, is analyzed in detail; this provides an alternative way to understand the breaking of $\mathrm{CP}$ symmetry at least in the topologically trivial sector. We note that the conflict with $\mathrm{CP}$ symmetry could be regarded as a topological obstruction. We also discuss the issues related to the definition of Majorana fermions in connection with the supersymmetric Wess-Zumino model on the lattice.

We generalize our previous work on $\pi \pi$ scattering to $K\pi$ scattering, and reanalyze the experiment data for $K\pi$ scattering below 1.6 GeV. Without any free parameter, we explain the $K\pi$ $I=3/2\mathrm{}$ S-wave phase shift very well by using t-channel $\rho$ and u-channel $K^{*}$ meson exchange. With the t-channel and u-channel meson exchange fixed as the background term, we fit the $K\pi I=1/2\mathrm{}$ S-wave data of the LASS experiment quite well by introducing one or two s-channel resonances. It is found that there is only one s-channel resonance between the $K\pi$ threshold and 1.6 GeV, i.e., $K_0^{*}\mathrm{}\left(1430\right)\mathrm{}$ with a mass around 1438–1486 MeV and a width of about 346 MeV, while the t-channel $\rho$ exchange gives a pole at $(450\mathrm{}–480i)$ MeV for the amplitude, rather uncertain due to the limitations of the approach used.

The nonleptonic weak decays of charmed mesons into a scalar meson and a pseudoscalar meson are studied. The scalar mesons under consideration are $\sigma$ [or $f_0\mathrm{}\left(600\right)\mathrm{}],$ $\kappa ,$ $f_0\mathrm{}\left(980\right),$ $a_0\mathrm{}\left(980\right)\mathrm{}$ and $K_0^{*}\mathrm{}\left(1430\right).$ A consistent picture provided by the data suggests that the light scalars below or near 1 GeV form an SU(3) flavor nonet and are predominately the $q^2{q}^2$ states, while the scalar mesons above 1 GeV can be described as a $q\overline{q}$ nonet. Hence, we designate $q^2{q}^2$ to $\sigma ,\kappa ,a_0\mathrm{}\left(980\right),f_0\mathrm{}\left(980\right)\mathrm{}$ and $q\overline{q}$ to $K_0^{*}.$ Sizable weak annihilation contributions induced from final-state interactions are essential for understanding the data. Except for the Cabibbo doubly suppressed channel $D^{+}\to f_0{K}^{+},$ the data of $\overrightarrow{D}\sigma \pi ,$ $f_0\pi ,$ $f_{0}K,$ $K_0^{*}\pi$ can be accommodated in the generalized factorization approach. However, the predicted rates for $\overrightarrow{D}{a}_0\pi ,$ $a_{0}K$ are too small by one to two orders of magnitude when compared with the preliminary measurements. Whether or not one can differentiate between the two-quark and four-quark pictures for the $f_0\mathrm{}\left(980\right)\mathrm{}$ produced in the hadronic charm decays depends on the isoscalar $f_0-\sigma$ mixing angle in the $q\overline{q}$ model.

We present a general procedure for incorporating higher-order information into the scale-setting prescription of Brodsky, Lepage and Mackenzie. In particular, we show how to apply this prescription when the leading coefficient or coefficients in a series in the strong coupling ${\alpha }_s$ are anomalously small and the original prescription can give an unphysical scale. We give a general method for computing an optimum scale numerically, within dimensional regularization, and in cases when the coefficients of a series are known. We apply it to the heavy quark mass and energy renormalization in lattice NRQCD, and to a variety of known series. Among the latter, we find significant corrections to the scales for the ratio of $e^{+}{e}^{-}$ to hadrons over muons, the ratio of the quark pole to $\overline{\mathrm{MS}}$ mass, the semileptonic B-meson decay width, and the top decay width. Scales for the latter two decay widths, expressed in terms of $\overline{\mathrm{MS}}$ masses, increase by factors of five and thirteen, respectively, substantially reducing the size of radiative corrections.

In a model of hadrons in which the hadron wave function at low $Q^2$ is represented by a hadron-like Fock state expansion, we calculate the $\pi$ and K parton distribution functions by comparing with the experimental data. We show that the model gives an accurate description of available data and, in addition, gives a clear prediction of the initial flavors to be considered at the low $Q^2$ scale where perturbative evolution starts.

We use a Landau theory and the $\epsilon$ expansion to study the superfluid phase transition of two-color QCD at a nonzero temperature T and baryonic chemical potential $\mu .$ At low T, and for $N_f$ flavors of massless quarks, the global $\mathrm{SU}\left({\mathrm{N}}_f\right)\times \mathrm{SU}\left({\mathrm{N}}_f\right)\times \mathrm{U}\mathrm{}\left(1\right)\mathrm{}$ symmetry is spontaneously broken by a diquark condensate down to $\mathrm{Sp}\left({\mathrm{N}}_f\right)\times \mathrm{Sp}\left({\mathrm{N}}_f\right)$ for any $\mu >0.\mathrm{}$ As the temperature increases, the diquark condensate melts, and at sufficiently large T the symmetry is restored. Using renormalization group arguments, we find that in the presence of the chiral anomaly term there can be a second order phase transition when $N_f=2\mathrm{}$ or $N_f>~6,$ while the transition is first order for $N_f=4.\mathrm{}$ We discuss the relevance of these results for the emergence of a tricritical point recently observed in lattice simulations.

