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
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 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 and the asymmetries should approach zero as .
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 [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- to
investigate single spin asymmetries.
Inclusive pion production exhibits surprisingly large single spin asymmetries at large values of , 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 (fig. 1) shows
Figure 1: Single spin asymmetry in inclusive production of
[8] and mesons [9].
a considerable rise above
, i.e. in the fragmentation region of
the polarized nucleon. It is positive for both
and mesons, while it has the opposite sign for
mesons.
The charged pion data taken in the range GeV
were split into two samples at = 0.7 GeV/c; the observed rise
is stronger for the high sample.
New results on the asymmetry in meson production were presented
recently [9]. The asymmetry is positive and the behaviour is compatible
with the one observed in and 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 dependence in the range
GeV/c, of the single spin asymmetry in
, , p and production in the central region
() [10].
The dependence measured for the 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 .
This appears to be in some contrast to the E704 data on the asymmetry
in the central region which shows a result compatible with zero up to
of about 4 GeV/c [12].
The values accessible with HERA- would be significantly larger than in all experiments performed up to now. The sensitivity of the asymmetry measurement in inclusive production of different particles at HERA- 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 (, ) plane as contours characterizing the sensitivity level in a bin of (GeV/c). 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.
Figure 2: Contours of the asymmetry sensitivity level
for inclusive production of different particles in the
plane. Only the following decay modes are taken into account:
, ,
, ,
,
.
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 dependence of all involved higher-twist
effects can be
Figure 3: Capability of HERA- to discriminate predictions
[14] for different .
measured with good accuracy ()
up to transverse momenta of about 810 GeV/c in the central region
and up to 56 GeV/c in the target fragmentation region.
Hence the -range where higher twist effects are expected to be essential
would be well covered.
The capability of HERA- to really prove a 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,
, 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-
(see fig. 2a,c).
A sizeable inclusive production of and hyperons
would allow to study the asymmetry in their production up to of about
56 GeV/c (fig. 2c). The measurement of the final-state
polarization via its decay would allow to study the polarization
spin transfer coefficient, . A recent study by E704 [15]
at moderate values of (0.11.5 GeV/c) showed a sizeable (up to 30%)
spin transfer from the incident polarized proton to the outgoing .
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
mesons is expected to be opposite
in sign to that of pions,
.
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- for measuring single spin asymmetries
in inclusive production of , , and
vector mesons are presented in fig. 2b. The sensitivity
for production is at a level comparable to that for pions (fig. 2a),
while for and mesons the reachable values are lower.
On the other hand, a study of the asymmetry in and production using
the decay channels and could be easier since the level of the expected combinatorial
background is smaller.
Also, the asymmetry in meson production could be useful
for a study of the strange quark polarization in a nucleon [6].
Inclusive direct photon production, ,
proceeds without fragmentation, i.e. the photon carries directly the
information from the hard scattering process. Hence this process
measures
a combination of initial 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 GeV/c in the central region
.
The experimental sensitivity of HERA-
was determined using cross-section calculations
for the two dominant hard subprocesses, i.e. gluon-Compton scattering
() and quark-antiquark annihilation
(),
and of background photons that originate mainly from and
decays.
It turns out that a good sensitivity (about 0.05)
can be maintained up to 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 ,
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, or )
using inclusive production of two pions on the transversely polarized
nucleon, .
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, , with respect to the polarization vector, ,
of the nucleon. The statistical sensitivity of HERA- remains to
be calculated.
The single spin asymmetries in inclusive J production
[2] and in Drell-Yan production,
, at small
transverse momenta [21], were
estimated at HERA- energy to be of the order of .
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 .
Large spin effects in proton-proton elastic scattering, , have been discovered many years ago. The single spin asymmetry was found significantly different from zero (see fig. 4). At HERA- energy one can measure the asymmetry in the range of (GeV/c) (see ref.[2, 3]).
Figure 4: Compilation of experimental data on the asymmetry in
elastic proton-proton scattering as a function of . In
addition the projected statistical errors attainable with
HERA- are shown.