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Observation of a New J PC = 1 \Gamma+ Exotic State
in the Reaction п \Gamma p ! п + п \Gamma п \Gamma p at 18 GeV/c
G. S. Adams, 4 T. Adams, 5 Z. Bar-Yam, 3 J. M. Bishop, 5 V. A. Bodyagin, 2 B. B. Brabson, 6 D. S. Brown, 7
N. M. Cason, 5 S. U. Chung, 1 R. R. Crittenden, 6 J. P. Cummings, 3;4 K. Danyo, 1 S. Denisov, 8 V. Dorofeev, 8
J. P. Dowd, 3 A. R. Dzierba, 6 P. Eugenio, 3 J. Gunter, 6 R. W. Hackenburg, 1 M. Hayek, 3;\Lambda E. I. Ivanov, 5 I. Kachaev, 8
W. Kern, 3 E. King, 3 O. L. Kodolova, 2 V. L. Korotkikh, 2 M. A. Kostin, 2 J. Kuhn, 4 R. Lindenbusch, 6 V. Lipaev, 8
J. M. LoSecco, 5 J. J. Manak, 5 J. Napolitano, 4 M. Nozar, 4 C. Olchanski, 1 A. I. Ostrovidov, 1;2;3 T. K. Pedlar, 7
A. Popov, 8 D. R. Rust, 6 D. Ryabchikov, 8 A. H. Sanjari, 5 L. I. Sarycheva, 2 E. Scott, 6 K. K. Seth, 7 N. Shenhav, 3; \Lambda
W. D. Shephard, 5 N. B. Sinev, 2 J. A. Smith, 4 P. T. Smith, 6 D. L. Stienike, 5 T. Sulanke, 6 S. A. Taegar, 5 S. Teige, 6
D. R. Thompson, 5 I. N. Vardanyan, 2 D. P. Weygand, 1 D. White, 4 H. J. Willutzki, 1 J. Wise, 7 M. Witkowski, 4
A. A. Yershov, 2 D. Zhao 7
(E852 Collaboration)
1 Brookhaven National Laboratory, Upton, New York 11973
2 Nuclear Physics Institute, Moscow State University, Moscow, Russia 119899
3 Department of Physics, University of Massachusetts Dartmouth, North Dartmouth, Massachusetts 02747
4 Department of Physics, Rensselaer Polytechnic Institute, Troy, New York 12180
5 Department of Physics, University of Notre Dame, Notre Dame, Indiana 46556
6 Department of Physics, Indiana University, Bloomington, Indiana 47405
7 Department of Physics, Northwestern University, Evanston, Illinois 60208
8 Institute for High Energy Physics, Protvino, Russia 142284
(September 25, 1998)
A partial-wave analysis of the reaction п \Gamma p ! п + п \Gamma п \Gamma p at 18 GeV/c has been performed on
a data sample of 250,000 events obtained by Brookhaven experiment E852. The expected J PC =
1 ++ a1(1260), 2 ++ a2(1320), and 2 \Gamma+ п2(1670) resonant states are clearly observed. The exotic J PC =
1 \Gamma+ wave produced in the natural parity exchange processes shows distinct resonance-like phase
motion around 1.6 GeV/c 2 in the aeп channel. A mass-dependent fit results in a resonance mass of
1593 \Sigma 8 +29
\Gamma47 MeV/c 2 and a width of 168 \Sigma 20 +150
\Gamma12 MeV/c 2 .
12.39.Mk, 13.25.Jx, 13.85.Hd, 14.40.Cs
Much progress has been made in recent years in
the theoretical description of hadrons which lie outside
the scope of the constituent quark model. QCD pre-
dicts the existence of multiquark qqqq and hybrid qqg
mesons as well as purely gluonic states. The most
suggestive experimental evidence for an exotic meson
would be the determination of quantum numbers J PC =
0 \Gamma\Gamma ; 0 +\Gamma ; 1 \Gamma+ ; 2 +\Gamma ,etc. A qq pair cannot form a state
with such quantum numbers.
