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Exotic J PC = 1 + Mesons at the Present Time
(discussion of some problems)
L. I. Sarycheva  and V. L. Korotkikh 
 Scobeltsyn Institute of Nuclear Physics, Moscow State University, Moscow 119899, Russia
Abstract. Some problems and questions on Exotic meson physics are presented. The particular
attention is given to the discrepancy between theory and experiment and to the interpretation of
experimental results.
INTRODUCTION
Not many physicits doubt that other forms of hadronic matter with gluonic de­
grees of freedom can exist. More than 170 cites are devoted to so called ``Non
q •
q­candidates''(see PDG [1]). A q •
q meson with orbital momentum l and total spin s
has a parity P = ( 1) l+1 and a charge conjugation C = ( 1) l+s . This excludes states
with J PC = 0 ; 0 + ; 1 + ; 2 + etc. Resonances with these exotic quantum numbers
could be Hybrids (bound state of quark, antiquark and gluon) or multiquark states. The
lightest state is expected to be a 1 + state. The last years give the experimental evidence
of two such states at mass 1.4 GeV/c 2 and 1.6 GeV/c 2 [2, 3, 4, 5, 6, 7, 8, 9].
THEORY AND EXPERIMENT DISCREPANCY
Four experimental group are more active in Exotic state study last time. The results
on the 1 + exotics of BNL (6 USA and 2 Russian institutions), VES (IHEP, Russia),
GAMS (IHEP, Russia) and Crystall Barrel (CERN) are demonstrated in Table 1.
The results of the experiments of the various reactions, on the different targets and
at the different beam energies are remarkably coincident. It removes such kind of ques­
tions as the correct calculation of the different apparatus acceptance, some distinctions
of partial wave analysis, the different background contributions. So the evidences of
1 + exotic states at mass 1.4 GeV/c 2 (p 1 (1400)) and 1.6 GeV/c 2 (p 1 (1600)) are very
weighable.
On the other hand the theoretical predictions (see review [10] and numerical cites
in it) are indeterminate because the nonperturbative effects are very strong for light
mesons. More exact QCD lattice gauge theory (LGT) predicts lightest hybrid masses
between 1.7 GeV/c 2 and 2.1 GeV/c 2 . The estimations of famous flux­tube model (FTM)
are close to LGT. The lightest gluonic hybrid J PC = 1 + has a mass around 1.9 Gev/c 2 .
It is larger than the experimental values for J PC = 1 + (Table 1). Other models such as a
bag model, a diquark cluster model, QCD sum rules (see cites in [10]) predict the mass
of 1 + hybrid in large mass range 1.4 to 2.0 GeV/c 2 . The theoretical result is very strong

TABLE 1. Evidence for J PC = 1 + exotics
Experiment Mass (MeV/c 2 ) Width (MeV/c 2 ) Decay mode Reaction
p 1 (1400)
BNL--94 [2] 137016 +50
30 38540 +65
105 hp p p ! hp p
BNL--95 [3] 1359 +16+10
14 24 314 +31+9
29 66 hp p p ! hp p
CBar [4] 14002020 31050 +50
30 hp •
pn ! p p 0 h
CBar [5] 136025 22090 hp 0 •
pp ! p 0 p 0 h
GAMS [6] 1370 fixed 300125 hp 0 p p ! hp 0 n
p 1 (1600)
BNL [7] 15938 +29
47 16820 +150
12 rp p p ! p + p p p
BNL [8] 159710 +45
10 3404050 h 0 p p p ! h 0 p p
VES [9] 161020 29030 rp, h 0 p, b 1 p p Be ! rp(h 0 p;b 1 p)X
model dependent. So, the first problem is that the theory gives larger value of 1 + exotic
meson or the accuracy of theoretical predictions is lower than the experimental ones.
The second problem is the discrepancy concerning the branching ratio. For example,
the FTM predicts that J PC = 1 + exotic state has a dominant b 1 p decay with rp weak
and hp and h 0 p very small decay branching [10]. VES result shows the branching of
p 1 (1600) ! f , where f is (b 1 p);(h 0 p);(rp) [11]:
G(p 1 (1600) ! f ) =
8
<
:
1; b 1 p;
1:0 0:3; h 0 p;
1:6 0:4; rp:
Either these three modes are not all due to a hybrid exotic, or our understanding of hybrid
decay is inaccurate.
There is another question concerning to the 1 + exotic decay. The state p 1 (1400)
decays to hp and not to h 0 p (Table 1). The state p 1 (1600) decays quite invert. p and h
belong to an octet and h 0 is a singlet of SU(3). E.Klempt [12] showed that J PC = 1 +
state cannot decay into two octet pseudoscalar mesons in the limit of flavor symmetry.
But it is possible the 1 + octet to decay to h 0 p. So, p 1 (1600) may be the octet state and
p 1 (1400) must be a multiplet of higher order. The easiest choice is a decuplet, which can
describe (q •
q+q •
q) states. The decuplet cannot possible be a hybrid: gluonic excitations
do not contribute to the flavor. The strange phenomenon that the p 1 (1600) does not
decay into hp thus provides the clue for the interpretation of the p 1 (1400) as decuplet
state [12]. The h--h 0 mixing can destroy this rule. So, S.U. Chung[13] suggested that
p 1 (1400) could be a complicated mixture (q •
q+ gluon) hybrid and a (q •
q+q •
q) state .

