Measurement of Polarised Parton Distributions
at HERMES
Antje Bruell
(on behalf of the HERMES collaboration)
Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
Abstract. During the last years the HERMES collaboration has measured inclusive and semiinclusive double-spin asymmetries in deep inelastic scattering on polarised hydrogen and deuterium
targets in the kinematic range 0.02 < x < 0.6 and 1 GeV 2 < Q2 < 10 GeV2 . With the installation
of a Ring Imaging Čerenkov detector in 1998, charged pions and kaons could be identified and
for the first time allowed to separately determine the polarisations of all valence and sea quark
distributions. Of special interest are the difference between the polarisation of the u- and d- sea
quarks where various phenomenological models predict a significant flavour asymmetry and the
polarisation of the strange quarks which have been suggested to have a negative contribution to the
nucleon spin.
INTRODUCTION
The study of the spin structure of the nucleon has attracted great interest since the EMC
experiment [1] reported that only a small fraction of the spin of the proton is carried
by the spins of the quarks. Several experiments at CERN, SLAC and DESY have since
confirmed this result. To further investigate the spin structure of the nucleon, both the
SMC experiment and the HERMES experiment have measured not only inclusive deepinelastic scattering but also semi-inclusive channels, in which a final state hadron is
detected in coincidence with the scattered lepton. As the identity of fast hadrons from
the fragmentation process is correlated with the flavour of the struck quark this “flavourtagging” can be used to determine the polarised parton distribution functions for each
quark flavour.
Assuming factorisation of the hard scattering and fragmentation processes, the photoabsorption double spin asymmetry A h1 for the production of a hadron of type h can be
written in LO QCD as
Ah1 (x, z, Q2) =
zmax h
2
2
2
1 + R(x, Q2 ) ∑ f e f ∆q f (x, Q ) zmin D f (z, Q )dz
.
zmax h
1 + γ2
D f (z, Q2)dz
∑ f e2f q f (x, Q2 ) zmin
(1)
Here q f (x, Q2 ) denote the unpolarised parton densities, ∆q f (x, Q2 ) = q↑f (x, Q2 ) −
q↓f (x, Q2 ) are the helicity dependent quark distributions, and R = σ L /σT is the ratio
of the longitudinal and transverse virtual photon absorption cross sections. The fragmentation functions Dhf (z, Q2) represent the probability that a struck quark of flavour f
fragments into a hadron of type h with energy E h and fractional energy z = Eh /ν .
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
343
SEMI-INCLUSIVE ASYMMETRIES
At HERMES, longitudinally polarised positrons of 27.5 GeV are scattered deepinelastically on polarised pure atomic hydrogen and deuterium gas targets. A large
acceptance forward spectrometer with excellent lepton/hadron separation detects the
scattered positrons in coincidence with final state hadrons. For the HERMES data on a
longitudinally polarised hydrogen target a threshold Cerenkov detector provided pion
identification for momenta above 4 GeV. Since the installation of the RICH detector in
1998, data have been collected on a longitudinally polarised deuterium target and pions,
kaons and protons are identified over the entire momentum range.
In Fig. 1 the semi-inclusive asymmetries for charged hadrons, pions and kaons are
presented as a function of x. Deep-inelastic scattering events were selected by imposing the kinematical constraints Q 2 > 1 GeV2 , W 2 > 10 GeV2 and y < 0.85. To enhance
the contribution of hadrons from the current fragmentation region and to supress contributions from exclusive events, the selection criteria 0.2 < z < 0.8 and x F > 0.1 were
applied. A Monte Carlo simulation was used to correct the asymmetries for kinematic
smearing in the variable x due to instrumental resolution and QED radiative effects.
h+
π+
0.8
A1,p
0.8
A1,p
0.6
HERMES prelim.
0.6
HERMES prelim.
(refined analysis)
0.4
0.4
0.2
SMC
0.2
0
0
h-
π−
0.8
A1,p
0.8
A1,p
0.6
HERMES prelim.
0.6
HERMES prelim.
(refined analysis)
0.4
0.4
0.2
SMC
0.2
0
0
0.02
0.1
0.7
0.02
0.1
x
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
0.02
h+
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
0.6
A1,d
HERMES prelim.
SMC
h-
A1,d
0.4
HERMES prelim.
SMC
0.7
x
0.6
0.5
0.4
0.3
0.2
0.1
0
-0.1
0.6
π+
A1,d
HERMES prelim.
π−
A1,d
0.4
-0.4
0.02
K-
A1,d
0
-0.2
-0.2
0.7
HERMES prelim.
0.2
0.2
0
0.1
K+
A1,d
0.1
x
0.7
x
-0.4
0.02
0.1
0.7
x
FIGURE 1. Semi-inclusive asymmetries for charged hadrons, pions and kaons on hydrogen (top panels)
and deuterium (bottom panels) targets.
The most striking feature of the new preliminary HERMES results is the difference
between the negative kaon asymmetry which is found to be consistent with zero over the
entire x range and all other asymmetries which are positive for x > 0.1.
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HELICITY DEPENDENT QUARK DISTRIBUTIONS
After integration over Q2 , Eq. 1 can be rewritten for any set of measured asymmetries
A(x) = P(x) · Q(x)
.
(2)
The vectors A(x) and Q(x)
contain the measured inclusive and semi-inclusive asymmetries from the different targets and the polarisations ∆q
q of the different quark flavours to
be extracted, respectively. The elements of the matrix P(x) depend on the fragmentation
functions, the unpolarised parton densities and the cross section ratio R(x, Q 2 ). The matrix P(x) also contains the influence of the limited acceptance of the spectrometer and
was determined from a Monte Carlo simulation of the HERMES experiment where the
fragmentation process was modelled in the LUND string model with parameters tuned
to the HERMES hadron multiplicities [2]. The CTEQ5L parametrisation [3] was used
for the unpolarised quark distributions.
