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Partial-Wave Analysis of the jï + ï \Gamma System Produced in the
Reaction ï \Gamma
p ! jï +
ï \Gamma
n at 18 GeV/c
Version 0.1
E852 Collaboration
J. J. Manak, T. Adams, J. M. Bishop, N. M. Cason, E. I. Ivanov, J. M. LoSecco,
A. H. Sanjari, W. D. Shephard, D. L. Stienike, S. A. Taegar, D. R. Thompson
University of Notre Dame
S. U. Chung, R. W. Hackenburg, C. Olchanski, D. P. Weygand, H. J. Willutzki
Brookhaven National Laboratory
B. B. Brabsen, R. R. Crittenden, A. R. Dzierba, J. Gunter, R. Lindenbusch, D. R. Rust,
E. Scott, P. T. Smith, T. Sulanke, S. Teige
Indiana University
S. P. Denisov, V. A. Dorofeev, I. A. Kachaev, V. V. Lipaev, A. V. Popov, D. I. Ryabchikov
IHEP Protvino
Z. Bar-Yam, J. P. Dowd, P. Eugenio, M. Hayek, W. Kern, E. King
University of Massachusetts Dartmouth
V. A. Bodyagin, O. L. Kodolova, V. L. Korotkikh, M. A. Kostin, A. I. Ostrovidov,
L. I. Sarycheva, N. B. Sinev, I. N. Vardanyan, A. A. Yershov
Moscow State University
D. S. Brown, T. K. Pedlar, K. K. Seth, J. Wise, D. Zhao
Northwestern University
1

G. S. Adams, J. P. Cummings, J. Kuhn, J. Napolitano, M. Nozar, J. A. Smith,
D. B. White, M. Witkowski
Rensselaer Polytechnic Institute
(January 21, 1998)
Abstract
A partial-wave analysis of 9082 jï + ï \Gamma n events produced in the reaction
ï \Gamma p ! jï + ï \Gamma n at 18:3 GeV/c has been carried out using data from ex-
periment 852 at Brookhaven National Laboratory. The data is dominated
by J PC = 0 \Gamma+ partial waves consistent with observation of the j(1295)
and the j(1440). The mass and width of the j(1295) was determined to
be 1282 \Sigma 5 MeV and 66 \Sigma 13 MeV respectively while the j(1440) was ob-
served with a mass of 1404 \Sigma 6 MeV and a width of 80 \Sigma 21 MeV. Other
partial waves of importance include the 1 ++ and the 1 +\Gamma waves. Results of
the partial wave analysis are combined with results of other experiments to
estimate f 1 (1285) branching fractions. These values are considerably different
from current values determined without the aid of amplitude analyses.
Typeset using REVT E X
2

I. INTRODUCTION
This paper presents results of a partial-wave analysis of the jï + ï \Gamma system in the 1.21
to 1.53 GeV/c 2 mass region. Specifically the reaction
ï \Gamma p ! jï + ï \Gamma n; j ! 2fl (1)
is examined at 18.3 GeV/c. The data sample was collected during the summer of 1994 using
the Multi-Particle Spectrometer (MPS) at the Alternating Gradient Synchrotron (AGS)
facility of Brookhaven National Laboratory (BNL).
The identification of the isoscalar members of the J PC = 0 \Gamma+ and 1 ++ nonets has been
the subject of considerable interest, particularly with regard to searches for exotic mesons.
It is known that some such states have a 0 (970)ï decay modes. Since the a 0 (970) couples to
both jï and to KK final states, comparison of the resonances produced in the jï + ï \Gamma and
KKï reactions can lead to important information with regard to this identification.
The jï + ï \Gamma system is complicated, characterized by the large range of accessible quantum
numbers (J PC = 0 \Gamma+ , 0 \Gamma\Gamma , 1 \Gamma\Gamma , 1 +\Gamma , 1 ++ , 2 \Gamma\Gamma . . . ), a large number of possible jï and ïï
intermediate isobars (a 0 , a 2 , f 0 =oe, ae, f 2 ), and the presence of overlapping resonances (f 1 ,
j(1295)).
Historically, the region around the 1.3 GeV/c 2 enhancement in the jï + ï \Gamma and KKï mass
spectra was called the D region. Most early analyses of this region [1--6] made the assumption
that a single state existed in the D region in the presence of an incoherent (non-interfering)
background. The problem was then the determination of the appropriate quantum numbers
of this state and its branching ratio to jï + ï \Gamma . Most early experiments showed a preference
for J PC = 1 ++ quantum numbers of the D, now referred to as the f 1 (1285).
Later, sufficiently high statistics were collected to carry out a partial wave analyses of
the jï + ï \Gamma system. Stanton et al. [7] performed an analysis of the reaction ï \Gamma p ! jï + ï \Gamma n
at 8.45 GeV/c. The D region was fit with a combination of 0 \Gamma+ , 1 ++ , and 1 +\Gamma partial waves.
Their analysis suggested the presence of a new state with J PC = 0 \Gamma+ , the j(1295) in the D
3

