Next-to-leading order photon structure functions

PROCEEDINGS SUPPLEMENTS EI.S EVI ER

Nuclear Physics B (Proc. Suppl.) 39B,C (1995) 38~40

Next-to-leading order photon structure functions W.L. van Neerven Instituut Lorentz, University of Leiden, P.O. Box 9506, 2300 RA Leiden, The Netherlands We present a complete next-to-leading order (NLO) QCD analysis of the photon structure functions F~(x, Q2) and F[(x, Q2). All contributions due to light partons and heavy quarks have been included.

We will present the most important results obtained from a complete NLO analysis of the photon structure functions F~(x, Q2) and F[(x, Q2) for a real photon target.In leading order one has to compute the following partonic subprocesses [1].

in the MS-scheme the photon structure functions take the following form

(1)

Where f [ denotes the parton density in the photon for which we choose the parametrization in [1]. The hadronic and pointlike components of the photon are described by the hadronic coefficient functions Ck,i and the photonic coefficient functions Ck,-r respectively.These functions depend on the factorization (= renormalization) scale/~ for which we choose p = @Furthermore we make a distinction between heavy quark and light parton contributions.Choosing the number of light flavours to be equal to three we have presented plots for the LO and NLO structure functions in riga ( F ; ) and fig.2 ( F [ ) for Q2 = 5.9 (GeV/c) 2 ( P L U T O data).From our calculations we can draw the following conclusions. In the kinematical range under investigation 0.03 < x < 0.8 and 0.7(GeV/c) 2 < Q2 < 390 (GeV/c) 2 among the heavy flavours only charm contributes and it constitutes about 30 % of the total structure function in LO as well as NLO.The difference between LO and NLO is only conspicuous below the charm thresh-

7" + 7---+ q + q. 7" +g--'* q + q.

(2)

Here 7* denotes the virtual photon with mass Q and 7 stands for the (almost) on-shell photon. The gluon indicated by g originates from the on-shell photon and its contribution to the cross section in (2) is described by introducing the gluon density in the photon.The quarks in the final state can be light as well as heavy and are denoted by q.The next-to- leading order processes, calculated in [2], are given by 7" + 7 ---~ q + q + g .

(3)

7* + g ---* q + ~l+ g.

(4)

7*+q(q)---~q+q +q(q).

(5)

After coupling constant renormalization and mass factorization which are both carried out

= i=q,g

+ck,.,(&/t?).

0920-5632/95/$09.50 © 1995 Elsevier ScienceB.V. All rights reserved.

SSD10920-5632(95)00039-9

g' ®

(6)

V~L. van Neerven/Nuclear Physics B (Proc. Suppl.) 39B, C (1995) 3 ~ 4 0

old and the order o~, corrections to the charm component amount to about 20-30 %.The bulk of the charm contribution can be attributed to photonic charm production (1) and (3) except for x < 0.01 where hadronic charm production (processes (2),(4) and (5)) becomes dominant.This is important because the photonic charm coefficient function is independent of the factorization scale so that charm production can be predicted with a high degree of accuracy.Therefore it will provide us with a good test of perturbative QCD. Finally there is a considerable improvement in the factorization scale dependence of the whole structure function while going from its LO to the NLO description.

References [1] M. Gltick, E. R.eya and A. Vogt , Phys. Rev. D46 (1992) 1973. [2] E. Laenen, S. Riemersma, a. Smith and W.L. van Neerven, Phys. Rev. D49 (1994) 5753.

39

W.L. van Neerven/Nuclear Physics B (Proc. Suppl.) 395, C (1995) 38-40

40

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.Solid line : ;long dashed line : F;'(CO); 2

s h o r t d a s h e d line : N L O c h a r m c o n t r i b u t i o n s ; d o t t e d line : L O c h a r m c o n t r i b u tions. T h e d a t a are f r o m P L U T O .

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