Several isovector 1 \Gamma+ exotic candidates have been re-
ported recently. A 1 \Gamma+ signal in the jп channel has
been seen by several groups. Although early measure-
ments [1,2] were inconclusive, the most recent measure-
ments [3,4] have presented strong evidence for a 1 \Gamma+ state
near 1.4 GeV/c 2 . Another 1 \Gamma+ state with a mass of
1.6 GeV/c 2 was observed in the j 0 п [2] and aeп [5] chan-
nels. Additionally, a state with resonant phase behavior
has been seen above 1.9 GeV/c 2 in the f 1 п [6] channel.
Theoretical predictions for the mass of the lightest 1 \Gamma+
hybrid meson are based on various models. The flux tube
model [7,8] predicts 1 \Gamma+ states at 1.8--2.0 GeV/c 2 . Sim-
ilar results are obtained in the calculations based upon
lattice QCD in the quenched approximation [9]. Earlier
bag model estimates suggest somewhat lower masses in
the 1.3--1.8 GeV/c 2 range [10]. QCD sum-rule predic-
tions vary widely between 1.5 GeV/c 2 and 2.5 GeV/c 2
[11]. The diquark cluster model [12] predicts the 1 \Gamma+
state to be at 1.4 GeV/c 2 . Finally, the constituent gluon
model [13] concludes that light exotics should lie in the
region 1.8--2.2 GeV/c 2 . Most of these models predict the
dominance of such decay modes of the hybrid meson as
b 1 (1235)п or f 1 (1285)п, with small (but non-negligible)
aeп decay probability [14].
In this letter we present experimental evidence for
an isovector 1 \Gamma+ exotic meson produced in the reaction
п \Gamma p ! п + п \Gamma п \Gamma p. Experiment E852 was performed at
the Multi-Particle Spectrometer facility at Brookhaven
National Laboratory (BNL). The experimental appara-
tus is described elsewhere [3,15,16]. A п \Gamma beam of mo-
mentum 18.3 GeV/c and a liquid hydrogen target were
used. The trigger was based on the requirement of
three forward-going charged tracks and one charged re-
coil track. Seventeen million triggers of this type were
recorded by the experiment during the 1994 run. After
reconstruction, 700,000 events with the correct topology
remain. Of these, 250,000 events remain after kinematic
cuts are applied to insure an exclusive sample of events
with a proton recoil.
1

Figure 1 shows the п + п \Gamma п \Gamma and п + п \Gamma mass spectra.
The well-known a 1 (1260), a 2 (1320), and п 2 (1670) reso-
nances dominate the three-pion spectrum. The two-body
mass spectrum shows clear evidence for the ae(770) and
f 2 (1270) isobars.
A partial-wave analysis of these data was performed
using a program developed at BNL [17]. Each event is
considered in the framework of the isobar model: an ini-
tial decay of a parent particle into a пп isobar and an un-
paired pion followed by the subsequent decay of the iso-
bar. Each partial wave ff is characterized by the quantum
numbers J PC [isobar]LM ffl --- here J PC are spin, parity
and C-parity of the partial wave; M is the absolute value
of the spin projection on the quantization axis; ffl is the
reflectivity (and corresponds to the naturality of the ex-
changed particle); L is the orbital angular momentum
between the isobar and the unpaired pion.
The spin-density matrix is parameterized in terms of
the complex production amplitudes V kffl
ff for wave ff with
reflectivity ffl [18]. These amplitudes are determined from
an extended maximum likelihood fit. The index k corre-
sponds to the different possibilities at the baryon vertex
and defines the rank of the spin-density matrix. This
rank does not exceed two for the proton-recoil reaction
(from proton spin-non-flip and spin-flip contributions).
It was determined that a fit with the spin-density matrix
of rank one presented here adequately describes the data.
