P H Y S I C A L R E V I E W D V O L U M E 11, N U M B E R 9

Suppressed $ photoproduction: A test for the charm hypothesis*

C. E. Carlson Department of Physics, The College of William and Mary, Williamsburg, Virginia 23185

P. G. 0. Freund The Enrico Fermi Institute and the Department of Physics, The University of Chicago, Chicago, Illinois 60637

(Received 13 January 1975)

The prediction of our previous paper about the suppression of the photoproduction of a cZ vector meson (c = charmed quark) is compared with recent information on the $I particle. The theoretical foundations of the argument are closely aqalyzed. The predicted value u(yp -3 +p) / u(yp -3 pp) -- 4.4 X lo-' [i.e., u(yp + J,p) -- 7 nb] is shown to be very different from what one would expect with the color interpretation of I). Preliminary experimental data seem to confirm this strong suppression of + photoproduction and with it the charm hypothesis (though we cannot rule out the idea that the J, is, say, an intermediate weak boson).

In 1972 we argued1 that the search for hadrons energy range a r e to a good approximation diffrac- containing charmedZ quarks i s best pursued i n the tive (i .e. , Pomeron-dominated) and therefore at lepton-antilepton channels. The part ic les to be t - 0 they a r e purely imaginary. For comparison searched for a r e the cc ( c = charmed quark) coun- let us a l so recal l that t e r p a r t of the p , w, and 9 vector mesons and i t s radial excitations. An obvious interpretation of the 4 (or J ) part ic les discovered by the BNL and SLAC groups3 i s that they a r e precisely these cT; ( l b ) vector mesons. Unfortunately, other explanations, such a s assigning the new part ic les to color oc te t s , a r e possible.

In I we showed that, in the cF interpretat ion, tensor dominance of the ~ o m e r o n " - ~ leads to a remarkable suppression of 4 photoproduction com- pared to p photoproduction. No s imi la r suppres - sion occurs in the color interpretation. In this sense 4 photoproduction can be viewed a s the crucial experiment to distinguish between these two (at p resen t leading) interpretat ions of the new part ic les . Even the meager existing information on 4 photoproduction speaks strongly against the color interpretat ion, while the charm in te rpre ta - tion can account fo r these data. In view of the r e - vived in te res t i n this problem, we shall reca l l h e r e our reasoning and spell out our assumptions in careful detail .

In the vector -dominance model of photoproduc- tion

where 3mp2 y , and 2 v%m, y L a r e the p-7 and 4-y transition matr ix elements , respect ively, and a,,, and opP a r e the $p and p,b total c r o s s sect ions. ' One a s s u m e s here that (Assumption A ) the pp - pp and qp - 4 p amplitudes in the relevant

(the $7 amplitude i s - ~ 5 m , ~ h r , ) .

Our argument now concentrates on the two fac- t o r s appearing on the right-hand s ides of Eqs. (1). The crucial factor i s the square of the rat io of the total c r o s s sections. To understand this , let us f i r s t give a qualitative argument. Diffraction i s essentially shadow scat ter ing. A p meson inter - ac t s with a proton predominantly by exchanging S = C = 0 mesons (S= s t rangeness , C = charm) and producing various final s ta tes . A q meson con- tains no S = 0 quarks and therefore must exchange predominantly s t range ( 1 S / = 1) mesons with a p ro- ton. Similar ly, a $ meson contains no C' = 0 quarks and exchanges predominantly charmed ( 1 C 1 = 1) mesons with a proton. Now, charmed mesons a r e heavier than s trange mesons, which in turn a r e heavier than nonstrange mesons. Therefore the energy denominators (or alternatively the lower Regge intercepts) will suppress the reaction r a t e s for s t rangeness exchange and even more for charm exchange. The corresponding shadow scat ter ing will a l so be suppressed. It i s thus c lea r that

Thls chain of inequalities can be sharpened , ' through the use of tensor -dominated Pomeron dynamics, into quantitative predictions for the rat ios a,, up, and U,,'U,~. The b a s i s of the ten- s o r -dominated Pomeron" s i s the quark-model

