Transverse Polarisation of Λ and Λ̄ Hyperons in
Quasi-Real Photon Nucleon Scattering
Antje Bruell
(on behalf of the HERMES collaboration)
Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA
Abstract. The transverse polarisation in inclusively produced Λ and Λ̄ hyperons has been studied at HERMES using the 27.5 GeV positron beam of the HERA accelerator at DESY. The
average transverse polarisations were found to be PnΛ = 0.055 ± 0.006 (stat) ± 0.016 (syst) and
PnΛ̄ = −0.043 ± 0.013 (stat) ± 0.012 (syst) for Λ and Λ̄, respectively. The dependence of PnΛ and
PnΛ̄ on the transverse momentum p T and on the hyperons’ light-cone momentum fraction ζ has
been investigated. The measured polarisations for Λ and Λ̄ exhibit different behavior in the current
and target fragmentation regions.
INTRODUCTION
At the beginning of the Fermilab hyperon program [1] it was believed that spin effects
in hadronic reactions should be of little importance at high energies. As helicity is
conserved in the limit of massless quarks, helicity-flip amplitudes, when calculated
in perturbative QCD, are greatly suppressed at high energies. It was thus surprising
that a significant polarisation was measured for Λ’s produced by 300 GeV unpolarised
protons scattered from an unpolarised beryllium target [2]. The measured Λ polarisation
was transverse, negative and directed opposite to the normal (n̂ = p̂ beam × p̂Λ ) of the
production plane. This transverse “self-polarisation” of Λ’s and other hyperons has
now been investigated in many scattering experiments with a wide variety of hadronic
beams [3]. The polarisation of Λ’s is almost always found to be negative (as in the
original pN experiment) and to increase linearly with the transverse momentum p T up
to pT 1 GeV/c where a plateau is reached. Also, a linear rise with xF is observed: the
polarisation is most pronounced when the hyperons are produced in the forward region,
where current-quark fragmentation is dominant. One notable exception to this rule is the
positive polarisation measured in K − p scattering, where a similar rise with pT but the
opposite sign of the polarisation is observed.
While hyperon polarisation has been studied extensively in hadron-hadron reactions, very little experimental information exists about the effect in photo- and electroproduction. Transverse polarisation in the inclusive photoproduction of neutral strange
particles was investigated 20 years ago at CERN [4] and SLAC [5]. However, the statistical quality of these data is rather poor. No significant p T dependence was observed
in either experiment. The SLAC experiment, however, reported a tendency for negative
polarisation values in the forward region.
CP675, Spin 2002: 15th Int'l. Spin Physics Symposium and Workshop on Polarized Electron
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548
TRANSVERSE Λ AND Λ̄ POLARISATION AT HERMES
The HERMES experiment offers an excellent opportunity to measure transverse Λ
polarisation in the reaction γ ∗ N → ΛX . The yields in this inclusive reaction, where the
beam positrons are scattered at very small angles and are not detected by the HERMES
spectrometer, originate mainly from the photoproduction peak in the cross-section at
Q2 ≈ 0 and are much higher than in the semi-inclusive case. The analysis presented here
combines all data collected at HERMES in the years 96-00. The sample includes data
taken with both longitudinally polarised hydrogen and deuterium targets and a variety of
unpolarised targets. The polarisation of the positron beam was always longitudinal but
was frequently reversed, resulting into a negligible value of the product PBPT .
Events containing Λ and Λ̄ hyperons were identified through the reconstruction of
secondary vertices from oppositely charged hadron tracks. The secondary vertex was
required to be at least 10 cm away from the upstream end of the target and the Λ decay
products were identified using a Cerenkov detector. For the polarisation analysis, Λ and
Λ̄ events within a ±2.5σ invariant mass window of the fitted peak were chosen and the
background was estimated using a side-band subtraction method.
