The Physics Programme of HERMES Run-II
Delia Hasch
(On behalf of the HERMES Collaboration)
INFN - Laboratori Nazionali di Frascati, 00044 Frascati, Italy
Abstract. The HERMES experiment has started its Run-II which is expected to run at least until
2006. The physics programme for this Run is based on two major axes of research: transversity
and exclusive reactions. In the first phase the HERMES target will provide transversely polarized
hydrogen atoms. The main aim of this part is to measure single-spin asymmetries in the semiinclusive production of hadrons. From these asymmetries the transversity distribution h 1 x will be
determined. This is the last twist-2 quark distribution function, which has not been measured at all
up to now. Data from the first run of HERMES with a longitudinally polarized target suggest that
this transversity distribution is accessible. During the last 2 years of the run a new recoil detector
will be installed surrounding the HERMES target. The aim is to fully determine the kinematics
for exclusive reactions by detecting also the slow recoil nucleon. This will enable HERMES to
make virtually background-free measurements of exclusive reactions, in particular of Deeply Virtual
Compton Scattering (DVCS).
INTRODUCTION
Historically, the investigation of the spin structure of the nucleon in electron scattering has been synonymous with inclusive measurements. In recent times, semi-inclusive
measurements have substantially extended the understanding of the nucleon spin. From
inclusive and semi-inclusive polarized deep inelastic scattering (DIS) the helicity distributions for u and d quarks are now known with reasonably good precision, while only a
first glimpse has been obtained for the sea-quark and gluon helicity distributions. Moreover, the transversity distribution h 1 (also denoted as helicity-flip distribution δ q) as well
as the contribution from the orbital angular momentum of quarks and gluons are still
unknown. While the experimental hunt for the former started very recently, a possible
measurement of the latter is still under discussion on both theoretical and experimental grounds. The transversity distribution h 1 represents the transverse spin distribution
of quarks in a nucleon polarized transversely to the virtual photon in the infinite momentum frame [1]. Transversity is a chiral-odd distribution which implies that it is not
directly observable in an inclusive measurement as chirality is conserved in electromagnetic and strong interactions. Therefore, a second chiral-odd object has to be involved
in the process. In semi-inclusive scattering this may be a chiral-odd fragmentation function, the so-called Collins function [2].
Nowadays exclusive processes, where all reaction products are detected, are becoming
a promising and powerful experimental tool to access further information about the spin
structure of the nucleon. The recently developed formalism of Generalised Parton Distributions (GPDs) [3] provides a unified description of inclusive and exclusive processes
CP675, Spin 2002: 15th Int'l. Spin Physics Symposium and Workshop on Polarized Electron
Sources and Polarimeters, edited by Y. I. Makdisi, A. U. Luccio, and W. W. MacKay
© 2003 American Institute of Physics 0-7354-0136-5/03/$20.00
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which takes into account the dynamical correlations between partons of different momenta in the nucleon. The well-known parton distributions and form factors turn out to
be the limiting cases and moments of GPDs. A particular feature in the context of spin
physics is that the second moment of the sum of the two unpolarized GPDs give the total
angular momentum carried by quarks [4].
THE HERMES EXPERIMENT
The HERMES experiment has been taken data at the HERA accelerator in Hamburg,
Germany since 1995. HERMES records the scattering of the longitudianally polarized
electron or positron beam of 27.6 GeV from polarized gas targets internal to the beam
pipe. Pure atomic H, D and 3 He have been used as well as a variety of unpolarized
nuclear targets. Featuring polarized beams and targets and an open-geometry spectrometer with good particle identification (PID), HERMES is well suited to a study of the
spin-dependent azimuthal moments of the SIDIS cross-section. The PID capabilities
of the experiment were significantly enhanced in 1998 when the threshold Čerenkov
detector (used to identify pions above a momentum of 4 GeV) was upgraded to a Ring
Imaging system (RICH). This new detector provides full separation between charged
pions, kaons and protons over essentially the entire momentum range of the experiment.
