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Target Mass Corrections for Polarized Structure Functions and New Sum Rules.pdf

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Target Mass Corrections for Polarized Structure Functions and New Sum Rules

a r X i v : h e p - p h / 9 8 1 2 4 7 8 v 1 2 2 D e c 1 9 9 8 DESY 98-181 hep-ph/9812478 December 1998 Target Mass Corrections for Polarized Structure Functions and New Sum Rules Johannes Blu?mlein and Avtandil Tkabladze1 DESY Zeuthen, D-15738 Zeuthen, Germany Abstract The target mass corrections are calculated for all structure functions of neutral and charged current deep inelastic scattering in lowest order in the coupling constant. Representations of the correction to the twist–2 and twist–3 contributions are derived both in Mellin-n and x-space. The impact of the target mass corrections on the general relations between the twist–2 and twist–3 parts of the structure functions is studied and three new relations between the twist–3 contributions are derived. 1 Alexander von Humboldt Fellow 1 1 Introduction Deep inelastic lepton–nucleon scattering provides one of the cleanest possibilities to study the nucleon structure at short distances. The light–cone expansion [1] proved to be one of the most powerful techniques in the Bjorken limit, Q2, P.q → ∞, x = Q2/2P.q = const., to derive the structure of the scattering cross sections, relations between the structure functions and their scaling violations. The early unpolarized deep inelastic scattering experiments [2] and most of the experiments, in which polarized lepton scattering off a polarized target [3, 4] has been studied so far, operated in the range of lower values of Q2. In this domain nucleon–mass corrections cannot be neglected. The target mass effects of O((M2/Q2)k) form one contribution to the power corrections. Unlike the case for dynamical higher twist effects [5–7] the target mass corrections can be calculated in closed form in all orders in M2/Q2 for deep inelastic structure functions. Because the product of a mass factor Mk and a genuine twist–l operator forms an operator of twist τ = k + l the individual terms in the Taylor–expansion in M2/Q2 of the target mass corrections mix with the dynamical