Exclusive Electroproduction of Vector and
Pseudoscalar Mesons at HERMES
Christian Schill
(for the HERMES collaboration)
INFN-Laboratori Nazionali di Frascati, 00044 Frascati, Italy
Abstract. The exclusive production of vector and pseudoscalar mesons in deep-inelastic lepton
scattering gives a mean to access the recently introduced generalized parton distributions (GPDs).
The GPDs provide a unified description of hadronic structure, which can be investigated with many
different reactions. Recent results are presented on the exclusive electroproduction of π mesons
and on diffractive ρ 0 and φ production on the proton, collected by the HERMES collaboration at
DESY. The experimental results for the ρ 0 and φ cross section are compared to calculations based
on a description of the reactions in terms of GPDs. It is shown that quark exchange is the dominant
production mechanism for ρ 0 production, while for φ production only gluon exchanges contributes.
For exclusively produced π , an asymmetry in the azimuthal distribution around the virtual photon
direction has been observed which depends on the orientation of the target spin.
INTRODUCTION
Recently, a growing interest has appeared for the generalized parton distributions
(GPDs) of the nucleon, which provide a unified formalism for the description of inclusive deep-inelastic scattering, deeply-virtual compton scattering, exclusive meson
production and electromagnetic form factor measurements [1]. In contrast to the usual
parton distribution functions, which can be interpreted as probabilities to find a parton
of a certain momentum fraction x and with a certain spin orientation in the nucleon,
generalized parton distributions describe the correlation between two partons with
different momenta x ξ and x ξ .
There exist four chirally-even GPDs for each quark flavor q. The functions H q and
q
H̃ conserve the nucleon helicity, E q and Ẽ q do not conserve it. In the forward limit,
ξ 0 and t 0, the GPDs are equivalent to the ordinary parton densities. Here, t is
the squared four-momentum transfer to the nucleon. However, the generalized parton
distributions contain more information. It was shown that the second moment of the
GPDs can be related to the total angular momentum of quarks and gluons in the nucleon
[2]. Through their dependence on t, GPDs describe also transverse degrees of freedom
in the nucleon.
The exclusive production of a vector or pseudoscalar meson M in deep-inelastic
electron nucleon scattering is a way to experimentally gain information about GPDs:
e p e p M
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
308
(1)
The total cross section for this reaction can be factorized into a hard lepton scattering
coefficient, which can be calculated in QCD, the wave function of the produced meson,
and GPDs in quadratic combinations [3]. It turned out that the produced meson acts
as a helicity filter. For the production of vector mesons the cross-section contains the
unpolarized GPDs H q and E q , for pseudoscalar mesons the polarized ones H̃ q and Ẽ q .
So far, very few experimental data exist for exclusive reactions. The reasons are the
small cross-sections involved and the high missing mass resolution required to ensure
exclusivity.
In this contribution, experimental data are presented for the exclusive production of
ρ 0 , φ and π mesons. These data have been collected by the HERMES experiment at
DESY in Hamburg. A 27.5 GeV polarized electron or positron beam in the HERA storage ring at DESY is scattered off a longitudinally polarized or unpolarized hydrogen gas
target. The HERMES forward spectrometer [4] features excellent particle identification
capabilities. It can detect the scattered lepton and identifies pions, kaons and protons in
a wide momentum range.
VECTOR MESON PRODUCTION
In this section data are presented on the above mentioned exclusive ρ 0 and φ production
off the proton. The factorization of the cross-section has only been proven for scattering
longitudinally polarized virtual photons [3]. In order to obtain information about the
longitudinal part of the total cross section, the spin density matrix elements of the
produced meson have been extracted from its decay angle distribution [5]. Assuming
that the helicity of the virtual photon is entirely transferred to the produced meson (the
so called s-channel helicity conservation), the longitudinal cross-section can be derived
from the measured total one by using these matrix elements. The ratio of the longitudinal
04 ε 1 r 04 , where
to the transverse part of the cross-section is given by: R σ L σT r00
00
04
ε is the virtual-photon polarization parameter and r 00 is one of the spin density matrix
elements.
The results on the longitudinal cross section for ρ 0 and φ production [6] are shown
in figure 1, compared with a model calculation in the framework of GPDs [7, 8]. The
HERMES kinematic region covers an intermediate range of W between 4 and 6 GeV,
where W is the photon-nucleon center-of-mass energy. Besides the dominant quark
exchange, also gluon exchange needs to be considered in the calculation. In the case
of ρ 0 production the gluon exchange contribution becomes relevant only at large Q 2 and
W . As can be seen in figure 1 (left panel), the prediction for the ρ 0 cross section is in
agreement with the data.
For the φ production cross section shown in figure 1 (right panel), only gluon exchange should contribute, since the proton contains only a small amount of s quarks.
This is confirmed by the good agreement between data and the model calculation.