In September 2000 HERMES completed its first phase of data taking, using
longitudinally-polarized targets. HERMES is now entering its second running phase
which will continue until at least 2006. The main physics subject of the period 2002
to 2004 will be measurements from transversely-polarized hydrogen target with the
specific goal of exploring the transversity structure function. In 2004 a recoil detector
surrounding the target will be installed, allowing to fully determine the kinematics for
exclusive reactions by detecting also the slow recoil nucleon. In conjunction with high
density unpolarized nuclear targets, HERMES will be well suited for measurements of
exclusive reactions with a recoiling proton in the final state in 2005 and 2006.
FUTURE TRANSVERSITY MEASUREMENTS
The Collins mechanism, proposed as a means to access to h 1 , manifests itself in an
azimuthal single-spin asymmetry which could be observed in semi-inclusive meson
electroproduction. The moment of this asymmetry is related to the product of h 1 x
and the Collins fragmentation function (FF) H
1 z, where the latter correlates the
angular distribution of the produced hadrons with the transverse spin of the primary
quark. HERMES has made the first measurements of single-spin azimuthal asymmetries
(SSA) for semi-inclusive pion and kaon production in DIS, using an unpolarized beam
and longitudinally polarized proton and deuteron targets [5, 6]. The observed sin φ
dependence of the asymmetry can be well described by model calculations based on
the Collins mechanism. The results imply that the Collins FF could be sizeable, hence
forseen measurement of h1 with a transversely polarized target at HERMES is very
promising. However, it cannot be excluded that at least part of the observed asymmetries
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2.5
(z)/Du1(z)
0.2<z<0.3
0.3<z<0.5
0.5<z<0.7
0.7<z<1.0
3
b)
2.4
1.8
0.4
1.2
0.2
0.6
0
10
x
1
0.5
0
-1
c)
2
1.5
(1)u
0.6
a)
H⊥1
0.8
δu(x)
ATπ
+
1
10
0
-1
0
0.5
1
x
z
FIGURE 1. a) The weighted asymmetry A T x for different intervals of z; b) the transversity distribution
1u
δ ux, and c) the ratio of the fragmentation functions H z to Du1 z as they would be measured by
1
HERMES. The asterisk in b) shows the normalization point.
is due to the interaction of the struck quark with the target remnant in the final state
through the exchange of a single gluon [7]. This mechanism was shown [8] to be
identical to the already known Sivers effect [9]. By scattering on a transversely polarized
target, it will be possible to distinguish the Collins and Sivers mechanism through their
different dependence on the angle φS between the transverse target polarization vector
and the lepton scattering plane.
For the particular case of an unpolarized beam and a transversely (with respect to the
incoming lepton momentum) polarized target (T) the following weighted asymmetry is
sensitive at leading twist to the product of h 1 x and H
1 z [10]
Ê
AT Ê
P dφ d2 P M sinφ dσ dσ Ê
Ê h
dφ d2 P dσ dσ PT Dnn 1
h1 x z H
z 1
f1 x D1 z
(1)
Here () denotes target up (down) transverse polarization, Mh is the mass of the
produced hadron, PT is the magnitude of the target polarization, D nn is the transverse spin
transfer coefficient and D1 z is the familiar unpolarized FF. The angle φ is the azimuthal
angle between the transverse target polarization vector and the transverse momentum P
of the produced hadron relative to the virtual photon direction. To evaluate the level of
accuracy that could be obtained for a measurement of AT , simulations [11] were done
assuming a target polarization of PT 75% and 7.0 million reconstructed DIS events.
Assuming u-quark dominance for π electroproduction, the asymmetry is given by
AπT PT
1u z
δ ux H1
Dnn ux Duz 1
(2)
The expected asymmetry AπT x as it would be measured by HERMES is presented in
Fig. 1a) for different intervals of z. The factorized form of the expression in Eq. 2 with
respect to the variables x and z allows the reconstruction of the shape for both of the
unknown functions δ u and H11u zDu1 z, while the relative normalization cannot be
fixed without further assumptions. The normalization ambiguity has been resolved by
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assuming δ ux 025 ∆ux 025, as indicated by the asterisk in Fig. 1b). A very
good statistical precision is expected for a first measurement of the x- and z-dependence
of the transversity distribution δ ux and of the ratio of the fragmentation functions
H11u zDu1 z.
