LETTEtCE AL Nuovo ClMENTO VOL. 3, N. 17 22 Aprile 1972

The Reaction e+e---> ~:+~-7:+7:- and the p'-Meson.

A. BnAMbN (*) and lVI. GREC0

Laboratori Nazionali de~ C N E f f - Fraseati

(ricevuto il 27 Dicembr6 1971)

In the preceding letter BARBARIlgO et al. (~) have reported on the observation of the process

(1) e+e- .-+ ~+7r-~+r

at total c.m. energies of the colliding beams 2E = %/s ranging from 1.2 to 2.4 OeV. The quantum numbers of the 4r: final state are well defined: JP~ = 1--, G = ~- and consequently I = 1, the same ones of the p-meson. The actual results however can be hardly understood under the assumption that reaction (1) proceeds only through a p intermediate state, because of the smallness of the cross-section at the total energies of 0.99 GeV (the AC0 results (~)), 1.2 and ~ 2 . 0 GeV. The threshold in fact for 4~ production is 0.6 GeV roughly, while the AI= (3.4) mode has a smoother energy behaviour than the experiment actually shows.

On the other hand, an attractive and at the same time natura l explanation of the data can be given assuming the existence of a new vector meson, the p'. This meson has been suggested by several theoretical models (s) and introduced by the authors (e) some time ago as a possible explanation of the rather high cross-sections observed in the multi-hadron production at ADONE.

In the present note we reexamine the previous a t tempt in light of new experimental information and analyse the implications concerning process (1).

The starting point of our model is to get an estimate of the coupling constans of the p' with the photon, gp'v = em#/]o',2 and with the mesons involved in its different decay modes. This was achieved (see ref. (s) for more details) by fitting the available experimental results concerning the decay rates of some pseudoscalar and vector

(*) O n leave of absence f r o m D e p a r t a m e n t o de Fis ica T6orica , Ba rce lona . (1) G. BARBARINO, F. CERADINI, ~ . CONVERSI, M. GRILLI, ~E. IABOCCI, 1V~. NIGRO, ~ . PAOLUZI, ~R. SAN- TONICO, P. SPILLAI~TINI, L. TRASATTI, V. VALENTE, R . VISENTIN a n d G. T. ZORN: Lett. Nuovo Cimento, 3, 689 (1972). (~) J . LEFRAN~OIS: t a l k g iven a t t h e 1971 Intern. Syrup. on Electron and Photon Interactions at High Energies, Cornell Un ive r s i t y ( I thaca , 1971). (3) J . LAYSSAC a n d F. M. RENARD: Lett. Nuovo Cimento, 1, 197 (1971). ( ') M. T. VAITGH~r a n d P. J . POLITO: Left. Nuovo Cime~o, 1, 74 (1971). (s) G. VENEZIAHO: NUOVO Cimento, 5 7 A , 190 (1968); J . A . SHAPIRO: Phys. Rev., 179, 1345 (1969). (~) A. B ~ 0 N a n d M. GRECO: Left. Nuovo Cimonto, 1, 739 (1971).

693

694 ~. BRAM6N and ~. eR~CO

mesons in t he spir i t of a vec to r -dominance mode l general ized wi th t he inclusion of these new states. In par t icular , for our ac tua l purposes, i t suffices to consider the chain of processes (~)

(2) r ~ + ~ - ~ , ~.._> =oy, =O~yy,

which are s imply re la ted by VMD and whose expe r imen ta l va lues are f i rmly estab- l ished (8). By using the old 0 R S A Y results (9) for the p h o t o n - v e c t o r - m e s o n couplings, AUOUSTIN et al. (~0) showed t h a t a d i sagreement be tween t h e VMD predic t ions and the expe r imen ta l values, of roughly a fac tor of two, was ob ta ined a t each s tep of t he chain (2). W e showed (a) t h a t t he exis tence of a new vec tor none t could res tore t he a g r e e m e n t i f the coupl ing cons tan ts of t he new mesons sat isfy the re la t ion

(3) ~ go'~o~ /o , , , ~ 0.2 g ~ l~'

I f howeve r t he new 0 R S A Y d a t a (n), now in a g r e e m e n t wi th those of NOVOSIBIRSK (~2), where used, t he d i sagreement in ref. (lo) would be reduced to a fac tor 1.4 rough ly a t each step. Correspondingly, in our ex t ended vec tor -dominance mode l the p a r a m e t e r

in t roduced in (3) should be g iven by

(4) ~ _ - - 0 . 1 2 .

