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Single Spin Asymmetries

A study of single spin asymmetries in inclusive particle production is considered now as a way to investigate higher twist effects: there might be twist-3 dynamical contributions or hard scattering higher twists; there might also be intrinsic tex2html_wrap_inline445 effects, both in the quark fragmentation process and in the quark distribution functions. The contributions of the different effects are process dependent and therefore a comparative study of single spin asymmetries in different processes might be a unique way of understanding the origin and the importance of higher twist contributions in large tex2html_wrap_inline447 inclusive production.
There exists no consistent theoretical understanding yet of the role of higher twist contributions in single spin asymmetries. Existing phenomenological models predict a size of these asymmetries ranging from a few to tens of percent. Higher twist contributions should die out with increasing tex2html_wrap_inline447 and the asymmetries should approach zero as tex2html_wrap_inline451. There is, however, another approach in which single spin asymmetries are associated with the manifestation of non-perturbative dynamics and the asymmetries would be large even at high tex2html_wrap_inline447 [6]. Among them, instantons are becoming increasingly interesting as possible sources for single spin asymmetries [7].
In the following we discuss the capability of HERA-tex2html_wrap_inline455 to investigate single spin asymmetries.

Inclusive pion production tex2html_wrap_inline457 exhibits surprisingly large single spin asymmetries at large values of tex2html_wrap_inline459, as it was measured a few years ago by the E704 Collaboration using a transversely polarized 200 GeV beam [8]. For any kind of pions the asymmetry tex2html_wrap_inline461 (fig. 1) shows

  figure686
Figure 1: Single spin asymmetry in inclusive production of tex2html_wrap_inline463 [8] and tex2html_wrap_inline465 mesons [9].

a considerable rise above tex2html_wrap_inline467, i.e. in the fragmentation region of the polarized nucleon. It is positive for both tex2html_wrap_inline469 and tex2html_wrap_inline471 mesons, while it has the opposite sign for tex2html_wrap_inline473 mesons. The charged pion data taken in the range tex2html_wrap_inline475 GeV were split into two samples at tex2html_wrap_inline447 = 0.7  GeV/c; the observed rise is stronger for the high tex2html_wrap_inline447 sample.
New results on the asymmetry in tex2html_wrap_inline465 meson production were presented recently [9]. The asymmetry is positive and the behaviour is compatible with the one observed in tex2html_wrap_inline471 and tex2html_wrap_inline469 production (cf. fig.1).
There exist many results on asymmetry measurements in inclusive particle production at smaller energies. Recently, a new experiment with a 40 GeV polarized proton beam published data on the tex2html_wrap_inline447 dependence in the range tex2html_wrap_inline489 GeV/c, of the single spin asymmetry in tex2html_wrap_inline491, tex2html_wrap_inline493, p and tex2html_wrap_inline497 production in the central region (tex2html_wrap_inline499) [10]. The tex2html_wrap_inline447 dependence measured for the tex2html_wrap_inline469 asymmetry is compatible with older data obtained at beam energies of 13.3 and 18.5 GeV/c [11] if plotted as a function of tex2html_wrap_inline505. This appears to be in some contrast to the E704 data on the tex2html_wrap_inline471 asymmetry in the central region which shows a result compatible with zero up to tex2html_wrap_inline447 of about 4 GeV/c [12].

The tex2html_wrap_inline447 values accessible with HERA-tex2html_wrap_inline455 would be significantly larger than in all experiments performed up to now. The sensitivity tex2html_wrap_inline515 of the asymmetry measurement in inclusive production of different particles at HERA-tex2html_wrap_inline455 was calculated using the inclusive differential cross-sections obtained with the Monte-Carlo program PYTHIA 5.6 [13]. The results are shown in fig. 2 in the (tex2html_wrap_inline459, tex2html_wrap_inline447) plane as contours characterizing the sensitivity level tex2html_wrap_inline523 in a bin of tex2html_wrap_inline525 (GeV/c)tex2html_wrap_inline527. For produced particles lines of constant polar angle in the laboratory system are shown; they are given for pions, but represent also a good approximation for heavier particles.

