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Further Study of 1 \Gamma+ Exotic Meson in the Reaction ú \Gamma p ! jú \Gamma p at 18 GeV=c
V. L. Korotkikh for the E852 Collaboration
Nuclear Research Institute of Moscow State University, Moscow 117321, Russia
E­mail:vlk@lav1.npi.msu.su
ABSTRACT
Details of the analysis of the jú \Gamma system studied 1 in the reaction ú \Gamma p !
jú \Gamma p at 18 GeV=c are given. The amplitude analysis indicates the presence
of interference between the a 2 (1320) and a J PC = 1 \Gamma+ wave between 1.2 and
1.6 GeV=c 2 . The phase difference between these waves shows phase motion not
attributable solely to the a 2 (1320). The data can be fitted by interference between
the a 2 (1320) and an exotic 1 \Gamma+ resonance with M = (1370 \Sigma16 +50
\Gamma30
) MeV=c 2
and \Gamma = (385 \Sigma40 +65
\Gamma105 ) MeV=c 2 .
1. Introduction
The jú system is particularly interesting in searching for exotic (or non­qq)
mesons because the system has spin (J), parity (P), and charge­conjugation (C) in
the sequence J PC = 0 ++ ; 1 \Gamma+ ; 2 ++ ; 3 \Gamma+ ::: for ` = 0; 1; 2; 3; ::: . (Here ` is the orbital
angular momentum of the jú system.) A qq meson with orbital angular momentum L
and total spin S must have P = (\Gamma1) L+1 and the neutral member of its isospin mul­
tiplet must have C = (\Gamma1) L+S . A resonance with a quantum number in the sequence
J PC = 0 \Gamma\Gamma ; 0 +\Gamma ; 1 \Gamma+ ; 2 +\Gamma ; 3 \Gamma+ \Delta \Delta \Delta does not satisfy these conditions and must be exotic.
Having isospin I=1, such a resonance could not be a glueball (2g; 3g; : : :), but it could
be a hybrid (qqg) or a multiquark (qqqq) state.
Several experiments, 2--5 prior to the publication of the E852 results, 1 had studied
the jú final state, and observed an enhancement in the P wave around 1.4 GeV=c 2 .
However, they reached conflicting conclusions.
The first credible claim for a 1 \Gamma+ exotic resonance was made by our experiment
at BNL. 1 In this paper we present some details of the analysis. We note that since the
publication of our letter, an independent confirmation of our results has come from a
new measurement by the Crystal Barrel collaboration. 6
2. Data and PWA
Our data sample was collected in the first data run of E852 at the Alternat­
ing Gradient Synchrotron (AGS) at Brookhaven National Laboratory (BNL) with the
Multi­Particle Spectrometer (MPS) augmented by additional detectors. The details of
the E852 apparatus are given elsewhere. 7

Of the 47 million triggers, 47,235 events were reconstructed 1 which were consistent
with the reaction
ú \Gamma p ! jú \Gamma p (1)
at 18 GeV=c, with the decay mode j ! flfl.
The background is approximately 7% at 1.2 GeV=c 2 , and only 1% at 1.3 GeV=c 2 .
A partial­wave analysis (PWA) 8--10 based on the extended maximum likelihood
method has been used to study the spin­parity structure of the jú \Gamma system.
The partial waves are parameterized in terms of the quantum numbers J PC as
well as m, the absolute value of the angular momentum projection, and the reflectivity
ffl. 11 In our naming convention, a letter indicates the angular momentum of the partial
wave in standard spectroscopic notation, while a subscript of 0 means m = 0, ffl = \Gamma1,
and a subscript of +(\Gamma) means m = 1, ffl = +1(\Gamma1). Thus, S 0 denotes the partial wave
having J PC m ffl = 0 ++ 0 \Gamma , while P \Gamma signifies 1 \Gamma+ 1 \Gamma , D+ means 2 ++ 1 + , and so on.
The results of the PWA fit for the D+ and P+ intensities and the phase difference
between these amplitudes, \Delta\Phi, are shown in Fig.1.
3. Leakage
The Monte­Carlo study shows that the intensity and phase motion of the P+ wave
do not have the characteristics of a wave which is artificially generated from a pure D+
wave due to possible incomplete knowledge of the resolution or detection inefficiency.
This does not preclude the possibility of some leakage of D+ wave to P+ wave being
present in the data and distorting the results of the mass dependent fit 1 (MDF). In
this section, we describe a test which has been carried out to study the sensitivity of
our MDF results to possible residual leakage being present in the data.
The fit has been carried out is a mass dependent partial wave analysis (MDPWA).
In such a fit, the PWA is carried out so that all jú \Gamma mass bins are fit simultaneously
and are tied together with a mass­dependent function for each partial wave. That is,
the extended maximum likelihood function is generalized to include mass dependence:
lnL /
n
X
i
lnI(\Omega i ; w i ) \Gamma
Z
d\Omega\Gamma w
j(\Omega ; w)
I(\Omega ; w): (2)
The free parameters in the fit include, in addition to the amplitudes of the partial
waves, the Breit­Wigner masses, widths, and intensities as well as mass­independent
production amplitude phases.
The results of the MDPWA fit are shown as the smooth curves in Fig.1. Also
shown as the points with error bars are the results of the standart PWA. 1 It is clear
that the two analyses give consistent results.
4. Conclusion
The results of the MDPWA fit are given in Table 1, where they are compared
with those of the combined PWA and mass dependent fit (PWA+MDF). The results
are quite compatible when one takes into account the systematic errors. The biggest
difference is in the fitted width of the P+ state which is larger for the MDPWA.

