Deep exclusive charged π electroproduction above the resonance region Murat M. Kaskulov ∗ and Ulrich Mosel Institut f¨ ur Theoretische Physik, Universit¨ at Giessen, D-35392 Giessen, Germany (Dated: November 16, 2018) A description of exclusive charged pion electroproduction ( e, e $^{′}$π$^{±}$) off nucleons at high energies is proposed. The model combines a Regge pole approach with residual effect of nucleon resonances. The exchanges of π (140), vector ρ (770) and axial-vector a$_{1}$ (1260) and b$_{1}$ (1235) Regge trajectories are considered. The contribution of nucleon resonances is described using a dual connection between the exclusive hadronic form factors and inclusive deep inelastic structure functions. The model describes the measured longitudinal, transverse and interference cross sections at JLAB and DESY. The scaling behavior of the cross sections is in agreement with JLAB and deeply virtual HERMES data. The results for a polarized beam-spin azimuthal asymmetry in ( ⃗ e, e $^{′}$π$^{±}$) are presented. Model predictions for JLAB at 12 GeV are given. PACS numbers: 12.39.Fe, 13.40.Gp, 13.60.Le, 14.20.Dh At JLAB the exclusive reaction p ( e, e ′ π $^{+}$) n has been studied for a wide range of photon virtualities Q 2 at an invariant mass of the π $^{+}$n system around the onset of deep inelastic scattering (DIS) regime, W ≃ 2 GeV [1– 5]. A separation of the cross section into the trans- verse σ$_{T}$ , longitudinal σ$_{L}$ and interference σ$_{TT}$ and σ$_{LT}$ components has been performed. The CLAS data for the polarized beam single-spin asymmetry in p ( ⃗ e, e ′ π $^{+}$) n are also available [6]. The HERMES data at DESY [7] extend the kinematic region to much higher values of W 2 > 10 GeV 2 toward the true DIS region Q 2 ≫ 1 GeV 2 and much higher values of − t . The cross section for p ( e, e ′ π $^{+}$) n has also been measured above the resonance region at the Cambridge Electron Accelerator (CEA) [8], in p ( e, e ′ π $^{+}$) n and n ( e, e ′ π − ) p at the Wilson Synchrotron Laboratory at Cornell [9–11] and DESY [12–16]. see Ref. [4] and references therein. Previous measure- ments [1, 2, 11] at smaller and much higher values of Q 2 show a similar problem in the understanding of σ$_{T}$ . Al- ready from values of Q 2 > 0 . 6 GeV 2 the meson-exchange and/or Regge pole models are not compatible with the measured interference σ$_{TT}$ and σ$_{LT}$ cross sections and the extraction of the pion form factor relies on the fit to the longitudinal cross section σ$_{L}$ only [5]. A remarkably rich experimental data base obtained for N ( e, e ′ π ) N ′ above the resonance region remains unexplained [3, 4]. On the other hand, a detailed knowledge of the p ( e, e ′ π $^{+}$) n re- action above the resonances √$_{s >}$ 2 GeV is mandatory for the interpretation of the color transparency signal ob- served in this reaction off nuclei [23, 24]. A possible description of σ$_{T}$ at JLAB has been pro- posed in Ref. [25]. The approach followed there is to complement the hadron-like interaction types in the t - channel, which dominate in photoproduction and low Q 2 electroproduction, with the direct interaction of virtual photons with partons followed by string (quark) fragmen- tation into π $^{+}$n . Then σ$_{T}$ can be readily explained and both σ$_{L}$ and σ$_{T}$ can be described from low up to high values of Q $^{2}$. In [25] the reaction p ( e, e ′ π $^{+}$) n is treated as an exclusive limit, z → 1, of semi-inclusive DIS The longitudinal cross section σ$_{L}$ is generally thought to be well understood in terms of the pion quasi-elastic knockout mechanism [17] because of the pion pole at low − t . If true, this makes it possible to study the charge form factor of the pion at momentum transfer much bigger than in the scattering of pions from atomic electrons [18]. On the other hand, the transverse cross section σ$_{T}$ is predicted to be suppressed by ∼ 1 /Q 2 with respect to σ$_{L}$ for sufficiently high values of Q 2 and W [19]. On the experimental side, however, the JLAB data show that at forward angles σ$_{T}$ is large. For instance, at Q 2 = 3 . 91 GeV 2 [3] σ$_{T}$ is by about a factor of two larger than σ$_{L}$ and at Q 2 = 2 . 15 GeV 2 it has same size as σ$_{L}$ in agreement with previous JLAB measurements [1]. in the spirit of an exclusive-inclusive connection [26]. The transverse cross section in n ( e, e ′ , π − ) p has been pre- dicted to be smaller than in p ( e, e ′ , π $^{+}$) n . The model [27] has also been applied to values of ( Q $^{2}$, W ) in the DIS re- gion at HERMES [7]. In [27] σ$_{T}$ in DIS gets much smaller in the forward π + production, but still dominates the off- forward region. There is a long standing issue concerning the reaction mechanisms contributing to deeply virtual π electropro- duction above the resonance region [20–22]. The models which describe ( e, e ′ π ± ) in terms of hadronic degrees of freedom fail to reproduce σ$_{T}$ observed in these reactions, However, in [25, 27] the transverse cross section σ$_{T}$ it- self was modeled and the solution of the problem on the amplitude level is still missing. Both the soft hadronic and hard partonic parts of the amplitude can in prin- ciple interfere making non-additive contributions to σ$_{L}$ and to interference σ$_{TT}$ and σ$_{LT}$ cross sections. One might describe this transverse strength in the language of perturbative QCD by considering higher twist correc- $^{∗}$Electronic address: kaskulov@theo.physik.uni-giessen.de p ( $_{e, e}$′$_{π}$ $^{+}$) X $^{z}$→ 1 −→ p ( $_{e, e}$′$_{π}$ $^{+}$) n (1) I. INTRODUCTION arXiv:1001.1952v1 [hep-ph] 12 Jan 2010