Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://lav01.sinp.msu.ru/~vlk/prepr1mnpl.ps Äàòà èçìåíåíèÿ: Mon Aug 10 18:24:22 1998 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 19:47:47 2012 Êîäèðîâêà:

hep­ex/9705011
15
May
1997
Evidence for Exotic Meson Production in the Reaction
ú \Gamma p ! jú \Gamma p at 18 GeV=c
D. R. Thompson, 1 G. S. Adams, 7 T. Adams, 1 Z. Bar­Yam, 4 J. M. Bishop, 1 V. A. Bodyagin, 5
D. S. Brown, 6 N. M. Cason, 1 S. U. Chung, 2 J. P. Cummings, 4 S. P. Denisov, 3 V. A. Dorofeev, 3
J. P. Dowd, 4 P. Eugenio, 4 R. W. Hackenburg, 2 M. Hayek, 4 E. I. Ivanov, 1 I. A. Kachaev, 3
W. Kern, 4 E. King, 4 O. L. Kodolova, 5 V. L. Korotkikh, 5 M. A. Kostin, 5 J. Kuhn, 7
V. V. Lipaev, 3 J .M. LoSecco, 1 J. J. Manak, 1 J. Napolitano, 7 M. Nozar, 7 C. Olchanski, 2
A. I. Ostrovidov, 5 T. K. Pedlar, 6 A. V. Popov, 3 D. I. Ryabchikov, 3 A .H. Sanjari, 1
L. I. Sarycheva, 5 K. K. Seth, 6 W. D. Shephard, 1 N. B. Sinev, 5 J. A. Smith, 7 D. L. Stienike, 1
C. Strassburger, 2; \Lambda S. A. Taegar, 1 I. N. Vardanyan, 5 D. P. Weygand, 2 D. B. White, 7
H. J. Willutzki, 2 J. Wise, 6 M. Witkowski, 7 A. A. Yershov, 5 D. Zhao, 6
The E852 Collaboration
1 University of Notre Dame, Notre Dame, IN 46556, USA
2 Brookhaven National Laboratory, Upton, Long Island, NY 11973, USA
3 Institute for High Energy Physics, Protvino, Russian Federation
4 University of Massachusetts Dartmouth, North Dartmouth, MA 02747, USA
5 Moscow State University, Moscow, Russian Federation
6 Northwestern University, Evanston, IL 60208, USA
7 Rensselaer Polytechnic Institute, Troy, NY 12180, USA
(May 16, 1997)
1

Abstract
The jú \Gamma system has been studied in the reaction ú \Gamma p ! jú \Gamma p at 18 GeV=c.
A large asymmetry in the angular distribution is observed indicating interfer­
ence between L­even and L­odd partial waves. The a 2 (1320) is observed in the
J PC = 2 ++ wave, as is a broad enhancement between 1.2 and 1.6 GeV=c 2 in
the 1 \Gamma+ wave. The observed phase difference between these waves shows that
there is phase motion in addition to that due to a 2 (1320) decay. 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 .
13.60.Le, 13.85.Fb, 14.40.Cs
Typeset using REVT E X
2