We apply the linked dipole chain model to hadronic collisions using a modified version of the LDCMC Monte Carlo program. In particular, we investigate the effects of multiple scatterings, which in this framework are reformulated in terms of the production of multiple chains of dipoles. We find, among other things, that this way of describing multiple scatterings is less sensitive to the treatment of soft, nonperturbative, scatterings. Although the results presented here are only at the parton level, by comparing with the corresponding results from PYTHIA we are confident that our model will be able to describe the essential features of high-energy hadronic collisions, including the underlying events and jet-pedestal effects in high-$p_{\perp }$ events. The model should also be applicable to estimates of the transverse energy flow in high-energy heavy ion collisions, of interest in analyses of signals for quark-gluon plasma formation.

Using light-front dynamics, we consider a simplified constituent model for relativistic strong decays of hybrid mesons made of a quark, an antiquark, and a gluon. We demonstrate that special relativity imposes significant constraints on the few-constituent approximation. In particular, for a hybrid meson decaying into two mesons through dissociation of a spinless constituent gluon into a quark-antiquark pair, the simplified model is shown to respect Lorentz invariance if the distance between quark and antiquark in the hybrid is several times smaller than the distance between the pair and the gluon. This suggests that the quark and antiquark in the hybrid could originate from a gluon in a gluonium state made of two gluons in this effective theory.

We derive the imaginary part of the potential nonrelativistic QCD (pNRQCD) Hamiltonian up to order ${1/m}^4,$ when the typical momentum transfer between the heavy quarks is of the order of ${\Lambda }_{\mathrm{QCD}}$ or greater, and the binding energy E much smaller than ${\Lambda }_{\mathrm{QCD}}.$ We use this result to calculate the inclusive decay widths into light hadrons, photons and lepton pairs, up to $\mathcal{O}({\mathrm{mv}}^3\times ({\Lambda }_{\mathrm{QCD}}^2{/m}^2,E/m\left)\right)$ and $\mathcal{O}{(mv}^5)$ times a short-distance coefficient, for $S-$ and P-wave heavy quarkonium states, respectively. We achieve a large reduction in the number of unknown nonperturbative parameters and, therefore, we obtain new model-independent QCD predictions. All the NRQCD matrix elements relevant to that order are expressed in terms of the wave functions at the origin and six universal nonperturbative parameters. The wave-function dependence factorizes and drops out in the ratio of hadronic and electromagnetic decay widths. The universal nonperturbative parameters are expressed in terms of gluonic field-strength correlators, which may be fixed by experimental data or, alternatively, by lattice simulations. Our expressions are expected to hold for most of the charmonium and bottomonium states below threshold. The calculations and methodology are explained in detail so that the evaluation of higher order NRQCD matrix elements in this framework should be straightforward. An example is provided.

We present a calculation of the complete $\mathcal{O}\left(\alpha \right)$ electroweak radiative corrections to the Møller scattering process $e^{-}{e}^{-}\to e^{-}{e}^{-},$ including hard bremsstrahlung contributions. We study the effects of these corrections on both the total cross section and polarization asymmetry measured in low energy fixed target experiments. Numerical results are presented for the experimental cuts relevant for E-158, a fixed target $e^{-}{e}^{-}$ experiment being performed at SLAC; the effect of hard bremsstrahlung is to shift the measured polarization asymmetry by $\approx +4\%.\mathrm{}$ We briefly discuss the remaining theoretical uncertainty in the prediction for the low energy Møller scattering polarization asymmetry.

A Majorana neutrino is characterized by just one flavor diagonal electromagnetic form factor, the anapole moment, which in the static limit corresponds to the axial vector charge radius $〈r_A^2〉.$ Experimental information on this quantity is scarce, especially in the case of the tau neutrino. We present a comprehensive analysis of the available data on the single photon production process $e^{+}{e}^{-}\to \nu \overline{\nu }\gamma$ off Z resonance, and we discuss the constraints that these measurements can set on $〈r_A^2〉$ for the $\tau$ neutrino. We also derive limits for the Dirac case, when the presence of a vector charge radius $〈r_V^2〉$ is allowed. Finally, we comment on additional experimental data on ${\nu }_{\mu }$ scattering from the NuTeV, E734, CCFR, and CHARM-II Collaborations, and estimate the limits implied for $〈r_A^2〉$ and $〈r_V^2〉$ for the muon neutrino.

An exact representation of the causal QED fermion Green’s function, in an arbritrary external electromagnetic field, derived in Fried, Gabellini, and McKellar, and which naturally allows for nonperturbative approximations, is here used to calculate nonperturbative approximations to the Green’s function in the simple case of a constant external field. Schwinger’s famous exact result is obtained as the limit as the order of the approximation approaches infinity.

Radiative decays of the radially excited charmonium resonance, $\psi \mathrm{}\left(2S\right),$ into $\pi \pi ,$ $K\overline{K}$ and $\eta \eta$ final states have been measured in a sample of $4.02\times {10}^6$ $\psi \mathrm{}\left(2S\right)\mathrm{}$ events collected by the BES Collaboration. The branching ratios $B\left(\psi \mathrm{}\right(2S)\mathrm{}\to \gamma f_2\mathrm{}(1270\left)\mathrm{}\right)=(2.12\mathrm{}\pm 0.19\pm 0.32)\times {10}^{-4}$ and $B\left(\psi \mathrm{}\right(2S)\mathrm{}\to \gamma f_0\mathrm{}(1710\left)\mathrm{}\right)\times B\left(f_0\mathrm{}\right(1710)\mathrm{}\to K^{+}{K}^{-})=(3.02\mathrm{}\pm 0.45\pm 0.66)\times {10}^{-5}$ are obtained. When compared to the corresponding radiative $J/\psi$ decays, the observed $\psi \mathrm{}\left(2S\right)\mathrm{}$ radiative decay rates into $\gamma f_2\mathrm{}\left(1270\right)\mathrm{}$ and $\gamma f_0\mathrm{}\left(1710\right)\mathrm{}$ are consistent with the prediction of the “12%” rule.