Screening of Coulomb Impurities in Graphene

We calculate exactly the vacuum polarization charge density in the field of a subcritical Coulomb impurity, $Z|e|/r$, in graphene. Our analysis is based on the exact electron Green's function, obtained by using the operator method, and leads to results that are exact in the parameter $Z\alpha$, where $\alpha$ is the "fine structure constant" of graphene. Taking into account also electron-electron interactions in the Hartree approximation, we solve the problem self-consistently in the subcritical regime, where the impurity has an effective charge $Z_{eff}$, determined by the localized induced charge. We find that an impurity with bare charge Z=1 remains subcritical, $Z_{eff} \alpha < 1/2$, for any $\alpha$, while impurities with $Z=2,3$ and higher can become supercritical at certain values of $\alpha$.Comment: 4 pages, 2 figure

The early evolution of the earth, the beginning of its geological history: how and when the granitoid magmas appeared

The Earth has a number of differences from the planets of the Solar System and other star-planetary systems. These differences were acquired during its formation and geological history. In the early Chaotic eon occurred the accretion of the Earth, the separation of the primary substance of the Earth into a mantle and a nucleus, a satellite of the Earth - the Moon appeared. 4500 Ma ago in the Gadey aeon the geological history of the Earth began. At this time, the endogenous processes on the Earth were controlled to a great extent by meteorite-asteroid bombardments, which caused large-scale melting and differentiation of the upper shells of the Earth. In the magmatic chambers differentiation proceeded until the appearance of melts of granitoid composition. The continental crust of Gadey time was almost completely destroyed by meteoric bombardments, the last heavy bombardment occurred at the end of the Gadey aeon 4000-3900 Ma ago. The geological situation of the Gadey time can be judged only from the preserved zircons from the rocks of that epoch. In particular, their geochemical features indicate that the Earth has an atmosphere. The Gadey eon was replaced by the Archean one, from which the processes of self-organization began to predominate on the Earth. At this time, a crust composed of komatiite-basalt and tonalite-trondhjemite-granodiorite (TTG) series of rocks was formed. In its formation, the processes of sagduction (vertical growth of the crust) over the rising mantle plumes was played the leading role. At the same time the lower basaltic crust was bured in the mantle, eclogitized and melted, which led to the appearance of the sodium series of TTG rocks. At the end of the Archean 3.1-3.0 Ga tectonics of the cover (LID tectonics), which determined the style of the structure and development of the Archean crust, is replaced by the tectonics of small plates, which was later replaced by modern tectonics - the tectonics of plates combined with mantle plumes

Study of Gluon versus Quark Fragmentation in Υ→ggγ\Upsilon\to gg\gamma and e+e−→qqˉγe^{+}e^{-}\to q\bar{q}\gamma Events at \sqrt{s}=10 GeV

Using data collected with the CLEO II detector at the Cornell Electron Storage Ring, we determine the ratio R(chrg) for the mean charged multiplicity observed in Upsilon(1S)->gggamma events, to the mean charged multiplicity observed in e+e- -> qqbar gamma events. We find R(chrg)=1.04+/-0.02+/-0.05 for jet-jet masses less than 7 GeV.Comment: 15 pages, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Resonant Structure of τ→3ππ0ντ\tau\to 3\pi\pi^{0}\nu_{\tau} and τ→ωπντ\tau\to \omega\pi\nu_{\tau} Decays

The resonant structure of the four pion final state in the decay $\tau \to 3\pi\pi^0\nu_\tau$ is analyzed using 4.27 million $\tau^+\tau^-$ pairs collected by the CLEO II experiment. We search for second class currents in the decay $\tau \to \omega\pi\nu_\tau$ using spin-parity analysis and establish an upper limit on the non-vector current contribution. The mass and width of the $\rho'$ resonance are extracted from a fit to the $\tau \to \omega\pi\nu_\tau$ spectral function. A partial wave analysis of the resonant structure of the $\tau \to 3\pi\pi^0\nu_\tau$ decay is performed; the spectral decomposition of the four pion system is dominated by the $\omega\pi$ and $a_1 \pi$ final states.Comment: 34 pages postscript, also available through http://w4.lns.cornell.edu/public/CLN

