2 research outputs found
The Kinetic Interpretation of the DGLAP Equation, its Kramers-Moyal Expansion and Positivity of Helicity Distributions
According to a rederivation - due to Collins and Qiu - the DGLAP equation can
be reinterpreted (in leading order) in a probabilistic way. This form of the
equation has been used indirectly to prove the bound
between polarized and unpolarized distributions, or positivity of the helicity
distributions, for any . We reanalize this issue by performing a detailed
numerical study of the positivity bounds of the helicity distributions. To
obtain the numerical solution we implement an x-space based algorithm for
polarized and unpolarized distributions to next-to-leading order in ,
which we illustrate. We also elaborate on some of the formal properties of the
Collins-Qiu form and comment on the underlying regularization, introduce a
Kramers-Moyal expansion of the equation and briefly analize its Fokker-Planck
approximation. These follow quite naturally once the master version is given.
We illustrate this expansion both for the valence quark distribution and
for the transverse spin distribution .Comment: 38 pages, 27 figures, Dedicated to Prof. Pierre Ramond for his 60th
birthda
The Three Loop Equation of State of QED at High Temperature
We present the three loop contribution (order ) to the pressure of
massless quantum electrodynamics at nonzero temperature. The calculation is
performed within the imaginary time formalism. Dimensional regularization is
used to handle the usual, intermediate stage, ultraviolet and infrared
singularities, and also to prevent overcounting of diagrams during resummation.Comment: ANL-HEP-PR-94-02, SPhT/94-054 (revised final version