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Hybrid and Glueball Production on
Nuclear Target
V.L.Korotkikh, L.I.Sarycheva
Moscow State University, Institute of Nuclear Physics
119899, Moscow, Russia
e­mail: vlk@lav.npi.msu.su
Abstract. We propose an experiment at moderate energies in which A­
dependence of Exotic meson production is measured. The main aim of such
study is the measurement of the interaction cross­section of Exotic resonances
with nucleon. Such information is very interesting for the expected Hybrids and
Glueballs. There is no experimental or theoretical information on the Hybrid­
nucleon and Glueball­nucleon cross­section up to now.
The measurement of A­dependence is now a standard method of study of the
resonance propagation through the nuclear matter. As a rule the people take
some definite characteristic (for example, x) of resonance process production
and measure the A ff(x) ­dependence. Lets mention here the numerous works
on the charmonium production and its interpretation ( see [1] and references
in it).
We remember also the classic works on the photoproduction of ae; OE and !
mesons (see the review [2] and references in it), where the cross­section of
vector mesons with nucleon was determined from nuclear experiments. The
cross­section of 3ú­ system with nucleon was measured in the process ú \Gamma +A !
ú + ú \Gamma ú \Gamma +A 0 at 15, 23, 40 GeV/c in works [3--6]. There turned out to be very
different results for the spin­parity states J PC of system. The charge exchange
reaction ú \Gamma +A ! ae 0 +A 0 at 3.7 GeV/c [7] was studied as the example of the
clear incoherent nuclear process and the ae 0 N ­ cross­section was determined
from A­dependence.
The reaction p +A ! p + ú +X at 9.0 GeV/c was investigated by Moscow
State University group [8]. It was shown how important to select incoher­
ent events by the condition q L r A ? 1, where q L is the longitudinal transfer
momentum and r A is the nuclear radius. This condition allows us to give a
simple and clear interpretation of the way how we determine the cross­section
of hadron system interaction with nucleon by analogy with the beam weak­

ness method. From the condition we localize the inelastic interaction region
\Deltaz ' ¯ h=\Deltap !! ¯ hr a and can consider the nuclear thickness after interaction
as matter thickness, which weakness the ``beam'' of produced system. The
authors have shown that (pú)N­cross­section is the same as the pN ­ cross­
section.
Last time the interest in the resonance production on nuclear targets is
increased. We mention here two theoretical works. One of them [9] is devoted
to the problem of j meson interaction with light nuclei. Another work [10]
studies the deformation of the mass distribution of ae meson decay products
in its passing through nuclear matter.
We propose to study the exotic meson production on nuclei at moderate
energy. The credible evidence of Exotics production in the process ú \Gamma +
p ! ú \Gamma j + p at 18 GeV/c (E852 collaboration [11]) and at 37 GeV/c (VES
collaboration [12]) was published . The possible interpretation of the exotic
state with quantum numbers J PC = 1 \Gamma+ and mass m = 1:37GeV=c 2 is the
bound state of quark­antiquark­gluon system jqqg ? (Hybrid meson, HYB) or
4­quark system jqqqq ?. Another kind of Exotics is a Glueball, GLU, which
is the bound state of two or more gluons, jgg ?; jggg ?; ::: .
So, we suggest to study the reaction
ú +A ! R(J PC ) +A 0 ; (1)
where R is HYB, GLU or 4­quark resonance system and A = H;C; Al; Cu;P b.
The notation A 0 means that we consider the incoherent process.
It gives us an unique possibility to extract the exotic meson ­ nucleon cross­
section oe(R; N) from A­dependence. At present time there is no experimental
or theoretical information on this cross­section. If the exotic meson is a real
strong interaction particle then its cross­section interaction with nucleon must
be approximately equal to oe(ú; N ). If it is not so and the observable wide
bump of decay particle mass distribution is the background than oe(R; N) will
be large then oe(ú; N ). Such kind of effect was shown in [13] from the analysis of
(3ú)N \Gamma cross­section. Behind the A 1 resonance region the oe(3ú; N) becomes
to be equal to twice of oe(ú; N ).
The interesting effect was observed in the reaction ú \Gamma +A ! ú + ú \Gamma ú \Gamma +A 0
[6]. The enhancement of 0 \Gamma S and 1 + S wave phase motion with 3ú \Gamma mass
system compared with hydrogen target is found. The same is seen for 1 + S
wave with increasing of target atomic weight. The authors of the work [6] have
claimed that the nuclear matter selects the particle system produced within
it enhancing the resonant state contribution in respect of the background.
Another interpretation of the effect is given in the work [14] as the inelastic
shadowing manifestation.
We have to underline the next points of the study of exotic meson production
on nuclei. The exotic production is very rare process. It needs the high
statistics measurements such as E852 data [11] or VES data [12]. Now the

