πN sigma term and chiral-odd twist-3 distribution function e(x) of the nucleon in the chiral quark soliton model

Abstract

The isosinglet combination of the chiral-odd twist-3 distribution function e u (x) + e d (x) of the nucleon has outstanding properties that its first moment is proportional to the well-known πN sigma-term and that it contains a δ-function singularity at x = 0. These two features are inseparably connected in that the above sum rule would be violated, if there is no such a singularity in e u (x) + e d (x). Very recently, we found that the physical origin of this δ-function singularity can be traced back to the long-range quark-quark correlation of scalar type, which signals the spontaneous chiral symmetry breaking of the QCD vacuum. The main purpose of the present paper is to give complete theoretical predictions for the chiral-odd twist-3 distribution function e a (x) of each flavor a on the basis of the chiral quark soliton model, without recourse to the derivative expansion type approximation. These theoretical predictions are then compared with the empirical information extracted from the CLAS data of the semi-inclusive DIS processes by assuming the Collins mechanism only. A good agreement with the CLAS data is indicative of a sizable violation of the πN sigma-term sum rule, or equivalently, the existence of a δ-function singularity in e u (x) + e d (x).

Transverse momentum distributions of quarks in the nucleon from the chiral quark soliton model

“…(The use of more time consuming double-subtraction scheme is mandatory, however, for some special parton distribution functions containing quadratic divergences. An example is the chiral-odd twist-3 unpolarized distribution functions eðxÞ investigated in [56][57][58][59]. )…”

Semi-inclusive deep-inelastic scattering in Wandzura-Wilczek-type approximation

“…The degrees of freedom in this model are quarks, antiquarks, and Goldstone bosons, which are strongly coupled (the coupling constant is ∼ 4) and has to be solved using nonperturbative techniques (expansion in 1/N c , where N c is the number of colors) with the nucleon described as a chiral soliton. In general, the model predicts non-zero tilde-terms, for instanceẽ a (x) = 0 [98][99][100]. However, despite strong interactions in this effective theory, the tilde termf ⊥q (x, k 2 ⊥ ) vanishes exactly in this model [93] and the WW-type approximation (3.3b) becomes exact at the low initial scale of this model of µ 0 ∼ 0.6 GeV.…”

Recent progress in QCD condensate evaluations and sum rules

“…After obtaining m 2 , |λ| 2 can be easily extracted from Eq. (193). As a result, m 2 and |λ| 2 become functions of M 2 and s th , which are parameters that physical observables should not depend on.…”