Small-xnonlinear evolution with impact parameter and the structure function data

Abstract

The nonlinear Balitsky-Kovchegov equation at small x is solved numerically, incorporating impact parameter dependence. Confinement is modeled by including effective gluon mass in the dipole evolution kernel, which regulates the splitting of dipoles with large sizes. It is shown, that the solution is sensitive to different implementations of the mass in the kernel. In addition, running coupling effects are taken into account in this analysis. Finally, a comparison of the calculations using the dipole framework with the inclusive data from HERA on the structure functions F2 and FL is performed.

BFKL Pomeron: modeling confinement

“…Therefore, the BFKL Pomeron with the modified kernel reproduces the main features of the soft Pomeron that has been found both from N=4 SYM theory [34][35][36][37] and from the high energy Reggeon phenomenology [31,32]: the large value of the Pomeron intercept (ω 0 ≈ 0.2−0.3) and α ′ IP = 0. These both conclusions are in agreement with the numerical solution of the modified BFKL and BK equations [14,15]. ¶ In the first preprint version of this paper the equation for the saturation scale was written incorrectly as N BF KL We consider as one of the results of this paper that we developed several methods to solve the modified BFKL equation analytically (semi-classical and diffusion approximations).…”

“…As has been mentioned above the numerical calculations in Refs. [14][15][16][17] show that such a modification of the BFKL kernel leads the exponential decrease of the scattering amplitude at large values of the impact parameter. Actually, we can see this directly from the equation (see Eq.…”

“…Therefore, we have to find how confinement of quarks and gluons being of non-perturbative nature, will change the large b behaviour of the scattering amplitude in the region where this amplitude is small. This complicated problem in spite of numerous attempts [4,[14][15][16][17][18][19][20], has not been solved. However we learned several lessons from these tries.…”

“…However, such way of including the non-perturbative large b behaviour does not work [4,[14][15][16][17] in the case of the BFKL and BK evolutions [11,28]. Since we are interested in the behaviour of the scattering amplitude at large b where this amplitude is small, we need to find a way to introduce the non-perturbative corrections directly to the BFKL kernel.…”

“…It has been checked by numerical calculations (see Refs. [14][15][16][17]) that if we modify the BFKL kernel introducing by hand a function that suppressed the production of the dipoles with sizes larger than 1/µ sof t , the resulting scattering amplitude has the exponential decrease at large impact parameters.…”