TY - JOUR

T1 - Evolution paths for small-x structure functions

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.

UR - http://www.scopus.com/inward/record.url?scp=0001295926&partnerID=8YFLogxK

U2 - 10.1016/0550-3213(91)90463-8

DO - 10.1016/0550-3213(91)90463-8

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AN - SCOPUS:0001295926

SN - 0550-3213

VL - 357

SP - 167

EP - 184

JO - Nuclear Physics, Section B

JF - Nuclear Physics, Section B

IS - 1

ER -