Nonlinear GLR-MQ evolution equation and <math><msup><mi>Q</mi><mn>2</mn></msup></math> -evolution of gluon distribution function

In this paper we have solved the nonlinear Gribov–Levin–Ryskin–Mueller–Qiu (GLR-MQ) evolution equation for the gluon distribution function <math><mrow><mi>G</mi><mo stretchy="false">(</mo><mi>x</mi><mo>,</mo><msup><mi>Q</mi><mn>2</mn></msup><mo stretchy="false">)</mo></mrow></math> and studied the effects of the nonlinear GLR-MQ corrections to the Leading Order (LO) Dokshitzer–Gribov–Lipatov–Altarelli–Parisi (DGLAP) evolution equations. Here we have incorporated a Regge-like behavior of gluon distribution function to obtain the solution of the GLR-MQ evolution equation. We have also investigated the <math><msup><mi>Q</mi><mn>2</mn></msup></math> -dependence of the gluon distribution function from the solution of the GLR-MQ evolution equation. Moreover it is interesting to observe from our results that nonlinearities increase with decreasing correlation radius ( <math><mi>R</mi></math> ) between two interacting gluons. The results also confirm that the steep behavior of gluon distribution function is observed at <math><mrow><mi>R</mi><mo>=</mo><mn>5</mn><mspace width="0.166667em"/><msup><mrow><mi mathvariant="normal">GeV</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></math> , whereas it is lowered at <math><mrow><mi>R</mi><mo>=</mo><mn>2</mn><mspace width="0.166667em"/><msup><mrow><mi mathvariant="normal">GeV</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></math> with decreasing <math><mi>x</mi></math> as <math><msup><mi>Q</mi><mn>2</mn></msup></math> increases. In this work we have also checked the sensitivity of <math><msub><mi mathvariant="italic">λ</mi><mi mathvariant="normal">G</mi></msub></math> in our calculations. Our computed results are compared with those obtained by the global DGLAP fits to the parton distribution functions viz. GRV, MRST, MSTW and with the EHKQS model