The question of whether or not hadrons outside the scope of the constituent quark
model exist is one whose answer speaks directly to the fullness of our understanding of
quantum chromodynamics (QCD) [1]. However, non­qq mesons (or exotic mesons) have
proven difficult to distinguish from the many conventional qq states which populate the
various mesonic spectra. For this reason, much attention has been focused on those states
with manifestly exotic J PC quantum numbers.
A qq meson with orbital angular momentum ` and total spin s must have P = (\Gamma1) `+1
and C = (\Gamma1) `+s . Thus a resonance with J PC = 0 \Gamma\Gamma , 0 +\Gamma , 1 \Gamma+ , 2 +\Gamma , ... must be exotic.
Such a state could be a gluonic excitation such as a hybrid (qqg) or glueball (2g; 3g; :::), or
a multiquark (qqqq) state. In a relative P wave (L=1), the jú \Gamma system has J PC = 1 \Gamma+ .
Having isospin I=1, it could not be a glueball, but it could be a hybrid or a multiquark
state.
Production and decay properties of exotic states have been predicted using several models
[2, 3, 4, 5, 6, 7, 8]. A calculation based upon the MIT bag model predicts [3] that a 1 \Gamma+
hybrid (qqg) will have a mass near 1.4 GeV=c 2 . On the other hand, the flux­tube model [4, 5]
predicts the mass of the lowest­lying hybrid state to be around 1:8 GeV=c 2 . Characteristics
of bag­model S­wave multiquark states (which would have J P = 0 + , 1 + , or 2 + ) have been
predicted[7] but those for a 1 \Gamma state have not. Finally, recent lattice calculations[8] of the
1 \Gamma+ hybrid meson estimate its mass to be in the range of 1.7 to 2.1 GeV.
The jú system has been studied in several recent experiments, with apparently incon­
sistent results. Alde et al. [9], in a study of ú \Gamma p interactions at 100 GeV/c at CERN
(the GAMS experiment), claimed to observe a 1 \Gamma+ state in the jú 0 system at 1.4 GeV=c 2
produced via unnatural parity exchange (the P 0 partial wave---the naming convention is
discussed below) [10]. Aoyagi et al. [11], in a ú \Gamma p experiment at 6.3 GeV/c at KEK, ob­
served a rather narrow enhancement in the jú \Gamma system at 1.3 GeV=c 2 in the natural parity
exchange 1 \Gamma+ spectrum (P+ ). Beladidze et al. [12], in the VES experiment at IHEP, (ú \Gamma N
interactions at 37 GeV/c) also reported a P+ signal in the jú \Gamma state, but their signal was
broader and had a significantly different phase variation from that of the KEK experiment.
3

While the phase difference between the P+ and D+ waves was independent of jú mass in
the KEK analysis, that phase difference did show significant mass dependence in the VES
analysis. (Since the phase variation for the D+ wave follows a classic Breit­Wigner pattern
for the a 2 (1320) meson, the phase difference between these waves can determine the phase
variation of the unknown P+ wave.)
Here we study the jú \Gamma system in the reaction ú \Gamma p ! jú \Gamma p at 18 GeV=c. Our data
sample was collected in the first data run of E852 at the AGS at Brookhaven National
Laboratory with the Multi­Particle Spectrometer (MPS) [13] using a liquid hydrogen target.
The MPS, which was equipped with six drift­chamber modules [14] and three proportional
wire chambers, was augmented by: a four­layer cylindrical drift chamber surrounding the
target [15]; a soft­photon detector consisting of 198 blocks of thallium­doped cesium iodide
[16] also surrounding the target; a window­frame lead­scintillator photon­veto counter; a
large drift chamber; and a 3045­element lead­glass detector (LGD) [17] downstream of the
MPS. Further details are given elsewhere [18].
A total of 47 million triggers which required one forward­going charged track, one recoil
charged track, and an LGD trigger­processor signal enhancing high electromagnetic effective
mass was recorded. Of these, 47,200 events were reconstructed which were consistent with
the jú \Gamma p (j ! 2fl) final state. These events satisfied topological and fiducial volume cuts,
as well as energy/momentum conservation for production and for the j ! 2fl decay with a
confidence level ? 10%[19]. The 2fl mass resolution at the j mass is oe = 0.03 GeV=c 2 .
The a 2 (1320) is the dominant feature of the jú \Gamma mass spectrum shown in Fig. 1a. Back­
ground has been estimated using side bands in both the 2­fl mass distribution and the
missing­mass distribution, thus taking into account background from non­j sources as well
as from sources due to production of other final states. The background level is approxi­
mately 7% at 1.2 GeV=c 2 , falling to 1% at 1.3 GeV=c 2 .
The acceptance­corrected distribution of jt 0 j = jtj \Gamma jtj min , where t is the the four­
momentum­transfer, is shown for jt 0 j ? 0:08(GeV=c) 2 in Fig. 1b. (Our acceptance is quite
low below 0.08 (GeV=c) 2 due to a trigger requirement.) The shape of this distribution is con­
4

