Lineshape of the Lambda(1405) Hyperon Measured Through its Sigma0 pion0 Decay

Abstract

The pp -> p K+ Y0 reaction has been studied for hyperon masses m(Y0)<1540 MeV/c2 at COSY-Juelich by using a 3.65 GeV/c circulating proton beam incident on an internal hydrogen target. Final states comprising two protons, one positively charged kaon and one negatively charged pion have been identified with the ANKE spectrometer. Such configurations are sensitive to the production of the ground state Lambda and Sigma0 hyperons as well as the Sigma0(1385) and Lambda(1405) resonances. Applying invariant- and missing-mass techniques, the two overlapping excited states could be well separated, though with limited statistics. The shape and position of the Lambda(1405) distribution, reconstructed cleanly in the Sigma0 pion0 channel, are similar to those found from other decay modes and there is no obvious mass shift. This finding constitutes a challenging test for models that predict Lambda(1405) to be a two-state resonance.

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arXiv:0705.1039v2 [nucl-ex] 15 Jan 2008
Lineshape of the Λ(1405) Hyperon Measured
Through its Σ0π0Decay
I.Zychora, M.B¨ uscherb, M.Hartmannb, A.Kacharavac,d,
I.Keshelashvilib,c, A.Khoukaze, V.Kleberf, V.Koptevg,
Y.Maedah, T.Mersmanne, S.Mikirtychiantsg, R.Schleichertb,
H.Str¨ oherb, Yu.Valdaug, C.Wilkini,∗
aThe Andrzej So? ltan Institute for Nuclear Studies, 05-400´Swierk, Poland
bInstitut f¨ ur Kernphysik, Forschungszentrum J¨ ulich, 52425 J¨ ulich, Germany
cHigh Energy Physics Institute, Tbilisi State University, 0186 Tbilisi, Georgia
dPhysikalisches Institut II, Universit¨ at Erlangen-N¨ urnberg, 91058 Erlangen,
Germany
eInstitut f¨ ur Kernphysik, Universit¨ at M¨ unster, 48149 M¨ unster, Germany
fPhysikalisches Institut, Universit¨ at Bonn, 53115 Bonn, Germany
gHigh Energy Physics Department, Petersburg Nuclear Physics Institute, 188350
Gatchina, Russia
hResearch Center for Nuclear Physics, Osaka University, Ibaraki, Osaka 567-0047,
Japan
iPhysics and Astronomy Department, UCL, London, WC1E 6BT, UK
Abstract
The pp → pK+Y0reaction has been studied for hyperon masses m(Y0) ≤ 1540MeV/c2
at COSY-J¨ ulich by using a 3.65GeV/c circulating proton beam incident on an in-
ternal hydrogen target. Final states comprising two protons, one positively charged
kaon and one negatively charged pion have been identified with the ANKE spectrom-
eter. Such configurations are sensitive to the production of the ground state Λ and
Σ0hyperons as well as the Σ0(1385) and Λ(1405) resonances. Applying invariant–
and missing–mass techniques, the two overlapping excited states could be well sep-
arated, though with limited statistics. The shape and position of the Λ(1405) distri-
bution, reconstructed cleanly in the Σ0π0channel, are similar to those found from
other decay modes and there is no obvious mass shift. This finding constitutes a
challenging test for models that predict Λ(1405) to be a two-state resonance.
Key words: Hyperon resonances, line shapes
PACS: 14.20.Jn, 13.30.-a
Preprint submitted to Elsevier1 February 2008