Table 1. Comparison of the results of the PWA combined with a separate mass dependent fit
(MDF) with those of the MDPWA with leakage.
Meson Mass (MeV=c 2 ) Width (MeV=c 2 )
a 2 (1320) E852 (PWA+MDF) 1317 \Sigma1 \Sigma2 127 \Sigma2 \Sigma2
E852 (MDPWA) 1313 \Sigma1 119 \Sigma2
ú 1 (1400) E852 (PWA+MDF) 1370 \Sigma16 +50
\Gamma30
385 \Sigma40 +65
\Gamma105
E852 (MDPWA) 1369 \Sigma14 517 \Sigma40
Table 2. Comparison of the results of E852 and the Crystal Barrel for the parameters of the
J PC = 1 \Gamma+ resonance.
ú 1 (1400) Mass (MeV=c 2 ) Width (MeV=c 2 )
E852 1370 \Sigma16 +50
\Gamma30
385 \Sigma40 +65
\Gamma105
Crystal Barrel 1400 \Sigma20 \Sigma20 310 \Sigma50 +50
\Gamma30
Our fitted parameters for the J PC = 1 \Gamma+ resonance are compared in Table 2 with
values recently reported by the Crystal Barrel experiment. 6 That experiment reports
that a J PC = 1 \Gamma+ resonance in the jú channel is required to fit their data in the
annihilation channel pn ! ú \Gamma ú 0 j. Their fitted parameters are very consistent with
those determined from our mass­dependent analysis.
So, since the resonance state has J PC = 1 \Gamma+ , it is manifestly exotic.
This research was supported in part by the US Department of Energy and the
Russion State Committee for Science and Technology.
References
1. D.R. Thompson et al., Phys. Rev. Lett. 79, 1630 (1997).
2. D. Alde et al., Phys. Lett. B 205, 397 (1988).
3. G.M. Beladidze et al., Phys. Lett. B 313, 276 (1993).
4. H. Aoyagi et al., Phys. Lett. B 314, 246 (1993).
5. C. Amsler et al., Phys. Lett. B 333, 277 (1994).
6. A. Abele et al., Phys. Lett. B 423, 175 (1998).
7. S. Teige et al., ``Properties of the a 0 Meson'', submitted to Phys. Rev.
8. S.U. Chung, ``Formulas for Partial­Wave Analysis'', Brookhaven BNL­QGS­
93­05, unpublished (1993).
9. S.U. Chung, Phys. Rev. D 56, 7299 (1997).
10. J.P. Cummings and D.W. Weygand, ``The New BNL Partial Wave Analysis
Program'', Brookhaven Report BNL­64637, unpublished (1997).
11. S.U. Chung and T.L. Trueman, Phys. Rev. D 11, 633 (1975).

Fig. 1. The fit results of the MDPWA (curves) and the mass independent PWA results
(crosses) for the jú \Gamma system: a) P+ , b) D+ intensities and c) their relative phase \DeltaOE(P + \Gamma
D+ ). Fig.1a also shows the contributions of the 1 \Gamma+ signal intensity (1), the sum (2) of the
leakage and the (signal ­ leakage) interference term and the complete 1 \Gamma+ wave (3).