Because of the parity-violating nature of the weak decay Λ → pπ − , protons are
preferentially emitted along the spin direction of their parent Λ. The angular distribution
of the decay products of the Λ may thus be used to measure its polarisation:
dN
dN0
=
(1 + α PnΛ cos θ p ),
dΩ p dΩ p
(1)
where the symbol dN0 /dΩ p denotes the distribution for the (isotropic) decay of an
unpolarised Λ sample, θ p is the angle of proton emission relative to the n̂ axis in the Λ
rest frame and α = 0.642 ± 0.013 [6] is the analysing power of the parity-violating weak
decay. Using the up/down mirror symmetry of the HERMES acceptance, the polarisation
of the Λ hyperons is determined from the measured cos θ p and cos θ p2 moments [7]:
PnΛ =
1 cos θ p .
α cos2 θ p (2)
Averaged over the full kinematic range of the data, the transverse polarisation of the
Λ and Λ̄ hyperons was measured to be
PnΛ = +0.055 ± 0.006 (stat) ± 0.016 (syst),
PnΛ̄ = −0.043 ± 0.013 (stat) ± 0.012 (syst).
(3)
The systematic uncertainty was estimated by measurements of the false “transverse
polarisation” of Ks0 mesons, and of hadron-hadron pairs which did not originate from
Λ(Λ̄) decay. The average virtual photon energy was determined from a Monte Carlo
simulation based on the PYTHIA 6.2 event generator to be ν = 16 GeV.
The good statistical quality of the HERMES data set allows to study the dependence
of the Λ and Λ̄ polarisation on certain kinematic variables. An approximate measure of
whether the hyperons were produced in the forward or backward region in the centerof-mass frame of the γ ∗ N reaction is the light cone momentum fraction of the beam
549
1
Λ/Λ ratio
0.8
20
18
-
xF (γp)
positron carried by the outgoing Λ or Λ̄. In a Monte Carlo simulation this variable
ζ ≡ (EΛ + pzΛ )/(EB + pB ) has been found to be correlated to xF (Fig. 1a). In particular,
all events at ζ ≥ 0.25 are produced in the forward hemisphere (xF > 0). This correlation
between ζ and xF is also reflected in the ratio of Λ to Λ̄ yields observed in the data after
background subtraction (Fig. 1b): above ζ = 0.25, the ratio of Λ to Λ̄ yields is constant
indicating similar production mechanisms for the two hyperons. At lower values of ζ
the ratio increases dramatically, most likely due to differences between the Λ and Λ̄
formation mechanisms in the target- and current-quark fragmentation regions.
0.6
16
14
0.4
12
0.2
10
0
8
6
-0.2
PYTHIA
4
-0.4
2
-0.6
0
0.1
0.2
0.3
0.4
0.5
ζ
a)
0
0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6
0.6
ζ
b)
γ ∗N
FIGURE 1. (a) Correlation between x F , evaluated in the
center-of-mass frame, and the light-cone
fraction ζ determined in the eN frame, as determined from a PYTHIA Monte Carlo simulation. (b) Ratio
of Λ to Λ̄ yields versus the light cone fraction ζ .
HERMES PRELIMINARY
ep → Λ X
10
Λ
Pn (%)
In Fig. 2 the Λ and Λ̄ polarisations are shown as a function of ζ . A clear difference between the Λ polarisation at low and high ζ is observed. While the Λ and Λ̄ polarisations
are similar at high ζ , at low values of ζ they are of opposite sign.
7.5
5
2.5
0
-2.5
-5
-7.5
-10
-
ep → Λ X
0
0.1
0.2
0.3
0.4
0.5
0.6
ζ=(EΛ+pz)/(Eb+pb)
FIGURE 2. (a) Transverse polarisation of Λ and Λ̄ hyperons as a function of the light cone momentum
fraction ζ = (EΛ + pzΛ )/(EB + pB).