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The excited states of the nucleon are a topical field of research, since the
full spectrum contains deep-rooted information about the underlying strong
colour force acting between the quarks and gluons. In addition to searching
for missing resonances predicted by quark models [1], it is important to un-
derstand the structure of certain well established states, such as the Λ(1405)
hyperon resonance.
Although a four–star resonance [2], and known already for many years, the dy-
namics of the Λ(1405) are still not fully understood. Within the quark model
it can be explained as a P–wave q3baryon [3]. It is also widely discussed
as a candidate for a¯KN molecular state [4], or for one with a more intrin-
sic q4¯ q pentaquark structure [5]. If the Λ(1405) is a dynamically generated
resonance produced via ¯KN rescattering within a coupled–channel formal-
ism [6,7], it may consist of two overlapping I = 0 states [8,9,10]. Its decay
spectrum would then depend upon the production reaction. Due to the open-
ing of the¯KN channels, the Λ(1405) lineshape is not represented satisfactorily
by a Breit–Wigner resonance [4,11,12,13]. Nevertheless, if the Λ(1405) were a
single quantum state, as in the quark model or molecular pictures, its lineshape
should be independent of the production method.
Part of the difficulty in elucidating the nature of the Λ(1405) is due to it
overlapping the nearby Σ0(1385). The interference between these two states
can distort significantly the Σ+π−and Σ−π+spectra [6], for which there are
experimental indications [14]. This interference can be eliminated by taking
the average of Σ+π−and Σ−π+data [11] but the cleanest approach is through
the measurement of the Σ0π0channel, since isospin forbids this for Σ0(1385)
decay. This is the technique that we want to develop here and, although our
statistics are rather poor, these are already sufficient to yield promising results.
We have used data obtained during high statistics φ–production measurements
with the ANKE spectrometer [15] to study the excitation and decay of low–
lying hyperon resonances in pp collisions at a beam momentum of 3.65 GeV/c
in an internal–ring experiment at COSY–J¨ ulich. A dense hydrogen cluster–jet
gas target was used and over a four–week period this yielded an integrated
luminosity of L = (69 ± 10) pb−1, as determined from elastic pp scattering
that was measured in parallel and compared with the SAID 2004 solution [16].
The detection systems of the magnetic three–dipole spectrometer ANKE si-
multaneously register and identify both negatively and positively charged par-
ticles [17]. Forward (Fd) and side–wall (Sd) counters were used for protons,
telescopes and side–wall scintillators for K+, and scintillators for π−. Since
the efficiencies of the detectors are constant to 2% (σ) across the momentum
range of registered particles, any uncertainty in this can be neglected in the
∗Corresponding author.
Email address: cw@hep.ucl.ac.uk (C.Wilkin).
2

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further analysis.
The basic principle of the experiment is the search for four–fold coincidences,
comprising two protons, one positively charged kaon and one negatively charged
pion, i.e., pp → pK+pπ−X0. Such a configuration can correspond, e.g., to the
following reaction chains involving the Σ0(1385) and Λ(1405) as intermediate
states:
(1) pp → pK+Σ0(1385) → pK+Λπ0→ pK+pπ−π0
(2) pp → pK+Λ(1405) → pK+Σ0π0→ pK+Λγπ0→ pK+pπ−γπ0.
In the Σ0(1385) case, the residue is X0= π0, while for the Λ(1405), X0= π0γ.
The resonances overlap significantly because the widths of 36MeV/c2for
Σ0(1385) and 50MeV/c2for Λ(1405) are much larger than the mass differ-
ence [2]. The strategy to discriminate between them is to: (i) detect and
identify four charged particles pFd, pSd, K+and π−in coincidence, thereby
drastically reducing the accidental background at the expense of statistics,
(ii) select those events for which the mass of a (pSdπ−) pair corresponds to
that of the Λ, (iii) select the mass of the residue m(X0) to be that of the π0
to tag the Σ0(1385), and m(X0) > m(π0) + 55MeV/c2for the Λ(1405).
Figure 1a shows the two–dimensional distribution of the four–particle missing
mass MM(pK+π−p) of the pSdπ−pairs versus the invariant mass M(pSdπ−).
A vertical band corresponding to the Λ, is visible around a mass of 1116MeV/c2.
The features of this band are illustrated clearly in the projection onto the
M(pSdπ−) axis shown in Fig. 1b. The Λ peak, with a FWHM of ∼ 5MeV/c2,
sits on a slowly varying background, much of which arises from a false pπ−
association (the combinatorial background).
Data within the invariant–mass window 1112–1120MeV/c2were retained for
further analysis and, in Fig. 2, MM(pFdK+) is plotted against MM(pK+pπ−)
for these events. The triangular–shaped domain arises from the constraint
MM(pFdK+) ≥ MM(pK+pπ−)+m(Λ). Despite the lower limit of 50MeV/c2
on MM(pK+pπ−), there is a background from Σ0production at the bot-
tom of the triangle, but this can be easily cut away. The enhancement for
MM(pFdK+) ∼ 1400MeV/c2corresponds to Σ0(1385) and Λ(1405) produc-
tion. The two vertical bands show the four–particle missing–mass MM(pK+pπ−)
criteria used to separate the Σ0(1385) from the Λ(1405). The left band is op-
timised to identify a π0whereas, in view of the missing–mass resolution, the
right one selects masses significantly greater than m(π0).
Since the properties of the Σ0(1385) are undisputed [2], we first present and
discuss results for this hyperon as a test case for the Λ(1405) analysis. In
Fig. 3 we show the experimental missing–mass MM(pFdK+) spectrum for
3

