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The OZI rule does not apply to baryons
Volume 217, number 1,2
PHYSICS LETTERS B
19 January 1989
THE OZI RULE DOES NOT APPLY TO BARYONS John ELLIS CERN, CH- I 211 Geneva 23, Switzerland Erwin G A B A T H U L E R Physics Department, University of Liverpool, Liverpool L69 3BX, UK and Marek K A R L I N E R J,2 SLAC, Stanford, CA 94309, USA Received 28 October 1988
Determinations of the x-N a-term and the EMC measurement of deep inelastic polarized i.tp scattering and various theoretical arguments indicate that baryons contain a significant number of strange quark-antiquark pairs. Their presence gives rise to additional connected diagrams which evade the Okubo-Zweig-Iizuka (OZI) rule for meson-baryon couplings, and explain the apparent violation of the OZI rule seen in the reaction pp~0~+x - as well as the process pp~pp0 + pions, and the backward peak seen in pp~K+K -. We catalogue predictions, based on moments of deep inelastic structure functions, for the OZI-evadingcouplings to baryons of 0-+, 0+ +, and 2 + + and other mesons. Processes where these predictions can be tested include backward meson production in x-N scattering as well as pp annihilation and pp scattering.
According to the Naive Quark Model ( N Q M ) ~ the proton wave function contains just two u quarks and one d quark. This model gives a good general picture o f h a d r o n structure at large distances (small mom e n t u m transfers Q2), while probes of shorter distance (larger Q2) reveal more constituents, notably a sea of (tq ( q = u , d, s) pairs and gluons, qualitatively as expected on the basis of perturbative Q C D [2 ]. However, there are now two experimental indications that these non-na]'ve constituents are present already at large distances (small Q2). One indication comes from determinations of the ~ - N sigma term [31 ~2:
Work supported by the Department of Energy, contract DEAC03-76SF00515. 2 Address after 1 October 1988: School of Physics and Astronomy, Tel-AvivUniversity, 69978 Tel-Aviv,Israel. ~ Fora review see ref. [ 1]. ,2 Fora recent review see ref. [4]. 0 3 7 0 - 2 6 9 3 / 8 9 / $ 03.50 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division )
L"~N= ~(mu + m d ) ( P l ( ~ l u + d d ) ] p ) ,
(l)
which is a factor of about 2 larger than the value expected from the G e l l - M a n n - O k u b o mass formula and the assumption ( p [gslp) = 0 , motivated by the NQM. The value (1) of X ~N indicates instead that
[5] (Pl (gslp) (Pl ( ~ u + a d + g s ) l p )
~_0.21.
(2)
A second indication comes from the recent EMC m e a s u r e m e n t of deep inelastic polarized ~tp scattering [ 6 ], which indicates that [ 7 ] A s = --0.24_+0.07,
(3)
where (PIgYtYsslp) - 2 s / A s : As_=As- (c~s/2zc)AG [ 8 - 1 0 ] , where As is the fraction of the proton spin carried by strange quarks and antiquarks, and AG is 173
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the fraction of the proton spin carried by gluons ~3 In addition to these experimental facts, there are strong indications from lattice gauge theory ( L G T ) that quark loops are important in baryon physics. Hadron spectrum calculations done in an approximation where quark loops are neglected (the so-called "quenched" approximation) consistently obtain too big a ratio of m p / m o. More recently, attempts were made to compute the n - N sigma term in the quenched approximation [ 14,15 ]. These too, gave a value substantially smaller than the one obtained from n - N scattering~4. Given that quark loops, i.e. non-valence quarks, are important, we would like to know whether non-valence s quarks are roughly as important as the non-valence u and d. One might have expected some suppression of s quark loops relative to those of u and d, because rn~ >> mu,d. Phenomenologically, this suppression seems to be a moderate effect. Whenextracting ( m u + m a ) / m ~ f r o m m~mK 2 2 [17],it is usually assumed that the vacuum expectation values of all three flavors are roughly of the same magnitude,
(au)o~(ad)o~(gS)o.
(4)
QCD sum rules [18] and instanton liquid calculations [ 19 ] give (gS)o 0.sz
(5)
These estimates are supported indirectly by the consistency of (mu + md)/ms with the values of mu.a.s deduced from elsewhere, for example from baryon masses. Since ( p Igs [p ) represents the perturbation of (gs)o in the neighborhood of the proton, one could expect ( P l ~ s l P ) ~ (p[fm, a d l p ) if (5) holds. Thus the proton wave function seems to contain a significant fraction of gs pairs, even when probed at large distances (small Q2). Although a surprise for
~3 From now on, we shall drop the tildes on As etc. We note in passing that AG_~ 0 in one interpretation [ 11 ] of the Skyrme model [ 12 ]. (For the three flavor extension of the model see ref. [13].) ~4 See however ref. [ 16] for a recent discussion of experimental uncertainties in determining the a-term.