Observation of Radiative Leptonic Decay of the Tau Lepton

Using 4.68 fb^{-1} of e^+e^- annihilation data collected with the CLEO II detector at the Cornell Electron Storage Ring (CESR) we have studied tau radiative decays tau -> mu nu nu gamma and tau -> e nu nu gamma. For a 10 MeV minimum photon energy in the tau rest frame, the branching fraction of radiative tau decay to a muon or electron is measured to be (3.61+-0.16+-0.35)*10^{-3} or (1.75+-0.06+-0.17)*10^{-2}, respectively. The branching fractions are in agreement with the Standard Model theoretical predictions.Comment: 11 pages postscript, also available through http://w4.lns.cornell.edu/public/CLN

Two-Body B Meson Decays to η\eta and η′\eta^{'} -- Observation of B→ηB\to \eta{'}K$

In a sample of 6.6 million produced B mesons we have observed decays B -> eta' K, with branching fractions BR(B+ -> eta' K+ = 6.5 +1.5 -1.4 +- 0.9) x $10^{-5}$ and BR(B0 -> eta' K0 = 4.7 +2.7 -2.0 +- 0.9) x $10^{-5}$. We have searched with comparable sensitivity for 17 related decays to final states containing an eta or eta' meson accompanied by a single particle or low-lying resonance. Our upper limits for these constrain theoretical interpretations of the B -> eta' K signal.Comment: 12 page postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Measurement of the Bˉ→Dℓνˉ\bar{B}\to D\ell\bar{\nu} Partila Width and Form Factor Parameters

We have studied the decay $\bar{B} \to D\ell\bar{\nu}$, where $\ell=e or \mu$. From a fit to the differential decay rate $d\Gamma/dw$ we measure the rate normalization ${\cal F}_D(1)|V_{cb}|$ and form factor slope $\hat{\rho}^2_D$, and, using measured values of $\tau_B$, find $\Gamma(\bar{B} \to D\ell\bar{\nu}) = (12.0 \pm 0.9 \pm 2.1) ns^{-1}$. The resulting branching fractions are ${\cal B}(\bar{B}^0 \to D^+\ell^-\bar{\nu})=(1.87 \pm 0.15 \pm 0.32)$ and ${\cal B}(B^- \to D^0\ell^-\bar{\nu})=(1.94 \pm 0.15 \pm 0.34)$. The form factor parameters are in agreement with those measured in $\bar{B} \to D^*\ell\bar{\nu}$ decays, as predicted by heavy quark effective theory.Comment: 11 pages, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Study of Semileptonic Decays of B Mesons to Charmed Baryons

Using data collected by the CLEO II detector at the center-of-mass energy on or near the Upsilon(4S) resonance, we have determined the 90% confidence level upper limit B(Bbar --> Lambda_c^+ e- X)/B(Bbar --> Lambda_c^+ X, Lambdabar_c^- X) < 0.05 for electrons with momentum above 0.6 GeV/c. We have also derived the ratio B(B^- --> Lambda_c^+ pbar e- nubar_e)/B(Bbar --> Lambda_c^+ pbar X) < 0.04 at the 90% confidence level and measured the ratio B(Bbar --> Lambda_c^+ pbar X)/B(Bbar --> Lambda_c^+ X, Lambdabar_c^- X) = 0.57 +- 0.05 +- 0.05.Comment: 9 page postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Further Search for the Two-Photon Production of the Glueball Candidate fJ(2220)f_{J}(2220)

The CLEOII detector at the Cornell e+ e- storage ring CESR has been used to search for the two-photon production of the $f_J(2220)$ decaying into pi+ pi-. No evidence for a signal is found in data corresponding to an integrated luminosity of 4.77/fb and a 95% CL upper limit on $\Gamma_{two-photon} * BR{pi+ pi-}$ of 2.5 eV is set. If this result is combined with the BES Collaboration's measurement of $f_J(2220) -> pi+ pi-$ in radiative $J/\psi$ decay, a 95% CL lower limit on the stickiness of the $f_J(2220)$ of 73 is obtained. If the recent CLEO result for \Gamma_{two-photon} * BR{\K_S K_S} is combined with the present result, the stickiness of the $f_J(2220)$ is found to be larger than 102 at the 95% CL. These results for the stickiness (the ratio of the probabilities for two-gluon coupling and two-photon coupling) provide further support for a substantial neutral parton content in the $f_J(2220)$.Comment: 8 pages, postscript file also available through http://w4.lns.cornell.edu/public/CLN