region as well as the f 1 (1285). In addition, it was suggested that the fit could be improved
considerably if the 0 \Gamma+ partial waves were not allowed to interfere with the other waves in
the fit.
The KEK-E179 collaboration performed two partial wave analyses [20,21] of the same
reaction at 8 GeV/c. They too used a set of 0 \Gamma+ , 1 ++ , and 1 +\Gamma partial waves to describe the
D region. Their analysis observed the f 1 (1285) and j(1295) in the D region. Their analysis
also suggested the presence of an additional state, the j(1440) located in what has been
called the E region.
II. APPARATUS
Figure 1 shows the experimental layout. The detector system consists of a charged-
particle spectrometer and a downstream 3045-element lead-glass electromagnetic calorimeter
(LGD) [8] [9] to provide neutral particle detection.
An 18.3 GeV/c ï \Gamma beam is incident on the 30-cm liquid-hydrogen target located at the
center of the MPS magnet. Surrounding the target is a 198-element thallium-doped cesium
iodide cylindrical veto array (CsI) [10] used in off-line analysis to reject events with wide-
angle, low-energy photons from baryonic resonance decay. Between the target and the CsI
is a four-plane cylindrical drift chamber (TCYL) [11] for triggering on recoil charged tracks.
The downstream half of the magnet is equipped with three proportional wire chambers
(TPX1-3) for triggering on forward charged-track multiplicity, and six drift chamber modules
(DX1-6) for measuring the momentum of forward charged tracks. Also in the magnet is a
window-frame lead-scintillator sandwich photon veto counter (DEA) which covers the solid-
angle gap between the CsI and the LGD. Two scintillation counters are mounted on DEA, a
window-frame counter (CPVC) to distinguish between charged and neutral particles hitting
DEA, and a rectangular counter (CPVB) which covers the hole in the DEA and is used, in
conjunction with CPVC, to veto charged tracks in the all-neutral trigger. Beyond the magnet
and just upstream of the LGD is a final drift chamber (TDX4) consisting of two X-planes,
4

and two scintillation counters (BV and EV) for vetoing non-interacting beam particles and
elastic-scatter events. Further details regarding the equipment are given elsewhere [12].
III. DATA SELECTION AND PROPERTIES
The trigger for the jï + ï \Gamma topology required a ?
Cerenkov-tagged ï \Gamma incident on the target,
two charged tracks emerging from the target, no charged recoil track, and an effective mass
greater than that of the ï 0 in the LGD as determined by a hardware processor. Some 48
million triggers of this type were taken. From these, a final sample of 9082 events consistent
with reaction 1 were selected by requiring:
ffl less than 20 MeV in the CsI to enhance recoil neutron events over N \Lambda events;
ffl exactly two photons (j) reconstructed in the LGD;
ffl a reconstructed beam track;
ffl two forward charged tracks of opposite charge;
ffl no recoil charged track;
ffl a 3-constraint SQUAW [13] kinematic fit to reaction 1 with a confidence level greater
than 7%;
ffl jtj ! 3 GeV 2 /c 2 after kinematic fitting.
The two-gamma mass distribution for about 10% of the data is shown before and after
the data selection cuts in Fig. 2. 1 The j signal is nearly background free after cuts.
The corrected mass distribution for these events is shown in Figure 3. Evident is the
j 0
which, when fit to a Gaussian, yields a mass of 961 MeV with oe =10 MeV, indicative
1 A cut was made on the missing-mass-squared distribution in Fig. 2b to simulate the effect of the
SQUAW kinematic fitting.
5

