Measurement

Direct photon production in pp interactions is dominated by the quark-gluon Compton subprocess, and the asymmetry is directly sensitive to the polarized gluon distribution. Indeed, the NLO calculation [24] of prospects for the inclusive photon production study with HERA- showed a sufficient statistical accuracy of HERA- to discriminate between different polarized gluon distribution functions.

The production of quarkonium states, in particular inclusive production, is a similarly clean tool to measure the polarized gluon distribution. For the production of quarkonia with above 1.5 GeV the subprocess provides the main contribution. Because of the relatively large quark mass the production cross section and the expected asymmetry are supposed to be calculable perturbatively. The expected asymmetry is proportional to and the projected statistical accuracy of HERA- allows for a very good discrimination between different parametrizations of [3].

  
Figure 1: The asymmetry and projected statistical errors for production at HERA- and two different energies at RHIC as a function of .

The expected double spin asymmetry for production at RHIC energies is much smaller. In fig. 1 predictions at HERA- and two different RHIC energies are shown with projected statistical errors. In the statistically accessible interval the asymmetry ranges between 0.08 and 0.10 at HERA-, but only between 0.01 and 0.03 at RHIC energies. It is likely that the fixed target experiment at HERA might accomplish a more significant measurement of the charmonium production asymmetry.

The inclusive two-jet production involves several hard subprocesses (gg, gq, qq scattering) with gluons. The extraction of the two-jet production cross-section at the given HERA- fixed target kinematics is problematic, as was described in some more detail in ref. [2]. As a possible way out one may presumably replace the two jets by two correlated high hadrons opposite in azimuth.
The asymmetry in open charm production could possibly be measured using as a tag a high single muon or electron-muon pairs from charm decays. This option, as well as two-jet production, needs further study.

The complete kinematics of the underlying hard 22 subprocess can be reconstructed if the away-side jet in the production of photon or is measured, as well. In this case the asymmetry can be directly related to the polarized gluon distribution [2]. Using this approach photon plus jet production was discussed in Ref. [3] as a tool to directly measure G/G. In fig. 2 the projected statistical sensitivity of HERA- for the measurement, on the present level of understanding, is shown vs. in conjunction with predicted errors for STAR running

  
Figure 2: Typical predictions for the polarized gluon distribution (LO calculations from Ref. [27]) confronted to the projected statistical errors expected for HERA- and RHIC experiments.

at RHIC at 200 GeV c.m. energy [26]. The errors demonstrate clearly that in the region a significant result from photon plus jet production can be expected from HERA- with an accuracy being about competitive to that predicted for RHIC.

In plus jet production the quark-gluon subprocess contributes only about 10% to the asymmetry compared to the gluon-gluon fusion subprocess. The prospect of a measurement at HERA- is shown as an additional entry in fig. 2. Although the interval () explored by both HERA- and RHIC is quite comparable, the different transverse momentum ranges accessed (2...8 GeV at HERA-; 10...40 GeV at RHIC) make both measurements indeed complementary; would be studied by HERA- in the pQCD onset region whereas the RHIC experiments will explore in the deep perturbative region.