Volume 24B, number 8 PHYSICS LETTERS 17 April 1967

NEUTRAL NON STRANGE 0- MESON PHOTOPRODUCTION AND REGGE POLES

P. DI VECCHIA and F. DRAG0 Laboratori Nazionale de1 CNEN, Frascati, Roma, Italy

Received 18 February 1967

Photoproduction of neutral non strange O- mesons is considered in the framework of Regge theory. Sym- metry relations between coupling constants are widely used. The results are in good agreement with the available experimental data.

Recent measurements [l] of photoproduction at high energy stimulated the application of the Regge pole theory to this problem [2-41. In particular the no photoproduction has been considered in ref. 2, in which the contribution of the w pole to the Reggeized CGLN invariant amplitudes [5] is cal- culated. The authors, assuming for the w trajec- tory the same as for the p, fit their results to the experimental data; moreover for Eyab = 2 GeV they introduce a direct channel resonance obtain- ing a better agreement at larger momentum trans- fer.

Fig.la. do/d(t[ for y + p --) p + r” as a function of -t.

The X0 photoproduction has been treated with Regge poles by Drechsler [4], considering only the contribution of the p trajectory in the crossed channel.

In this paper we present an analysis of the process

y+p+M” +Pt (1)

where MO can be r”, no or X0. Our aim is to show that, introducing the p and w trajectories in the crossed channel and assuming suitable re-

r

I 1 I I I I 1

3 4 5 6 7 8 9 1

E* pev

Fig. lb. Integrated ~0 photoproduction cross section for 1 t ( c 0.5 CRV8.

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Volume 24B, number 8 PHYSICS LETTERS 17 April 1967

Table 1

w*

, I --__

gv(gT) = electrical (magnetic) nucleon Vertex Coupling constants for vector exchange, y= (gT/gv).

p = transition magnetic moment.

Lations between the quantities involved, it is pos- sible to reduce greatly the number of parameters in Regge pole phenomenology. The results so ob- tained are in good agreement with the available experimental data.

The Regge pole contribution to our process can be caIcuIated using the heIicity representation [6] * in the t-channel p + p - Mo + y together with crossing relations [7]. It can be shown that the

* Our normalization convention here is different from that of Jacob and Wick [6]. The two are related by

F xp; vp = (dd F~u?;p.

I I I

0.1 a2 a3 0.4 a5 -t [GQ

Fig. 2.a. da/d\ t ) for y + p 9 p + q” as a function of 4.

