L E T T E R E AL NUOVO CIMENTO VOL. 19, N. 5 4 Giugno 1 9 7 7

Relative Strengths of Pomeron and Other Particle Couplings.

S. IwAo

Department o] Physics, College o] .~iberal Arts, Kanazawa University - Kanazawa

(ricevuto il 3 Marzo 1977)

AMALDI et al. (1) have discussed extensively the diffraction of hadronie waves, where the so-called pomeron exchange plays the fundamental role. The factorization and universality of pomeron couplings for diffractive processes were summarized as one of the topics. This is confined to the resume of many authors up to tha t time at PS and SLAC-LINAC energy region. I t would be very dcsirabIe to investigate the validity of such nice features up to much higher energies. In principle some of the basic relative coupling strengths of pomeron and other particles can be studied by comparing the properly integrated differential cross-sections for meson-baryon and baryon-baryon scatterings. Recently AYRES et al. (2,s) reported the extensive data suitable for that purpose at five incident momenta ranging from 50 GeV/c to 175 GeV/c and the lab- oratory energies from 140 GeV to 175 GeV for the elastic and single diffractive scat- terings, respectively.

The purpose of this paper is to investigate the universality of the relative coupling strengths of the pomeron and of other particles from both elastic and diffractive processes in the wide range of energies by making use of available information. I t was found that the universali ty of the coupling strengths under the factorization hypothesis holds in a certain accuracy. A new coupling strength is derived. The relative pomeron-quark coupling strengths are discussed. They will serve for finding new information.

(1) U. A~I~DI , /~ I . JACOB a n d G. 1W~TTHI~E : Di//rae$ion ol Igadronic Waves, to be p u b l i s h e d in Ann. Rev. Nucl. Sci. , 26, 1976. (u) D . S . AYRES, R . DIEBOLD, S . J . I~ACLAY, D. CUTTS, R . E. LANOU j r . , L . J . LEVINSON, J . T. MASSIMO, J . LITT, R . ~[EUNIOR, M. SOGARD, B. GITTEL~IAN, E . C. LOH, A. E . BRENNER, J . E . ELIAS, G. MIKENBERG, L . GUERRIERO, P . LAVOPA, G. !~IAGGI, C. DE ~ARZO, F. POSA, S . SELVAGGI, P . SPINELLI, F . WALDNER, D. S. BARTON, J . BUTLER, J . FINES, J . I . FRIEDMAN, H . W . KENDALL, B . NELSON, L. ROSENSON, R . VERDIER, B. GOTTSCHA~K, R . L . ANDERSON, D. GUSTAVSON, K . RICH, D. M. RITSON a n d G. A. WEITSCH: 7 ~ p , K ~ p , p p a n d PP e las t ic scattering f rom 50 ~o 175 GeV/c , F e r r a i l a b - P U B - 7 6 / 6 6 - E X P (August 1976). (a) D. S. ~YRES, R . DIEBOLD, D. C u T r s , R . E . LANOU, L . J . LEVINSON, J . T. ~rlASSII~IO, J . LITT, R . I~[EUNIER, B. GrrrEL~IAN, ~ . SOOARD, A . E. BEENNER, J . E. ELIAS, S . MIKENBERG, C. DE I~ARZO, L . GUERRIERO, P . LAYOPA, G. I~LkGGI, F . POSA, G. SELVAGOI, D. S. BARTON, J . BUTLER, J . FINES, J . I . FRIEDI~IAN, H . W . KENDALL, B. NELSON, L . ROSENSON, R . VERDIER, S . GOTTSCHALK, R . l , . ANDERSON, D. GUSTAVSON, • . RICI~[, D. M. RITSON, S . A . WEITSCE~ a n d E. C. LO~: Phys. Rev. Left. ,37, 1724: (1976).

157

1 5 8 s . i w A o

The elastic and diffract ive processes are

(1) a + b ~ a -kb ,

(2) a + b ~ a + X

and

(3) a + b ~ Y + X

t y p e react ions. I n the l a t t e r two cases the i nva r i an t masses of X and Y are res t r ic ted for t h e m o m e n t a t r e la t ive ly low values. The q u a n t u m n u m b e r exchanged in the reac- t ion is t h a t of v a c u u m as far as the in terna l one concerns. The pomeron domina t ed p a r t of t he cross-section shows the forward peak. I n the diffract ive processes the da ta are g iven somet imes in t e rms of da/dt'dM~, where t ' : t + I r is . and M x is the in- v a r i a n t mass of the sys tem X. The phenomenolog ica l pa ramet r i za t ion of the cross- sect ion near the forward region m a y be re la ted to the wel l -known Reggeized ampl i tude or to t he analogue of opt ical-dif f ract ion ampl i tude (1). We are only in te res ted in the rela- t ive coupl ing s t rengths of t he pomeron and par t ic les so we shall confine ourselves how to ex t r ac t the quan t i t y of in te res t f rom the na ive expe r imen ta l ly pa rame t r i zed cross- sections. The mos t c o m m o n pa ramet r i za t ion for small-It ' I region m a y be m a d e by

