Analysis of the small- x behavior of gluon distribution and a search for gluon recombination

The behavior of gluon distributions in the small- x region are semi-numerically predicted by using the nonlinear Gribov–Levin–Ryskin and Mueller–Qiu (GLR–MQ) evolution equation with the nonlinear shadowing term incorporated. It is interesting to observe that gluon recombination at the twist-4 level lowers the rapid growth of gluon densities with decreasing x compared to the linear DGLAP evolution. The nonlinear gluon density functions are calculated and compared with different parameterizations as well as models. Results show that our predictions for the gluon density function are comparable with different parameterizations. We make a deliberate attempt to explore the effect of nonlinear or shadowing corrections and we observe that nonlinear effects play a vital role in the kinematic region of small- x ( <math altimg="si1.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>≤</mo><msup><mrow><mn>10</mn></mrow><mrow><mo>−</mo><mn>3</mn></mrow></msup></math> ) and <math altimg="si2.gif" xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup></math> ( <math altimg="si3.gif" xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>≤</mo><msup><mrow><mi>Q</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>≤</mo><mn>20</mn><msup><mrow><mtext> GeV</mtext></mrow><mrow><mn>2</mn></mrow></msup></math> )