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2
), MeV/c
-π
p
+
MM(p K
100
150
200
250
300
350
400
a)
2
), MeV/c
-π
Sd
M(p
11001110112011301140
2
ENTRIES / 10 MeV/c
50
100
150
200
250
300
350
400
b)
Fig. 1. a) Missing mass MM(pK+pπ−) versus invariant mass M(pSdπ−). The
shaded vertical box shows the band used to select the Λ. b) The projection of
all the events from panel a) onto the M(pSdπ−) axis shows a clear Λ peak with a
FWHM projection of ∼ 5MeV/c2and a slowly varying background.
events within the π0–band of Fig. 2. When this is fit with a Breit–Wigner
distribution plus a linear background, a mass of M = (1384 ± 10)MeV/c2
and a width of Γ ∼ 40MeV/c2are obtained, in good agreement with the
PDG values [2]. The resonance is located half way between the Σπ and¯KN
thresholds, indicated by arrows in Fig. 3, and no significant influence of either
threshold is observed in the data.
To investigate possible contributions to the spectrum other than from the
Σ0(1385) excitation, Monte Carlo simulations were performed for backgrounds
from non–resonant and resonant production. The first group of reactions in-
cludes processes such as pp → NK+πX(γ) and pp → NK+ππX(γ), with X
4

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2
), MeV/c
-π
p
+
MM(p K
50100150200250300350400
2
), MeV/c
+
K
Fd
MM(p
1200
1300
1400
1500
1600
0
π
=
0
X
γ
0
π
=
0
X
Fig. 2. Missing mass MM(pFdK+) versus MM(pK+pπ−). A clear concentration of
π0events is seen, though with a central value of the mass ∼ 8MeV/c2too high, a
deviation that is consistent with the resolution expected for a four–particle missing
mass. The left shaded vertical box covers this π0region and the right one has
MM(pK+pπ−) > 190MeV/c2originating, e.g., from π0γ and ππ.
representing any allowed Λ or Σ hyperon. The second group comprises Λ(1405)
and Λ(1520) hyperon production. The simulations, based on the GEANT3
package, were performed in a similar manner to those in Ref. [18]. Events were
generated according to phase space using relativistic Breit–Wigner parametri-
sations for the known hyperon resonances [2]. Their relative contributions were
deduced by fitting the experimental data, giving the results shown by the his-
tograms of Fig. 3. Also included is a small contribution from the Λ(1405)
channel, arising from the tail of the missing–mass events in Fig. 2 leaking into
the π0region. As expected, the Σ0(1385) peak dominates over a small and
smooth background.
In order to estimate the total Σ0(1385) production cross section we used the
overall detector efficiency of ∼ 55% and the cumulative branching ratio of
56% for the Σ0(1385) decay chain corresponding to reaction (1). With the
calculated acceptance of ∼ 2×10−6and the number of Σ0(1385) events equal
to 170 ± 26, we find
σtot(pp → pK+Σ0(1385)) = (4.0 ± 1.0stat± 1.6syst)µb.
at pbeam = 3.65GeV/c. The systematic uncertainty in the fitting procedure
and cross section evaluation was estimated by varying some of the event selec-
tion parameters, such as the width of the MM(pK+pπ−) bands or the range
5