The experimental acceptance was taken into account
by means of Monte Carlo normalization integrals as de-
scribed in [17]. Relativistic Breit-Wigner functions with
standard Blatt-Weisskopf factors were used in the de-
scription of the ae(770), f 2 (1270), and ae 3 (1690) isobars.
The п + п \Gamma S-wave parameterization was based on the K-
matrix formalism [19]. The results presented here were
obtained in a fit with the K-matrix parameterization
based on the modified ``M'' solution of [20].
The partial-wave analysis was performed in 40 MeV/c 2
mass bins and for 0:05 ! \Gammat ! 1:0 (GeV=c) 2 . Goodness-
of-fit was estimated by a qualitative comparison of the
experimental moments H(LMN ) with those predicted
by the PWA fit [18]. These moments are the integrals of
the D L
MN (ff; fi; fl) functions of three Euler angles taken
over the experimental or predicted angular distributions.
It was determined that a minimal set of 21 partial waves
is required in order to achieve a reasonable agreement be-
tween the experimental and predicted moments. This set
takes into account all relevant decay modes of the known
resonances. It includes three 0 \Gamma+ waves, four 1 ++ waves,
three 1 \Gamma+ waves, two 2 ++ waves, seven 2 \Gamma+ waves, one
3 ++ wave, and a non-interfering isotropic wave (which
turned out to be rather small). The 1 \Gamma+ waves were
found to be essential for the description of the moments.
The acceptance-corrected numbers of events for the
major non-exotic spin-parity states predicted by the
PWA fit are shown in Fig. 2. The J PC = 1 ++ wave
corresponding to the a 1 (1260) meson is dominant and
accounts for almost half of the total number of events in
the sample. The a 2 (1320) is prominent in the J PC = 2 ++
waves, and the п 2 (1670) dominates the J PC = 2 \Gamma+
waves. The J PC = 0 \Gamma+ spectrum is quite complex. Its
shape below 1.6 GeV/c 2 is very sensitive to the choice of
the п + п \Gamma S-wave parameterization. Despite this com-
plexity, the п(1800) state is clearly seen in the spectrum.
The intensities of the exotic waves are shown in Fig.
3. All three 1 \Gamma+ [ae(770)]P waves with M ffl = 0 \Gamma ; 1 \Gamma ; 1 +
(denoted as P 0 , P \Gamma , and P+ ) show broad enhancements
in the 1.1--1.4 GeV/c 2 and 1.6--1.7 GeV/c 2 regions. At
the same time, the 1 \Gamma+ [f 2 (1270)]D1 + wave (not shown)
is consistent with zero.
The phase difference between the 1 \Gamma+ [ae(770)]P 1 +
wave and all other significant natural parity exchange
waves indicates a rapid increase in the phase of the 1 \Gamma+
wave across the 1.5--1.7 GeV/c 2 region; this is consistent
with resonant behaviour. Some of these phase differences
are shown in Figs. 4 and 5.
Extensive studies have been made to test the stability
of the results with respect to the assumptions made in
the analysis. It was found that no significant change in
the 1 \Gamma+ waves takes place by inclusion of rank 2 in the
spin density matrix, by different choice of the пп S-wave
parameterization, by exclusion of the events from the re-
gions with a relatively large uncertainty in the instru-
mental acceptance, or by making PWA fits in restricted
regions of t.
The impact of the finite resolution and acceptance of
the apparatus on the 1 \Gamma+ signal was estimated by the
following method. Monte Carlo events were generated in
accordance with the spin-density matrix found in the fit
of the real data, except for the matrix elements corre-
sponding to the 1 \Gamma+ waves which were set to zero. The
Monte Carlo simulation of the instrumental acceptance
and resolution was applied to the generated events. In-
tensities of the 1 \Gamma+ waves found in the partial-wave fit
of this sample are shown as shaded histograms in Fig.
