Chiral perturbation theory for nucleon generalized parton distributions
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THE EUROPEAN PHYSICAL JOURNAL A
Chiral perturbation theory for nucleon generalized parton distributions M. Diehl1 , A. Manashov2 , and A. Sch¨afer3,a 1 2 3
Theory Group, Deutsches Elektronen-Synchroton DESY, 22603 Hamburg, Germany Institut f¨ ur Theoretische Physik, Universit¨ at Regensburg, 93040 Regensburg, Germany Department of Theoretical Physics, Sankt-Petersburg State University, St.-Petersburg, Russia Received: 4 September 2006 / c Societ` Published online: 27 September 2006 – ° a Italiana di Fisica / Springer-Verlag 2006 Communicated by U.-G. Meißner ˜ E ˜ of the Abstract. We analyze the moments of the isosinglet generalized parton distributions H, E, H, nucleon in one-loop order of heavy-baryon chiral perturbation theory. We discuss in detail the construction of the operators in the effective theory that are required to obtain all corrections to a given order in the chiral power counting. The results will serve to improve the extrapolation of lattice results to the chiral limit. PACS. 12.38.-t Quantum chromodynamics – 12.38.Bx Perturbative calculations – 12.39.Fe Chiral Lagrangians
1 Introduction In recent years one has learned that many aspects of hadron structure can be described in the unifying framework of generalized parton distributions (GPDs). This framework allows one to combine information which comes from very different sources in an efficient and modelindependent manner. The field was pioneered in [1–3] and has evolved to considerable complexity, reviewed, for instance, in [4–7]. As GPDs can be analyzed using standard operator product expansion techniques [1, 8], their moments can be and have been calculated in lattice QCD [9]. Lattice calculations of well-measured quantities can be used to check the accuracy of the method, which may then be employed to evaluate quantities that are much harder to determine experimentally. This complementarity is especially valuable in the context of GPDs, because experimental measurements as, e.g., in [10] may not be sufficient to determine these functions of three kinematic variables in a model-independent way. Moreover, several moments of GPDs admit a physically intuitive interpretation in terms of the spatial and spin structure of hadrons, see, e.g., [2, 11–13]. A notorious problem of lattice QCD is the need for various extrapolations from the actual simulations with finite lattice spacing, finite volume and unphysically heavy quarks to the continuum, infinite volume and physical quark masses. Simple phenomenological fits are often still a
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sufficient in view of the general size of uncertainties, but with increasing numerical precision more reliable methods have to be applied. Chiral perturbation theory (ChPT) provides such a method [14]. Describing the exact lowenergy limit of QCD it predicts the functional form for the dependence of observables on the finite volume and the pion mass [15] and also the finite lattice spacing [16]. At a given order in the expansion parameter, ChPT defines a number of low-ener
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