174
19 January 1989
the NQM ~5, the indications (2), (3) of strange quarks in the proton are expected in models based on approximate chiral symmetry, i,e. light quarks: mu,d,s<< AQCD. The Skyrme model, [ 12,13 ] which correctly reproduces the low-energy behavior of the QCD lagrangian in the limit of chiral symmetry, mu,d.s--'O, and a large number of colors, Nc--.oe, predicts [5] 0.23 for the right-hand side ofeq. (2). In addition, there are other model-independent predictions for the strange content of the proton, given by all chiral soliton theories of which the Skyrme model is the simplest representative. One such model-independent prediction is [ 20 ] Aura 4 g A ,
Ad=
-
3 , ~gA
AS =
--
l • ~gA
(6)
With gA = 1.25 taken from experiment ~6, (6) yields Au=0.71,
Ad=--0.54,
As=--0.18,
(7)
to be compared with the values [ 6 ] Au=0.73 +-0.07, As= --0.24+_0.07,
Ad=--0.52+_0.07, (8)
extracted from experiment [ 6 ]. The usual 1/Nc argument indicating that non-valence dlq pairs are suppressed in mesons [ 21,22 ] does not carry over immediately to baryon wave functions [23 ]. Quark-antiquark pairs are visualized as being generated by the splitting of gluons. In the 1~No expansion, baryons contain Arc quarks in a first approximation, and therefore the number ofgluon exchange diagrams is enhanced by O(N~) relative to their number in flq mesons. Color matching reduces this enhancement to O(Nc), a factor which carries over to the number of~lq pairs relative to their abundance in mesons. Gluons are enhanced relative to qq pairs by O(Nc) in both mesons and baryons ~7, indicating that neglecting gluons may not be a good initial ap~5 In the NQM language this means that the constituent quarks are objects which contain a substantial admixture of gs pairs. The traditional successes of the NQM, such as mass and magnetic moment calculations, remain unaffected by this fact. As we point out, however, there are experimental phenomena where the presence of ss pairs does make a difference. ~ We take gA from experiment since while (6) is a model-independent prediction, the value of gA is in general modeldependent. ~7 The same is also true in the vacuum, but this does not prevent the non-zero value of ( q q ) o from being important!
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PHYSICS LETTERS B
proximation to the baryon wave-function. Nevertheless, we still expect clq pairs to be O(Nc) more important in baryons than in mesons. The fact that the proton wave function contains gs pairs even at large distances (low Q2) implies that gs mesons can couple directly via connected diagrams to non-strange baryons, as in fig. 1a, thus evading the naYve form of the O k u b o - Z w e i g - I i z u k a ( O Z I ) rule [24], which implicitly assumes that such couplings can only occur via disconnected diagrams, as in fig. lb. Experimentally, the OZI rule is known to work well for m e s o n - m e s o n couplings, where it is theoreticallyj ustified by the 1/iV,, expansion. [21,22 ]. However, as argued above, this justification does not extend to meson-nucleon couplings and, as we will see, there are several published experimental claims to see violations of the OZI rule for m e s o n - n u c l e o n couplings. Most of the evidence for OZI evasion in m e s o n baryon couplings comes from lop annihilation both at rest and in flight. Several experiments have compared the rates for the OZI-forbidden process lop~ 0rt+rt and the OZI-allowed process lop-,o~Tt+:t -. The general conclusion has been that Rg-~r(lop--, 0n+~ )/cr(15p-,o~+~t - ) is larger than the ratio (7 _ 2 ) X 1 0 -3 [(1.5_+3:3×10 31 expected on the basis of the departure from ideal mixing in the 0 and co me-
19 January 1989
sons calculated using first-order SU (3) breaking in a quadratic (linear) mass formula. For example, ref. [25] finds that R g = ( 1 9 + _ 5 ) X l 0 -3 forpp = (0.70-0.76) GeV
(9)
after making a phas :-space correction. Ref. [ 25 ] also finds that the CM angle distribution of the 0 differs from that of the o, which has a small amount of forward-backward peaking ~s. Ref. [25] therefore claims that the OZI rule is violated in the reaction f)p--,07t+rt -, and finds an amplitude ratio < 0.05
~ A (pp~ss+X)__ A ( 1 5 p ~ u + X) + A (r)p-~dd+ X) <0.22
(10) that apparently violates the OZI rule, with the precise value of the ratio depending on the relative phase o f the amplitudes. Other measurements give R g = ( 1 5 _ + 3 ) X l 0 -3
(lla)
(ref. [26] ), Rg__ (19+v5)×10
3
(llb)
(ref. [27] ),
Rg= ( 3 0 +
7 ) × 10 --~
(1 lc)
(ref. [28 ] ),
Rg =
g u
g
,
u
m-
d
~
u
=
d
u
(a)
(I) f ' . . .