of the resolution of the apparatus in the 1 GeV/c 2 mass region. An enhancement in the D
region 2 is observed which, when fit to a Gaussian plus a linear background, yields a mass of
1278 MeV and oe = 20 MeV.
Shown in Figs. 4a and 4b respectively are the jï \Gamma and jï + effective mass distributions
respectively for a three-body mass between 1.2 and 1.54 GeV/c 2 . Seen in each spectrum are
a 0 (980) peaks. If we restrict ourselves to the D region (1.2-1.35 GeV/c 2 ), show in figure 5,
we can see that the two body mass distributions vary as a function of jïï mass. Specifically
an asymmetry is observed between the of a +
0 and a \Gamma
0 . This asymmetry is due to due to the
interference between odd and even isospin states and is well-described in the partial-wave
analysis described in the next section.
The ï + ï \Gamma effective mass distribution for the 1.1-2.0 GeV/c 2 three-body mass region is
shown in Fig. 4c. Evident is a distorted ae(770) signal due to its proximity to threshold.
For the following analysis, 9,082 events were selected from the above data set in the
low-mass region. These events have 1:205 ? M(jïï) ? 1:535GeV/c 2 .
IV. PARTIAL-WAVE ANALYSIS
A. Fitting Procedure
The formalism used in this analysis is based on the papers of Chung [14] and Chung and
Trueman [15]. The analysis techique involved the use of the reflectivity basis to describe the
individual partial waves and the maximization of an extended log likelihood function in the
fitting proceduere. The procedure and analysis programs are described by Cummings and
Weygand [16].
Due to the large number of possible partial waves accessible to the jï + ï \Gamma system, a
complete analysis requiring all possible isobars and partial waves is not practical given the
2 A detailed description of the Dalitz plot in the D region is given is elsewhere [12].
6

limited statistics. In principal one would like to include all possible isobars: a 0 ; a 2 ; f 0 ; ae; f 2
and a large set of partial waves (J ! 4). Because this analysis is in the low-mass region, we
can eliminate the a 2 and the f 2 isobars. Furthermore, we choose to consider only amplitudes
with J ! 2 since there are no known states 3 with higher spin in this low-mass region which
decay to jïï.
An incoherent background was included in some fits. This was represented by a single
real parameter with no angular dependence associated with it (other than the acceptance of
the apparatus). While the final fit did not contain a background term, its use was explored
in the fitting process. The background is in many ways similar to a non-interfering J = 0,
oej partial wave, making them quite difficult to differentiate.
In principal, a rank 2 fit is required to describe the data to account for the presence
of spin-flip and non-flip amplitudes generated at the baryon vertex. Fits were attempted
for both rank 1 and 2. The likelihood function was improved greatly when the fit rank
was increased to two. In addition, rank 1 fits to the data became unstable in the absence
of a background wave. Furthermore, when a background was included, it had unexpected
structure in the D and E regions and occurred at a higher level than anticipated. All of this
information suggested that a rank 2 fit was required to fit the data, and rank 1 fits were not
used.
The ae isobar was modeled by a relativistic Breit-Wigner with parameters extracted from
the Particle Data Book [17]. For the final fit the a 0 was modeled as a Breit-Wigner form
with a mass of 980 MeV and a width of 72 MeV. The ïï S-wave (the oe=f 0 ) was represented
by a parameterization of the ï + ï \Gamma S-wave provided by K. L. Au et al. [18]. Alternate
parameterizations of the a 0 and the oe=f 0 were explored [19]. However it was found that the
particular choice of parameterization had little effect on the final result.
3 The f 2 (1270) could in principle reach this final state through the a 2 ï mode, but this is highly
suppressed by phase space.
7