sistent with previous experiments and has been shown to be consistent with natural­parity
exchange production in Regge­pole phenomenology [20, 21].
The acceptance­corrected distribution of cos `, the cosine of the angle between the j and
the beam track in the Gottfried­Jackson frame [22] of the jú \Gamma system, is shown in Fig. 2a
for 1:22 ! M(jú \Gamma ) ! 1:42 GeV=c 2 . There is a forward­backward asymmetry in cos `. The
asymmetry for j cos `j ! 0:8 is plotted as a function of jú \Gamma mass in Fig. 2b. The asymmetry
is large, statistically significant and mass dependent. Since the presence of only even values
of L would yield a symmetric distribution in cos `, the observed asymmetry requires that
odd­L partial waves be present to describe the data.
A partial­wave analysis (PWA) [23, 24] 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 (which is positive (negative)
for natural (unnatural) parity exchange [25]). 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. We consider partial waves with m Ÿ 1, and we assume that the
production spin­density matrix has rank one.
The experimental acceptance is determined by a Monte Carlo method. Peripherally­
produced events are generated [26] with isotropic angular distributions in the Gottfried­
Jackson frame. After adding detector simulation [27], the Monte Carlo event sample is
subjected to the same event­selection cuts and run through the same analysis as the data.
The experimental acceptance is then incorporated into the PWA by using these events to
calculate normalization integrals (see ref. [23]).
Goodness­of­fit is determined by calculation of a ü 2 from comparison of the experimental
moments with those predicted by the results of the PWA fit. A systematic study has been
performed to determine the effect on goodness­of­fit of adding and subtracting partial waves
5

of J Ÿ 2 and m Ÿ 1. All such waves have been included in the final fit. We have also
performed fits including partial waves with J = 3 and J = 4. Contributions from these
partial waves are found to be insignificant for M(jú \Gamma ) ! 1:8 GeV=c 2 . Thus, PWA fits
shown or referred to in this letter include all partial waves with J Ÿ 2 and m Ÿ 1 (i.e.
S 0 , P 0 , P \Gamma , D 0 , D \Gamma , P+ , and D+ ). The background described above was included as a
non­interfering, isotropic term of fixed magnitude.
The results of the PWA fit in 40 MeV=c 2 bins for 0:98 ! M(jú \Gamma ) ! 1:82 GeV=c 2 and
0:10 ! jtj ! 0:95 GeV 2 are shown in Fig. 3a­c. Here, the acceptance­corrected numbers
of events predicted by the PWA fit for the D+ and P+ waves and their phase difference
\Delta\Phi(D + \Gamma P+ ) are shown as a function of M(jú \Gamma ). There are eight ambiguous solutions
in the fit [24, 28, 29], each of which leads to the same angular distribution. We show the
range of fitted values for these ambiguous solutions in the vertical rectangular bar at each
mass bin, and the maximum extent of their errors is shown as the error bar. The a 2 (1320)
is clearly observed in the D+ partial wave (Fig. 3a). A broad peak is seen in the P+ wave
at about 1:4 GeV=c 2 (Fig. 3b). \Delta\Phi(D + \Gamma P+ ) increases through the a 2 (1320) region, and
then decreases above about 1.5 GeV=c 2 (Fig. 3c). The intensities for the waves of negative
reflectivity (not shown) are generally small and are all consistent with zero above about 1.3
GeV=c 2 .
These results are quite consistent with the VES results[12]. In particular, the shape of
the phase difference is virtually identical to that reported by VES. (The magnitude of the
phase difference is shifted by about 20 ffi relative to that of VES.)
Consistency checks and tests of the data have been carried out to determine whether the
observation of the structure in the P+ wave could be an artifact due to assumptions made in
the analysis or to acceptance problems. These include: fitting the data in restricted ranges of
the decay angle; inclusion of higher angular momentum states; fitting the data with various
t cuts; fitting the data using different parametrizations of the background; making cuts on
other kinematic variables such as the ú \Gamma p or the jp effective masses; and fitting data using
events with j ! ú + ú \Gamma ú 0 decays (with rather different acceptance from the 2fl events). The
6

