Twist-4 effects and Q dependence of diffractive DIS

In this letter we report the direct perturbative QCD evaluation of twist-4 effects in diffractive DIS. They are large and have a strong impact on the Q dependence of diffractive structure functions at large β. Based on the AGK rules, we comment on the possible contribution from diffractive higher twists to ∝ 1 Q corrections to proton structure function at small x. These corrections to the longitudinal structure function FL may be particularly large. E-mail: [email protected] 1 Supported by the EU Program ERBFMBICT 950427 1 The direct calculation of higher twist corrections to the proton structure function (SF) remains one of challenges of perturbative QCD (pQCD) description of inclusive deep inelastic scattering (DIS) ([1, 2], for phenomenological estimates based on departures from the DGLAP evolution see [3]). In a striking contrast to inclusive proton SF, twist-4 (T4) corrections to diffractive SF, F D(3) i (xIP, β, Q ), (i = L, T ), are genuinely short distance dominated [4, 5] and thus calculable from the first principles of pQCD. Furthermore, they are strongly enhanced by the gluon SF of the proton squared [6], F D(3) i (T4; xIP, β, Q ) ∝ 1 Q G(xIP, Q ). (Hereafter x,Q, β and xIP = x β are standard diffractive DIS variables and G(x,Q) = xg(x,Q)). For instance, for β ∼ > 0.9, the twist-4 longitudinal diffractive SF was found to be comparable to, and even exceeding, the leading twist-2 (T2) transverse SF over a broad range of Q, making questionable [6, 7, 8, 9] applications of the standard DGLAP evolution to diffractive SF. In this letter we extend our early analysis of twist-4 longitudinal diffractive SF [6] to similarly enhanced twist-4 contribution to the large-β transverse diffractive SF . It enters F D(3) T (xIP, β, Q ) with negative sign and, as the higher twist dies out at largeQ, the transverse SF F D(3) T (xIP, β, Q ) will rise with increasing Q. We present for the first time an analysis of the β and Q dependence of compensations of the longitudinal and transverse twist-4 SF’s in F D(3) 2 = F D(3) T + F D(3) L , which completes the evaluation of driving twist-4 terms in F D(3) 2 . We compare our results with the H1 experimental data on F D(3) 2 [11]. Based on a connection between diffractive DIS and unitarity corrections to the proton SF suggested by the Abramovski-Gribov-Kancheli (AGK) rules [12, 13, 14], we evaluate the unitarity-driven diffractive twist-4 corrections to the small-x proton SF, which is potentially very large in the proton longitudinal SF FL. The underlying pQCD subprocess for diffractive DIS at large β is the excitation of the qq̄ Fock states of the photon γp → Xp, where X = qq̄ [5]. The relevant pQCD diagrams are shown in Fig. 1. In what follows, z and (1 − z) are the fractions of the (light–cone) momentum of the photon carried by the quark and antiquark, respectively, ~k is the relative transverse momentum in the qq̄ pair, M = (mf + k )/z(1 − z) is the invariant mass of the diffractive system, ~p⊥ is the (p,p’) momentum transfer and t = −~ p⊥ . The contribution of The preliminary results from this study have been reported at DIS’97 [9]. Related results were presented at DIS’97 by J.Bartels and M.Wüsthoff [10].