F r o m this resul t and by assuming mp,~_ 1.6 GeV, we pred ic t the pa r t i a l w id th of the p'-+~T:-->~:+~:-~o~ ~ decay mode to be

(5) 2 4 [I~ n§

and there fore a fac tor of 3 smaller t h a n our prev ious resul t (e). B y means of usual S U 3 and phase-space eva lua t ion techniques and in t roduc ing the expe r imen ta l value F ( ~ - ~ = + ~ - ~ ~ _~ 10 MeV we ob ta in for t he main 9"-~ VP decay modes

= lio'y (6) r(p'-~ ~ ) = 24 ~ l , ~ I rl ' K*K) = Jl 'y

where all t he widths are expressed in MeV. W e h a v e also e s t ima ted for t he pseudoscalar- pseudosealar decays modes F(p ' ->PP)~_8( /p , / ]p ) ~ MeV, which is compat ib le wi th t he esper imenta l in format ion avai lable (~3). B y adding all these ra tes for t he decays p ' -> VP, PP , we ob ta in Fvp.pp --~43(/p,//~) 2 MeV-- ~ 215 MeV where t he va lue (fp,//o)2~-. 5,

(~) A similar analysis of the three related processes has been done by R. A. BRANDT and G. PREPA o RATA: Phys. Rev. Le~., 25, 1530 (1970), by using operator product expansions techniques. (8) PARTICLE DATA GROUP: R ~ . Mod. Phi /s . , 43 (Apri l 1971). (9) See for instance ref. (~). (xo) j . E . AUGUSTIN, D. BENAKSAS, J . C. BIZOT, J . BUON, B. DELCOURT, V. GRACCO, J . HAISSINSKI, J . JEAN JEAN, D. LALANNE, F. LAPLAHCHE, J . LEFRAN~OIS, P . LEBK~LANN, P. MARIN, ]~. NGUYEN NGOC, J . PEREZ-Y-JORBA, F. ~ICHARD, F. RUMPF, E* SILVA, S. TAVERIW[ER a n d I). TREILLE.* P h y s . Le f t . , 28 B, 5O3 (1969). (1~) See ref. (2). (~2) See, for example, R. 1V[ARSHALL: Proeegdi~g8 of thg DaTesbury ~ y Week~7~[ (June 1970). (xa) A. BRAlVI~N and M. GRECO: Journ. Phys., C 3, 93 (1971)~

TE[E REACTION e + e - - - > ~+7~-T~+~ - AND THE ~ ' -MESON 6 9 ~

estimated in ref. (e), has been tentat ively used. Fur ther decay modes are therefore required if the total p' width is about 0.35 GeV. This value is roughly confirmed by the new results (x4) on the reaction yp-->pzc+z:-r:+r:-, besides those of the preceding letter, both experiments suggesting a sizeable p'-+~+~-z:+~ - decay mode.

More in detail, DAVlEI~ et al. (~4) have studied the just mentioned reaction at photon energies up to 18GeV, showing evidence for a 4 ~ enhancement centered at (1.6 4- 0.1) GeV with a width of (0.5 4- 0.1) GeV and the following properties: a) the corresponding cross-section of (0.9 4- 0.2) vb is energy independent above 6 GeV; the slope parameter of da/dt is (5.8 4- 0.4) (GeV) -~, very near to the value (6.6 4- 0.4) (GeV) -~ for the analogous slope in the reaction yp ~ pop at the same energies.

This effect can be understood in terms of diffractive production of a p' which sub- sequently decays into four pions. By assuming the equality of the elastic p-nucleon and p'-nucleon cross-sections, as can be expected from the quark model, and neglecting nondiagonal terms pp--> p'p with respect to the diagonal ones pp-> pp and p'p-+ p'p we easily obtain

(7) F(p'-~ 4=~)

~_ (0.08 • 0.02

where we have used for the p-photoproduction cross-section the value % = 12 ~b (15). If is easy to evaluate the implications of this result in the 4~ ~ production in e+e -

annihilation, by using the expression for the e+e--~ p '-+[ cross-section

(8) m,.,~p 1 T'(o,..+~) (7~(8) 1 6 z 2 ~ 2

We find

(9) (re%-~an q- (m~,) = (1.6 -4- 0.5). 10 -3~ cm 3 .

The energy dependence is shown in Fig. 1 (*) and it is compared with the experiments. Looking at this Figure it should be realized also the presence of a background essentially coming from the AI~ contribution of the p tail previously discussed, which can be roughly estimated to be about 5 nb in the average.

In order to have more precise information on the four pions p'-decay modes, we have studied the reaction p'-+ pT:T: with techniques of finite-energy sum rules, similar to the approach used in p~ scattering. We omit the details, which will be discussed elsewhere. The preliminary results of this analysis are /~(p'-+pr:+r:-)~ 30([p,/]o) ~ MeV and F(p'---> p~7: e) ~ 12([p,/]p) 2 MeV in rough agreement with eq. (7).

We are now able to estimate the strength of the pCphoton coupling by adding all the different decay rates to a total width of ~ 0.35 GeV. We obtain (]p,/]p)2~_ 4. This value is consistent with the typical limits given in t]~e literature, using however realistic assumption on the p' width and on the branching ratio to two pions (13).