partial wave analysis (PWA) is the only way to extract such kind of the rare
contributions.
PWA of multiparticle systems produced on nuclear target is difficult. The
physical background is large. We need to select the events from production
on one nucleon of nucleus. The direct way is to register the nucleon recoil by
the experimental way. But such processes of the quasi­elastic knock out of
nuclear nucleon have small cross­section.
Another way is to measure the cross­section when we don't pay attention
on nuclear state and add up the events with any final state of nucleus. Let's
see the region jtj r 2
A ?? 1 where jtj ' q 2 = q 2
T + q 2
L is a square of full
momentum transfer. It was shown in the classic Glauber's work [15] that the
nuclear incoherent cross­section of particle scattering is proportional to the
cross­section on hydrogen target
doe A
dt
(t) = doe H
dt
(t) N(A) (2)
where the number N(A) depends on the atomic weight A.
We take advantage of this fact and suggest to study from the experimental
data the model independent ratio
R(A; Ü ) =
doe A
dÜ (Ü )
doe H
dÜ (Ü )
(3)
for the same configuration Ü = ft; m; :::g of decay particle kinematical quanti­
ties on nuclear and Hydrogen targets. The ratio has the definite A­ dependence
which can be interpreted by theoretical models.
For example the generalization of Glauber's model to the production of
particle R with helicity – in the reaction ú \Gamma +A ! R 0 (–) +A 0 on nucleus A
with Z protons is [16,17]
doe A
dt
(t) ae –– 0
A (t) = Z
A
doe H
dt
(t) ae –– 0
H (t) N(A;
oe – + oe – 0
2
) (4)
Here ae –– 0
(t) is a spin­density matrix and oe – = oe – (R; N) is the R­nucleon
cross­sections for given helicity, which are free parameters. The authors [16,17]
have considered the different corrections on Pauli principle, multiple scatter­
ing, contributions of helicity flip amplitudes and others.
We should like to pay attention on the correction of the inelastic shadowing.
It includes the effect of the inelastic intermediate states in nuclear multiple
collisions. At the moderate energy 7­18 GeV this effect is supposed to be
small. It is the energy region E ! E crit where the total contribution of planar
amplitudes is presented as Glauber formula [18]. At higher energies it is
necessary to take into account the inelastic shadowing .

The study of the incoherent cross­section of Exotic state production has a
definite advantage compared with coherent cross­section. The rules of quan­
tum select for coherent events, when the final and initial nuclear have the same
quantum numbers, dictates to produce the states with J P = 0 \Gamma ; 1 + ; 2 \Gamma ; ::: for
incident ú. So we can't see the exotic states such as J P = 0 +\Gamma ; 1 \Gamma+ ; 2 +\Gamma ; ::: .
There are not such restrictions for the incoherent events.
We suggest to study the reactions ú + A ! R(J PC ) + A 0 and to measure
the incoherent cross­section in the region jtj ? 0:1(GeV=c) 2 at energy 7­18
GeV. The analysis of A­ dependence of the same final configurations of decay
particle kinematical quantities on Hydrogen and nuclear targets allows us to
get the unique information on the exotic meson interaction with nucleon.
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