To determine the appropriate waves over the low-mass region, a fit was performed using a
coarse bin width of 50 MeV with all waves with J ! 2 included. Waves were then discarded
from the fit if their removal had little effect on the value of the likelihood function (j\DeltaLj ! 5).
Selected waves were then re-introduced in the fit to insure the stability of the solution. In
total, several hundred different sets of partial waves were fit. For each combination of partial
waves, the binning, t cuts, starting values, and starting point were varied to insure stability
of the final solution. The set of waves chosen for the final fit is shown in Table I.
For the final fit, a bin width of 30 MeV was chosen. This was seen as a compromise
between achieving adequate statistics in each mass bin and acquiring the best possible
resolution in the D and E regions. The starting values of the fit were randomly chosen and
the entire spectrum was re-fit several times to insure stability with the finer bin width. For
bin widths below 30 MeV the fits often became unstable, converging to different solutions
depending upon the starting values.
It is interesting to note that the final waves selected for the low mass-region are consistent
with those used by Stanton et al. [7] and by Fukui et al. [20]. The only exception is that we
do not use a 1 +\Gamma a 0 ï wave. We found that the fit could not distinguish this wave from the
1 +\Gamma aej wave in the D region. Due to the unambiguous presence of the aej partial wave at
higher mass, it was decided not to include the 1 +\Gamma a 0 ï partial wave in the final set.
B. Results of Partial Wave Analysis
1. J PC = 0 \Gamma+ Partial Waves
The fitted intensity distribution for the 0 \Gamma+ a 0 ï wave as a function of jï + ï \Gamma effective
mass is shown in Fig. 6a. A sharp peak in the D region is evident, consistent with the
observation of j(1295) ! a 0 ï. Some intensity is seen extending out to 1.4 GeV/c 2 . It
should be noted that the majority of the signal for this wave comes from the second rank of
the fit. This indicates a different production mechanism than that for the 1 +\Gamma and the 1 ++
8

waves (which are produced dominantly in the first rank) and means that these latter waves
do not interfere with the 0 \Gamma+ wave.
Shown in Fig. 6b, the 0 \Gamma+ oej wave is double-peaked, with enhancements in both the D
and E regions. This structure is suggestive of j(1295) and j(1440) production. In fact, the
majority of the structure seen in the E region is associated with this wave. This result, is
somewhat inconsistent with previous analyses [20,21], which observe the presence of a oej
decay of the j(1440), but do not see it dominating the structure in the E region.
As was mentioned above, second-rank fits were required to obtain good fits to the data.
A large portion of the 0 \Gamma+ signal occurred in the second rank, with the largest proportion
in the 0 \Gamma+ oej partial wave in the E region. Because these waves do not interfere with the
other dominant waves in the fit, reliable relative phase motion could not be obtained.
The result of adding the two 0 \Gamma+ waves coherently in each rank and then adding the
sums incoherently is shown in Fig. 6c. Peaks in the D and E regions are clearly visible,
and constructive interference occurs within each rank. The spectrum was fit to two spin-0
Breit-Wigners plus a quadratic background. Fitted values of the masses and widths are
given in Table II. In addition, the a 0 ï=oej branching ratio can be determined from Fig. 6
for both the j(1295) and the j(1440). These values are also given in Table II.
2. J PC = 1 ++ Partial Waves
Shown in Fig. 7a is the 1 ++ a 0 ï partial wave intensity distribution. This wave shows
evidence for the f 1 . However, the amount of f 1 signal is surprisingly small (600 counts in
the peak bin) compared with the 0 \Gamma+ intensity. No significant structure was observed at
higher mass.
Figure 7b shows the 1 ++ oej partial wave intensity distribution. This wave was necessary
to the fit for bins above 1.45 GeV/c 2 .
Shown in Fig. 7c is the coherent sum of the 1 ++ partial waves. This sum displays a peak
in the vicinity of the f 1 and a slow rise at high mass. When a comparison to the coherent
9