results are very stable and, in particular, the behavior of \Delta\Phi(D + \Gamma P+ ) does not change in
any of these checks.
Fits were also carried out on Monte Carlo events generated with a pure D+ wave to
determine whether P+­wave structure could be artificially induced by acceptance effects,
resolution, or statistical fluctuations. We do find that some P+ intensity can be induced by
resolution and/or acceptance effects. Such ``leakage'' leads to a P+ wave that mimics the
generated D+ intensity (and in our case would therefore have the shape of the a 2 (1320))
with a \Delta\Phi(D + \Gamma P+ ) that is independent of mass. Neither property is seen in our result.
In an attempt to understand the nature of the P+ wave observed in our experiment,
we have carried out a mass­dependent fit to the results of the mass­independent amplitude
analysis. The fit has been carried out in the jú mass range from 1.1 to 1.6 GeV=c 2 . The
input quantities to the fit included, in each mass bin, the P+­wave intensity; the D+­wave
intensity; and the D+ \GammaP + phase difference. Each of these quantities was taken with its error
and correlation coefficients from the result of the amplitude analysis. In this fit, we have
assumed that the D+­wave and the P+­wave decay amplitudes are resonant and have used
relativistic Breit­Wigner forms[30] for these amplitudes. We introduce a constant relative
production phase between the P+­wave and D+­wave amplitudes. The parameters of the fit
included the D+­wave mass, width and intensity; the P+­wave mass, width and intensity;
and the D+ \GammaP + production phase difference. One can view this fit as a test of the hypothesis
that the correlation between the fitted P­wave intensity and its phase (as a function of mass)
can be fit with a resonant Breit­Wigner amplitude.
Results of the fit are shown as the smooth curves in Fig. 3a, b, and c. The mass and
width of the J PC = 2 ++ state (Fig. 3a) are (1317 \Sigma1 \Sigma2) MeV=c 2 and (127 \Sigma2 \Sigma2) MeV=c 2
respectively [31]. (The first error given is statistical and the second is systematic [32].) The
mass and width of the J PC = 1 \Gamma+ state as shown in Fig. 3b are (1370 \Sigma16 +50
\Gamma30
) MeV=c 2
and (385 \Sigma40 +65
\Gamma105
) MeV=c 2 respectively. Shown in Fig. 3d are the Breit­Wigner phase
dependences for the a 2 (1320) (line 1) and the P+ waves (line 2); the fitted D+ \GammaP + production
phase difference (line 3); and the fitted D+ \GammaP + phase difference (line 4). (Line 4, which is
7

identical to the fitted curve shown in Fig. 3c, is obtained as line 1 \Gamma line 2 + line 3.)
The fit to the resonance hypothesis has a ü 2 =dof of 1.49. The fact that the production
phase difference can be fit by a mass­independent constant (of 0.6 rad) is consistent with
Regge­pole phenomenology [33] in the absence of final­state interactions. If one fits the
data to a non­resonant (constant phase) P+ wave, and also assumes a Gaussian intensity
distribution for the P+ wave, one obtains a fit with a ü 2 =dof of 1.55. In this case, the
observed phase dependence on mass is attributed to a rapidly varying production phase
[34]. Such a phase variation cannot be excluded, but is not expected for any known model.
Note that for this non­resonant hypothesis one must have a separate hypothesis for the
observed structure in the P+ intensity --- a structure which is explained naturally by the
resonance hypothesis. We thus conclude that there is credible evidence for the production
of a J PC = 1 \Gamma+ exotic meson.
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, the US Department of Energy, and the Russian State
Committee for Science and Technology.
8

