Pion parton distribution function in the valence region

Abstract

The parton distribution function of the pion in the valence region is extracted in a next-to-leading order analysis from Fermilab E-615 pionic Drell-Yan data. The effects of the parameterization of the pion's valence distributions are examined. Modern nucleon parton distributions and nuclear corrections were used and possible effects from higher twist contributions were considered in the analysis. In the next-to-leading order analysis, the high-x dependence of the pion structure function differs from that of the leading order analysis, but not enough to agree with the expectations of pQCD and Dyson-Schwinger calculations.The pion has a central role in nucleon and nuclear structure. The pion has not only been used to explain the long-range nucleon-nucleon interaction, but also to explain the flavor asymmetry observed in the quark sea in the nucleon. Experimental knowledge of the parton structure of the pion arises primarily from pionic Drell-Yan scattering [1,2,3,4] from nucleons in heavy nuclei. Recently, the shape of the extracted pion parton distribution function (PDF) at high-x, where x is the fraction of the pion momentum carried by the interacting quark, i.e. Bjorken-x, has been questioned [5].The anomalously light pion mass is believed to arise from dynamical chiral symmetry breaking. Any model of the pion must account for its dual role as a quarkantiquark system and the Goldstone boson of dynamical chiral symmetry breaking. Theoretical descriptions of pionic parton structure at high-x disagree. The parton model [6], perturbative quantum chromodynamics (pQCD) [7,8] and some non-perturbative calculations such as Dyson-Schwinger Equation (DSE) models [5,9,10,11,12] indicate that the high-x behavior should be near (1 − x) a , with a 2. In contrast, relativistic constituent quark models [13,14], Nambu-Jona-Lasinio models with translationaly invariant regularization [15,16,17,18], Drell-Yan-West relation [19,20] and even duality arguments [21] favor a linear high-x dependence of (1 − x). Instanton-based models appear to lie in between these two [22]. Lattice calculations yield only the moments of the distributions and not the PDFs themselves [23,24].While the PDFs for the nucleon are now well determined by global analyses of a wide range of precise data (see e.g. [25,26,27]) the pion PDFs are very poorly known. Presently there are only two experimental techniques to access quark distributions in the pion: the deep inelastic scattering from the virtual pion cloud of the proton for which data is available in the low-x, sea region (3 × 10 −4 ≤ x ≤ 0.01) [28,29], and the Drell-Yan mechanism which provides data in the valence region (0.2 ≤ x ≤ 0.99). Unfortunately there is no overlap between these two experimental techniques.A previous leading order (LO) analysis of pionic Drell-Yan data by J. Conway et al. (Fermilab E615) [1] sug-

Diffractive excitation of heavy flavors: Leading twist mechanisms

“…The same problem appears in the Drell-Yan reaction at x F → 1, as is seen in data [23]. Therefore, one should not rely on QCD factorization at large x F → 1.…”

“…Now we are in the position to group the longitudinal amplitudes in a similar form to the transverse ones, getting the light-cone distribution amplitudes corresponding to the bremsstrahlung and production mechanisms, 23) where the longitudinal distribution amplitudes Φ L read, .24) …”

Nucleon and pion distribution functions in the valence region

“…The consideration of NNLO, as well as NLO diagrams, also leads to a simple factorization of the cross-section and an approximate factor of two for K. The factorization scheme dependence of the K-factor is described at length in (van Neerven and Zijlstra, 1992). We note in addition that the K factor depends on kinematics, a fact shown in (Wijesooriya et al, 2005) to be important at very high x for pionic Drell-Yan studies.…”

Hadron properties and Dyson–Schwinger equations

“…It would be very interesting to know, e.g., how, if at all, the distribution functions of a Goldstone mode differ from those of other hadrons. Calculation [91] and experiment [92] together are needed to address that issue.…”