DATA INTERPRETATION
Background
Are there exotic mesons (see Table 1) the new physical effects or is it a background
display? The people ask this question because the data background and exotic signal
is comparable in hp , rp and hp 0 systems. The situation is more better in h 0 p
system because here the p 1 (1600) contribution is comparable with a 2 (1300) [8]. The
ground answer is that the PWA is studying an interference effect of weak (say P­
wave) with a strong wave (D­wave). And the interference contribution is larger than
the background. But the questions are remained. Let doesn't discuss the incoherent
isotropical background B INC (m), which adds to common distribution
W (m;W) = jD(m)I D (W)+P(m)I P (W)j 2 +B INC (m): (1)
Here m is a mass of meson system, W are particle decay angles. I D (W) and I P (W) is a
wave decay amplitudes. Each wave has its own background:
D(m) = f (D)
BW (m)+B (D)
COH (m);
P(m) = f (P)
BW (m)+B (P)
COH (m):
(2)
The authors [2] used the real and mass independent background B (D)
COH and no back­
ground in P­wave. The description of experimental intensities and relative phase is good
with Breit­Wigner amplitudes f (D)
BW (m) and f (P)
BW (m). Such simplest model is used in other
works [3, 6, 7, 8, 9]. The remain questions are the next. Can we describe data without
resonant BW in P­wave, but with the complex background B (D)
COH in D­wave and with
some mass dependence phase of this background? How it could be interpretated? What
is the contribution B (P)
COH (m) in the P­wave and has it the mass dependent phase? Theory
could help, but it has to suggest description of two wave simultaneously at least.
Non­resonant Deck­type background
The authors [14] suggested a new interpretation of p 1 (1400). They used K­matrix ap­
proach, which connects various channels of reaction. Model has many free parameters. It
describes approximately the peak at m= 1:4 GeV/c 2 by the interference of a Deck­type
background with a real hybrid at m = 1:6 GeV/c 2 . But such kind of approach cannot
describe the Exotics of the Crystal Barrel experiment (Table 1) in the annihilation •
pp
and •
pn.

SOME PROBLEMS OF DATA ANALYSIS
The angular distribution in PWA is a sum
W (W) = Å
e;k
j e U k (W)j 2 +B INC : (3)
There is no interference between waves with different reflectivities e = 1, which
are coincides with a naturalities h of exchanged particles. Also are for the non­spinflin
(k = 1) and the spinflip (k = 2) nucleon amplitude. It is direct consequence of parity con­
servation in the production process. One of the problem is that the ambiguous solutions
appear particularly when there are many unnatuarally (h = 1) parity exchange (UNPE)
waves for the quasi­two­body reactioms. If their contributions are small smeared be­
tween solutions as it is for hp [2], rp [7], h 0 p [8], then they don't strongly affect
the NPR waves. In these cases the people average ambiguous solutions of NPE waves,
But the interpretation problem of 1 + UNPE waves in rp system is remained. Its con­
tribution is very unstable and there is no strong partner wave in UNPE sector to set its
resonance nature. Exotic 1 + of UNPE is seen in rp BNL data at 18 GeV/c and doesnt
seen in rp VES data at 18 GeV/c. But both experiments see 1 + NPE wave.
The interesting suggestion to select the physical solution between ambiguous so­
lutions is made by Sadovsky [6] on the example hp 0 by the help of Gersten's root
motion. He reanalysed GAMS data and now he claims that the 1 + exotic state at
m = 1:4GeV=c 2 decay to the channel hp 0 .
There is also a problem of the spin­density matrix rank. If we set only the spinflip
or only non­spinflip amplitudes, then we have rank=1 [2]. It may be not right if the
mechanism of p 1 and a 2 production is different. Definite indication is seen in the
different t­dependence of h 0 p events in the region of p 1 (1600) and a 2 mesoms [8].
The slope of t­dependence of p 1 (1600) is smaller comparing with the slope of a 2 .
If the production of p 1 and a 2 is caused by the different Regions or the different
Region combinations, then it may be a reason of different the spinflip and non­spinflip
amplitudes.
REFERENCES
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