(it) M. I)AVIER, I . DERADO, D. C. FRIES, F. F. L Iu , !~. F. MOZLEy, A. (3. ODIAI~, J . PARK, W. P. SWAN- SON, F. VILLa a n d D. YOU~CT: SLAC P r e p r i n t ( June 1971). (i~) j . PARK, lYE DAVlER, I . DER&DO, D. C. FRIED, F. F. LIU, 1~. F. ~V~OZLEY, A. C. ODIAlq, W~ P. SWAIq- SO~r F: VILLA a n d D. u S L A C - P U B - 9 7 2 (1971). (*) The e x p e r i m e n t a l po in t s a r e t a k e n f r o m ref. (1).

696 A. BRAMSN and ~. ~RECO

We discuss now briefly the implications of our last result on proton Compton scat- tering and vector-meson photoproduetion, where discrepancies of the order of factors of two are observed for the ppho ton coupling constants when compared to the values found in e+e - annihilation.

h0

3O

10

0

T I

1.0 1.5

T

1

2.0 2E(GeV)

:Fig. 1. - e + e - - ~ = + = - g + ~ - ; | A C O , �9 B o s o n g r o u p , x q v-= * e x p e r i m e n t .

T I I I rl

2.5

From the VDM model follows the relation

(lo) ~. ~ 4 1 do ~

where do'~ denotes the forward cross-section and ~v the ratio of the real to the imag- inary part. I t is well known tha t the value of ]~/4~ obtained through eq. (10), from the total yp cross-section and from photoproduction data is smaller by a factor of about two than the results from e+e - colliding beams. More explicitly one gets /~/4~ = = 1.4 ~ 0.2 to be compared with the value 2.56 ~ 0.22 (,1). Since eq. (10) is based on VMD alone the disagreement has to be a t t r ibuted to a failure of the model. The situation substantially changes in the presence of higher vector mesons coupled to the photon. Let us in fact extend the sum over the vector mesons in eq. (10), by including as next step the p' and its SU3 partners. By using the above value (]p,//p)2 ~ 4 and as- suming doZ/dt(yp--> p'p) = (/o/]r da~ PP) the r.h.s, of eq. (10) rises by a factor 1.25, to be compared with 1.35 approximately.

This improvement of the VMD results suggests that moderate but significant cor- rections can arise from the continuum of higher-mass states, and underlines the fact that the hadronic properties of the photon cannot only be described by the nearby vector mesons, namely p, r and ~. Similar conclusions have been obtained by ALTARELI and PI~m~ARATA (is) who have estimated the contribution from the continuum by using the operator expansions near the light-cone.

I t is very tempting to speculate on what can be the overall contribution of the vector mesons coupled to the photon. Should the naive relation ]p(n)/]~ = 2 ~ be true

(z~) G. ALTA~RJELLI and G. PI~EpAR4TA: University of Rome preprint n. 300 (1971).

THE REACTION e + e - - - > ~ : + ~ - ~ + ~ - AND THE p ' -MESON 6 9 ~

for every s tate n, the eq. (10) has to be replaced by

(11) ~tot(YP) = C ~ V=p.o,q~

/~T4~ ~ + ~ dt (vp-~Vp/ 1 + u . . . .

= 4 ~r ~ 1 / . o 4 1 d ~ 3 v=p.~.~ ~ 1~/4~ 1 + ~ dt ( y p ~ V p ) ,

in very good agreement with experiment . This leads to an effective p-photon coupling measured in photon-nucleon reactions

\4z /e l f ~ 4 \4~ j 0ff

where the value ]~/4z = 2.56 has been used. The value (12) is in surprising agreement with different high-energy results (t~) on photoabsorpt ion and Compton scat ter ing experiments.

Finally, we observe tha t exper imenta l evidence in favour of the 1- ( ~ 1680) but against the 1- ( ~ 1250) is predic ted in some Veneziano-type form factors (is), which allow the photon to couple only to the even daughters of the p-meson.

We are very grateful to Y. SRIVASTAVA for interest ing discussions and for a crit ical reading of the manuscript. One of us (A.B.) acknowledge s G.I .F.T. for financial support .

(1~) D. O. CALDWELL, V. B. ELINGS, W. P . HESSE, R . J . ~r F. V. MURPHY, B. W. WORSTER a n d D. E. YOUNT: Phys. Rev. Lets 25, 609 (1970); G. BUSCHHORN, L. CRIEGEE, L. ]:)UBAL, G. I~RANKE, G. GEWENIGER, P. HEIDE, R . KOTTHAUS, G. POELZ, U. TIMM, K . WEGENER, H . WERNER, • . WOUG a n d W . ZIM~ERMANN: Phys. Left., 33 B, 241 (1970). (tO See, fo r example , H . SUURA: Phys. Rev. Lett., 23, 551 (1969),