Recent Results on Photoproduction of Vector Mesons and Mass Dependent Pomeron Trajectory



Shaukat Ali and Muhammad Ali

Theory Group, Department of Space Science,

University of the Punjab, Lahore.



ABSTRACT

It is shown that the recent results on photoproduction of vector mesons can be

naturally explained by using a mass dependet pomeron trajectory.

Regge theory [1] has been successful in describing soft hadron-hadron interactions. Elastic

photoproduction of 0 and mesons is well described [2] as a diffractive process in the framework of the

Vector Dominance Model (VDM) [3] and Regge theory [1]. Soft diffraction can be described by the exchange

of a soft pomeron Regge trajectory (t) = (0) + /t with an intercept (0) = 1.08 and slope / = 0.25 GeV-2.

This trajectory is also sometimes referred to as the nonperturbative Pomeron. However, the steep energy

behaviour of the elastic J / photoproduction cross section at HERA, cannot be described in the Regge

picture by a pomeron trajectory with an intercept of 1.08. The cross section for this reaction rises faster than

expected from a `soft' diffractive reaction. While the cross section of elastic photoproduction of the three

lightest vector mesons 0, and , rises like W0.22 [4] that of the J / rises like W0.640.13 [5] or W0.920.14 [6].

This indicates that the intercept of the exchanged `object' in the latter reaction is larger than 1.08 but in order

to measure the intercept from the cross section behavior one needs information also on the slope /.

We have argued that [7] the elastic photoproduction of 0, and meson ( soft diffractive

photoproduction ) as well as that of the J / photoproduction ( hard diffractive process) can be described by

assuming mass dependent expression for the pomeron trajectory in the frame work of Regge theory [1]. It is

interesting that the elastic photoproduction data of 0, and J / vector meson, recently measured by ZEUS

Collaboration [8] up to -t = 3 GeV2 and at average centre of mass energy <W> = 94 GeV agree well with our

fit except 0 . A careful analysis shows that some other quantity also plays role in these reactions. Thus in

order to fit the experimental data, we also have to consider the role of isospin I in the amplitude. We have

shown that by proposing the isospin dependent residue function of the form exp (-3It) in the framework of

Regge theory, these measurements for all the three reactions along with the previous results at high energies

can be explained by using the mass dependent pomeron trajectory.

We suggest a simple expression as

(t) = (1 + fm) + (a/m)t

where intercept (0) = 1+ fm and slope / = a/m GeV-2, f = 0.05 GeV-1, a = 0.20 GeV-1 and m is the mass of

the vector meson involved in the process p Vp. For lighter vector meson 0 and this expression behaves


like a soft pomeron trajectory and for elastic J/ photoproduction behaves like a hard pomeron trajectory.













The differential cross-section results for p p The differential cross-section results for p J/p

By using this simple expression, the differential cross sections of the soft and hard diffractive

reactions, p Vp, V = 0, and p J/p along with the previous results at high energies are explained.

The differential cross-section results for p 0p and p p reactions calculated by using mass dependent

pomeron trajectory are compared with the recently measured experimental data [8]. The agreement is quite

good. Next we compare the predictions of our calculations with the experimental data [8] for p J/p

reaction. The theoretical predictions of the model are in good agreement with the experimental data. The

intercept of the exchange pomeron in this reaction is 1.153 and slope is about .07t which is very small as

compared to soft pomeron, giving the evidence for no shrinkage. This can be interpreted as indication that for

the reaction p J/p diffusion from small to large size configuration is only a small correction up to W =

94 GeV. Thus the process is hard and fully calculable in purturbative QCD

ACKNOWLEDGMENT: We are grateful to Professor M. Saleem for drawing our attention to this

problem.

REFERENCES

1. P.D.B.Colliins, An Introduction to Regge Theory and High Energy Physics, Cambridge

University Press (1957); T.Regge, Nuovo Cim.14 (1959) 951; 18(1960) 947.

2. J.A.Crittenden, Exclusive Production of Neutral Vector Mesons at the Eelectron-Proton

Collider HERA, Springer Tracts in Modern Physics, Volume 140 (Springer, Berlin

Heidelberg, 1997).

3. J.J.Sakurai, Ann. Phys. 11 (1960) 1; J.J.Sakurai, Phys.Rev.Lett.22 (1969) 981.

4. ZEUS Collab. M.Derrick et al. Z.Phys. C69 (1995) 39; ZEUS Collab. M.Derrick et al.

Z.Phys.C73 (1996) 73; ZEUS Collab. M.Derrick et a., Phys.Lett. B377 (1996) 259; HI

Collab. S.Aid et al., Nucl. Phys. B463 (1969) 3.

5. HI Collab. S.Aid et al., Nucl. Phys. B472 (1996) 3.

6. ZEUS Collab. M.Derrick et al., Zeit. Phys. C75 (1997) 215.

7. A. Shaukat, R.Haris, J.Sc. Res. XXIX (2000)1 31

8. ZEUS Collab. J.Breitweg et al., DESY 99-160 (1999).