550
15
Pn (%)
HERMES PRELIMINARY
12.5
Λ
ζ<0.25
ζ>0.25
HERMES PRELIMINARY
10
Λ
Pn (%)
The dependence of PnΛ on the transverse momentum p T of the Λ (defined with respect
to the eN system rather than the unavailable γ ∗ N system) has also been explored. This
dependence is shown in Fig. 3 for the two intervals ζ < 0.25 and ζ > 0.25. In both
regimes the Λ polarisation rises with p T , particularly for the forward-going hyperons
where this behavior is more pronounced. This kinematic dependence is reminiscent
of the linear rise of hyperon polarisation with p T , up to pT ≈ 1 GeV, that has been
consistently observed in the forward production of hyperons in hadronic reactions.
In the forward region the Λ̄ polarisation is consistent with zero, also in agreement
with hadronic reactions. In the backward region, however, the measured Λ̄ polarisation
favours a negative value.
10
7.5
Λ
7.5
5
5
Λ
2.5
2.5
0
0
-2.5
-2.5
-5
-
Λ
-5
-7.5
-7.5
-10
-
Λ
0
0.2
0.4
0.6
0.8
1
1.2
-10
1.4
0
pT (GeV)
0.2
0.4
0.6
0.8
1
1.2
1.4
pT (GeV)
FIGURE 3. Transverse polarisation of Λ and Λ̄ hyperons as a function of p T for the intervals ζ < 0.25
(left panel) and ζ > 0.25 (right panel).
DISCUSSION
In contrast to the negative values observed in almost all other reactions, the transverse Λ
polarisation measured at HERMES is found to be positive. Furthermore, a negative Λ̄ polarisation was measured, in contrast to the zero values measured in other reactions. This
negative value, however, appears to arise principally from the data in the “backwardproduction” region ζ < 0.25. It may thus be a consequence of the complex and poorly
understood mechanism of the target fragmentation.
The positive Λ polarisation measured at HERMES can possibly be related to the structure of the photon: at the energy of the HERMES experiment, the hadronic component
of the photon contributes about 80% of the total γ p cross section. Thus a substantial
fraction of the Λ and Λ̄ hyperons might be produced in the interaction of qq̄ pairs (or of
resonant ρ 0 , ω or Φ mesons) with the target. Consequently, the transverse Λ polarisation measured in the forward region might be related to the one measured in the reactions
π ± p → ΛX or K ± p → ΛX . Among these reactions, only Λ production from a K − beam
shows a clear polarisation signal, which also is the only hadronic measurement show-
551
ing a positive value of the polarisation. Fitting the p T dependence of the Λ polarisation
observed in the HERMES forward region with the same functional form as observed in
the K − p reaction results into a good description (i.e. both experiments found an almost
linear rise with pT ) if a relative contribution of the K − meson to the photon of about 7%
is assumed. In this approach, the quarks and anti-quarks in the photon beam are on an
equal footing, and the Λ and Λ̄ polarisations should thus become similar at large ζ . This
trend is qualitatively supported by the data (Fig. 2). Conversely, Λ and Λ̄ polarisation
are seen to differ in the target fragmentation region, where quarks and anti-quarks are
distinguished by the target.
No theoretical calculation is yet able to explain all existing data on Λ and Λ̄ polarisation. The model of DeGrand and Miettinen [8], however, can at least account for
the relative signs and magnitudes of the polarisations in numerous hadron-to-hyperon
transitions. In this model of proton-proton scattering, the forward-going Λ’s are formed
from the recombination of a high-momentum valence (ud) 0 diquark from the beam with
a strange sea quark from the target. The negative Λ polarisation then arises from the
acceleration of the strange quark, via the Thomas precession effect. The positive Λ polarisation observed with K − beams is conversely indicative of the deceleration of valence
strange quarks from the beam. The positive polarisation observed in the HERMES photoproduction data might therefore indicate that the γ → ss̄ hadronic component of the
beam is the dominant source of inclusive Λ production.
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