Baryon octet distribution amplitudes in Wandzura-Wilczek approximation

Hard exclusive processes give us a unique possibility to study the 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 nonperturbative 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 Q is large, the dominant contributions to an amplitude come from DAs of lowest possible twist. The highertwist DAs give rise to the power-suppressed corrections. The factorization approach works quite well for the mesons but for baryons it encounters conceptual difficulties. Namely, it has been shown in Refs. [7–10] that the soft rescattering processes produce contributions that break the factorization theorems; see for a detailed discussion Refs. [11–13]. A quantitative description of the nucleon electromagnetic form factors has been achieved in the framework of the light-cone rules [14–16] by taking into account the power-suppressed [17–20] and next-to-leading-order [21,22] corrections. As it has been shown, the powersuppressed corrections, which are parameterized by the higher-twist nucleon DAs, give a sizable contribution for moderate Q ∼ 2–5 GeV. 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. [18,19,22,23], and references 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 [24]. For mesons, the genuine higher-twist DAs often appear to be smaller than the corresponding WW terms (see, for example, [25,26]). In many cases, keeping only the WW terms one gets a quite good approximation for the highertwist 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 long ago. A detailed discussion of the method can be found in Ref. [25]. We also mention that WW corrections to the generalized parton distributions have been derived in [27–31] and the relevant problem of WW contributions has been considered in Refs. [32–37]. The situation with baryon DAs is more complicated because they are determined by matrix elements of threeparticle (three-quark) operators. Until now the WW corrections were only known for the first few moments of the nucleon DAs [17,18]. The effective technique that allows one to calculate the WW terms for the multiparticle DAs was developed in [38,39]. 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 [38,39]. In the recent paper [40] the first results of the lattice calculation of the baryon octet DAs moments have been presented. Keeping in mind ongoing progress in lattice calculations, one can expect that information on highertwist DAs will be available soon. Therefore, in the present paper, we derive the WW corrections to the higher-twist baryon octet DAs. The paper is organized as follows: in Sec. II we recall the basics of the spinor formalism and fix our notations. In Sec. III, we give the definitions of the DAs for the baryon octet. Sections III A and III B contain the analysis of the mixed chirality DAs up to twist 5 and in Sec. III C we consider the chiral DAs of twist 4 and 5. The Appendixes contain the SUFð3Þ relations between different DAs and explicit expressions for the few first polynomials entering the expansion of baryon DAs. PHYSICAL REVIEW D 93, 034024 (2016)