REFERENCES
\Lambda Visitor
[1] N. Isgur et al., Phys. Rev. Lett. 54, 869 (1985).
[2] N. Isgur and J. Paton, Phys. Rev. D 31, 2910 (1985).
[3] T. Barnes et al., Nucl. Phys. B 224, 241 (1983).
[4] F.E. Close and P.R. Page, Nucl. Phys. B 443, 233 (1995).
[5] T. Barnes et al., Phys. Rev. D 52, 5242 (1995).
[6] M. Chanowitz and S. Sharpe, Nucl. Phys. B 222, 211 (1983).
[7] R.L. Jaffe, Phys. Rev. D 15, 267 (1977).
[8] P. Lacock, et al., Phys. Rev. D 54, 6997 (1996); C. Berbard, et al., Nucl. Phys. B (Proc.
Suppl) 53, 228 (1997).
[9] D. Alde et al., Phys. Lett. B 205, 397 (1988).
[10] The result was later brought into question. See Y.D. Prokoshkin and S.A. Sadovskii,
Physics of Atomic Nuclei 58, 606 (1995).
[11] H. Aoyagi et al., Phys. Lett. B 314, 246 (1993).
[12] G.M. Beladidze et al., Phys. Lett. B 313, 276 (1993).
[13] S. Ozaki, ``Abbreviated Description of the MPS'', Brookhaven MPS note 40, unpublished
(1978).
[14] S.E. Eiseman et al., Nucl. Instr. & Meth. 217, 140 (1983).
[15] Z. Bar­Yam et al., Nucl. Instr. & Meth. A 386, 253 (1997).
[16] T. Adams et al., Nucl. Instr. & Meth. A 368, 617 (1996).
[17] R.R. Crittenden et al., Nucl. Instr. & Meth. A 387, 377 (1997).
9

[18] S. Teige et al., Proceedings of the Fifth International Conference on Calorimetry in High
Energy Physics, eds. Howard A. Gordon and Doris Rueger (World Scientific, Signapore,
1995) 161.
[19] O.I. Dahl et al., ``SQUAW kinematic fitting program'', Univ. of California, Berkeley
Group A programming note P­126, unpublished (1968).
[20] A.C. Irving and R.P. Worden, Phys. Rep. 34, 117 (1977).
[21] E.J. Sacharidis, Lett. Nuovo Cimento 25, 193 (1979).
[22] The Gottfried­Jackson frame is a rest frame of the jú \Gamma system in which the z­axis is
in the direction of the beam momentum, and the y­axis is in the direction of the vector
cross­product of the target and recoil momenta.
[23] S.U. Chung, ``Formulas for Partial­Wave Analysis'', Brookhaven BNL­QGS­93­05, un­
published (1993).
[24] S.U. Chung, ``Amplitude Analysis for Two­pseudoscalar Systems'', Brookhaven BNL­
QGS­97­041 (1997); submitted to Phys. Rev.
[25] S.U. Chung and T.L. Trueman, Phys. Rev. D 11, 633 (1975).
[26] J. Friedman, ``SAGE, A General System for Monte Carlo Event Generation with Pre­
ferred Phase Space Density Distributions'', Univ. of California, Berkeley Group A program­
ming note P­189, unpublished (1971).
[27] Two independent detector simulation methods, GEANT (``GEANT Detector Descrip­
tion and Simulation Tool'', CERN program Library Long Writeups Q123, unpublished
(1993)) and the E852 software package SAGEN were used with no significant changes in
results.
[28] S.A. Sadovsky, ``On the Ambiguities in the Partial­Wave Analysis of ú \Gamma p ! jú 0 n
Reaction'', Inst. for High Energy Physics IHEP­91­75, unpublished (1991).
10

