Formulas for Continued Fractions. An Automated Guess and Prove Approach

We describe a simple method that produces automatically closed forms for the coefficients of continued fractions expansions of a large number of special functions. The function is specified by a non-linear differential equation and initial conditions. This is used to generate the first few coefficients and from there a conjectured formula. This formula is then proved automatically thanks to a linear recurrence satisfied by some remainder terms. Extensive experiments show that this simple approach and its straightforward generalization to difference and $q$-difference equations capture a large part of the formulas in the literature on continued fractions.Comment: Maple worksheet attache

Reflection groups in hyperbolic spaces and the denominator formula for Lorentzian Kac--Moody Lie algebras

This is a continuation of our "Lecture on Kac--Moody Lie algebras of the arithmetic type" \cite{25}. We consider hyperbolic (i.e. signature $(n,1)$) integral symmetric bilinear form $S:M\times M \to {\Bbb Z}$ (i.e. hyperbolic lattice), reflection group $W\subset W(S)$, fundamental polyhedron \Cal M of $W$ and an acceptable (corresponding to twisting coefficients) set P({\Cal M})\subset M of vectors orthogonal to faces of \Cal M (simple roots). One can construct the corresponding Lorentzian Kac--Moody Lie algebra {\goth g}={\goth g}^{\prime\prime}(A(S,W,P({\Cal M}))) which is graded by $M$. We show that \goth g has good behavior of imaginary roots, its denominator formula is defined in a natural domain and has good automorphic properties if and only if \goth g has so called {\it restricted arithmetic type}. We show that every finitely generated (i.e. P({\Cal M}) is finite) algebra {\goth g}^{\prime\prime}(A(S,W_1,P({\Cal M}_1))) may be embedded to {\goth g}^{\prime\prime}(A(S,W,P({\Cal M}))) of the restricted arithmetic type. Thus, Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type is a natural class to study. Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type have the best automorphic properties for the denominator function if they have {\it a lattice Weyl vector $\rho$}. Lorentzian Kac--Moody Lie algebras of the restricted arithmetic type with generalized lattice Weyl vector $\rho$ are called {\it elliptic}Comment: Some corrections in Sects. 2.1, 2.2 were done. They don't reflect on results and ideas. 31 pages, no figures. AMSTe

Experimental search for muonic photons

We report new limits on the production of muonic photons in the CERN neutrino beam. The results are based on the analysis of neutrino production of dimuons in the CHARM II detector. A $90\%$ CL limit on the coupling constant of muonic photons, $\alpha_{\mu} / \alpha < (1.5 \div 3.2) \times10^{-6}$ is derived for a muon neutrino mass in the range $m_{\nu_{\mu}} = (10^{-20} \div 10^5)$ eV. This improves the limit obtained from a precision measurement of the anomalous magnetic moment of the muon $(g-2)_\mu$ by a factor from 8 to 4

Leading-order QCD Analysis of Neutrino-Induced Dimuon Events

The results of a leading-order QCD analysis of neutrino-induced charm production are presented. They are based on a sample of 4111 \numu- and 871 \anumu-induced opposite-sign dimuon events with $E_{\mu 1},E_{\mu 2} > 6~{\rm GeV}$, $35 5.5\,{\rm GeV^2}$, observed in the CHARM~II detector exposed to the CERN wideband neutrino and antineutrino beams. The analysis yields the value of \linebreak the charm quark mass $m_c=1.79\pm0.38\,{\rm GeV}/c^2$ and the Cabibbo--Kobayashi--Maskawa matrix element $|V_{cd}|=0.219\pm0.016$. The strange quark content of the nucleon is found to be suppressed with respect to non-strange sea quarks by a factor $\kappa =0.39\pm0.09$

Observation of weak neutral current neutrino production of J/ψJ/\psi

Observation of \jpsi production by neutrinos in the calorimeter of the CHORUS detector exposed to the CERN SPS wide-band \numu beam is reported. A spectrum-averaged cross-section $\sigma^{\mathrm{J/\psi}}$ = (6.3 $\pm$ 3.0) $\times \mathrm{10^{-41}~cm^{2}}$ is obtained for 20 GeV $\leq E_{\nu} \leq$ 200 GeV. The data are compared with the theoretical model based on the QCD Z-gluon fusion mechanism

The CHORUS neutrino oscillation search experiment

The CHORUS experiment has successfully finished run I (320~000 recorded \numu\ CC in 94/95) and performed half of run II (225~000 \numu\ CC in 96). The analysis chain was exercised on a small data sample for the muonic \tdecay\ search using for the first time fully automatic emulsion scanning. This pilot analysis, resulting in a limit \sintth \leq 3 \cdot 10^{-2}, confirms that the CHORUS proposal sensitivity (\sintth \leq 3 \cdot 10^{-4}) is within reach in two years

Measurements of the leptonic branching fractions of the τ\tau

Data collected with the DELPHI detector from 1993 to 1995 combined with previous DELPHI results for data from 1991 and 1992 yield the branching fractions B({\tau \rightarrow \mbox{\rm e} \nu \bar{\nu}}) = (17.877 \pm 0.109_{stat} \pm 0.110_{sys} )\% and $B({\tau \rightarrow \mu \nu \bar{\nu}}) = (17.325 \pm 0.095_{stat} \pm 0.077_{sys} )\%$

Measurement of the Quark and Gluon Fragmentation Functions in Z0Z^0 Hadronic Decays

The fragmentation functions and multiplicities in $b\overline{b}$ and light quark events are compared. The measured transverse and longitudinal components of the fragmentation function allow the gluon fragmentation function to be evaluated