Measurements of Gluon Polarization

As mentioned above, the experiment E704 at FNAL has measured the for multi-photon production in polarized pp collisions at GeV [5]. The multi-photons are presumably originated in the electromagnetic part of the jet energy. Since jet-production is highly dominated by the gluon-gluon scattering and gluon-quark scattering, the asymmetry is quite sensitive to the gluon polarization. The measured asymmetries have been compared with the model predictions. This is one of the constraints currently available.

Several groups have analyzed experimental data on asymmetry to extract gluon polarization. For example, Ball, Forte, Ridolfi performed next-to-leading order (NLO) analysis of the experimental data and concluded that most probable size of the gluon polarization is around [13]

One of the most reliable channels to measure the gluon polarization is high prompt photon production. The production cross section measured at CERN and FNAL has been used to extract gluon distribution.

The production in pp collision is dominated by the gluon Compton process followed by annihilation process. Our Monte Carlo simulation study by PYTHIA [14] shows about 90% of the production originates in the gluon Compton process. If the polarization of the anti-quark is small, actually this can be checked in weak boson production, the contribution of annihilation process to the asymmetry can be negligible, and the asymmetry can be written at the leading order (LO) as

Since partonic level asymmetry is calculated in QCD, and quark polarization has been measured in pol-DIS experiments, thus gluon polarization can be extracted from the experimentally measured asymmetry, .

For the complete reconstruction of the partonic level kinematics, the detection of the quark jet is desirable. The STAR detector system is advantageous in the jet detection due to its hermetic coverage. The jet finding efficiency with STAR detector in pp collision at GeV is about 50-85% depending on the of jet with the resolution of 30% [15]. In the PHENIX detector system, the reconstruction of the quark jet momentum is very difficult. The momentum fraction carried by initial gluon, however, can be estimated with full-fledged Monte Carlo simulation like PYTHIA and plotted as a function of photon in Figure 4.

The yield has been calculated using PYTHIA utilizing parton distribution set GRV94LO [16] and listed in Table iv for both 200 GeV and 500 GeV. In addition, the sensitivity of the gluon polarization measurement has been evaluated assuming the product of . The results are summarized in Table iv.

  
Table iv: Sensitivity summary for the measurements of gluon polarization via prompt production.

The main difficulty in the detection of the prompt photon in pp collision is the huge background from . Basically invariant mass of two photons should be useful to identify the origin, but not perfect. In the low region, the fake photon due to one photon missing the detector is dominant. In the higher region, two photons from neutral meson tend to merge into one cluster within a finite resolution of the detector and fake single photon. Even a severe background from radiative decay of the mesons is expected to to be reducible significantly by requiring isolation of the photon from other particles. Indeed, the simulation studies using PYTHIA shows that the detection of prompt photon will be feasible in the region, 1030 GeV/c.

  
Figure 4: Correlation between Bjorken-x and transverse momentum of photon.

For further test of the measurement of gluon polarization, we are investigating the asymmetry for open heavy quark and heavy quarkonium productions. Especially recent studies show that dimuon production in pp collision at GeV is dominated by coincidental semi-leptonic decay of D-mesons. Since the production of charm quark in pp collision is dominated by gg scattering, the asymmetry for the production is sensitive to polarized gluon density. The next-to-leading order calculation of the asymmetry is partially done [17,18]. In addition, charmonium production has been quoted to be very sensitive to the polarized gluon density for long time basing on LO calculations [19,20,21]. Recent CDF data have, however, shown that LO calculation of the cross section significantly underestimates experimentally measured cross sections [22]. It seems that any model on the production has failed to reproduce the every aspects of the production, such as rapidity distribution, distribution, and polarization of the charmonia. Since various higher mass states contribute to production, measurement of the asymmetry for production has been proposed and the study is underway [23].