FUTURE MEASUREMENTS OF EXCLUSIVE REACTIONS
Experimental information on GPDs can be obtained by measuring cross sections or
asymmetries of exclusive reactions with different final states. Due to the experimental
difficulties arising from the small cross sections involved and the high energy resolution
required, first results in this field are appearing only now.
The theoretically cleanest way to access GPDs appears to be using DVCS process, i.e.
the hard exclusive leptoproduction of real photons with the target nucleon remaining
intact. Since the Bethe-Heitler (BH) process has an identical final state, the amplitudes
of both processes add coherently, and the interference between them can be used to
access the DVCS amplitude. The leading order and leading twist interference term [12]
I ∝ el
1
cos φ ReM̃ 11 Pl sin φ
ε ε 1
1ε
ImM̃ 11
ε
(3)
depends on the charge and the helicity of the incident lepton with polarization Pl . Here,
ε is the polarization parameter of the virtual photon.
Experimental results of exclusive measurements at HERMES have been reported on this
conference [13, 14]. However, the missing mass resolution of the HERMES spectrometer is not sufficient to exactly identify exclusive events individually and to separate
them from non-exclusive events, like e.g. from those events where an intermediate ∆resonance was created. Therefore exclusivity could be better established only on the
level of a data sample by restrictive cuts and/or by background estimation and subtraction. The upgrade of the spectrometer with a recoil detector planned for 2004 will substantially improve this situation by establishing exclusivity on the event level for exclusive reactions with a recoiling proton in the final state. The HERMES recoil detector [15]
will basically consist of a barrel of detectors around the target region. This will allow the
detection of the slowly recoiling proton at large angle without interfering with the acceptance of the high momentum mesons and photons in the HERMES spectrometer. The
recoil detector will consist of two layers of silicon detectors surrounding the target cell
inside the beam vacuum and two layers of scintillating fibre detector in a longitudinal
magnetic field of about 1 Tesla. The combination of both detectors allows for tracking
in the momentum range of 0.1 P 1.4 GeV. Particle identification is provided via the
energy deposition. Additional scitillators will be used for π 0 detection through their decay photons. The exclusive final state will be selected by applying co-planarity cuts, i.e.,
ensuring that the recoiling proton is in the same plane as the produced meson or photon.
For exclusive production of photons used to study the DVCS-BH interference, it is estimated that the background due to ∆ production (the primary contaminating process) can
be reduced to 1%.
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→+
Ach (φ)
ALU (φ)
0.6
e p→e pγ
+
0.2
±
0.4
±
e p→e pγ
0.15
0.1
0.2
0.05
0
-0.05
0
-0.1
-0.2
-0.15
-0.2
-0.4
-0.25
-0.6
-3
-2
-1
0
1
2
-0.3
3
φ, rad
-3
-2
-1
0
1
2
3
φ, rad
FIGURE 2. Projections of statistical accuracies (closed circles) for measurements of the beam-spin
(left) and beam-charge (right) azimuthal asymmetries for hard electroproduction of photons as function
of the azimuthal angle φ . The HERMES results from existing data are shown as open circles. The curves
represent various GPD model predictions.
Fig. 2 shows the projected accuracy for measurements of beam-spin and beamcharge asymmetries associated with the DVCS-BH interference for one year of highluminosity running (corresponding to 2 fb 1 ) with the HERMES recoil detector. The
calculations [16] were performed using different GPD parameterizations as shown by
the different curves in Fig. 2. The open points shows the HERMES results [17, 13] from
the 1996/97 data taking periods representing 0.13 fb 1 for the beam-spin asymmetry and
from the 1998/2000 data taking periods for the beam-charge asymmetry. The remarkable
improved accuracy in measuring the variable t with the recoil detector will allow one to
study kinematic dependences of the asymmetries.
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