94 research outputs found
Factorial correlators: angular scaling within QCD jets
Factorial correlators measure the amount of dynamical correlation in
multiplicity between two separated phase-space windows. We present the
analytical derivation of factorial correlators for a QCD jet described at the
double logarithmic (DL) accuracy. We obtain a new angular scaling property for
properly normalized correlators between two solid-angle cells or two rings
around the jet axis. Normalized QCD factorial correlators scale with the
angular distance and are independent of the window size. Scaling violations are
expected beyond DL approximation, in particular from the subjet structure.
Experimental tests are feasible, and thus welcome.Comment: preprint SACLAY-T00-182, TSL/ISV-00-0239; 18 pages, latex, 4 figures;
submitted to Eur. Phys. J.
On positive functions with positive Fourier transforms
Using the basis of Hermite-Fourier functions (i.e. the quantum oscillator
eigenstates) and the Sturm theorem, we derive the practical constraints for a
function and its Fourier transform to be both positive. We propose a
constructive method based on the algebra of Hermite polynomials. Applications
are extended to the 2-dimensional case (i.e. Fourier-Bessel transforms and the
algebra of Laguerre polynomials) and to adding constraints on derivatives, such
as monotonicity or convexity.Comment: 12 pages, 23 figures. High definition figures can be obtained upon
request at [email protected] or [email protected]
Eigenmodes of Decay and Discrete Fragmentation Processes
Linear rate equations are used to describe the cascading decay of an initial
heavy cluster into fragments. This representation is based upon a triangular
matrix of transition rates. We expand the state vector of mass multiplicities,
which describes the process, into the biorthonormal basis of eigenmodes
provided by the triangular matrix. When the transition rates have a scaling
property in terms of mass ratios at binary fragmentation vertices, we obtain
solvable models with explicit mathematical properties for the eigenmodes. A
suitable continuous limit provides an interpolation between the solvable
models. It gives a general relationship between the decay products and the
elementary transition rates.Comment: 6 pages, plain TEX, 2 figures available from the author
Factorial Moments of Continuous Order
The normalized factorial moments are continued to noninteger values of
the order , satisfying the condition that the statistical fluctuations
remain filtered out. That is, for Poisson distribution for all .
The continuation procedure is designed with phenomenology and data analysis in
mind. Examples are given to show how can be obtained for positive and
negative values of . With being continuous, multifractal analysis is
made possible for multiplicity distributions that arise from self-similar
dynamics. A step-by-step procedure of the method is summarized in the
conclusion.Comment: 15 pages + 9 figures (figures available upon request), Late
Geometric scaling as traveling waves
We show the relevance of the nonlinear Fisher and Kolmogorov-Petrovsky-
Piscounov (KPP) equation to the problem of high energy evolution of the QCD
amplitudes. We explain how the traveling wave solutions of this equation are
related to geometric scaling, a phenomenon observed in deep-inelastic
scattering experiments. Geometric scaling is for the first time shown to result
from an exact solution of nonlinear QCD evolution equations. Using general
results on the KPP equation, we compute the velocity of the wave front, which
gives the full high energy dependence of the saturation scale.Comment: 4 pages, 1 figure. v2: references adde
Diffractive SUSY particle production at the LHC
We give detailed predictions for diffractive SUSY Higgs boson and top squark
associated productions at the LHC via the exclusive double pomeron exchange
mechanism. We study how the SUSY Higgs cross section and the signal over
background ratio are enhanced as a function of tangent beta in different
regimes. The prospects are particularly promising in the ``anti-decoupling''
regime, which we study in detail. We also give the prospects for a precise
measurement of the top squark mass using the threshold scan of central
diffractive associated top squark events at the LHC.Comment: 14 pages, 6 fig
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