406

Table 2

~~~

For the w-C~ mixing angle we assumed cos h = m, sen X = l/\Fj; CY is theq o - X0 mixing angle: using the Gell-Mann/Okubo mass formula and the actual mass of q” and X0, one gets: cos IY = 0.98, sen CY = f 0.18.

contribution of a Reggeized vector meson to the helicity amplitudes, for azimutal angle equal to zero, is given by [7]

where q,q’ = initial, final momenta in the crossed channel c. m. system, z = cosQt, I = Regge tra- jectory, M = nucleon mass. The d&functions in eq. (2) are not the ordinary reduced rotation ma- trices, and are defined in ref. 7.

The momentum transfer distribution for the process (1) is then

6 [&bJ ------ -m--r--~--

0.15

a 10 o1 a05

L I I .-L__L___I__I--_-A_-_ . ̂ _ -

Fig., 2b. Integrated qO-photoproduction cross section for ItI 6 0.5 GeV2. The value sina=+0.18 is used.

Volume 24B, number 7 PHYSICS LETTERS 3 April 196’7

da nt -_=-.-2

dt c ‘yp _+Ft(w) 2

K2S hel. Xh;lJ!J xx;/.l/Q ’ (3)

where K is the initial momentum in the production channel.

The C~X;~F are the residue functions from which we have explicitly factorized the threshold behavior (qq’/&Z2)ff: they are determined by the type of interaction and contain the coupling con- stants and some kinematical factors. We assume that the functions ClO;$$, ClO, _g _g,,C_lO;++, C-10, _$ -$ contain a factor [a(, + 115 and the remaining others a factor (Y(Q, + 1). Roughly speak- ing, the [(Y(LY+I)]P comes from the fact that (Y=O is a sense-nonsense [8] value for Ft lo. I 1, while

,22

the LY(Q+ 1) factor comes from the fact that (Y =0 is a nonsense-nonsense value for Ft 10; $ _+ [91*

We make now a pole approximation in the t- plane: i. e. we require that the Regge amplitude, eq. (2) reduces to the simple Born term for

B t - mex *. The result of the matching at the pole is presented in table 1.

From the experimentally known decay width [ll] I@- ~7) = 1.27 k 0.22 MeV we get for the wny vertex p =0.94 GeV-1 **. The transition mag- netic moments for the other vertices VMy can be found assuming the SU(6)Wsymmetry [e. g. 121 and are given in table 2. For the Vpp vertex, as- suming pure F-coupling, we obtain also from SU(6)W [13]:

= 3gvp, g’p = 0 V

W gT =;g,“T gc” = 0

T

(4)

g{ is well known experimentally: g2/4n = 0.74 [e. g. 141. The yp parameter can be connected with the electromagnetic structure of the baryons ob- taining [e.g. 151 yp = 3.7.

We first discuss a”-production. We assumed for the p the trajectory found by Logan and Ser- torio [16]:

cr&) = 0.58 + 0.90t t in GeV2

(compare also ref. 17). The ~-trajectory is not well known: it has

been studied by Phillips and Rarita [18]; how-

* rhis method has been successfully applied several times [e. g. 3,101: it permits to assign a definite phy- sical interpretation to the residue of the Regge pole in the J-plane.

** The transition magnetic moment p is defined by the phenomenological Lagrangian f?= 1_1e pvp’% A a w 71. Its dimension is a length in the natural V “8 *. sys em o units

(E=c=l).

1 1 \ ,, 1 0.1 0.2 0.3 0.4 0.5 0.6

-t pJ2]

Fig, 3a. da/d/t/ for y+ p -+p + X0 as a function of 4.

L , 1

/ 0.01'

/ I I 1 I

6.

I I ET [W]

I

2 3 4 5 7 6 9 10

Fig. 3b. Integrated X0-photoproduction cross section for Jtl SO.5 GeV2. Th e upper curve refers to sina = = -0.18, the lower to sina = +0.18. The two experimen- tal points refer to the total photoproduction cross sec-

tion.

ever in their paper Regge-poles are used in a way which is quite different from our approach, so that their parametrization cannot be used di- rectly in our work. If however we tentatively as- sume a straight w-trajectory with the intercept and slope given by them, we obtain the right be- havior and order of magnitude for the cross sec- tion. We can improve the agreement fitting crw(t) with the available data at 3 GeV, getting

cyw(t) = 0.60 + 0.75 t .

The results given in fig. 1 are in good agree- ment with the experimental data up to t =

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Volume 24B, number 8 PHYSICS LETTERS 17 April 1967

= -0.5 GeV2: obviously it is possible to improve the agreement fitting some of the many param- eters involved, but in this paper we are not so much interested in the phenomenological descrip- tion, as in the question to what extent a Regge picture, complemented by symmetry relations, may be applicable for inelastic processes like photoproduction, in spite of the difficulties en- countered by the model in the elastic case. For larger values of t our simple model with con- stant residues is no longer able to fit do/dt with sufficient accuracy; however our model may be still valid at larger momentum transfer, but at these energies the resonance effects can be im- portant, as suggested in ref. 2.

It should be noted that the contribution of the p trajectory, though small, is not at all negli- gible.

We give also the cross section for the no and X0 photoproduction, figs. 2 and 3, for which there are practically no data at high energy.

In order to test better the theory, it should be interesting to obtain other experimental data at higher energies where the resonance effects are less pronounced.

The polarization of the recoil proton results very small in our model: this may be easily un- derstood since the p and w trajectories are very close and have the same signature. However this result is probably not reliable in the energy range covered by the experiments where the resonances should contribute to the polarization (compare ref. 16).

t*

References 1.

2.

3. 4. 5.

6. 7. 8.

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***

M. Braunschweig, D. Hussmann, K. Ltibelsmeyer and D. Schmitz, Phys. Letters 22 (1966) 705; German Bubble chamber collaboration: Nuovo Ci- mento 46 (1966) 795; V. B. Elings, K. J. Cohen, D.A. Garelick, S. Homma, R. A. Lewis. P. D. Luckev and L. S. Osborne. Phvs. Rev. Letters 16 (1966) 474.

I ”

M. P. Lecher and H. Rollnik. Phvs. Letters 22 (1966) I I

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