Bjorken sum rule in QCD frameworks with analytic (holomorphic) coupling

We investigate the polarized Bjorken sum rule (BSR) in three approaches to QCD with analytic (holomorphic) coupling: Analytic Perturbation Theory (APT), Two-delta analytic QCD (2[Formula: see text]anQCD) and Three-delta lattice-motivated analytic QCD in the three-loop and four-loop MOM scheme (3l3[Formula: see text]anQCD, 4l3[Formula: see text]anQCD). These couplings do not have unphysical (Landau) singularities, and have finite values when the transferred momentum goes to zero, which allows us to explore the infrared regime. With the exception of APT, these theories at high momenta practically coincide with the underlying perturbative QCD (pQCD) in the same scheme. We apply them in order to verify the Bjorken sum rule within the range of energies available in the data collected by the experimental JLAB collaboration, i.e. [Formula: see text] and compare the results with those obtained by using the perturbative QCD coupling. The results of the new frameworks with respective couplings (2[Formula: see text] and 3[Formula: see text]) are in good agreement with the experimental data for [Formula: see text] already when only one higher-twist term is used. In the low-[Formula: see text] regime [Formula: see text], we use [Formula: see text]PT-motivated expression or an expression motivated by the light-front holography (LFH) QCD used earlier in the literature.

Singular analytic linear cocycles with negative infinite Lyapunov exponents

We show that linear analytic cocycles where all Lyapunov exponents are negative infinite are nilpotent. For such one-frequency cocycles we show that they can be analytically conjugated to an upper triangular cocycle or a Jordan normal form. As a consequence, an arbitrarily small analytic perturbation leads to distinct Lyapunov exponents. Moreover, in the one-frequency case where the $k$th Lyapunov exponent is finite and the $(k+1)$st negative infinite, we obtain a simple criterion for domination in which case there is a splitting into a nilpotent part and an invertible part.

A Method for Retrieving the Ground Flash Fraction and Flash Type from Satellite Lightning Mapper Observations

An analytic perturbation method is introduced for retrieving the lightning ground flash fraction in a set of N lightning flashes observed by a satellite lightning mapper. The value of N must be large, typically in the thousands, and the satellite lightning optical observations consist of the maximum group area (MGA) produced by each flash. Moreover, the method subsequently determines the flash type (ground or cloud) of each of the N flashes. Performance tests of the method were conducted using simulated observations that were based on Optical Transient Detector (OTD) and Lightning Imaging Sensor (LIS) data. It is found that the mean ground flash fraction retrieval errors are below 0.04 across the full range 0–1 under the nominal conditions defined. In general, it is demonstrated that the retrieval errors depend on many factors (i.e., the number N of satellite observations, the magnitude of random and systematic instrument measurement errors, the ground flash fraction itself, and the number of samples used to form certain climate distributions employed in the method). The fraction of flashes accurately flash typed by the method averaged better than 78%. Overall, the accuracy of ground flash fraction and flash-typing retrievals degrade as the simulated population ground and cloud flash MGA distributions become more identical. Finally, because the analytic perturbation method was found to be quite robust (i.e., it performed well for several arbitrary underlying MGA distributions), it is not restricted to the lightning problem studied here but can be applied to any inverse problem having a similar problem statement.