  figure48
Figure 2: Contours of the asymmetry sensitivity level tex2html_wrap_inline523 for inclusive production of different particles in the tex2html_wrap_inline531 plane. Only the following decay modes are taken into account: tex2html_wrap_inline533, tex2html_wrap_inline535, tex2html_wrap_inline537, tex2html_wrap_inline539, tex2html_wrap_inline541, tex2html_wrap_inline543. Lines of constant laboratory angles of the particles are shown and marked with their values in units of mrad.

Experimentally, it is not a simple task to measure single spin asymmetries in the fragmentation region of the polarized nucleon in a fixed target experiment at 820 GeV. This region lies either at very large laboratory angles (a few tens of degrees) if a combination of polarized target and unpolarized beam is used, or it is at very small angles (a few mrad) for the other combination, unpolarized target and polarized beam (see fig. 2). The question how close to the HERA proton beam particles can be measured deserves a special study.
As can be seen from fig. 2, the combined tex2html_wrap_inline447 dependence of all involved higher-twist effects can be

  figure687
Figure 3: Capability of HERA-tex2html_wrap_inline455 to discriminate predictions [14] for different tex2html_wrap_inline447.

measured with good accuracy (tex2html_wrap_inline551) up to transverse momenta of about 8tex2html_wrap_inline55310 GeV/c in the central region tex2html_wrap_inline555 and up to 5tex2html_wrap_inline5536 GeV/c in the target fragmentation region. Hence the tex2html_wrap_inline447-range where higher twist effects are expected to be essential would be well covered. The capability of HERA-tex2html_wrap_inline455 to really prove a tex2html_wrap_inline447 dependence in the fragmentation region of the polarized nucleon is shown in fig. 3, where the curves were obtained [3] assuming a non-zero quark distribution analysing power, tex2html_wrap_inline565, according to Ref. [14]. The curves and the projected statistical errors in fig. 3 are drawn for the combination of polarized proton beam and unpolarized target and the minimal pion detection angle was assumed to be 5 mrad.
A measurement of the asymmetry in the inclusive production of particles with different quark contents may allow to study a flavour dependence of the higher twist contributions. In particular, it would be interesting to compare the asymmetry for pions and kaons what appears possible at HERA-tex2html_wrap_inline455 (see fig. 2a,c).

A sizeable inclusive production of tex2html_wrap_inline569 and tex2html_wrap_inline571 hyperons would allow to study the asymmetry in their production up to tex2html_wrap_inline447 of about 5tex2html_wrap_inline5536 GeV/c (fig. 2c). The measurement of the final-state tex2html_wrap_inline577 polarization via its decay would allow to study the polarization spin transfer coefficient, tex2html_wrap_inline579. A recent study by E704 [15] at moderate values of tex2html_wrap_inline447 (0.1tex2html_wrap_inline5531.5 GeV/c) showed a sizeable (up to 30%) spin transfer from the incident polarized proton to the outgoing tex2html_wrap_inline569.

The study of polarization asymmetries in inclusive vector meson production is especially attractive as these particles are produced `more directly' in comparison to pions which are mainly decay products of heavier particles. Comparing asymmetries in vector and pseudoscalar meson production can provide information on the magnitude of the asymmetry in quark scattering [16]. If the asymmetry is generated only during the fragmentation of polarized quarks, the asymmetry of tex2html_wrap_inline587 mesons is expected to be opposite in sign to that of pions, tex2html_wrap_inline589. On the contrary, if the quark scattering asymmetry were the dominating one, the asymmetries of pseudoscalar and vector mesons would not differ substantially.
The statistical sensitivity of HERA-tex2html_wrap_inline455 for measuring single spin asymmetries in inclusive production of tex2html_wrap_inline587, tex2html_wrap_inline595, and tex2html_wrap_inline597 vector mesons are presented in fig. 2b. The sensitivity for tex2html_wrap_inline587 production is at a level comparable to that for pions (fig. 2a), while for tex2html_wrap_inline595 and tex2html_wrap_inline597 mesons the reachable tex2html_wrap_inline447 values are lower. On the other hand, a study of the asymmetry in tex2html_wrap_inline595 and tex2html_wrap_inline597 production using the decay channels tex2html_wrap_inline611 and tex2html_wrap_inline535 could be easier since the level of the expected combinatorial background is smaller. Also, the asymmetry in tex2html_wrap_inline597 meson production could be useful for a study of the strange quark polarization in a nucleon [6].

