Abstract
In this paper we derived in QCD the BFKL linear, inhomogeneous equation for the factorial moments of multiplicity distribution($M_k$) from LMM equation. In particular, the equation for the average multiplicity of the color-singlet dipoles($N$) turns out to be the homogeneous BFKL while $M_k \propto N^k$ at small $x$. Second, using the diffusion approximation for the BFKL kernel we show that the factorial moments are equal to: $M_k=k!N( N-1)^{k-1}$ which leads to the multiplicity distribution:$ \frac{\sigma_n}{\sigma_{in}}=\frac{1}{N} ( \frac{N\,-\,1}{N})^{n - 1}$. We also suggest a procedure for finding corrections to this multiplicity distribution which will be useful for descriptions of the experimental data.
Highlights
We suggest a procedure for finding corrections to this multiplicity distribution which will be useful for descriptions of the experimental data
During the past several years a robust relation between the principle features of high energy scattering and entanglement properties of the hadronic wave function have been in focus of the high energy and nuclear physics communities [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]
In Ref. [5], it was proposed that parton distributions can be defined in terms of the entropy of entanglement between the spatial region probed by deep inelastic scattering (DIS) and the rest of the proton
Summary
During the past several years a robust relation between the principle features of high energy scattering and entanglement properties of the hadronic wave function have been in focus of the high energy and nuclear physics communities [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]. [5], it was proposed that parton distributions can be defined in terms of the entropy of entanglement between the spatial region probed by deep inelastic scattering (DIS) and the rest of the proton This approach leads to a simple relation S 1⁄4 ln N between the average number of color-singlet dipoles and the entropy of the produced hadronic state S. VI we suggest an approach to go beyond diffusion approximation, which cannot give a reliable description of the experimental data even in the leading order of perturbative QCD In this approach we propose to solve exactly the equations for the factorial moments and using the difference between the exact solution and Eq (2) [ΔMk 1⁄4 MkðexactÞ − Mk (Eq (2))] we develop the way to estimate the multiplicity distributions beyond diffusion approximation.
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