New exact analytical solution of the nonlinear Gribov-Levin-Ryskin-Mueller-Qiu equation

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Main Authors: Cai, Yanbing, Wang, Xiaopeng, Chen, Xurong
Format: Preprint
Published: 2024
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author Cai, Yanbing
Wang, Xiaopeng
Chen, Xurong
author_facet Cai, Yanbing
Wang, Xiaopeng
Chen, Xurong
contents The GLR-MQ equation is a nonlinear evolution equation that takes into account the shadowing effect, which tames the growth of the gluon at small-$x$. In this study, we analytically solve for the first time the nonlinear GLR-MQ equation using the homogeneous balance method. The definite solution of the GLR-MQ equation is obtained by fitting the MSTW2008LO gluon distribution data. We find that the geometric scaling is an intrinsic property of our analytical solution and the gluon distribution functions from our solution are able to reproduce the MSTW2008LO data. These results indicate that our analytical solution from the homogeneous balance method is valid to describe the gluon behavior at small-$x$. Moreover, the saturation scale $Q_s$ has been extracted from our analytical solution, we find that the energy-dependent saturation scale obeys the exponential law $Q_s^2\,\propto\,Q_0^2 e^{λY}$.
format Preprint
id arxiv_https___arxiv_org_abs_2401_15651
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle New exact analytical solution of the nonlinear Gribov-Levin-Ryskin-Mueller-Qiu equation
Cai, Yanbing
Wang, Xiaopeng
Chen, Xurong
High Energy Physics - Phenomenology
The GLR-MQ equation is a nonlinear evolution equation that takes into account the shadowing effect, which tames the growth of the gluon at small-$x$. In this study, we analytically solve for the first time the nonlinear GLR-MQ equation using the homogeneous balance method. The definite solution of the GLR-MQ equation is obtained by fitting the MSTW2008LO gluon distribution data. We find that the geometric scaling is an intrinsic property of our analytical solution and the gluon distribution functions from our solution are able to reproduce the MSTW2008LO data. These results indicate that our analytical solution from the homogeneous balance method is valid to describe the gluon behavior at small-$x$. Moreover, the saturation scale $Q_s$ has been extracted from our analytical solution, we find that the energy-dependent saturation scale obeys the exponential law $Q_s^2\,\propto\,Q_0^2 e^{λY}$.
title New exact analytical solution of the nonlinear Gribov-Levin-Ryskin-Mueller-Qiu equation
topic High Energy Physics - Phenomenology
url https://arxiv.org/abs/2401.15651