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2
), MeV/c
+
K
Fd
MM(p
1300 1350 1400 1450 15001550
2
ENTRIES / 10 MeV/c
10
20
30
40
50
60
0
π
=
0
X
NK
π Σ
Fig. 3. Missing–mass MM(pFdK+) distribution for the pp → pK+pπ−X0reaction
for events with M(pSdπ−) ≈ m(Λ) and for MM(pK+pπ−) ≈ m(π0). Experimental
points with statistical errors are compared to the shaded histogram of the fitted
overall Monte Carlo simulations. The simulation includes resonant contributions
(solid–black) and non–resonant phase–space production (solid–grey). The structure
in the latter arises from the various channels considered. Arrows indicate the Σπ
and¯KN thresholds.
for the Λ peak (see Fig. 1), or the non–resonant background in Fig. 3. The
cross section is only a little lower than at 6GeV/c, (7 ± 1)µb [19], whereas
that for pp → pK+Λ increases by a factor of four over a similar change in
excess energy [20].
Turning now to the Λ(1405), simulations show that the Σ0(1385) does not
contaminate the missing–mass MM(pK+pπ−) range above 190MeV/c2. This
point is crucial since it allows us to obtain a clean separation of the Σ0(1385)
and Λ(1405). There is the possibility of some contamination from the pK+Λ(ππ)0
channel but there is only a limited amount of the five–body phase space avail-
able near the maximum missing mass. Simulations also show that the ANKE
acceptance varies only marginally in the mass range around 1400MeV/c2. The
corresponding experimental missing–mass MM(pFdK+) spectrum is shown in
Fig. 4a. The asymmetric distribution, which peaks around 1400MeV/c2, has
a long tail on the high missing–mass side that extends up to the kinematical
limit.
In order to extract the Λ(1405) distribution from the measured Σ0π0decay,
a different strategy has been applied, where we first fit the non–resonant
contributions to the experimental data. The fit was performed for 1440 <
MM(pFdK+) < 1490MeV/c2to exclude heavier hyperon resonances, such
6

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2
ENTRIES / 10 MeV/c
10
20
30
40
50
γ
0
π
=
0
X
NK
π
Σ
a)
2
), MeV/c
+
K
Fd
MM(p
13001350 14001450 1500 1550
0
5
10
15
20
25
30
b)
Fig. 4. a) Missing–mass MM(pFdK+) distribution for the pp → pK+pπ−X0reac-
tion for events with M(pSdπ−) ≈ m(Λ) and MM(pK+pπ−) > 190MeV/c2. Exper-
imental points with statistical errors are compared to the shaded histogram of the
fitted non–resonant Monte Carlo simulation. b) The background–subtracted line-
shape of the Λ(1405) decaying into Σ0π0(points) compared to π−p → K0(Σπ)0[13]
(solid line) and K−p → π+π−Σ+π−[11] (dotted line) data.
as the Λ(1520). The resulting non–resonant background is indicated by the
shaded histogram in Fig. 4a. When this is subtracted from the data we obtain
the distribution shown as experimental points in Fig. 4b.
Our background–subtracted data exhibit a prominent structure around 1400MeV/c2.
There is no indication of a second near 1500MeV/c2, which might result
from the production of the Λ(1520) [11]. The excess of at most 20 events
for MM(pFdK+) > 1490MeV/c2leads to an upper limit for the Λ(1520) pro-
duction cross section of σtot <
0.2µb. The smallness of the signal in this
case would be largely due to the low branching of only 9% into this channel.
There is no evidence either for a significant contribution from the Y0∗(1480)
hyperon [18]. If this state were the same as the one–star Σ0(1480) of Ref.[2],
7

