L~TT:ERE AL NUOVO CIM]LNTO "VOL. 1, N. 18 1 Maggio 1971

H a d r o n P r o d u c t i o n in e+e - Col l i s ions and the E x i s t e n c e o f N e w Vec tor

Mesons .

A. BnA:ubN (*) and M. GRECO

Labor~ tor i N a z i o n a l i del C N E N - t%'ascati

(ricevuto il 15 Matzo 1971)

Recently some experimental effort has been devoted to search for additional vector mesons whose existence has been suggested by many theoretical models (1). Different experiments (2) looking at coherent photoproduction of high-mass pion pairs from nuclei have shown some evidence for a broad resonance in the mass range (1.4-?-1.6) GeV, although none of them has unambiguously established its mass and width. Furthermore the analysis of the four-piou mass spectrum produced ia the reac- tion -~p-->~+~-~+r:-p shows an enhancement at 1.55GeV having a width of (0.26 i 0.11) GeV (3.~).

In the present letter we assume the existence of a meson having the quantum numbers of the p, we call it p', and we discuss some consequences of its existence. First we re- examine the situation concerning the decays of the known pseudoscalar and vector mesons taking into account the contributions of the p' and its S U 3 partners. This enables us to have an estimate of how these new mesons couple to the photon and to the old ones. We study then the cross-sections for production of hadrons in e+e - col- lisions and predict their magnitude and behaviour at total energies of the colliding beams 2E ranging from 1.4 to 2.4 GeV.

A general analysis of the VMD predictions concerning the electromagnetic and strong decays of the k~ow~ ~eso~s has been recently m~d~ (s) showing that a reasonable agreement with the experimental data can be achieved. We now reconsider the whole

( ') O n leave of absence f r o m I n s t i t u t o de Fis ica Tebr ica , Ba rce lona . (~) N. N. I(HURI: Phys. Rev., 132, 914 (1963); D. Z. FREEDMAN a n d J . M. WANG: Phys. Rev., 153, 1596 (1967); G. VENEZIANO: Nt~ovo Cimento, 5 7 A , 190 (1968); J . A. SHAPIRO: Phys. Rer., 179, 1345 (1969); H . L. LIPK[Ig: Prooeedinys o/ the Lur~d I~ternational Co~]erence on Elementary Particles (Luad , 1970). (~) a) G. ~ICCLELLA~ r, N. MISTRY, P..'~[OSTEK, H . OGREN, A. OSBORNE, A. ~ILVERMAN, J . S~VARTZ, 1~. TALMAN a n d G. DIAMBR[NI-PALAZZ[ : Phys. R~_v. Lelt., 23, 718 (1909); b) F. BULOS et al. : S L A C - P U B - 7 5 1 (1970); c) H . ALVENSLEBEN, g . 5. BECKI~R, ~V. K . BERTRAM, M. (]HEN, K..]- . COHEN, R . T. EDWARDS, W. M. KNASEL, P~. MARS[IALL, D. J . QUINN, M. ROHDE, G. H . SANDERS, H. SCHUBEL a n d S. (2. C. TING : Phys. Rev. Left., 26, 273 (1971). (*) M. DAVIER el al.: S L A C - P U R - 6 6 6 {1969). (~) F o r a r ev iew of the e ~ p e r i ~ e n t a [ s i t u a t i o n see R . 5![ARSHAEL: Proceedlngs vf the Daresbt~ry ,b'fudy Weekend ( June 1970). (s) A. BARACCX a n d A. BRAMON: Nuovo Cimento, 6 9 A , 613 (1970).

739

740 A. BRA~CISN and ~. ~nnc0

s i tua t ion along the same lines by including these new vec tor mesons in order to es t imate t he va lue of some of the i r coupling constants .

The p-photon, p ' -photon couplings and the coupling constants among the dif- ferent S U a mult ip le ts invo lved in our model are defined as follows:

(1) go*=-- em~/lp , gp,,=- em~, / / z , ,

g =- g p ~ , h ~ g~,p.~ , ] =- - - g ~ p ~ , (2) g'=- gp~"~, g~,p'~, __ gp~'~

h ' = - , f ~

By means of the usual techniques of VMD and SU~ we obta in the decay rates for pro- cesses of the type V ~ 3 u , V - ~ : y and P ~ y y in t e rms of the products (*) g/]p, g ' / ] V , h/]p and h ' / ] V . F r o m the exper imenta l values (s) F(r l l . 7 M e V , F ( ~ - > 3 ~ ) = -- 0.73 MeV, F(o)-+~:0y) = 1.12 MeV and F ( ~ - ~ : ~ ~ 0 (< 0.014 MeV) and tak ing the o)-@ mix ing angle as p red ic ted by the quark model, i .e . sin 0 = 1/%/~, we obta in the following values expressed in (GeV)-~:

eg eh eg" eh" (3) - - = 0.59 , - - = 0.91 , - -~ - - - - 0 . 0 9 , - - = - - 0 . 1 9 .

lp l~ l~' l~'

W e check these results by eva lua t ing the decay ra te of the neut ra l pion. We obta in F( : :~ 8 .4eV in good agreement wi th the value F ( 7 : ~ ( 8 . 5 • 1 .7)eV quoted in ref. (6). We note tha t the in t roduc t ion of the new mesons, the i r couplings being (10- -20)% of the old ones, m a y be considered as a r a the r small correct ion to t he original VMD results.