Usua l ly n tcrnfinates at n ~ 2 which a l ready shows the v io la t ion f rom the l inear i ty of the pomeron t r a j ec to ry in the physical region.

F r o m the close examina t i on of the analysis of the da t a one finds t h a t a 1 ~ a 2 (factor 4 or more) and the mos t of the cross-section is covered by the cut-off of [t'lm,~ = 0.6 (GeV) 2. The p a r a m e t e r A and a~ are usual ly s-dependent quant i t ies , e.g., a 1 ----2a~(0)In (s/so) in t he Regge theory. I f we confine ourselves to t he above range of t ' we can a p p r o x i m a t e the in tegra ted cross-section by

A (5) - - ( 1 - - cxp [-- 0.6 az] )

�9 M~(max)~ or w i th the mul t ip l ica t ion factor i n - ) ~ 7 2 , - / ,

Mx(min) ]

which wil l be compared for va r ious processes at f ixed s. All the problems discussed in th is pape r will adop t the above formula when the da t a are pa ramet r i zed by differen- t ia l forms. Fo r a lmost all cases t he fac tor ( 1 - - e x p [ - -0 .6a~] ) i s close to 1. Above all the p a r a m e t e r a2 usual ly conta ins a larger error than t h a t for al and an in tegra l involv- ing the a 2 par t often makes obscure the re l iabi l i ty of t he final a n s w e r . W e consider therefore tha t our app rox ima t ion is good enough for our present purpose.

I n tab le I we tabu la te t he re la t ive coupling s t rengths for fixed s in uni ts of 2 ~PPD for processes of t ype (1) at va r ious CM energies. In the first 10 lines the p ro ton and the an t ip ro ton arc specifically des ignated by p+ and p- , respect ively . The first three columns arc ob ta ined f rom the pa rame t r i za t ion in ref. (~), whi le t he remain ing three columns correspond to those ci ted in a decade old book (4). The expe r imen ta l errors are omi t t ed f rom those calculated f rom recent analysis for s impl ic i ty and of the re la t ive ly increased

(~) S. GASIOROWICZ: Elementary Particle Physics (New York, N . Y . , 1966).

R E L A T I V E S T R E N G T t I S OF POMERON A N D O T t I E R P A R T I C L E C O U P L I N G S

TABLE I . -- Representative ratios o/ pomeron-hadron coupling strengths.

159

Elas t i c V s (GeV) fl~lfl~p elast ic v /~ (GeV) 2 2

p+p+ 9.78 1.00 p~p+ 3.94 1.0

11.5 1.00 4.41 1.0

13.8 1.00 5.24 1.0

16.3 1.00 5.93 1.0

18.2 1.00 6.40 1.0

p-p+ 9.78 1.07 p -p+ 4.04 1.3 ~ 0.1

11.5 0.982 4.43 1.3 + 0.1

13.8 1.12 5.08 1.2 ~ 0.1

16.3 1.06

18.2 0.986

~+p 9.73 0.424 ~.+p 3.81 0.47 ~ 0.02

11.5 0.443 4.30 0.42 -~ 0.01

13.7 0.453 5.15 0.41 ~ 0.02

16.2 0.476 5.86 0.39 • 0.02

18.2 0.466

~ - p 9.73 0.438 ~ - p 3.86 0.42 -E 0.02

l l . 5 0.444 4.32 0.41 :~ 0.01

13.7 0.449 5.19 0.42 ~ 0.02

16.2 0.472 5.91 0.41 i 0.02

18.2 0.464

K+p 9.75 0.294 K+p 3.84 0.29 ~_ 0.06

11.5 0.297 4.56 0.28 :t: 0.02

13.7 0.333 5.17 0.30 + 0.02

16.2 0.334

18.2 0.345

9.75 0.322 K - p 3.94 0.35 j : 0.10 K - p

11.5 0.332 4.38 0.29 ~ 0.09

13.7 0.338

16.2 0.350

18.2 0.355

prec i s ion of t h e da t a . More prec i se ly t h e a p p a r e n t d i s a g r e e m e n t of t he ca lcu la ted coupl ing s t r e n g t h s a m o n g d i f fe rent g roups is w i t h i n an e r ror of o r ig ina l p a r a m e t e r s . E x c e p t for

