1/f noise from nonlinear stochastic differential equations

We consider a class of nonlinear stochastic differential equations, giving the power-law behavior of the power spectral density in any desirably wide range of frequency. Such equations were obtained starting from the point process models of 1/f^b noise. In this article the power-law behavior of spectrum is derived directly from the stochastic differential equations, without using the point process models. The analysis reveals that the power spectrum may be represented as a sum of the Lorentzian spectra. Such a derivation provides additional justification of equations, expands the class of equations generating 1/f^b noise, and provides further insights into the origin of 1/f^b noise

Non-thermal recombination - a neglected source of flare hard X-rays and fast electron diagnostic

Context. Flare Hard X-Rays (HXRs) from non-thermal electrons are commonly treated as solely bremsstrahlung (f-f), recombination (f-b) being neglected. This assumption is shown to be substantially in error, especially in hot sources, mainly due to recombination onto Fe ions. Aims. We analyse the effects on HXR spectra and electron diagnostics by including non-thermal recombination onto heavy elements in our model. Methods. Using Kramers hydrogenic cross sections with effective Z, we calculate f-f and f-b spectra for power-law electron spectra, in both thin and thick target limits, and for Maxwellians, with summation over all important ions. Results. We find that non-thermal electron recombination, especially onto Fe, must, in general, be included together with f-f, for reliable spectral interpretation, when the HXR source is hot. f-b contribution is greatest when the electron spectral index is large, and any low energy cut-off small. f-b spectra recombination edges mean a cut-off in F(E) appears as a HXR feature at Photon energy = Ec + Vz, offering an Ec diagnostic. Including f-b lowers, greatly in some cases, the F(E) needed for prescribed HXR fluxes and, even when small, seriously distorts F(E) as inferred by inversion or forward fitting based on f-f alone. Conclusions. f-b recombination from non-thermal electrons can be an important contributor to HXR spectra and should be included in spectral analyses, especially for hot sources. Accurate results will require use of better cross sections than ours and consideration of source ionisation structure.Comment: 13 pages, 2 tables, 9 figures, Accepted for publication in A&

A Measurement of the Product Branching Ratio f(b->Lambda_b).BR(Lambda_b->Lambda X) in Z0 Decays

The product branching ratio, f(b->Lambda_b).BR(Lambda_b->Lambda X), where Lambda_b denotes any weakly-decaying b-baryon, has been measured using the OPAL detector at LEP. Lambda_b are selected by the presence of energetic Lambda particles in bottom events tagged by the presence of displaced secondary vertices. A fit to the momenta of the Lambda particles separates signal from B meson and fragmentation backgrounds. The measured product branching ratio is f(b->Lambda_b).BR(Lambda_b->Lambda X) = (2.67+-0.38(stat)+0.67-0.60(sys))% Combined with a previous OPAL measurement, one obtains f(b->Lambda_b).BR(Lambda_b->Lambda X) = (3.50+-0.32(stat)+-0.35(sys))%.Comment: 16 pages, LaTeX, 3 eps figs included, submitted to the European Physical Journal

B→KB\to K Transition Form Factor up to O(1/mb2){\cal O}(1/m^2_b) within the kTk_T Factorization Approach

In the paper, we apply the $k_T$ factorization approach to deal with the $B\to K$ transition form factor $F^{B\to K}_{+,0}(q^2)$ in the large recoil regions. The B-meson wave functions $\Psi_B$ and $\bar\Psi_B$ that include the three-particle Fock states' contributions are adopted to give a consistent PQCD analysis of the form factor up to ${\cal O} (1/m^2_b)$. It has been found that both the wave functions $\Psi_B$ and $\bar\Psi_B$ can give sizable contributions to the form factor and should be kept for a better understanding of the $B$ meson decays. Then the contributions from different twist structures of the kaon wavefunction are discussed, including the $SU_f(3)$-breaking effects. A sizable contribution from the twist-3 wave function $\Psi_p$ is found, whose model dependence is discussed by taking two group of parameters that are determined by different distribution amplitude moments obtained in the literature. It is also shown that $F^{B\to K}_{+,0}(0)=0.30\pm0.04$ and $[F^{B\to K}_{+,0}(0)/F^{B\to \pi}_{+,0}(0)]=1.13\pm0.02$, which are more reasonable and consistent with the light-cone sum rule results in the large recoil regions.Comment: 22 pages and 6 figure