Singlet parton densities beyond leading order

Two-loop QED corrections to the Altarelli-Parisi splitting functions

“…However, at O(α 2 ), they are the same and the equality can be used to achieve further simplifications. Moreover, at this order, it is verified that 28) due to charge conjugation invariance.…”

“…[18], we make use of the diagram-by-diagram classification available in the original NLO QCD results presented in refs. [27][28][29] and, then, we modified consistently their color structure to account for the gluon-photon replacement. In this case, we explicitly concentrate on the QED corrections, without including those arising from Weak bosons, which only become relevant for very extreme kinematical conditions, where their masses are neglected in comparison to other scales involved in the process.…”

“…We extract the O(α 2 S ) contributions from refs. [27,28] and the O(α α S ) ones from ref. [18]; the resulting plot is given in figure 1.…”

Analytic results for Higgs production in bottom fusion

“…This is reflected in the modified beta coefficient β ′ 0 = β 0 + 3C F . The two loop splitting function P (2) bb can be extracted from the results of [45,46].…”

Regge behaviour of distribution functions and evolution of gluon distribution function in next-to-leading order at low-x

“…The DGLAP evolution equation for gluon distribution function upto NLO has the standard form [5,6] ( ) ( ) have their forms as given in [5,6]. At low-x, for x 0, only gluon splitting function matters [6,7].…”