fle~a/flppp are t he p -p+ case a t low energies, ~ 2 n e a r l y c o n s t a n t for a wide range of energies. P e r h a p s , t h i s wil l ho ld w i t h i n a v a l i d i t y of p o m e r o n d o m i n a t e d Regge pole app roach . The r e l a t i ve s t r e n g t h s d iscussed a b o v e m a y also be ca lcu la ted a p p r o x i m a t e l y b y corn-

1 6 0 s . IW.~O

p a r i n g t h e c o r r e s p o n d i n g t o t a l e last ic cross-sect ions a t a p p r o p r i a t e energies w i t h o u t loss of gene ra l i t y , case w h e n we do n o t h a v e su i t ab l e p a r a m e t r i z a t i o n (see, l a t e r d i scuss ion) .

I f we use t he d a t a s u m m a r i z e d b y DIDDENS (5) for v / ~ = ( 8 . 7 2 . 9 . 0 8 ) G e V (near 2 z = 40 GeV/c) we f ind

(6) fl~,-v- : 0 .966 , fl~=+=+ = 0 .434, ~ - = - = 0.447 (0.453) , fleK~+~ = 0.311

a n d 2 f lPK-K- ~ 0.314

in u n i t s of 2 aga in neg lec t ing errors . These r e su l t s s u p p o r t t he goodness of resu l t s ~PPl} o b t a i n e d in t a b l e I . W e sha l l use t he c o n v e n t i o n of u n i t s s t a t e d above a n d neg lec t ing to wr i t e i t exp l ic i t ly in t h e sequal .

Now we w a n t to tes t , f i rs t of all, t h e u n i v e r s a l i t y of these c o n s t a n t s f rom di f f rac t ive processes a n d t h e n t u r n ou t a t t e n t i o n to p o m e r o n a n d o t h e r pa r t i c le coupl ings .

F r o m t y p e (2) processes a t V~s = (16.2--18.2) GeV for M ~ : (4- -9) (GeV) 2 of AYRES et al. (3) we f ind 0.886 4- 0.106, 0.582 4- 0.034, 0.530 4- 0.033, 0.344 4- 0.110 a n d 0.342 4- 0.034 cor respond ing , respec t ive ly , to t hose in eq. (6). A t PL : 16 GeV/c (1) we h a v e a more e l a b o r a t e d i f f rac t ive processes for X ~ p, ~ ( 1 4 0 0 ) , 2~(1520), 2~(1960) a n d ~')(2190), whe re flp~-~-2 is a l m o s t c o n s t a n t a n d i t s ave rage va lue is 0.460 4- 0.078 a t ~/~- = 5.64 GeV. S u m m a r i z i n g the above re su l t s a n d those in t ab l e I t h e un ive r - sa l i ty of fac tor ized p o m e r o n coup l ing s t r e n g t h s appl ies to t h e wide r ange of energies.

L e t us discuss f u r t h e r t h e less we l l - s tud ied quan t i t i e s . Aga in f rom t y p e (2) reac- t ions (1) we f ind 2 4- flev(o~"rO 0.11 0.02, ~" = flpr~+~-~ = 0.060 4- 0.006 a n d 0.048 4- 0.017 as ave rages for ~ / s - = ( 4 . 0 . 6 . 8 ) , ( 4 . 6 . 7 . 0 ) a n d ( 3 . 5 . 5 . 9 ) GeV, respec t ive ly . Here , t he las t v a l u e was o b t a i n e d f rom di f f rac t ive p h o t o - p - m e s o n p roduc t ions . H i g h - e n e r g y d a t a give , however , 2 flpv(=~+) = 0.053 • 0.015 a t ~ / ~ = 45 GeV (e) a n d fl~p(p~+~-) = = 0.0037 4- 0.0015 a t ~ / s = 31 GeV (7). W e t h i n k t h a t a n a p p a r e n t d i s c r e p a n c y is due to t h e lack of da ta .