sum of the 0 \Gamma+ partial waves (Fig. 6) is made one observes that the majority of signal in the
D and E regions arises not from 1 ++ partial waves but from the 0 \Gamma+ wave. This observation
is especially important to the D region, because some previous analyses used for branching
ratio estimates have assumed the D signal to be primarily 1 ++ , not 0 \Gamma+ .
3. aej Partial Waves
The intensity distribution for the 1 +\Gamma aej wave is shown in Fig. 8a. This wave was seen in
all previous analyses and is significant over the low mass region. Previous experiments [20]
have claimed this wave to be evidence for production of the b 1 (1235) with a aej decay mode.
However the lack of structure in the 1 +\Gamma wave and unclear phase motion discourage this
interpretation. It should be noted that this wave is essential for producing the a +
0 =a \Gamma
0
asymmetry observed in the data.
Shown in Fig. 8b is the 1 \Gamma\Gamma aej intensity distribution. This is the only negative reflectivity
partial wave and does not interfere with any other partial waves in the fit. The wave steadily
increases throughout the low-mass region and its behavior is consistent with it being the
low-mass tail of the ae(1700).
V. DISCUSSION OF THE F 1 (1285) BRANCHING FRACTIONS
The j(1295) production dominates the D peak, accounting for roughly 80% of the D
signal. This observation has implications on the f 1 ! jïï branching fraction. Previous
experiments [2] have determined the f 1 ! jïï branching fraction without the aid of a
partial wave analysis under the assumption that the D peak consists of a single f 1 state,
resting on top of an incoherent background. This assumption is clearly incorrect, and values
for the branching fractions must be corrected.
Corden et al. [2] studied the reactions ï \Gamma p ! jï + ï \Gamma n and ï \Gamma p ! KKïn at 15 GeV/c.
In their analysis they obtained a KKï=jïï branching ratio in the D region of 0:5 \Sigma 0:2
without the aid of a partial wave analysis. It is reasonable to assume that the relative
10

production of f 1 and j(1295) is the same in this experiment as in that of Ref. [2] since the
experiments are close in energy and are studying the same final state. It is also reasonable to
assume that the KKï decay mode is all due to f 1 decay since this reaction has been studied
using a partial wave analysis [22] with this conclusion. Thus the KKï=jïï branching ratio
of the f 1 should be adjusted by dividing the observed D-region KKï=jïï branching ratio by
the fraction of the D peak which is due to f 1 (1285) decay. We thus obtain (0:5 \Sigma 0:2)=0:2 =
2:5 \Sigma 1:0 for this branching ratio.
We can perform the same type of estimate using, instead of our own analysis, the results
of KEK-E179 [20] for the reaction ï \Gamma p ! jï + ï \Gamma n at 8.95 GeV/c. In that experiment, the
fraction of the D peak which is due to f 1 (1285) decay is 50%. Again using the results of
Corden et al. (although in this case the difference in the energies of the experiments is
larger) one can obtain an alternate estimate of the KKï=jïï branching ratio for f 1 decay
to be 1:0 \Sigma 0:4.
One can estimate the effect which these results can have on the f 1 (1285) branching
fractions by assuming that the D signal observed in the KKï, flae 0 , and 4ï decay modes is
due only to f 1 decay. This is the most reasonable for the KKï mode as mentioned above.
However, the other two decay modes (flae 0 , 4ï) have not been as thoroughly investigated 4 .
Specifically, using the quoted branching ratios of 0:33 \Sigma 0:04 for KKï=4ï and 0:45 \Sigma 0:18 for
flae 0 =2ï + 2ï \Gamma , the f 1 (1285) branching fractions can be calculated. In Table III are listed the
f 1 branching fractions calculated using KKï=jïï branching ratios of 2:5 \Sigma 1:0 (BNL-E852)
and 1 \Sigma 0:4 (KEK-E179) respectively.
Assigning systematic errors to these f 1 (1285) branching fractions is difficult due to the
undetermined uncertainties in branching ratios for the 4ï and flae 0 decay modes. However
it is clear from this exercise that the f 1 (1285) branching fractions as listed in the particle
4 Of these modes the 4ï branching fraction is most suspect due to the large number of interfering
partial waves which contribute to a 4ï data set.
11