In order to es t imate the coupling cons tants ]/]~ and ] ' l ip, we need to consider pro- cesses invo lv ing the ~ and ~' mesons for which the theore t ica l and exper imenta l situa- t ion is no t so clear. Assuming an ~-~' mix ing angle a = 10.4 ~ and tak ing the experi- m e n t a l results (s) F ( ~ - + y y ) = 1.01 keV and F(~-~r:+=-, l ) = 0.127 keV we deduce

(4) e]//7 ~ - - 0.14 (GeV) -z , e l ' l / V ~ 0.84 (GeV) -~ .

A new check of our values (3) and (4) is again possible by eva lua t ing the rad ia t ive decay rates of the ~ '-meson. We find F(~ ' -> yy) ~ 54 keV and R =- F(~ ' -+ 7:+rv-y)/F(~ ' --> yy) _~ _~ 2.4 in good agreement wi th the more recent expe r imen ta l resul ts (7) f rom which the values F (~ ' - ->yy) ,~p<400keV and R~p_~2.5 can be casfly deduced. We note f rom eqs. (4) t h a t the p' gives now an essential cont r ibut ion to reduce the value R _~ 14 previous ly ob ta ined in ref. (5). We finally emphasize tha t all the above results do not depend on the exac t value of the p' mass and wid th we have used, p rov ided rap, ~2m~.

We proceed now to inves t iga te the implicat ions of the p' in the product ion of hadrons in e+e - annihi la t ion. The to ta l cross-section for e + e - ~ p'--> (final s ta te f) at a to ta l energy 2E = ~ /~ a round the mass of the p' is g iven by

(5)

4

a t ( s ) : 1 6 ~ 2 ~ 2 m V 1 Fp,_,f e 2 '

(*) Amplitudes involving the ratio ]~/1~,, which we find to be small, have been neglected at this early stage. (6) PARTICLE DATA GROUP: Phys. Lelt. , 33 B, 1 (1970). (v) J. BENSINGER, A. ]~. ERWIN, ~[. A. THOI~[PSON and ~V. D. WALKER: Phys. Left . , 33 B, 505 (1970). See also D. BOLLINI, A. BUHLER-BROGLIN, P. DALP]AZ, T. ]~[ASSAM, F. NAVACH, F. L. NAVARRIA, M. A. SCItlgEE~ANN alld fix. ZICItICttI: Nuovo Cimeato, 5 8 A , 289 (1968).

I tADI%ON P R O D U C T I O N I N c + e - C O L L I S I O N S A N D T H E E X I S T E N C E E T C . 741

where ]~, is defined in eq. (1), Fp,~f is the decay ra te for 9 '-~ f and F~, is the ~' to ta l width . F r o m the exper imenta l evidence we roughly assume rag ,_ ~ 1 .5GeV and F r ~ 0.35 GeV. Le t us consider first the final s ta te f which gives rise to high mult i - plicit ies of p roduced par t ic les and can be re la ted to the above discussion on meson decays, namely r ~ : , ~ and ~ ' . F r o m eq. (5) i t follows t h a t the different p roduc t ion cross- sections depend only on the rat io 1~,~/]~,, which, apar t f rom phase-space factors, can be computed using the results of eqs. (3) and (4). We arc therefore able to predic t the magni tude and the energy behav iour of the to ta l cross-sections in the energy region around the mass of the ~'.

By means of the usual techniques to eva lua te the par t ia l decay rates we get the following values for the different peak cross-sections:

(6) { r162 = 3.6 �9 10 -a2 cm 2 ,

(~e+e-__~cp~(//bp,) ___~ 0.07" 10 -82 cln 2 ,

~r162 (m~,) _~ 0.2.10 -s2 cm 2 ,

ao~-~pn,(m~,) = 0.1.10 -3~ cm 2 .

