Evolution paths for small-x structure functions

E. M. Levin*, G. Marchesini, M. G. Ryskin, B. R. Webber

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We compare the solutions of the "one-loop" (summing αS ln″ Q2) and "all-loop" (including also α″S ln″ x) evolution equations for small-x structure functions. In the semi-classical approximation one can define evolution paths in the (ln x, ln Q2)-plane, which are helpful in understanding many features of the solutions. We compute the asymptotic form of the mean path and the dispersion of paths for both the one-loop and all-loop cases, and compare the results with those of Monte Carlo simulations. We also use the Monte Carlo simulations to study the infrared stability of small-x evolution. Our results explain why the one loop and all-loop solutions are similar, over a wide range of x and Q2, especially when the input structure function at low Q2 is a rapidly increasing function of 1 x.

Original languageEnglish
Pages (from-to)167-184
Number of pages18
JournalNuclear Physics, Section B
Issue number1
StatePublished - 24 Jun 1991
Externally publishedYes


FundersFunder number
Italian Ministcro della Pubblica lstruzione
Science and Engineering Research Council


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