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Abstract In this paper we found the multiplicity distribution of the produced gluons in deep inelastic scattering at large z= (Q²ₛ/Q²) \, \, \, \, 1 z = ln Q s 2 / Q 2 ≫ 1 where Qₛ Q s is the saturation momentum and Q² Q 2 is the photon virtuality. It turns out that this distribution at large n > n n > n ¯ almost reproduces the KNO scaling behaviour with the average number of gluons n (z²/2) n ¯ ∝ exp z 2 / 2 κ, where = 4. 88 κ = 4. 88 in the leading order of perturbative QCD. The KNO function (nn) = (-\, n/n) Ψ n n ¯ = exp - n / n ¯. For n n n ¯ we found that ₙ (z - 2 \, \, (n-1) ) / (n-1) σ n ∝ (z - 2 κ ln (n - 1) ) / (n - 1). Such small n determine the value of entropy of produced gluons SE = 0. 3\, z²/ (2\, ) S E = 0. 3 z 2 / (2 κ) at large z. The factor 0. 3 stems from the non-perturbative corrections that provide the correct behaviour of the saturation momentum at large b.
E. Levin (Fri,) studied this question.