2454 C . E . C A R L S O N A N D P . G . 0. F R E U N D

interpretat ion of duality. The Pomeron i s r e p r e - sented6 by the quark d iagram of Fig. l (a ) . Even without any detailed dynamics, i t i s obvious f r o m Fig. l ( a ) that the Pomeron couples to hadrons by f i r s t "transiting" to a q q s ta te with the appropriate quantum numbers , i .e. , an even-signature meson t rajectory such a s that of the f , f ' , and f , (their cF par tner ) . This is explicitly shown in Fig. l(b). We have

where y F v ( t ) i s the coupling of the Pomeron to the vector meson V(V=p, p, $). The assumption of tensor dominance4 (Assumption B) s t a t e s that

where a p ( t ) i s the Pomeron t ra jec tory , while a,, i s the leading even-signature meson t rajectory that couples to the vector meson V. The p meson con- tains only nonstrange quarks, s o that T , = j . Simi- l a r ly , T,= f ' and T, =f,. The (even-signature) T, t ra jectory i s known to be exchange-degenerate with the (odd-signature) V trajectory. Thus

1= aTv(mV2)= a T v ( 0 ) + a;my2

o r (5)

a T v ( 0 ) = 1 - a h n ~ y ' .

Using cr,(O) = 1 along with Eqs. (3) and (5) we then find

It is known experimentally that a; = &, s o that one predicts

This a g r e e s beautifully with the experimental r e - su l t

We now a s s u m e (Assumption C ) that

a;= a;, . (8)

Then

w2p %= =0.061, o r o,,= 1.6 m b . ~ P P m+

(9)

This then contributes a suppression factor of (0.061)2 = 3.8 x on the right-hand s ide of Eq. ( l a ) . This i s the crucial factor ' (it has been d l s - regarded in more recent l i terature8) .

FIG. 1. Tensor-dominated Pomeron in vector-meson (v) - proton scattering: (a) quark diagram, (b) "usual" diagram.

Concerning the factor y p L 'yLi12 in Eq. ( l a ) : From the experimental widths I?,,,+, = 6.5 keV and r, ,,+,- = 3 keV we ex t rac t

a s opposed to the symmetry value y p 2 / y , 2 = 1. In- se r t ing Eqs. (9) and (10) into ( l a ) we find

o r , in other words [using d a df ( y P - p P ) / , = , = 100 pb /GeV2],

This is essent ial ly the prediction of I. Now let us analyze the assumptions we made i n

deriving (11). Assumption A is s tandard and c e r - tainly good within 15% o r so. It becomes bet ter a s the energy increases . The assumption (B) of a tensor-dominated Pomeron considers the effect of the leading Regge t rajectory a T , ( t ) but neglects i t s daughters. F r o m the experimentally verified p r e - diction (7) i t i s c l e a r that this i s a good approxima- tion. The tensor -dominated Pomeron has numer - ous fur ther successful t es t s to i t s credi t . We men- tion here the identical spin s t ruc ture of the f Regge t e r m and the Pomeron t e r m i n nN s c a t t e r -

the observed diffraction dissociation in nN-A2N,7s4 and the c o r r e c t prediction of o,' a ,,."Similarly, exchange degeneracy, used in Eq. (5), i s well understood. As for Assumption C [Eq. (a ) ] , i t i s implied by the s t r ing picture of had- rons. Indeed, a' i s determined by the nature of the s t r ing , which in i t s turn is independent of the quarks a t i t s ends. Nevertheless, this assump- tion might be open to some question in view of the

11 - S U P P R E S S E D + P H O T O P R O D U C T I O N : A T E S T F O R T H E . . . 2455

la rge splitting between and 4': nz,,' - W L ~ 4 GeVZ. The formula Independent of the detailed shape of the 4 t ra jectory is the one obtained in t e r m s of affc(0) f r o m Eqs. (3) and (4):

For any empir ical value of af,(0) = a- (0) Eq. (4') yields a value for u,, 'up, which one can i n s e r t in Eq. ( l a ) to predict uYp, LP. Concerning Eq. (1): We note that f r o m the leptonic decays one findsg