T h e las t i n t e r e s t i ng q u a n t i t y is in the case for a = b = p a n d X = (AK +) for reac- t ion (2). W e find flrrtA~+)~ = 0.0013 4- 0.0004 as an ave rage a t ~/g = 45 a n d 53 GeV (s). The s ame q u a n t i t y a t m u c h lower ene rgy (an ave rage for %/s = 4.9 a n d 6.8 GeV) (9) is e s t i m a t e d to be 0.0017 4- 0.0006 a n d 0.0015 for M x < l . 8 GeV a n d 1.8 G e V < M x ~ < 2.0 GeV, respec t ive ly . In o rde r to get a f inal conc lus ion we need more da t a . How- ever , t h e good a g r e e m e n t f o u n d a b o v e encourages us to p u s h t h e s imi la r idea for a d d i t i o n a l s t u d y inc lud ing , e.g., h y p e r o n - n u c l e o n s c a t t e r i n g (see l a t e r discussion) .

Before go ing i n to t he d iscuss ion of p o m e r o n - q u a r k coup l ing le t us s h o r t l y t o u c h u p o n t h e doub le d i f f rac t ive process , eq. (3). T h e k n o w n reac t ion is exc lus ive ly con-

(~) A . N . DIDDENS: High energy, low mult ipl ici ty reactions, in X V I I International Con]erence o~ High- Energy Phys ics , ed i t ed b y J . 1%. S M I ~ , ( R u t h e r f o r d , 1974), p . 1-41-I-70. (6) H . DE I~ERRET, E. NAGY, M. I=~EOIJER, W. SCI~Mn)T-PARZEFALL, K . ]~. SCHUBERT, K . WINTER, A. BRANDT, H . DIBON, G. FLUGGE, F. NIBEROALL, P. E. SCHUMACI~ER, J . J , AUBERT, C. BROLL, G. (~()IGNET, J . ]~AVIER, L. MASSONNET, ~ . VIVARGENT, ~V. BARTL, H . EICHINOER, CH. GOTTFRIED a l ld G. NEUHOFER: Phys . Let t . . 63 B, 477 (1976). (~) M. DEEEA NEGRA, D. DRIJAHD, H . G. FISCHER, G. FONTAINE, H . FREHSE, P. FRENKns C. CHES o QUIRE, R . GOKIEEI, P. HAI~KE, ~V. HOF5IANN, W. ISENBECK, E. E. KLUOE, V. KORBEL, D. I~INGLIN, A . MINTEN, A. NORTON, A. PUTZER, m. SOSNO~u S. STEIN a n d D. ~VEGENER: Phys . Lef t , 6 5 B , 394 (1976). (s) L. BAKSAY, A. B~I~I, G. I~-. C~ANG, R . ELLIS, H . FOETH, S. V. FUNG, A. I~ERNAN, J . LAYTER, F. MULLER, B. NAROSKA, D. SHEX, A . STAUDE, P. STROLIN, V. TELEGDI a n d G. TRILLING: Phys . Let t . 6 4 B , 405 (1976), (~) $. ttOF3IANN, U. IDSCHOK, ]~. SCItR()DER, V. BLOBEL, H . FESEFELDT a n d J . SEYERLEIN: DiHraction dissociation in the reaction p p ~ pAK: + at 12 and 24 GeV/e, B O N N - H E - 7 6 - 2 0 , p r e p r i n t ( D e c e m b e r 1976).

RELATIVE STRENGTHS OF POMERON AND OTHER PARTICLE COUPLINGS 161

fined to t he case for X = Y = J~f'* (or nucleon and pions). The in tegra ted single and double di f f ract ive cross-sections for the S * case are known at PL = 300 GeV/c (~o). Com- bining these w i t h the known elast ic to ta l cross-section (n) a t the same m o m e n t u m we find fierY* = 0.11 :j: 0.01 and 0.15 :s 0.06 for the former and the la t te r reactions, re- spect ively . The va lue is again consis tent w i th t h a t e s t ima ted before. This fact is known b y m a n y au thors (~2,~a) and in te rp re ted in t e rms of t he re la t ion among elastic,

wi th in some factor. single and double diffract ive cross-sections, v i z . , a ~ % , d . = a,.d.

