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Abstract
Abstract The CCFM equation and its extended form with a quadratic term (KGBJS equation) are solved with fixed and running coupling constant. The solution of the KGBJS equation is compared to gluon densities resulting from the CCFM and BK equations. As the saturation scale Q s now becomes available as a function of the hard scale p we observe that low values of p impede its growth with $ \frac{1}{x} $ . Also, at values much larger than partons transversal momentum the saturation effects become independent on the hard scale what we call liberation of saturation scale. We also introduce the hard-scale-related saturation scale P s and investigate its energy dependence. We observe that the new scale as a function of x decreases starting from the value of transversal momentum of gluon.
Highlights
Equation is compared to gluon densities resulting from the CCFM and BK equations
As the saturation scale Qs becomes available as a function of the hard scale p we observe that low values of p impede its growth with
As the equation depends on a hard scale we introduce hard scale related saturation scale Ps
Summary
2.1 Hard emissions approximation and running coupling effects The KGBJS equation reads:. We see on figure 2 that the effect of running coupling constant as compared to the fixed value at αs = 0.2 leads to faster growth of the density and is more pronounced when the hard scale is larger. The solution with running αs on figure 2 at p = 1 GeV and around k = 50 GeV dominates over the constant αs solution and the difference grows bigger with higher k This is due to small values of αs(k2) entering the exponent in the Regge factor included in the initial condition. The variable p is larger than q than the theta function sets to one and the angular ordering is relaxed We expect this will have interesting implications for the saturation scale generated by the KGBJS equation.
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