The Kinetic Interpretation of the DGLAP Equation, its Kramers-Moyal Expansion and Positivity of Helicity Distributions

Details The Kinetic Interpretation of the DGLAP Equation, its Kramers-Moyal Expansion and Positivity of Helicity Distributions The Kinetic Interpretation of the DGLAP Equation, its Kramers-Moyal Expansion and Positivity of Helicity Distributions

2003-01-15

arxiv.org/abs/hep-ph/0301103v2

Int.J.Mod.Phys. A20 (2005) 4863-4898

Physics

High Energy Physics

High Energy Physics - Phenomenology

38 pages, 27 figures, Dedicated to Prof. Pierre Ramond for his 60th birthday

Scientific paper

10.1142/S0217751X05020951

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 $|\Delta f(x,Q)| < f(x,Q)$ between polarized and unpolarized distributions, or positivity of the helicity distributions, for any $Q$. 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 $\alpha_s$, 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 $q_V$ and for the transverse spin distribution $h_1$.

Affiliated with

Also associated with

No associations

Rating

The Kinetic Interpretation of the DGLAP Equation, its Kramers-Moyal Expansion and Positivity of Helicity Distributions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Kinetic Interpretation of the DGLAP Equation, its Kramers-Moyal Expansion and Positivity of Helicity Distributions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Kinetic Interpretation of the DGLAP Equation, its Kramers-Moyal Expansion and Positivity of Helicity Distributions will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-497914