Measurement of azimuthal asymmetries associated with deeply virtual Compton scattering on a longitudinally polarized deuterium target
Introduction
Generalized Parton Distributions (GPDs) provide a framework for describing the multidimensional structure of the nucleon [1], [2], [3]. GPDs encompass parton distribution functions and elastic nucleon form factors as limiting cases and moments, respectively. Parton distribution functions are distributions in longitudinal momentum fraction of partons in the nucleon, and are extracted from measurements of inclusive and semi-inclusive deep-inelastic scattering. Form factors are related to the transverse spatial distribution of charge and magnetization in the nucleon. Both form factors and (transverse-momentum-integrated) parton distribution functions represent one-dimensional distributions, whereas GPDs provide correlated information on transverse spatial and longitudinal momentum distributions of partons [4], [5], [6], [7], [8], [9]. Furthermore, access to the total parton angular momentum contribution to the nucleon spin may be provided by GPDs through the Ji relation [3].
Hard exclusive leptoproduction of a meson or photon, with only an intact nucleon or nucleus remaining in the final state, can be described in terms of GPDs. GPDs depend on four kinematic variables: t, x, ξ, and . In this case, t is the Mandelstam variable, or the squared four-momentum transfer to the target, given by , where p () is the initial (final) four-momentum of the target. In the ‘infinite’ target-momentum frame, x and ξ are related to the longitudinal momentum of the parton involved in the interaction as a fraction of the target momentum. The variable x is the average momentum fraction and the variable ξ, known as the skewness, is half the difference between the initial and final momentum fractions carried by the parton. The evolution of GPDs with , with the difference between the four-momenta of the incident and scattered leptons, can be calculated in the context of perturbative quantum chromodynamics as in the case of parton distribution functions. This evolution has been evaluated to leading order [1], [2], [3], [10] and next-to-leading order [11], [12], [13] in the strong coupling constant . The skewness ξ can be related to the Bjorken scaling variable through in the generalized Bjorken limit of large , and fixed and t. There is currently no consensus as to how to define ξ in terms of experimental observables; hence the experimental results are typically reported as projections in . The entire x dependences of GPDs are generally not experimentally accessible, an exception being the trajectory [14], [15].
GPDs can be constrained through measurements of cross sections and asymmetries in exclusive processes such as exclusive photon or meson production. In this paper, the Deeply Virtual Compton Scattering (DVCS) process, i.e., the hard exclusive production of a real photon, is investigated using a longitudinally polarized deuterium target.
The spin-1/2 nucleon is described by four leading-twist quark-chirality-conserving GPDs H, E, and [1], [2], [3], [16]. In contrast, DVCS leaving the spin-1 deuteron intact requires nine GPDs: , , , , , , , and [17], [18], [19]. In the forward limit of vanishing four-momentum transfer to the target nucleon ( and ), the pairs of GPDs (H, ) and (, ) reduce respectively to quark number density and helicity distributions. In this limit the GPD , sensitive to tensor effects in the deuteron, reduces to the tensor structure function , which was measured in inclusive deep-inelastic scattering on a tensor polarized deuterium target [20]. Both and are associated with the 5% D-wave component of the deuteron wave function in terms of nucleons [22]. In addition to GPD , they both contribute to the beam-helicity and beam-charge asymmetries. The term with GPD dominates in the beam-helicity ⊗ tensor asymmetry in DVCS from a longitudinally polarized deuterium target at very small values of t [18]. At this kinematic condition, the asymmetry with respect to target polarization is dominated by the term with GPD . Thus, the measurement of certain asymmetries in DVCS on a polarized deuterium target may provide new constraints for these GPDs.
This paper reports the first observation of azimuthal asymmetries with respect to target polarization alone and with respect to target polarization combined with beam helicity and/or beam charge, for exclusive electroproduction of real photons from a longitudinally polarized deuterium target. The asymmetries arise from the DVCS process where the photon is radiated by the struck quark, and its interference with the Bethe–Heitler (BH) process where the photon is radiated by the initial or final state lepton. The resulting asymmetries combine contributions from the coherent process , and the incoherent process where in addition a nucleon may be excited to a resonance. The coherent reaction contributes mainly at very small values of t, while the incoherent process dominates elsewhere. It is natural to model the incoherent process as scattering on only one nucleon in the deuteron, while the other nucleon acts as a spectator. Monte Carlo simulations in HERMES kinematic conditions [23] suggest that the proton contributes about 75% of the incoherent yield and the neutron about 25%, and included in these, nucleon resonance production contributes about 22% of the incoherent yield. The incoherent reaction on a proton dominates that on a neutron because of the suppression of the BH amplitude on the neutron by the small elastic electric form factor at low and moderate values of the momentum transfer to the target. The dependence of the measured asymmetries on the kinematic conditions of the reaction is also presented and these results on the deuteron are compared where appropriate with the corresponding results obtained on a longitudinally polarized hydrogen target [24].
