Eur. Phys. J. C 69, 425-431 (2010)
https://doi.org/10.1140/epjc/s10052-010-1413-4

Decoupling the NLO coupled DGLAP evolution equations: an analytic solution to pQCD

¹ Department of Physics and Astronomy, Northwestern University, Evanston, IL, 60208, USA
² Department of Physics, University of Wisconsin, Madison, WI, 53706, USA
³ Department of Physics, Astronomy and Geosciences, Towson University, Towson, MD, 21252, USA
⁴ Department of Physics and Astronomy, University of Kansas, Lawrence, KS, 66045, USA

mblock@northwestern.edu

Received: 7 July 2010
Revised: 26 July 2010
Published online: 21 August 2010

Abstract

Using repeated Laplace transforms, we turn coupled, integral-differential singlet DGLAP equations into NLO (next-to-leading) coupled algebraic equations, which we then decouple. After two Laplace inversions we find new tools for pQCD: decoupled NLO analytic solutions , . , are known NLO functions and , are starting functions for evolution beginning at . We successfully compare our u and d non-singlet valence quark distributions with MSTW results (Martin et al., Eur. Phys. J. C 63:189, 2009).