3. Considerable leakage from the non-exotic waves to
the 1 \Gamma+ waves is evident below 1.4 GeV/c 2 . An addi-
tional study has identified the 1 ++ [ae(770)]S0 + wave as
a primary source of this leakage at small values of the
three-pion effective mass. Leakage from the 2 ++ and
2 \Gamma+ waves turned out to be negligible. The presence of
leakage prevents us from drawing any conclusion about
the nature of the low-mass enhancement in the 1 \Gamma+ spec-
trum. However, the second peak in the 1 \Gamma+ intensities
at 1.6 GeV/c 2 (where resonant behavior is observed) is
not affected by the leakage problem.
We have also studied how our results for the exotic 1 \Gamma+
wave are affected by the choice of the partial waves used
in the PWA fit. Numerous wave sets (J ? 4, jM j ? 1,
with up to 42 waves in a set) were tried in the fits. The
resonant phase motion of the 1 \Gamma+ wave was present in all
fits, although the magnitude and width of the peak in the
1 \Gamma+ intensity varied. These variations lead to the rather
2

large model-dependent systematic uncertainties which we
assign to the parameters of the 1 \Gamma+ state.
To determine the resonance parameters, a se-
ries of two-state и 2 fits of the 1 \Gamma+ [ae(770)]P 1 + and
2 \Gamma+ [f 2 (1270)]S0 + waves as a function of mass was made.
The latter wave was chosen as an anchor because it
is a major decay mode of the п 2 (1670), the only well-
established resonance in the vicinity of 1.6 GeV/c 2 . An
example of such a fit is shown in Fig. 5. The и 2 function
of the fit is и 2 =
P
Y i
T E i \Gamma1 Y i , where Y i is a 3-element
vector consisting of the differences between measured and
parameterized values for the intensities of both waves
and the phase difference between them in the mass bin i,
and E i is a 3 \Theta 3 error matrix for these values calculated
through Jacobian transformation from the error matrix of
production amplitudes found in the maximum likelihood
fit. Both waves are parameterized with relativistic Breit-
Wigner forms including Blatt-Weisskopf barrier factors.
In addition to Breit-Wigner phases, a production phase
difference which varies linearly with mass is assumed.
The fit yields и 2 = 25:8 for 22 degrees of freedom, with
the production phase difference between the two waves
being almost constant throughout the region of the fit.
If instead the 1 \Gamma+ wave is assumed to be non-resonant
(with no phase motion), then the fit has и 2 = 50:8 for 22
degrees of freedom, and requires a production phase with
a slope of 7.6 radians/(GeV/c 2 ). Such rapid variation of
the production phase makes a non-resonant interpreta-
tion of the 1 \Gamma+ wave unlikely.
The fitted mass and width of the 1 \Gamma+ state are
M=1593 \Sigma 8 +29
\Gamma47 MeV/c 2 and \Gamma=168 \Sigma 20 +150
\Gamma12 MeV/c 2 .
The error values correspond to statistical and systematic
uncertainties, respectively. The systematic errors were
estimated by fitting the PWA results obtained for differ-
ent sets of partial waves and different rank of the PWA
fit.
Unfortunately, there are no significant waves in
the unnatural parity exchange sector with which to
conduct phase studies of the 1 \Gamma+ [ae(770)]P 0 \Gamma and
1 \Gamma+ [ae(770)]P 1 \Gamma waves [see Fig. 3(a)]. Moreover, the ab-
sence of interference with a strong wave leads to much
greater instability in the magnitude of these small waves
in different fits. Nevertheless, the shape of the 1 \Gamma+ in-
tensity distribution in unnatural parity exchange remains
comparable with that in natural parity exchange.
In summary, we have performed a partial-wave analysis
of the reaction п \Gamma p ! п + п \Gamma п \Gamma p. All expected well-
known states (a 1 , a 2 , and п 2 ) are observed. In addition,
the natural parity exchange partial wave with manifestly
exotic quantum numbers J PC = 1 \Gamma+ shows structure in
the intensity and phase motion which are consistent with
a resonance at 1.6 GeV/c 2 decaying into the aeп channel.