309
ρ0p) [µb]
100
<Q2> = 2.3 GeV2
<Q2> = 4.0 GeV2
σL(γ*p
10-1
HERMES
E665
101
101
W [GeV]
FIGURE 1. In the left panel the longitudinal cross section for exclusive ρ 0 production is compared to
the results of a GPD-based calculation [7, 8]. The dotted curves represent the gluon-exchange contribution,
the dashed curves the quark-exchange and the solid curves their sum. In the right panel, the longitudinal
cross section for exclusive φ production is shown together with the results of a GPD-based calculation
[7, 8], involving only gluon exchange.
PSEUDOSCALAR MESON PRODUCTION
Only a quadratic combination of GPDs appears in the unpolarized cross section for exclusive meson leptoproduction. Considering in addition the polarization degree of freedom helps to disentangle the various contributions by measuring further quantities. It
has been shown that for exclusive π production from a transversely polarized nucleon
the interference between the two polarized GPDs H̃ q and Ẽ q can lead to a large asymmetry in the distribution of the azimuthal angle φ [9, 10, 11]. Here, φ is the angle of
the outgoing meson around the direction of the virtual photon with respect to the lepton
scattering plane, as shown in figure 2.
At HERMES, exclusive meson production has been studied using a longitudinally
polarized hydrogen target [12]. With respect to the virtual photon, however, the target
polarization vector has a certain transverse component as well.
M
φ
e’
e
γ
FIGURE 2. Definition of the azimuthal angle φ for exclusive leptoproduction of the meson M.
310
0.6
a)
1500
0.4
Nπ
1000
0.2
A(φ)
500
0
b)
Nπ+ - Nπ-
200
0
-0.2
0
-0.4
-0.6
0
1
-3
2
MX [GeV]
-2
-1
0
φ [rad]
1
2
3
FIGURE 3. Left panel: a) Missing mass spectra for π (filled circles) and π (open circles) electroproduction on the proton [12]. The histogram is a Monte Carlo prediction for exclusive π production.
b) Difference between the π and the normalized π distribution. The curve is a Gaussian fit to the data,
the dotted line indicates the nucleon mass. Right panel: Longitudinal target-spin asymmetry for exclusive
φ sin φ .
π production. The curve is a fit to the data with the function Aφ A sin
UL
In the present setup, the identification of exclusive events is not possible on an eventby-event basis since the missing mass resolution of the spectrometer is limited to about
230 MeV for this process. However, the background of non-exclusive events can be
subtracted from the data. As an estimate for the non-exclusive background for π production, the π yield was used, since exclusive production of π is forbidden on
the proton due to charge conservation. In the upper part of the left panel of figure 3, the
π and π missing mass spectra are displayed. In the lower part the difference of the
π and the normalized π spectrum is shown. A clear peak of exclusive π production
can be seen at the mass of the proton.
The φ -dependence of the cross section can be described by a cross section asymmetry
defined as follows:
Aφ 1 N φ N φ Pt Abg φ Nbg
Pt N φ N φ Nbg
(2)
where N (N ) is the number of events with the direction of the target spin parallel
(anti-parallel) to the electron beam momentum and Pt the target polarization. Nbg is the
number of events of the non-exclusive background estimated from π production and
Abg is the non-exclusive background asymmetry of π , estimated for 13 Mx 20
GeV. The HERMES data are displayed in the right panel of figure 3. The measured
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asymmetry shows a clear φ -dependence and can be parameterized by the function
φ
sin φ
Aφ Asin
UL
(3)
φ 018 005stat 001syst.
with Asin
UL
For this experimental result there exist no theoretical predictions yet, due to the above
mentioned two components of the target polarization vector in the center-of-mass frame.
For a longitudinally polarized target the polarized cross section σ S has the form
φ
σS ∝ ST σL SL σLT Asin
sin φ
UL
(4)
with contributions from the longitudinal (L) virtual photon amplitude and from the interference (LT) of the longitudinal and the transverse photon amplitude. The longitudinal
SL and transverse ST components of the target polarization vector are determined in
the photon-nucleon center-of-mass frame. For a quantitative model calculation of the
measured asymmetry, an evaluation of the term σ LT is necessary, which requires a nextto-leading twist calculation [11], that is not yet available. For a entirely transversely
polarized target the second term in equation (4) vanishes and only leading twist amplitudes contribute [9, 10]. New measurements at HERMES with a transversely polarized
hydrogen target, which have started in 2002, will provide a more direct access to GPDs.
SUMMARY AND OUTLOOK
In this contribution results from the HERMES experiment for the exclusive electroproduction of ρ 0 , φ and π mesons on the proton have been presented. Some of these results
show a good agreement with model calculations performed in the framework of generalized parton distributions. To obtain more information on these functions data on many
different exclusive reactions will be needed. In 2004, HERMES will continue measuring exclusive reactions with the help of a new recoil detector, which will allow better
identification of exclusive reactions [13]. In addition, measurements with a transversely
polarized hydrogen target have started in 2002. This will result in the first experimental information about transverse azimuthal target spin asymmetries, which have been
predicted to be large [9].
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