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arXiv 1801.06360hep-ph
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非线性GLR-MQ发展方程首阶以上解的唯象研究

On phenomenological study of the solution of nonlinear GLR-MQ evolution equation beyond leading order

M. Lalung, P. Phukan, J. K. Sarma

摘要:

利用Gribov-Ryskin-Levin-Mueller-Qiu(GLR-MQ)演化方程,在胶子($\sim 1/Q$)横向尺寸不变的条件下,对次领先阶(NLO)和次领先次领先阶(NNLO)胶子分布函数$G(x,Q^2)$的小x行为进行了唯象研究.我们考虑了胶子-胶子分裂函数$P_{gg} (z)$和强耦合常数$α_s (Q^2)$的NLO和NNLO修正。我们提出了基于胶子密度$G(x,Q^2)$的Regge类近似的半解析解,这些解在光子虚度$(Q^2)$的中等范围和小Bjorken变量$(x)$下是有效的.研究小-x下胶子复合效应引起的非线性效应是非常有趣的,它最终抑制了线性DGn演化方程所预测的胶子密度向小-x方向的不寻常增长。

英文摘要:

We present a phenomenological study of the small-x behaviour of gluon distribution function $G(x,Q^2)$ at next-to-leading order (NLO) and next-to-next-to-leading order(NNLO) in light of the nonlinear Gribov-Ryskin-Levin-Mueller-Qiu (GLR-MQ)evolution equation by keeping the transverse size of the gluons ($\sim 1/Q$) fixed. We consider the NLO and NNLO corrections, of the gluon-gluon spitting function $P_{gg} (z)$ and strong coupling constant $α_s (Q^2)$. We have suggested semi-analytical solutions based on Regge like ansatz of gluon density $G(x,Q^2)$, which are supposed to be valid in the moderate range of photon virtuality$(Q^2)$ and at small Bjorken variable$(x)$. The study of the effects of nonlinearities that arise due to gluon recombination effects at small-x is very interesting, which eventually tames down the unusual growth of gluon densities towards small-x as predicted by the linear DGLAP evolution equation.

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