data book need to be corrected. The 4ï decay mode is probably the dominant decay mode
of the f 1 rather than the jïï mode.
VI. SUMMARY AND CONCLUSIONS
The low-mass partial wave analysis was performed on 9082 events in the 1.20--
1.54 GeV/c 2 mass interval. This analysis used a rank 2 fit with 30 MeV bins and a set
of 6 partial waves. The partial waves used in the fit were: 0 \Gamma+ a 0 ï, 0 \Gamma+ oej, 1 +\Gamma aej, 1 ++ a 0 ï,
1 ++ oej and 1 \Gamma\Gamma aej.
The D region was found to include a large contribution from the 0 \Gamma+ wave peaking
at a mass consistent with the presence of the j(1295). Some evidence of 1 ++ wave was
also seen, consistent with f 1 (1285) production. The fact that the region is dominated by
j(1295) production leads to significant changes in the f 1 (1285) branching fractions discussed
in Section V.
The j(1295) was seen to decay to both a 0 ï and oej. The a 0 ï=oej branching ratio for
j(1295) was estimated to be 0:48 \Sigma 0:22. The mass and width of the j(1295) were determined
to be 1282 \Sigma 5 MeV and 66 \Sigma 13 MeV respectively. This result is consistent with that of
Fukui et al. [20] who determined the mass and width of the j(1295) to be 1295 \Sigma 4 MeV
and 53 \Sigma 6 MeV.
The E region is dominated by a large 0 \Gamma+ f 0 =oej signal present in the second rank of the
fit. This signal is consistent with production of a single state, the j(1440). The mass and
width of the j(1440) are estimated to be 1404 \Sigma 6 MeV and 80 \Sigma 21 MeV. This result is
remarkably consistent with the Particle Data Group weighted average value for the mass
and width of the j(1440) of 1415 \Sigma 10 MeV and 60 \Sigma 20 MeV.
Previous analysis of the reactions ï \Gamma p ! KKïn and in J=/ decays have observed
0 \Gamma+ structures in the E region in the a 0 ï and K \Lambda K decay modes while studies of the
ï \Gamma p ! jï + ï \Gamma n reaction have yielded both a oej and an a 0 ï component of the E as in this
analysis. However, the oej signal in this analysis dominates the E region, while previous
12

analyses (KEK-E179) have suggested a larger a 0 ï component of the E. An estimate of the
j(1440) a 0 ï=oej branching ratio from this analysis is 0:15 \Sigma 0:04. The systematic errors are
unassigned but assumed to be large due to the difficulty of the fit in distinguishing 0 \Gamma+ a 0 ï
and 0 \Gamma+ oej waves from each other.
In addition to the f 1 (1285), j(1295) and the j(1440) contributions, a large, relatively
structureless signal in the 1 +\Gamma aej wave was observed throughout the low mass region. This
wave has also been observed in all previous partial wave analyses of the ï \Gamma p ! jï + ï \Gamma n
system. There is no obvious resonance interpretation of this structure, but its presence
is required to account for the large a +
0 =a \Gamma
0 production asymmetry seen in the D region,
indicative of odd-even isospin interference. A 1 \Gamma\Gamma aej partial wave is also seen in the low-
mass fit, consistent with the low-mass tail of the ae(1700).
We would like to express our deep appreciation to the members of the MPS group.
Without their outstanding efforts, the results presented here could not have been obtained.
We would also like to acknowledge the invaluable assistance of the staffs of the AGS and
BNL, and of the various collaborating institutions. This research was supported in part by
the National Science Foundation and the US Department of Energy.
13

REFERENCES
[1] J. H. Campbell et al, Phys. Rev. Lett. 22, 1204 (1969)
[2] M. J. Corden et al., Nucl. Phys. B 144, 153 (1978)
[3] O. I. Dahl et. al, PR, 1967, vol. 164, pp1377--1429
[4] R. Nacasch et. al, Nucl. Phys. B 203, 203 (1978)
[5] C. Defoix et. al, Nucl. Phys. B 44, 125 (1972)
[6] A. Gurtu et al., Nucl. Phys. B 151, 181 (1979)
[7] N. R. Stanton et al., Phys. Rev. Lett.42, 346 (1979)
[8] B. Brabson et al., Nucl. Instr. & Meth A 332, 419 (1993)
[9] R. R. Crittendon, Nucl. Instr. & Meth A, 387, 377 (1997)
[10] T. Adams et al., Nucl. Instr. & Meth A 386, 617 (1996)
[11] Z. Bar-Yam et al., Nucl. Instr. & Meth A 342, 398 (1994)
[12] S. Teige et al., to be published 1998
[13] O. I. Dahl et al., ``SQUAW kinematic fitting program'', Univ. of California, Berkeley
Group A programming note P-126, unpublished (1968).
[14] S.U. Chung, ``Formulas for Partial-Wave Analysis'', Brookhaven BNL-QGS-93-05, un-
published (1993).
[15] S.U. Chung and T.L. Trueman, Phys. Rev. D 111, 633 (1975)
[16] J. P. Cummings and D. P. Weygand, ``The New BNL Partial Wave Analysis Programs'',
BNL-64637, unpublished (1997).
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[18] K. L. Au et al., Phys. Rev. D 35, 1633 (1986)
14

