Higher twists in deep inelastic scattering

We perform an exploratory study of higher twist contributions to deep inelastic scattering. We estimate the size of two major sources of higher twist, namely absorptive corrections and the vector meson dominance (VMD) contribution. We find that they give a sizeable higher twist component of F2. For example at x = 0.01 it is about 8% (17%) at Q2 = 10 GeV2 (4 GeV2), reaching up to 27% at x = 10−4 and Q2 = 4 GeV2. At the smaller x value the largest contribution comes from absorptive corrections, while at the larger values of x the VMD term dominates. At large Q the cross section for deep inelastic scattering (DIS) is to a good approximation described by just the twist-2 component of the structure function. That is σT (γ p) = 4πα Q2 FT (x,Q ) (1) with FT ≃ F (2) T , where α is the electromagnetic coupling. Indeed in extracting parton distributions from DIS data it is commonly assumed that (1) is exact and that FT is given entirely by twist-2. To leading order in QCD we have F (2) T = ∑ q eqx[q(x,Q ) + q̄(x,Q)] (2) where q and q̄ are the quark and antiquark distributions and eeq is the charge of the quark. For sufficiently small values of Q the higher twist (4,6,...) components of FT , defined by FT = F (2) T + F (4) T Q2 + F (6) T Q4 + ..., (3) would be expected to give noticeable contributions to σT . Surprisingly, even though the DIS data have become much more precise, the recent global analyses still show no necessity for higher twist contributions — despite including data at remarkably low values of Q. Moreover parametric fits of F2 data [1] have found very small values of F (4) 2 at low x. Our objective is to explore the role, and to estimate the size, of the higher twist terms. ¿From the point of view of the Wilson Operator Product Expansion (OPE) the higher twist terms correspond to operators describing a larger number of partons. Say, for twist-4 we must consider operators with four quarks 〈N |qq̄qq̄|N〉 or four gluons 〈N |gggg|N〉, and so on. Strictly speaking for each new twist and new operator we have to specify a new input function which should be determined by a global fit to the DIS data. Unfortunately the data are not yet precise enough to determine more than the leading twist, F (2) T , decomposition in terms of partons. Rather we will discuss two effects which are expected to give the dominant twist-4 contributions in the HERA domain. The contributions arise from (a) absorption corrections and (b) the vector meson dominance (VMD) contribution. We estimate their size below, but first we show their 1/Q behaviour. At low x the behaviour of σT (γ p) is controlled by the evolution of gluons in the t channel. The evolution equation may be written xg(x,Q) = xg(x,Q0) + ∫ 1