QCD coherence in the structure function and associated distributions at small $x$

Details QCD coherence in the structure function and associated distributions at small $x$ QCD coherence in the structure function and associated distributions at small $x$

1994-12-20

arxiv.org/abs/hep-ph/9412327v1

Nucl.Phys. B445 (1995) 49-80

Physics

High Energy Physics

High Energy Physics - Phenomenology

LaTeX file of 27 pages

Scientific paper

10.1016/0550-3213(95)00149-M

We recall the origin of angular ordering of soft parton emission in the region of small $x$ and show that this coherent structure can be detected in associated distributions. For structure functions at small $x$ and at fixed transverse momentum the angular ordering is masked because of the complete inclusive cancellations of collinear singularities for \xt0. Therefore, in this case the dependence on the hard scale is lost and the angular ordered region becomes equivalent to multi-Regge region in which all transverse momenta are of the same order. In this limit one derives the BFKL equation. In general such a complete cancellation does not hold for the associated distributions at small $x$. The calculation, which requires an analysis without any collinear approximation, is done by extending to small $x$ the soft gluon factorization techniques largely uses in the region of large $x$. Since one finds angular ordering in the both regions of small and large $x$, one can formulate a unified evolution equation for the structure function, a unified coherent branching and jet algorithm which allows the calculation of associated distributions in all $x$ regions. Such a unified formulation valid for all $x$ is presented and compared with usual treatments. In particular we show that the associated distributions at small $x$ are sensitive to coherence. By replacing angular ordering with the multi-Regge region one neglects large singular contributions in the associated distributions.

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