Pion parton distributions in a nonlocal Lagrangian

Abstract

We use phenomenological nonlocal Lagrangians, which lead to non trivial forms for the quark propagator, to describe the pion. We define a procedure based on previous studies on non local lagrangians for the calculation of the pion parton distributions at low Q 2 . The obtained parton distributions fulfill all the wishful properties. Using a convolution approach we incorporate the composite character of the constituent quarks. We evolve, using the Renormalization Group, the calculated parton distributions to the experimental scale and compare favorably with the data and draw conclusions.PACS numbers: 11.10. St, 12.38.Lg, 13.60.Fz, 24.10.Jv I. INTRODUCTIONParton Distributions Functions (PDFs) and Generalized Parton Distributions (GPDs) [1,2,3], relating PDFs and electromagnetic form factors, encode unique information on the non perturbative hadron structure (for a recent review, see [4]). Any realistic model of hadron structure should be able to calculate them. We shall proceed in here to study the parton distribution functions of the pion in a previous developed formalism [5].From the experimental point of view the PDFs and GPDs of the pion are difficult to determine. Pions decay into muons or photons and therefore the pion distribution functions can not be obtained from direct DIS experiments. The pion parton distribution has been inferred from the Drell-Yang process [6,7,8] and direct photon production [9] in pion-nucleon and pion-nucleus collisions. These set of experiments have been analyzed in ref. [10] obtaining that the fraction of moment of each valence (anti)quark in the pion is about 0.23 for Q 2 = 4 GeV 2 . The parton distribution functions of the pion has been a subject of much discussion in the literature. In [11,12] calculations using quenched lattice QCD, for their lowest moments, were performed. The lack of sea quarks in the approximation implies a greater presence of valence quarks. Its PDFs [13,15] and GPDs [16] have been also calculated in the Nambu-Jona Lasinio (NJL) model [17]. In the chiral limit, its quark valence distribution is as simple as q (x) = θ (x) θ (1 − x) . Once evolution is taken into account, good agreement is reached between the calculated PDFs and the experimental results [13]. The pion PDFs and GPDs have also been calculated in a model with the simplest pseudoscalar coupling between the pion and the constituent quark fields [14], and in the instanton model, [19,20]. In ref.[19] the chiral limit result of the NJL model for PDFs changes such that q (x) goes to zero for x → 0 and x → 1. The pion PDFs have also been calculated in a spectral quark model [18]. Also, the pion PDFs have been calculated in a statistical model, without any dynamical assumption, obtaining quite reasonable results [21] . In [22] the GPDs of the pion are calculated in the bag model. A relevant contribution to the calculation of the pion GPDs on the light-front has been given by Tiburzi and Miller [23], and some remarks on the use of the light-front for calculating GPDs can be found in [24]. Looking f...

Distribution amplitudes of light mesons and the photon in the instanton model

“…Recently there have been published several papers [15][16][17][18], where in nonlocal models, similar to the one considered above, the distribution functions for pion and photon were treated inconsistently. Indeed, the typical expression (4) defining the distribution functions has two parts.…”

“…It is well known, that for example, the leading twist operators, entering the pion distribution amplitude and distribution function, are given by γ µ γ 5 and γ µ , correspondingly. Nevertheless, the authors of [15][16][17] included additional terms proportional to (k + k ) µ , where k and k are incoming and outgoing momenta of a quark. These additions in [15][16][17] modify the known results of the leading twist calculations.…”

“…Nevertheless, the authors of [15][16][17] included additional terms proportional to (k + k ) µ , where k and k are incoming and outgoing momenta of a quark. These additions in [15][16][17] modify the known results of the leading twist calculations. However, it is evident, see for example [1], that these additional terms contribute to twist-4 distributions and do not touch the leading twist-2 distributions.…”

Fragmentation functions and parton distribution functions for the pion with the nonlocal interactions

“…The Dyson-Schwinger (DS) method was applied to compute the valance-quark distribution function, resulting in relatively good agreement with the available experimental data for the pion and kaon [27]. Similarly, the pion parton distribution was studied with a nonlocal Lagrangian using the DS method [28]. In Ref.…”

Transversity Form Factors and Generalized Parton Distributions of the Pion in Chiral Quark Models

“…For the first part and within a non perturbative setup we apply chiral quark models which have proven to be very useful in the determination of the soft matrix elements entering various high-energy processes [1,2,5,[9][10][11][12][15][16][17]21,22,[25][26][27][28]30,32,33,36,40,[42][43][44][45][46][47][48][50][51][52]54,55]. We use the standard local Nambu-Jona-Lasinio (NJL) model with the Pauli-Villars regularization [49] and two versions of the nonlocal models, where the quark mass depends on the virtuality: the instanton-motivated model [23] and the Holdom-Terning-Verbeek (HTV) model [35] (these variants differ in the form of the quark-pion vertex).…”