Equation (2) has been solved for the vector Q(x)
by a least squares minimisation
technique. To avoid large uncertainties from correlations between the elements of the
Q(x),
the polarisation of the sea quarks was set to zero for x > 0.3.
x⋅∆u
0.2
0
x⋅∆d
–
–
∆u-∆d
0
-0.2
0.1
–
1.5
HERMES preliminary
(1996-2000)
–
x⋅∆u
1
2
Q = 2.5 GeV
0
0
–
x⋅∆d
-0.5
0
HERMES prelim.
-0.1
0.1
2
0.5
-0.1
0.1
–
∆u-∆d
2
[EPJ C14, 147 (2000)]
-1.5
Bourrely et al.
[EPJ C23, 487 (2002)]
0
2
Q = 2.5 GeV
-0.1
0.02
χQSM
-1
(1996-2000)
GRSV/(1+R)
BB
x⋅∆s
0.1
-2
2
0.7
0.02
x
0.1
0.7
x
FIGURE 2. Left: the x-weighted polarized quark distributions x ∆q(x) as a function of x, as extracted
from HERMES inclusive and semi-inclusive asymmetries on polarized hydrogen and deuterium targets.
All data are evolved to Q 2 = 2.5 GeV2 . The dashed curves represent the GRSV00 parametrisation [4], the
dot-dashed curves correspond to the results of a LO QCD analysis by Blümlein and Böttcher [5]. Right:
the difference ∆ū − ∆ d¯ at Q2 = 2.5 GeV 2 as a function of x in comparison to the predictions of two recent
phenomenological models [6, 7].
The resulting x-weighted polarised parton densities, evolved to Q 2 = 2.5 GeV2 , are
shown in Fig. 2. Also shown are two recent parametrisations from LO analyses of only
345
inclusive polarised deep-inelastic scattering data. Good agreement between the data and
the parametrisations is observed for the up and down quark polarisations. In contrast
to the parametrisations, the polarisation of the strange sea quarks extracted from the
HERMES asymmetries tends to be positive. Using the same fitting formalism, the value
of ∆ū − ∆d¯ was extracted (right panel of Fig. 2). No breaking of the flavor symmetry in
the light sea quark polarisation is observed at the present level of experimental accuracy.
FRAGMENTATION AT HERMES
To apply the concept of flavour-tagging in the determination of parton distributions the
fragmentation process has to be understood.
√ Especially at the relatively low center-ofmass energy of the HERMES experiment ( s ∼ 7 GeV), two important questions have
to be addressed:
•
•
do the hard and the soft processes factorise ?
can one clearly separate the current and the target fragmentation region ?
At present, the assumption of factorisation is supported by two measurements:
1. The measurement of the pion multiplicity [8]
The differential multiplicity, i.e. the number of pions produced in deep-inelastic
scattering normalised to the total number of inclusive deep-inelastic scattering
events has been determined for both neutral and charged pions. As expected from
isospin symmetry, the agreement between neutral and charged pions is excellent,
at least up z ∼ 0.7, where a possible contribution from exclusive channels might
become important. In the left panel of Fig. 3 the neutral pion multiplicities as
measured at HERMES are compared to the EMC measurements [9] as a function
of z. As a significant Q2 dependence of the fragmentation process is expected
by perturbative QCD, the HERMES results have been evolved from the average
measured Q2 of 2.5 GeV2 to the average Q2 of the EMC experiment (Q2 = 25
GeV2 ). The excellent agreement between the two experiments strongly supports
the fact that the fragmentation process at HERMES is essentially the same as for
the EMC experiment at a much higher center-of-mass energy.
2. The measurement of the flavour asymmetry in the light quark sea [10]
At HERMES the flavour asymmetry of the light quark sea has been determined
from the ratio of the differences between charged pion yields for proton and neutron targets. Using the factorised ansatz for semi-inclusive deep-inelastic scattering
one can derive an expression which factorises into two independent functions of x
and z and thus can be rearranged to extract the ratio (d(x) − u(x))/(u(x) − d(x)).
Plotting this quantity for fixed values of x as a function of z provides a test of the
assumed form of factorisation. As shown in the right panel of Fig. 3 no z dependence is observed, strongly supporting the assumption of factorisation between the
hard scattering process (depending on the parton distributions q i (x)) and the hadro±
nisation of the struck quarks (described by the fragmentation functions D πq (z)). It
346
(d-u)/(u-d)
π
(1/NDIS) dN /dz
should be noted, however, that the statistical precision of the data presented here
does not allow to exclude a z dependence of the order of 10-20%.
1
0
1
0
1
1
0
1
10
-1
0
1
0
10
-2
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.2
0.9
0.3
z
0.4
0.5
0.6
0.7
0.8
z
FIGURE 3. Left: multiplicity of neutral pions as a function of z, as measaured by HERMES and EMC.
The HERMES data have been evolved to Q 2 = 25 GeV2 , the average Q 2 of the EMC muon data. Right:
the flavour asymmetry of the light quark sea as extracted from HERMES semi-inclusive data as function
of z for different values of x.
The current and the target fragmentation region are expected to be reasonably separated if the rapidity difference is larger than about 4 [11]. For pions in the HERMES
kinematics this corresponds to the requirement of a minimum z value of about 0.2-0.3.
As all HERMES analyses of semi-inclusive events used for the extraction of parton
distributions have imposed a minimum z value of 0.2, contributions from the target fragmentation region are expected to be small.
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