We want to acknowledge the invaluable help of the staff
at the MPS facility in carrying out this experiment and
the assistance of the staffs of the AGS, BNL, and the
collaborating institutions. This research was supported
in part by the US Department of Energy, the National
Science Foundation, and the Russian State Committee
for Science and Technology.
\Lambda Permanent Address: Rafael, Haifa, Israel.
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3

4000
8000
1.0 1.5 2.0
10000
20000
0.5 1.0 1.5
Mass (GeV/c )
2
Events
/
(5
MeV/c
)
2 (a) (b)
a
a
f
p p
r r
1
2
2
2
FIG. 1. Experimental effective mass distribution without
acceptance correction: (a) п + п \Gamma п \Gamma mass spectrum, (b) п + п \Gamma
mass spectrum (two entries per event).
1.0 1.5 2.0
4000
8000
1.0 1.5 2.0
20000
40000
1.0 1.5 2.0
10000
20000
1.0 1.5 2.0
10000
20000
Mass (GeV/c )
2
Intensity
/
(40
MeV/c
)
2
(a) (b)
(c) (d)
0 -+ 1 ++
2 -+ 2 ++
FIG. 2. Combined intensities of all (a) 0 \Gamma+ waves, (b) 1 ++
waves, (c) 2 \Gamma+ waves, (d) 2 ++ waves.
1.0 1.5 2.0
2000
4000
1.0 1.5 2.0
500
1000
1500
Mass (GeV/c )
2
Intensity
(a) (b)
P , P P
-
o +
FIG. 3. Wave intensities of the 1 \Gamma+ [ae(770)]P exotic waves:
(a) the M ffl = 0 \Gamma and 1 \Gamma waves combined, (b) the M ffl = 1 +
wave. The PWA fit to the data is shown as the points with
error bars and the shaded histograms show estimated contri-
butions from all non-exotic waves due to leakage.
1.4 1.6 1.8
0
1
2
3
1.4 1.6 1.8
-3
-2
1.4 1.6 1.8
-3
-2
-1
0
1.4 1.6 1.8
2
3
4
1.4 1.6 1.8
-1
0
1
1.4 1.6 1.8
0
1
2
Mass (GeV/c )
2
Phase
Difference
(rad)
(a) (b)
(c) (d)
(e) (f)
FIG. 4. Phase difference between the
1 \Gamma+ [ae(770)]P 1 + wave and (a) the 0 \Gamma+ [f0(980)]S0 + wave, (b)
the 2 ++ [ae(770)]D1 + wave, (c) the 1 ++ [ae(770)]S0 + wave, (d)
the 1 ++ [ae(770)]S1 + wave, (e) the 2 \Gamma+ [ae(770)]P 0 + wave, (f)
the 2 \Gamma+ [f2(1270)]D0 + wave.
1.5 1.6 1.7 1.8
500
1000
1500
1.5 1.6 1.7 1.8
4000
8000
12000
1.5 1.6 1.7 1.8
2.2
2.6
3.0
1.5 1.6 1.7 1.8
1.0
2.0
Mass (GeV/c )
2
Mass (GeV/c )
2
Intensity
Phase
(rad)
(a) (b)
(c) (d)
Dj
j
1 -+ 2 -+
(1 -+ -2 -+ )
1
2
3
FIG. 5. A coupled mass-dependent Breit-Wigner fit of
the 1 \Gamma+ [ae(770)]P 1 + and 2 \Gamma+ [f2(1270)]S0 + waves. (a)
1 \Gamma+ [ae(770)]P 1 + wave intensity. (b) 2 \Gamma+ [f2(1270)]S0 + wave
intensity. (c) Phase difference between the 1 \Gamma+ [ae(770)]P 1 +
and 2 \Gamma+ [f2(1270)]S0 + waves. (d) Phase motion of the
1 \Gamma+ [ae(770)]P 1 + wave (1), 2 \Gamma+ [f2(1270)]S0 + wave (2), and
the production phase between them (3).
4