Section snippets
Scattering amplitudes
The DVCS process is currently the simplest experimentally accessible process that can be used to constrain GPDs. The initial and final states of DVCS are indistinguishable from those of the competing BH process. For a target of atomic mass number A and no target polarization component transverse to the direction of the virtual photon, the general expression for the cross section of the coherent reaction or incoherent reaction reads [18], [25]
The HERMES experiment
A detailed description of the HERMES spectrometer can be found in Ref. [30]. A longitudinally polarized positron or electron beam of energy 27.6 GeV was scattered off a longitudinally polarized deuterium gas target internal to the HERA lepton storage ring at DESY. The lepton beam was transversely self-polarized by the emission of synchrotron radiation [31]. Longitudinal polarization of the beam at the target was achieved by a pair of spin rotators in front of and behind the experiment [32]. The
Event selection
The data sets used in the extraction of the various asymmetries reported here are given in Table 1. In this analysis, it was required that events contain exactly one charged-particle track identified as a lepton with the same charge as the beam lepton, and one photon producing an energy deposition () in the calorimeter (preshower detector). The following kinematic requirements were imposed on the events, as calculated from the four-momenta of the incoming and outgoing lepton:
Extraction formalism
The simultaneous extraction of Fourier amplitudes of beam-charge and beam-helicity asymmetries combining data collected during various running periods at HERMES for both beam charges and helicities on unpolarized hydrogen or deuterium targets is described in Refs. [26], [27]. It is based on the maximum likelihood technique [41], which provides a bin-free fit in the azimuthal angle ϕ (see Ref. [42] for details). In this paper, data taken with a longitudinally polarized deuterium target were
Background corrections and systematic uncertainties
The asymmetry amplitudes are corrected for background contributions, mainly decays to two photons of semi-inclusive neutral mesons, using the method described in detail in Ref. [42]. The average contribution from semi-inclusive background is 4.6%. The contribution of exclusive pions is neglected, as it is found to be less than 0.7% in each kinematic bin, supported by studies of HERMES data [43]. After applying this correction, the resulting asymmetry amplitudes are expected to originate from
Single- and double-spin asymmetries
The results for the Fourier amplitudes of the single-charge asymmetries , and are presented in Fig. 1, Fig. 2, Fig. 3 as a function of −t, , or and are also given in Table 5. While the variable would be the appropriate choice to present experimental results for pure coherent scattering, the nucleonic Bjorken variable is the practical choice in this case where incoherent scattering dominates over most of the kinematic range. The
Summary
Azimuthal asymmetries with respect to target polarization alone and also combined with beam helicity and/or beam charge for hard exclusive electroproduction of real photons in deep-inelastic scattering from a longitudinally polarized deuterium target are measured for the first time. The asymmetries are attributed to the interference between the deeply virtual Compton scattering and Bethe–Heitler processes. The asymmetries are observed in the exclusive region of the
Acknowledgements
We gratefully acknowledge the DESY management for its support and the staff at DESY and the collaborating institutions for their significant effort. This work was supported by the Ministry of Economy and the Ministry of Education and Science of Armenia; the FWO-Flanders and IWT, Belgium; the Natural Sciences and Engineering Research Council of Canada; the National Natural Science Foundation of China; the Alexander von Humboldt Stiftung, the German Bundesministerium für Bildung und Forschung
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Cited by (0)
- 1
Now at: Brookhaven National Laboratory, Upton, NY 11772-5000, USA.
- 2
Now at: Massachusetts Institute of Technology, Cambridge, MA 02139, USA.
- 3
Now at: Institut für Physik, Universität Mainz, 55128 Mainz, Germany.
- 4
Now at: Institut für Kernphysik, Universität Frankfurt a.M., 60438 Frankfurt a.M., Germany.
- 5
Now at: Carnegie Mellon University, Pittsburgh, PA 15213, USA.