Inclusive direct photon production, tex2html_wrap_inline617, proceeds without fragmentation, i.e. the photon carries directly the information from the hard scattering process. Hence this process measures a combination of initial tex2html_wrap_inline445 effects and hard scattering twist-3 processes. The first and only results up to now were obtained by the E704 Collaboration [17] showing an asymmetry compatible with zero within large errors for tex2html_wrap_inline621 GeV/c in the central region tex2html_wrap_inline623.
The experimental sensitivity of HERA-tex2html_wrap_inline455 was determined using cross-section calculations for the two dominant hard subprocesses, i.e. gluon-Compton scattering (tex2html_wrap_inline627) and quark-antiquark annihilation (tex2html_wrap_inline629), and of background photons that originate mainly from tex2html_wrap_inline471 and tex2html_wrap_inline465 decays. It turns out that a good sensitivity (about 0.05) can be maintained up to tex2html_wrap_inline635 8 GeV/c. For increasing transverse momentum the annihilation subprocess and the background photons are becoming less essential; we expect to be able to detect a clear dependence on tex2html_wrap_inline447, of the direct photon single spin asymmetry.

There is an interesting possibility [18, 19] to extract the third twist-2 quark distribution function (quark transversity distribution, tex2html_wrap_inline639 or tex2html_wrap_inline641) using inclusive production of two pions on the transversely polarized nucleon, tex2html_wrap_inline643. This structure function describing basically the fraction of transverse polarization of the proton carried by its quarks is totally unknown at present. In inclusive lepton DIS its contribution is suppressed by a quark mass whereas it is in principle accessible in semi-inclusive DIS [5, 19, 20]. The asymmetry in inclusive two-pion production would be studied as a function of the angle of the normal of the two-pion plane, tex2html_wrap_inline645, with respect to the polarization vector, tex2html_wrap_inline647, of the nucleon. The statistical sensitivity of HERA-tex2html_wrap_inline455 remains to be calculated.

The single spin asymmetries in inclusive Jtex2html_wrap_inline651 production [2] and in Drell-Yan production, tex2html_wrap_inline653, at small transverse momenta [21], were estimated at HERA-tex2html_wrap_inline455 energy to be of the order of tex2html_wrap_inline657. Nevertheless, one may expect larger asymmetries as the calculations might still not be complete. The projected level of sensitivity can be taken from the section on double spin asymmetries as it is the same for both cases if the beam polarization is accounted for in case of tex2html_wrap_inline659.

Large spin effects in proton-proton elastic scattering, tex2html_wrap_inline661, have been discovered many years ago. The single spin asymmetry tex2html_wrap_inline461 was found significantly different from zero (see fig. 4). At HERA-tex2html_wrap_inline455 energy one can measure the asymmetry in the range of tex2html_wrap_inline667 (GeV/c)tex2html_wrap_inline527 (see ref.[2, 3]).

  figure123
Figure 4: Compilation of experimental data on the asymmetry in elastic proton-proton scattering as a function of tex2html_wrap_inline671. In addition the projected statistical errors attainable with HERA-tex2html_wrap_inline455 are shown.


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Next: References Up: No Title Previous: No Title

Vladislav Korotkov
Wed Feb 18 18:48:34 MET 1998