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the decay into Σ0π0would be forbidden. However, this state is also not seen
in the K−p → π0π0Λ reaction [21].
We finally turn to the contribution from lower missing masses. From the num-
ber of events with 1320 < MM(pFdK+) < 1440MeV/c2, equal to 156 ± 23,
we find a total production cross section of
σtot(pp → pK+Λ(1405)) = (4.5 ± 0.9stat± 1.8syst)µb
at pbeam= 3.65GeV/c. The cumulative branching ratio for the Λ(1405) decay
chain of reaction (2) of 21% and the acceptance of ∼ 4 × 10−6have been
included, as well as the overall detection efficiency of ∼ 55%.
The (Σπ)0invariant–mass distributions have been studied in two hydrogen
bubble chamber experiments. Thomas et al. [13] found ∼ 400 Σ+π−or Σ−π+
events corresponding to the π−p → K0Λ(1405) → K0(Σπ)0reaction at a beam
momentum of 1.69GeV/c. Hemingway [11] used a 4.2GeV/c kaon beam to
investigate K−p → Σ+(1660)π−→ Λ(1405)π+π−→ (Σ±π∓)π+π−. For the
Σ−π−π+π+final state, the Σ−π+mass spectrum is distorted by the confusion
between the two positive pions. Thus, in the comparison with our data, we
use only the Σ+π−distribution, which contains 1106 events [11].
In Fig. 4b our experimental points are compared to the results of Thomas
and Hemingway, which have been normalised by scaling their values down
by factors of ∼3 and ∼7, respectively. The effect of the¯KN threshold is
apparent in these published data, with the Λ(1405) mass distribution being
distorted by the opening of this channel. Despite the very different production
mechanisms, the three distributions have consistent shapes. A fit of one to
either of the others leads to a χ2/ndf of the order of unity though, as pointed
out in Ref. [6], for Σ+π−production [11] there is likely to be some residual
distortion from I = 1 channels. The K−p → Λ(1405)π0→ Σ0π0π0data
yield a somewhat different distribution [22] but, as noted in this reference, the
uncertainty as to which π0originated from the Λ(1405) “smears the resonance
signal in the spectra”. The situation is therefore very similar to that of the
Hemingway Σ−π−π+π+data [11] and such results can only be interpreted
within the context of a specific reaction model, such as that of Ref. [9].
Models based on unitary chiral perturbation theory find two poles in the neigh-
borhood of the Λ(1405) which evolve from a singlet and an octet in the exact
SU(3) limit [8,9]. One has a mass of 1390MeV/c2and a width of 130MeV/c2
and couples preferentially to Σπ. The narrower one, located at 1425MeV/c2,
couples more strongly to¯KN, whose threshold lies at ∼ 1432MeV/c2. Both
states may contribute to the experimental distributions, and it is their rel-
ative population, which depends upon the production mechanism, that will
determine the observed lineshape. Our experimental findings show that the
8

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properties (mass, width, and shape) of the Λ(1405) resonance are essentially
identical for these three different production modes.
In summary, we have measured the excitation of the Σ0(1385) and Λ(1405) hy-
peron resonances in proton–proton collisions at a beam momentum of 3.65GeV/c.
We have succeeded in unambiguously separating the two states through their
Λπ0and Σ0π0→ Λγπ0decay modes. Cross sections of the order of a few µb
have been deduced for both resonances. The Λ(1405), as measured through
its Σ0π0decay, has a shape that is consistent with data on the charged de-
cays [11,13], with a mass of ∼ 1400MeV/c2and width of ∼ 60MeV/c2. This
might suggest that, if there are two states present in this region, then the
reaction mechanisms in the three cases are preferentially populating the same
one. However, by identifying particular reaction mechanisms, proponents of
the two–state solution can describe the shape of the distribution that we have
found [10].
The Σ0π0channel is by far the cleanest for the observation of the Λ(1405)
since it is not contaminated by the Σ(1385) nor the confusion regarding the
identification of the pion from its decay. However, although we have shown that
the method works in practice, in view of our limited statistics, further data are
clearly needed. The decay Λ(1405) → Σ0π0→ Λγπ0can be detected directly
in electromagnetic calorimeters. Corresponding measurements are under way
in γp reactions (CB/TAPS at ELSA [23], SPring−8/LEPS [24]) and are also
planned in pp interactions with WASA at COSY [25].
We acknowledge many very useful discussions with E. Oset. We also thank all
other members of the ANKE collaboration and the COSY accelerator staff for
their help during the data taking. This work has been supported by COSY-
FFE Grant, BMBF, DFG and Russian Academy of Sciences.
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