[19] C. Amsler et al., Phys. Lett. B 335, 425 (1995)
[20] S. Fukui et al., Phys. Rev. B 267, 293 (1991)
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[22] A. Birman et al., Phys. Rev. Lett. 61, 1557 (1988)
15

FIGURES
FIG. 1. E852 Apparatus Layout
GeV
Events/MeV
GeV
Events/MeV
0
200
400
600
800
1000
1200
1400
0.4 0.6 0.8 1
0
50
100
150
200
250
0.4 0.6 0.8 1
FIG. 2. a: 2fl mass distribution before cuts, b: 2fl mass after data selection cuts
16

GeV
Events/10MeV
0
200
400
600
800
1000
0.8 1 1.2 1.4 1.6 1.8 2 2.2
FIG. 3. jï + ï \Gamma three body mass distribution
GeV
Events/10MeV
GeV
Events/10MeV
GeV
Events/10MeV
0
50
100
150
200
250
300
350
0.5 1 1.5
0
50
100
150
200
250
300
350
0.5 1 1.5
0
50
100
150
200
250
300
350
0.5 1
FIG. 4. a: jï \Gamma two-body mass distribution, b: jï + two-body mass distribution, c: ï + ï \Gamma
two-body mass distribution for the jï + ï \Gamma massregion between 1.2 and 1.54 GeV/c 2 .
17

GeV
Events/20MeV
GeV
Events/20MeV
GeV
Events/10MeV
0
50
100
150
200
250
300
350
0.5 1 0
50
100
150
200
250
300
350
0.5 1 0
50
100
150
200
250
300
350
0.5 1
FIG. 5. a: jï \Gamma two-body mass distribution (D region), b: jï + two-body mass distribution
(D region), c: ï + ï \Gamma two-body mass distribution for the jï + ï \Gamma mass region between 1.2 and
1.35 GeV/c 2 (D region).
GeV
Events/30
MeV
GeV
Events/30
MeV
GeV
Events/30
MeV
0
200
400
600
800
1000
1.3 1.4 1.5
0
250
500
750
1000
1250
1500
1750
2000
2250
1.3 1.4 1.5
0
500
1000
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FIG. 6. a: 0 \Gamma+ a 0 ï intensity, b: 0 \Gamma+ oej intensity, c: Total 0 \Gamma+ intensity
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FIG. 7. a: 1 ++ a 0 ï intensity, b: 1 ++ oej intensity, c: Total 1 ++ intensity
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FIG. 8. a: 1 +\Gamma aej intensity, b: 1 \Gamma\Gamma aej intensity (negative reflectivity partial wave)
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TABLES
TABLE I. Partial Waves Used in Final Fit
Isospin J PC Isobar l m ffl
1 1 \Gamma\Gamma ae 1 0 \Gamma1
0 0 \Gamma+ a 0 0 0 +1
0 0 \Gamma+ oe 0 0 +1
0 1 ++ a 0 1 0 +1
0 1 ++ oe 1 0 +1
1 1 +\Gamma ae 0 0 +1
TABLE II. Properties of the J PC = 0 \Gamma+ States
Mass (GeV/c 2 ) Width (GeV/c 2 ) a 0 ï=oej Branching Ratio
j(1295) 1:282 \Sigma 0:005 0:066 \Sigma 0:013 0:48 \Sigma 0:22
j(1440) 1:404 \Sigma 0:006 0:080 \Sigma 0:021 0:15 \Sigma 0:04
TABLE III. f 1 Branching Fractions
Decay Mode PDG BNL-E852 KEK-E179
4ï 29 \Sigma 6% 59 \Sigma 17\Sigma?% 53 \Sigma 21\Sigma?%
jïï 54 \Sigma 15% 8 \Sigma 3\Sigma?% 17:5 \Sigma 9\Sigma?%
flae 0 6:6 \Sigma 1:3% 13 \Sigma 8\Sigma?% 12 \Sigma 7\Sigma? %
KKï 9:7 \Sigma 1:6% 20 \Sigma 7\Sigma?% 17:5 \Sigma 7\Sigma?%
20