F r o m the analysis of F N A L elast ic da ta i t is na tu ra l to assume

(7a)

(7b)

and

(7c)

~2D+D+ 2 2 = ~ppp ~PD - P -

~2K+K+ 2 __ 2 2 = : ~PKK - - ~PDP flPK-K- "~ 0.330

on the average. coupling as

(Sa)

(8b)

and

(8c)

An inspect ion of these resul ts suggests us to choose the pomeron -qua rk

/~.~, = 3 / ~ . u . ,

prov ided t h a t flr~. = flFdd" Here, u, d and s denote three known quarks. Numerica l ly , we find

(9) flp~ --~ 0.377,6pp~, and tip,, ~ 0.237 flppp.

Making use of eqs. (7)-(9) and fac tor iza t ion hypothesis , we can pred ic t the elastic hyperon- nucleon sca t ter ing cross-sections at pomeron-domina ted region:

(10)

and

(11)

a (Ap-~ Ap) = a ( Z • Z• -- (2flPuu ~U flpss)z a(pp--*-pp) ~ O . 8 3 0 a ( p p ~ p p )

a(E-p--+ E-p) -- (flPu. + 2tiPs,) 2 a(pp-> pp) ~ 0.658a(pp--> p p ) .

Fo r the m o m e n t the forward dominance is observed only for A p ~ Ap scat ter ing a t PL = 2.88 and 4.25 GeV/c (v/s = 2.814 and 3.22 GeV, respect ive ly) Qa). The observed

(10) A. FIRESTONE, V. DAVIDSON, F . NAGY, C. PECK, A. SHENG, F. T. DAO, I t . I:~ANFT, J . LACH, E. ~r f . NEZRICK, ~k. DZIERBA~ n . POSTER a n d W. SLATER: Evidence /or double rill/faction in p p interact ions at 300 GeV/c, F E R M I L A B - P u b - 7 4 / 1 0 1 - E X P ( D e c e m b e r 1974). (11) E. Bxcc I , J . P . DROULES, E. FLA_MINIO, J . D. HANSEN a n d D. R . O. MORRIS0N: Compilat ion o/cross- sections I I I - p and ~ induced reactions, C E R N / H E R A 73-1 ( J u n e 1973). (13) j . W•ITMORE: P h y s . R e p . , 1 0 C , 273 (1974); 27.C, 187 {1976). (13) M. JACOB: Hadron phys ics at I S R energies, C E R N 74-15 ( J u l y 1974). (14) O. BENARY, N. BARACH-SCHMIDT, LEROY t~. PRICE, A. H . ROSENFELD a n d G. ALEXANDER: -~ com- Pila t ion ol Y,~V reactions, U C R L - 2 0 0 0 0 Y N ( J a n u a r y 1970).

1 6 2 s. i w A o

cross-scctions are 9 ~ 3 mb and 9 ~ 4 rob, respectively. The calculation on the r.h.s, of eq. (10) at the corresponding energies yields 13 mb and 10.5~:0.23 rob. The assumptions made in this treatment seem to be satisfied within an experimental error. A further experimental check on this problem at FNAL and CERN-SPS energies is very inter- esting to be performed. If the simple constructive phase assumed for pomeron-quark couplings holds in general including charmed c-quark (is), we can predict the lower l imit of the charmed-meson-baryon scattering cross-sections in pomeron dominance:

(12)

and

(13)

a(D-Lp---~ D• > �89 ~ r:p)

a(F:~p ~ F:~p) > ~ a ( n p ~ rip). ~p~

If the phase is destructive the inequality sign should be reversed. These two examples are shown as a matter of interest. No direct experimental check will easily be done in a near future.

We should like to speculate on the pomeron structure. If the coloured massless non-Abclian gauge gluons are responsible for the pomeron structure, three (or more} gluons with vacuum quantum number should be exchanged simultaneously between quarks. Such a conjecture must be reconciled with the coupling strength between single gluon and quark (~s). I t is hoped that a complete understanding of the diffrac- tive phenomena may be performed in the same line of thought.

(la) M. K . GAILLARD, B. W. LEE a n d J . L. RosNEI~: Rev . Mod . P h y s . , 47, 277 (1975), a n d r e f e r ences t h e r e i n e o n ~ i n e d ; A. DE ]~UJULA: Theoretical basis el the nel part ic les , i n X V I I I In terna t ivna l Con- ]erence on High-Energy Physics , Tb i l i s i , H U T P - 7 6 / A 1 6 7 ( J u l y 1976), a n d r e f e r ences t h e r e i n c o n t a i n e d . (1,) S. IWAO: Lef t . Naovo Cimento , 16, 486 (1976), a n d r e f e r ences t h e r e i n con t a ined .