The energy dependence of the to ta l cross-sections for r and 9"~' p roduc t ion in the range 1.4~<~/Y~<2.4 is shown in Fig. 1. I t is clear f rom this figure tha t the mode e+e--+r domina tes all o ther modes near the rap, peak, while the channel p'-+ p~'

~ . 3 E

0 I I I 14 16 18 20 2.2 2

~-(GeV)

Fig. I. - (lurve 1) eo~o+p-~'+~+~ -, curve 2) p.+~-, curve 3) (~o, curve 4) p~', curve 5) 7:+~-.

opens at 1.7 GeV approx ima t ive ly and domina tes thereaf ter . The ~:: and p-r modes are depressed because of the smallness of the i r coupling constants . The mult ipl ici t ies p roduced in t he final s ta te are easily found to be

r o I ~:+::-::0~o , 9 0 % ,

~:~176 , 10% ,

~+~- + n e u t r a l s , 26% ,

2(~+7: -) + n e u t r a l s , 6 2 % ,

3(~+r ~ or y , 1 2 % .

742 A. BRAMbN and M. GREr

As far as the react ion e + e - + p ' - ~ = + n - is concerned, for which the previous con- s iderat ions cannot apply, i t is possible to ex t rac t some informat ion f rom the experi- men ta l results on pion pair pho toproduc t ion f rom nuclei (3). By assuming t h a t t he enhancemen t observed in ref. (-~) is due to the p' and f rom the fact tha t the in ter ference be tween p and p' at the n~ 0, peak is small we obta in (*)

(7) F p , _ ~ = z _ 0.006 2"0' ]~'

and therefore Fo,~r:=/l" p, ~_ 5.6.10 -4 ]~;2. Subs t i tu t ing in eq. (5) we find for the cross- section at the peak a~+~-o=+~-(m~,)_~ 0.36-10 -a~ cm ~. The energy dependence of a~.~-(s) is shown in Fig. 1. The p' resonant cont r ibu t ion to the process e+e - ~ K+K - is obta ined from the preceding react ion e + e - - + u + n - by assuming SU3 symmet ry . We find ax+K-(m~,) ~ 0.09"10 -82 cm ~. By adding the cross-sections at(s) for the s tates f above considered we give in Fig. 1 the to ta l cross-section which is compared to the theore t ica l behav iour of ar I t is s t r ik ing to note how the different channels add toge ther for ~ / ~ 1 . 5 GeV to give in good approx imat ion a cross-section behav ing as 1/s.

W e add some remarks, also in order to clar ify the l imits of our model. By assuming the exis tence of a new vec tor meson hav ing a mass about 1.5 GeV we have shown t h a t t he theore t ica l s ta tus of the known meson decays is improved . The cross-sections for e+e - - + hadrons in t he range 1.4K ~/XK 2.4 GeV have been then predicted. However , we have so far neglec ted in ter ference contr ibut ions coming main ly f rom e+e- -+ p-+ tar: and e + e - ~ p-> ~+~:- (s). These addi t ional terms, which are negligible on the p' peak, can be present par t icu la r ly for c.m. energies smaller t han m0,. They can change s l ight ly our resul ts which represent the main cont r ibut ion to the product ion cross-sections. W e have also disregarded final s tates like p ' -~A~r : + or more sophis t icated ones because of t he lack of a clear exper imenta l and theore t ica l s i tuat ion, avoid ing in this w a y the in t roduc t ion of unknown free parameters . A precise eva lua t ion of these ex t r a t e rms should come from a detai led compar ison wi th exper iments .

An accura te knowledge of the to ta l peak cross-section will lead to a measure of ]0"" Should our results be confirmed wi thou t the need of fur ther addi t ional te rms, f rom eq. (5) and atot(~ ' ) - -~ 4.4-10 -32 em 2 we would get the rat io ]o"/]o2 2 ~ 5.

W e emphasize also tha t an i m p r o v e m e n t on the exper imenta l s i tua t ion concerning the ~ and ~' decays would lead to a be t t e r de te rmina t ion of the couplings ] and ] ' and therefore of our theore t ica l predict ions.

L e t us finally note t h a t according to our scheme the S U 3 par tners of the p', such as ta', could at least in pr inciple cont r ibu te to the e+e - annihi la t ion cross-sections. Since no expe r imen ta l in format ion is up to now available, we have comple te ly disregarded this k ind of contr ibut ions .

A more deta i led and wide analysis on the a r g u m e n t is ac tua l ly in progress.

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We thank the groups of A D O N E for discussions on the exper imenta l status. We are par t i cu la r ly grateful to C. BERNARDINI for a cr i t ical reading of the manuscr ip t and to M. BERNARDINI, F. FELICETTI, M. GRILLI and A. F. GRILLO for in teres t ing discussions. One of us (A.B.) acknovledges G . I .F .T . for financial support .

(*) We thank Dr. H. O~RE~" for clarifying discussions on this point. (8) J. LAYSSAC and F. M. RENARD: Left. Nttovo Cimento, 1, 197 (1971).