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BNL PREPRINT
BNL­QGS­98­0501
Study of ¯
pp Baryon Exchange Processes
V. L. Korotkikh 1;2
June 25, 1998
abstract
The cross­section of the process ¯
p + p ! X 0 + j is estimated, where the
exchange particle is a virtual N + (1535) and the X 0 can be the exotic meson.
1 Moscow State University, 119899 Moscow, Russia ; e­mail: vlk@lav1.npi.msu.su
2 Physics Department, Brookhaven National Laboratory, Upton, NY 11973­5000

It is suggested in reference [1] to study a process with baryon exchange in order to look
for the exotic mesons with unnatural quantum numbers J PC = 1 \Gamma+ .
The reaction
¯
p + p ! X 0 + j; X 0 ! ú \Sigma ae \Upsilon ; ae \Upsilon ! ú \Upsilon + ú 0 (1)
can be described in Regge pole model [2] by diagram in Fig. 1.
N + (1535)
p
p
X 0
h
p +
r ­
Fig.1. Production of a meson X 0 in a baryon­exchange process from ¯
pp interactions.
Since the branching ratio for N + (1535) ! p + j is in the 30--55% range, the contribution
of N + (1535) exchange is expected to be substantial.
Because the ¯
p + N + (1535) initial state is not an eigenstate of C, J PC ­exotic states are
now allowed. So, if ¯
p (J P = 1
2
\Gamma
) and N + (1535) (J P = 1
2
\Gamma
) are in a relative P­wave and
the total intrinsic spin is zero, i.e. S = 0, then the state X 0 can be both J PC = 1 \Gamma\Gamma and
J PC = 1 \Gamma+ . The latter of these cannot be a ¯
qq state, and therefore is an exotic state.
The aim of this note is an estimation of absolute cross­section of reaction (1) in terms of
its u\Gamma and also p lab \Gamma dependence.
We use the formulae of Regge model from reference [3], where a detailed study of the
backward scattering is presented. The backward meson scattering
ú \Gamma + p ! p + ú \Gamma (2)
is descibed by the diagram in Fig.2. The authors of [3] found the corresponding parameters
in order to fit data.
The amplitudes of the annihilation reaction (3), shown in Fig.3
¯
p + p ! ú + + ú \Gamma (3)
1

D 0 ,N 0
p ­
p
p
p ­
Fig.2. Backward scattering of meson.
are related to the amplitude of reaction (2), and in the limit of large energy, the cross­section
is equal to
d¯oe
du
(¯pp ! ú + ú \Gamma ) = 1
2
doe
du
(ú \Gamma p ! pú \Gamma ) (4)
D 0 ,N 0
p
p
p +
p ­
Fig.3. Annihilation reaction ¯
p + p ! ú + + ú \Gamma
We repeated Barger and Cline's [3] calculation of reaction (3) and received the same
2

results at 10 GeV with their parameters:
fi \Delta
8ú
= 0:10 GeV \Gamma1 ;
s 0 = 2:85 GeV 2 ;
ff \Delta (u) = 0:15 + 0:9 u:
(5)
The differential cross­section depends on these parameters as
d¯oe
du
= 389:3 ¯b
ú
2 s
/
fi \Delta
8ú
! 2
jR(ff; s)j 2 ;
R(ff; s) = (ff + 1=2) (ff + 3=2)
1 + e \Gammaiú(ff\Gamma1=2)
cos úff
`
s
s 0
' ff\Gamma1=2
;
(6)
where ff = ff(u) is the Regge trajectory of given baryon exchange.
The integral cross­section is
oe(s) =
Z doe
du
du (7)
with s ú (2 mN p lab ).
We assume that a good estimation of cross­section for reaction (1) will be the cross­section
of reaction (8), which is shown in Fig.4.
¯
p + p ! j + j (8)
N + (1535)
p
p
h
h
Fig.4. Annihilation reaction ¯
p + p ! j + j
3

For this reaction we use the next parameters:
fi N
8ú
= (0:10 GeV \Gamma1 ) BR(N(1535) ! p + j);
s 0 = 2:85 GeV 2 ;
ff N (u) = \Gamma1:62 + 0:9 u;
BR(N(1535) ! p + j) = 0:45 :
(9)
Parameters of the Regge trajectory of N(1535) baryon exchange were taken from reference
[4] and the branching of N(1535) from reference [5].
The results are presented in Fig.5 and Fig.6.
The integral cross­section is well approximated by
oe(p lab ) = 75:0
`
p lab
3:0GeV
' \Gamma5:0
¯b : (10)
References
[1] S.U.Chung et al.,'Search for Exotic Meson with ¯
p Beams', BNL­preprint QGS­98­021
[2] A.C.Irving and R.P.Worden, Phys. Rep. D34, 117 (1977).
[3] V.D.Barger, D.B.Cline,'Thenomenological theories of high energy scattering', W.A.
Benjamin, Inc., NY, 1969.
[4] P.Collins, 'An introduction to Regge theory and high energy physics', Cambridge uni­
versity press, 1977.
[5] Particle Data Group, Phys. Rep. D54, 1 (1996).
4

Fig.5. Differential cross­section of reaction ¯
p + p ! j + j at 4.0 GeV/c.
5

Fig.6. Integral cross­section of reaction ¯
p + p ! j + j.
6