Inser t ing this and Eq. (7) o r (7') into Eq. ( l b ) we find

a s opposed to the experimental value of = 0.27 for the left-hand side. Of course , in Eq. (12) y p and y , a r e determined on the meson m a s s shel l , while i n Eq, (13) they a r e needed a t F2 =O. It i s t rue , however, that this aspect of the vector-dominance model i s incompletely understood. All the s a m e , i t suppresses Q photoproduction even more than Eq. (13) and one could expect an e x t r a suppression even in the c a s e of Eq. (11). Whichever way we argue, however, we pred ic t a s t rong suppression of + photoproduction. To the extent that the t de- pendences a r e s imi la r , one predicts

With u(yp - p p ) - 16 lib this means u ( y p - +p) = 7 nb. Again, a s we have said, there could be a n ex t ra suppression due to symmetry breaking at the y# transition.

In the color interpretat ion of the $, y; would be f-dominated and one would not pick up the c r u - cial m , 4 / r r ~ w 4 fac tor , but only the rat io of 71 , /y,', , which has no reason to be small . Thus in the color interpretat ion one would expect a(?@- $ p ) to be of the o rder of n ~ i c r o b a r n s o r hltndreds of mnobavns. The upper bound1' of u(yp- 4p)< 29 nb and pre l im- inary resu l t s of fu r ther experiments on 4 photo- production a l l indicate a s t rong suppression of 4 photoproduction. They a r e certainly compatible with our prediction (14) ( see I). They speak against the color interpretation.

In a cautionary vein le t u s emphasize that smal l 4-photoproduction c r o s s sections would be ex- pected a l so in the more "exotic" case that $ turned out to be , s a y , a weak intermediate bo- son. In the la t ter c a s e one would, however, e x - pect a violation of pari ty , which would readily distinguish i t f r o m the charm interpretation.

Finally, le t us point out that in addition to i t s importance for the c h a r m hypothesis, the sup- pression of +,! photoproduction could provide the most d ramat ic test of the tensor-dominated Pom- eron.

*Work supported in part by a grant from the National Science Foundation: Contract No. MPS74-08833.

'c. Carlson and P. G. 0. Freund, Phys. Lett. E, 349 (1972). This paper will be referred to a s I from now on. We have switched here to the more conventional notation for the vector-meson-photon transition ampli- tudes in terms of reciprocals of the universal coupling constants Y p , Y Q, Y* . In the third line of text following Eq. (2) of I , the words "Eq. (1)" should read "Eq. (2)".

2 ~ . L. Glashow, J. niopoulos, and L. Maiani, Phys. Rev. D 2, 1285 (1970). This paper contains further refer- ences.

3 ~ . J. Aubert et a1 ., Phys. Rev. Lett. 2, 1404 (1974); J.-E. Augustin et a l . , ibid. 33, 1406 (1974).

4 ~ . Carlitz, M. B. Green, and A. Zee, Phys. Rev. Lett. 26, 1515 (1971); Phys. Rev. D 4, 3439 (1971). -

5 ~ . Lovelace, Phys. Lett. z, 500 (1971). 6 ~ . G. 0. Freund and R. J. Rivers, Phys. Lett. E,

510 (1969). 'P. G. 0. Freund, H, F. Jones, and R. J. Rivers, Phys,

Lett. e, 89 (1971). 'M. K. Gaillard, B. W. Lee, and 3 . Rosner, Rev. Mod.

Phys. 41, 277 (1975); A. De RUjula and S. L. Glashow, Phys. Rev. Lett. 34, 46 (1975); C. G. Callan, R. Le Kingsley, S. B. Treiman, F. Wilczek, and A. Zee, ibid. 34, 52 (1975).

$see, e.g., G. Wolf, in Proceedings of the 1971 Inter- national Symposium on Electron and Photon Interactions at High Energies, edited by N . B. Mistry (Laboratory of Nuclear Studies, Cornell Univ., Ithaca, N. Y., 1972), p. 189.

'OM. Perl, private communication.