Evolution paths for small-x structure functions

E. M. Levin; G. Marchesini; M. G. Ryskin; B. R. Webber

doi:10.1016/0550-3213(91)90463-8

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 journal › Article › peer-review

25 Scopus citations

Abstract

We compare the solutions of the "one-loop" (summing α_S 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 language	English
Pages (from-to)	167-184
Number of pages	18
Journal	Nuclear Physics, Section B
Volume	357
Issue number	1
DOIs	https://doi.org/10.1016/0550-3213(91)90463-8
State	Published - 24 Jun 1991
Externally published	Yes

Funding

Funders	Funder number
Italian Ministcro della Pubblica lstruzione
Science and Engineering Research Council

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10.1016/0550-3213(91)90463-8

Cite this

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title = "Evolution paths for small-x structure functions",

abstract = "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.",

author = "Levin, {E. M.} and G. Marchesini and Ryskin, {M. G.} and Webber, {B. R.}",

note = "Funding Information: * Research supported in part by the UK Science and Engineering Research Council and in part by the Italian Ministcro della Pubblica lstruzione.",

year = "1991",

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doi = "10.1016/0550-3213(91)90463-8",

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AU - Levin, E. M.

AU - Marchesini, G.

AU - Ryskin, M. G.

AU - Webber, B. R.

N1 - Funding Information: * Research supported in part by the UK Science and Engineering Research Council and in part by the Italian Ministcro della Pubblica lstruzione.

PY - 1991/6/24

Y1 - 1991/6/24

N2 - 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.

AB - 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.

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Evolution paths for small-x structure functions

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