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Particles and Fields
Eur. Phys. J. C 2, 569-579
DOI 10.1007/s100529800706

Four loop anomalous dimensions of gradient operators in $\bf {\phi^4}$ theory

S.É. Derkachov1 - J.A. Gracey2 - A.N. Manashov3

1 Department of Mathematics, St Petersburg Technology Institute, Sankt Petersburg, Russia (e-mail: derk@tu.spb.ru)
2 Theoretical Physics Division, Department of Mathematical Sciences, University of Liverpool, Liverpool, L69 7ZF,
United Kingdom (e-mail: jag@amtp.liv.ac.uk)
3 Department of Theoretical Physics, State University of St Petersburg, Sankt Petersburg, 198904 Russia
(e-mail: manashov@snoopy.phys.spbu.ru)

Received: 12 May 1997 / Published online: 20 February 1998

Abstract
We compute the anomalous dimensions of a set of composite operators which involve derivatives at four loops in $\overline{\mbox{MS}}$ in ${\phi^4}$ theory as a function of the operator moment n. These operators are similar to the twist-2 operators which arise in QCD in the operator product expansion in deep inelastic scattering. By regarding their inverse Mellin transform as being equivalent to the DGLAP splitting functions we explore to what extent taking a restricted set of operator moments can give a good approximation to the exact four loop result.


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