671 research outputs found
First Colonization of a Spectral Outpost in Random Matrix Theory
We describe the distribution of the first finite number of eigenvalues in a
newly-forming band of the spectrum of the random Hermitean matrix model. The
method is rigorously based on the Riemann-Hilbert analysis of the corresponding
orthogonal polynomials. We provide an analysis with an error term of order
N^(-2 h) where 1/h = 2 nu+2 is the exponent of non-regularity of the effective
potential, thus improving even in the usual case the analysis of the pertinent
literature. The behavior of the first finite number of zeroes (eigenvalues)
appearing in the new band is analyzed and connected with the location of the
zeroes of certain Freud polynomials. In general all these newborn zeroes
approach the point of nonregularity at the rate N^(-h) whereas one (a stray
zero) lags behind at a slower rate of approach. The kernels for the correlator
functions in the scaling coordinate near the emerging band are provided
together with the subleading term: in particular the transition between K and
K+1 eigenvalues is analyzed in detail.Comment: 32 pages, 8 figures (typo corrected in Formula 4.13); some reference
added and minor correction
Nonperturbative 2D Gravity, Punctured Spheres and -Vacua in String Theories
We consider a model of 2D gravity with the coefficient of the
Einstein-Hilbert action having an imaginary part . This is equivalent to
introduce a -vacuum structure in the genus expansion whose effect is to
convert the expansion into a series of alternating signs, presumably Borel
summable. We show that the specific heat of the model has a physical behaviour.
It can be represented nonperturbatively as a series in terms of integrals over
moduli spaces of punctured spheres and the sum of the series can be rewritten
as a unique integral over a suitable moduli space of infinitely punctured
spheres. This is an explicit realization \`a la Friedan-Shenker of 2D quantum
gravity. We conjecture that the expansion in terms of punctures and the genus
expansion can be derived using the Duistermaat-Heckman theorem. We briefly
analyze expansions in terms of punctured spheres also for multicritical models.Comment: 12 pages + 2 figures available upon request. LaTeX Fil
Thomae type formulae for singular Z_N curves
We give an elementary and rigorous proof of the Thomae type formula for
singular curves. To derive the Thomae formula we use the traditional
variational method which goes back to Riemann, Thomae and Fuchs.Comment: 22 page
Systems of Hess-Appel'rot type
We construct higher-dimensional generalizations of the classical
Hess-Appel'rot rigid body system. We give a Lax pair with a spectral parameter
leading to an algebro-geometric integration of this new class of systems, which
is closely related to the integration of the Lagrange bitop performed by us
recently and uses Mumford relation for theta divisors of double unramified
coverings. Based on the basic properties satisfied by such a class of systems
related to bi-Poisson structure, quasi-homogeneity, and conditions on the
Kowalevski exponents, we suggest an axiomatic approach leading to what we call
the "class of systems of Hess-Appel'rot type".Comment: 40 pages. Comm. Math. Phys. (to appear
Measurement of W Polarisation at LEP
The three different helicity states of W bosons produced in the reaction e+
e- -> W+ W- -> l nu q q~ at LEP are studied using leptonic and hadronic W
decays. Data at centre-of-mass energies \sqrt s = 183-209 GeV are used to
measure the polarisation of W bosons, and its dependence on the W boson
production angle. The fraction of longitudinally polarised W bosons is measured
to be 0.218 \pm 0.027 \pm 0.016 where the first uncertainty is statistical and
the second systematic, in agreement with the Standard Model expectation
Intercalibration of the barrel electromagnetic calorimeter of the CMS experiment at start-up
Calibration of the relative response of the individual channels of the barrel electromagnetic calorimeter of the CMS detector was accomplished, before installation, with cosmic ray muons and test beams. One fourth of the calorimeter was exposed to a beam of high energy electrons and the relative calibration of the channels, the intercalibration, was found to be reproducible to a precision of about 0.3%. Additionally, data were collected with cosmic rays for the entire ECAL barrel during the commissioning phase. By comparing the intercalibration constants obtained with the electron beam data with those from the cosmic ray data, it is demonstrated that the latter provide an intercalibration precision of 1.5% over most of the barrel ECAL. The best intercalibration precision is expected to come from the analysis of events collected in situ during the LHC operation. Using data collected with both electrons and pion beams, several aspects of the intercalibration procedures based on electrons or neutral pions were investigated
Search for Anomalous Couplings in the Higgs Sector at LEP
Anomalous couplings of the Higgs boson are searched for through the processes
e^+ e^- -> H gamma, e^+ e^- -> e^+ e^- H and e^+ e^- -> HZ. The mass range 70
GeV < m_H < 190 GeV is explored using 602 pb^-1 of integrated luminosity
collected with the L3 detector at LEP at centre-of-mass energies
sqrt(s)=189-209 GeV. The Higgs decay channels H -> ffbar, H -> gamma gamma, H
-> Z\gamma and H -> WW^(*) are considered and no evidence is found for
anomalous Higgs production or decay. Limits on the anomalous couplings d, db,
Delta(g1z), Delta(kappa_gamma) and xi^2 are derived as well as limits on the H
-> gamma gamma and H -> Z gamma decay rates
Measurement of W Polarisation at LEP
The three different helicity states of W bosons produced in the reaction e+
e- -> W+ W- -> l nu q q~ at LEP are studied using leptonic and hadronic W
decays. Data at centre-of-mass energies \sqrt s = 183-209 GeV are used to
measure the polarisation of W bosons, and its dependence on the W boson
production angle. The fraction of longitudinally polarised W bosons is measured
to be 0.218 \pm 0.027 \pm 0.016 where the first uncertainty is statistical and
the second systematic, in agreement with the Standard Model expectation
Neutral-Current Four-Fermion Production in e+e- Interactions at LEP
Neutral-current four-fermion production, e+e- -> ffff is studied in 0.7/fb of
data collected with the L3 detector at LEP at centre-of-mass energies
root(s)=183-209GeV. Four final states are considered: qqvv, qqll, llll and
llvv, where l denotes either an electron or a muon. Their cross sections are
measured and found to agree with the Standard Model predictions. In addition,
the e+e- -> Zgamma* -> ffff process is studied and its total cross section at
the average centre-of-mass energy 196.6GeV is found to be 0.29 +/- 0.05 +/-
0.03 pb, where the first uncertainty is statistical and the second systematic,
in agreement with the Standard Model prediction of 0.22 pb. Finally, the mass
spectra of the qqll final states are analysed to search for the possible
production of a new neutral heavy particle, for which no evidence is found
Measurement of Exclusive rho+rho- Production in Mid-Virtuality Two-Photon Interactions and Study of the gamma gamma* -> rho rho Process at LEP
Exclusive rho+rho- production in two-photon collisions between a quasi-real
photon, gamma, and a mid-virtuality photon, gamma*, is studied with data
collected at LEP at centre-of-mass energies root(s)=183-209GeV with a total
integrated luminosity of 684.8pb^-1. The cross section of the gamma gamma* ->
rho+ rho- process is determined as a function of the photon virtuality, Q^2,
and the two-photon centre-of-mass energy, W_gg, in the kinematic region:
0.2GeV^2 < Q^2 <0.85GeV^2 and 1.1GeV < W_gg < 3GeV. These results, together
with previous L3 measurements of rho0 rho0 and rho+ rho- production, allow a
study of the gamma gamma* -> rho rho process over the Q^2-region 0.2GeV^2 < Q^2
< 30 GeV^2
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