DESY 15-254 Baryon octet distribution amplitudes in Wandzura-Wilczek approximation

Hard exclusive processes give us unique possibility to study internal structure of hadrons. The theoretical description of exclusive processes is based on the QCD factorization approach [1–6]. Scattering amplitudes (decay amplitudes) in this approach are given by convolution of the coefficient function which can be calculated perturbatively with nonpertubative functions – the distribution amplitudes (DAs). In the infinite momentum frame DAs can be interpreted as the momentum fraction distributions of partons in hadrons. The DAs are usually classified according to their twist. In the QCD factorization approach, where the relevant Q2 is large, the dominant contributions to an amplitude come from DAs of lowest possible twist. The higher twist DAs give rise to the power suppressed corrections. The factorization approach works quite well for the mesons but for baryons it encounters conceptual difficulties (see Refs. [7–11]). Also one faces the difficulties in attempt to provide a quantitative description of the current experimental data, the electromagnetic nucleon form factors, in particular. A quantitative description of the nucleon electromagnetic form factors has been achieved in the framework of the lightcone rules (LCSR) [12–14] by taking into account the power suppressed [15–18] and next-to-leading order [19, 20] corrections. As it has been shown, the power suppressed corrections, which are parameterized by the higher twist nucleon DAs, give sizeable contribution for moderate Q2 ∼ 2−5GeV. Unfortunately, our knowledge of the nucleon (baryon) DAs is quite limited. Only the leading twist nucleon DA is known with some degree of certainty, while the estimates of the higher twist nucleon DAs are very poor (see e.g. Refs. [16, 17, 20, 21] and reference therein). At the same time, the higher twist DAs contain the contributions that are related to the lower twist DAs – the so-called Wandzura-Wilczek (WW) contributions [22]. For mesons, the genuine higher twist DAs often appear to be much smaller than the corresponding WW terms. In many cases, keeping only the WW terms one gets a quite good approximation for the higher twist DAs (the so-called WW approximation). The lowest twist meson DAs are defined by matrix elements of two-particle (quark-antiquark or gluon) light-ray operators. For such operators the WW contributions were calculated a long ago. A detailed discussion of the method can be found in Ref. [23]. We also mention here that WW corrections to the generalized parton distributions were derived in [24–28]. The situation with baryon DAs is more complicated because they are determined by matrix elements of three-particle (three-quarks) operators. Until now the WW corrections were only known for the first few moments of the nucleon DAs [15, 16]. The effective technique that allows one to calculate the WW terms for the multiparticle DAs was developed in [29, 30]. The approach is based on the spinor formalism and conformal wave expansion for the light-ray operators. Using this technique the WW corrections to the three-particle nucleon DAs were calculated up to twist-5 [29, 30]. In the present paper we, keeping in mind the recent progress in lattice calculations of the baryon DA moments [31], derive the SUF(3) baryon octet DAs in the WW approximation. The paper is organized as follows: in Sect. II we remind the basics of the spinor formalism and fix our notations. In Sect. III, we give the definitions of the DAs for the baryon octet. The subsections III A, III B contain the analysis of the mixed chirality DAs up to twist-5 and in the subsection III C we consider the chiral DAs of twist-4 and 5. The Appendices contain the SUF(3) relations between different DAs and explicit expressions for the few first polynomials entering the expansion of baryon DAs.