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

作者：Block Martin M^*; Durand Loyal; Ha Phuoc; Mckay Douglas W

来源：European Physical Journal C, 2010, 69(3-4): 425-431.

DOI：10.1140/epjc/s10052-010-1413-4

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 F(s)(x, Q(2)) = F(s)(F(s0)(x), G(0)(x)), G(x, Q(2)) = G(F(s0)(x), G(0)(x)). F(s), G are known NLO functions and F(s0)(x) = Fs(x, Q(0)(2)), G(0)(x) = G(x, Q(0)(2)) are starting functions for evolution beginning at Q(2) = Q(0)(2). 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). at large x, from jet data. For recent determinations of the gluon and quark distributions, see [1, 5].
We show that our analytic method determines the evolution of the singlet and gluon structure functions from arbitrary Q(0)(2) directly and individually, using as input F(s0)(x) = Fs(x, Q(0)(2)) and G(0)(x) = G(x, Q(0)(2)), with the guarantee that the evolved F(s)(x, Q(2)) and G(x, Q(2)) satisfy both of the NLO coupled DGLAP equations. Also calculated are NLO non-singlet functions, so that individual quark and gluon distributions are also analytically found from starting distributions of individual quark and gluon distributions. As numerical examples, we give the solutions for non-singlet NLO valence quark distributions, comparing them to the MSTW [1] published NLO valence quark distributions.

• 出版日期2010-10
• 单位西北大学