[29] E. Barrelet, Nuovo Cimento A 8, 331 (1972).
[30] For both D+ and P+ , a standard relativistic Breit­Wigner form was used with a mass­
dependent width. For the D+ wave, the Breit­Wigner form has been modified so as to
accomodate deviations of the observed shape of jD+ j 2 away from the a 2 mass from a pure
BW form, without altering its phase dependence. Details are given in an expanded paper
to be submitted for publication.
[31] Widths quoted do not take into account mass resolution. The accepted values for the
mass and width of the a 2 (1320) (R.M. Barnett et al., Phys. Rev. D 54, 1 (1996)) are 1318.1
\Sigma:7 MeV=c 2 and 107 \Sigma5 MeV=c 2 . Monte Carlo studies show that our fitted width, when
resolution effects are taken into account, would be 120 MeV=c 2 for a true width of 107
MeV=c 2 . Thus our measured value is somewhat higher than the current world average.
[32] The systematic errors are based on the range of values allowed by taking into account
the previously described ambiguous solutions. Details are given in an expanded paper to
be submitted for publication.
[33] The signature factor and the residue functions are at most t­dependent (not mass de­
pendent) (see ref. [20]).
[34] The fit requires a linear production phase difference with a slope of ­4.3 rad/GeV.
11

FIGURES
M(hp) GeV
1 . 0 1 . 4 1 . 8
3000
2000
1000
0
Events/.02
GeV a.)
Events/.02
GeV
2
3
1 0
0 . 0 0 . 4 0 . 8
b.)
1 0 4
|t'| (GeV/c) 2
FIG. 1. a.) The jú \Gamma effective mass distribution. b.) Distribution of jt 0 j = jtj \Gamma jtj min .
12

Asymmetry
M(hp) GeV
1 . 0 1 . 4 1 . 8
0 . 0
0 . 2
0 . 4
0 . 6 b.)
Events/.1
8000
6000
4000
2000
0
Cos q
­ 1 . 0 0 . 0 1 . 0
a.)
. 0
. 1
. 2
. 3
. 4
. 5
FIG. 2. Distributions of a.) the cosine of the decay angle in the Gottfried­Jackson frame for
events with 1.22 ! M(jú \Gamma ) !1.42 GeV=c 2 , and b.) the forward­backward decay asymmetry as a
function of M(jú \Gamma ). The asymmetry = (F \Gamma B)=(F +B) where F(B) is the number of events for
which the j's momentum is forward (backward) in the Gottfried­Jackson frame. The dashed curve
and the right­hand scale in a.) show the acceptance in this mass region.
13

M(hp) GeV
1 . 0 1 . 4 1 . 8
Phase
Difference
(rad)
0 . 0
0 . 4
0 . 8
1 . 2
DF(D ­ P )
+ +
4
1 2
8
0
x 10 3
D +
Events/.04
GeV
0
600
400
200
P +
Events/.04
GeV
M(hp) GeV
1 . 0 1 . 4 1 . 8
Phase
Difference
(rad)
0 . 0
1 . 0
2 . 0
3 . 0
a) b)
c ) d) 1
2
3
4
FIG. 3. Results of the partial wave amplitude analysis. Shown are a.) the fitted intensity
distributions for the D+ and b.) the P+ partial waves, and c.) \Delta\Phi(D + \Gamma P+ ), their phase difference.
The range of values for the eight ambiguous solutions is shown by the central bar and the extent
of the maximum error is shown by the error bars. Also shown as curves in a.), b.), and c.) are
the results of the mass dependent analysis described in the text. The lines in d.) correspond to
(1) the fitted D+ Breit­Wigner phase, (2) the fitted P+ Breit­Wigner phase, (3) the fitted D+ \GammaP +
relative production phase, and (4) the overall D+ \GammaP + phase difference as shown in c.) but with a
different scale.
14