U
ud
---
J~ d
="=
U
(b)
Fig. 1. (a) A connected diagram coupling a gs meson (e.g. 0, f' ) to a non-strange baryon via non-valence ss quarks, thereby evading the OZI rule. (b) A disconnected OZI-forbidden diagram contributing to the same vertex.
(12_+~) × 10 -3
( 1ld)
(ref. [27] ), at 15 momenta of 0, 1.2, 2.3, 3.6 GeV, respectively, also indicating that the OZI rule appears to be violated (see also ref. [29 ] ). Although fewer data are available, there is also evidence of an apparent violation of the OZI rule in the reaction 1 5 n ~ 0 ( o ) + r t - . The data o f ref. [30] correspond to [ 31 ] P (15N--, 9~ - ) = ( 8.8 _+2.2 ) × 10- 4, whilst those o f ref. [32] correspond [31] to P ( p N _ , c 0 7 z - ) = ( 6 . 6 + l . 1 ) × l 0 3, leading to the estimate
R~ n - O'(0~-) a(ort- )
0.13.
(12)
This surprisingly large ratio should be checked and the related reactions !0p--, 0(c0)r~ ° also measured, to ~8 Later we will give a qualitative explanation of this feature. 175
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PHYSICS LETTERS B
confirm the apparently large deviation ( 12 ) from the OZI rule. There is also evidence for a deviation from the naive form of the OZI rule in 15p annihilation to f ' ( 1 5 2 5 ) + p i o n s , compared with f(1275) or A2(1275) +pions. Ref. [28 ] finds R~
a(f'rc+rt-) - ( 2 9 _ + { ' ) × 1 0 -3
a(flt+~-)
(13)
to be compared with the ( 1 - 2 ) × 10-3 which would be expected from the ratio F ( f ' - , T t + T t - ) / F ( f ---, n + r t - ) . Other experiments also find surprisingly many f' final states, a(PP--*f'rt+rt- ) ~ 0.43 a(pp~flt+Tt )
14a)
(ref. [33] ), a(13P~ f'r~°) ~0.064 a (f)p--, ( f + A2)X ° )
14b)
(ref. [34] ), a(13P--+f'r~°) ~ 8 . 6 X 10 -3 a(pp-~A~ 7t-+)
(14c)
(ref. [ 34 ] ), indicating that the naWe OZI rule is also inapplicable to tensor meson couplings to baryons, possibly even to a greater extent than for vector mesons. On the other hand, the ratio of forward 7 z - p - , V n cross-sections, R; = a(Tt-p--,0n)/a(=-p--+mn) = (3.2+_0.4)X10 -3 at p = = 6 GeV [35], is in agreement with the OZ! rule and the expected deviation from ideal mixing ~9. Moreover, the natural spin-parity exchange ( N E X ) amplitudes for r t - p - , 0 n and mn have similar t-dependences, suggesting that the N E X m e s o n - m e s o n - r e g g e o n vertices obey the OZI rule, as expected. However, at lower energies [ 38-40] there is a relative enhancement of R~ since a(n-p--+Qn) falls more rapidly with p= than does a(rt-p--+t0n), and production has a broader t-distribution than does production. These observations are consistent with the appearance at lower energies o f subleading pieces ~gThere are also measurements of R~,=-a(n-p-*nOp)/ a(n-p-~nop)=(6_+3_+2)×10 -3 at p~=10 GeV, [36] and R'~.o~- a(n-p---}n+n-n-gp)/a(n p~n+~-n-cop) =5+_~X 10 - 3 at p== 19 GeV [37], which are also in agreement with the OZI rule. 176
19 January 1989
in the amplitude which evade the OZI rule and could be associated with baryonic vertices. More evidence against the naive OZI rule comes from p p - , p p ( 0 or m)nrt reactions. One experiment at p v = 2 4 GeV finds [41 ]
P a(pP-*pPg, ppO(~+rc- ), ppO ( ~ % z - ) 2 ) a(pp--,ppo, ppm (~+rt - ), ppm(n+rt - )2) =(19+7)X10
-3 ,
(15)
while another experiment at pp = 10 GeV finds [ 36 ] O )) = ( 2 0 +-9 + 8 ) X 1 0 R ~ = aa (( pP pP ~~ pP pPm
-3
(16)
The former experiment [41 ] indeed claims on the basis of a comparison between the ratio ( 16 ) and the corresponding ratio for incident pions that "... ~ is produced also from strange quarks in the incident particle, with protons containing more ~s pairs than pions". In addition to the above pieces of evidence that the naive OZI rule is violated in m e s o n - b a r y o n cou-
$ p
d,
.
K"
~'
~s= ,%
tl K"
(a)
~ d
ig-- O, (,... d
(hi Fig. 2. (a) A connected diagram contributing to a backward peak in the region 0p-+K-K + via non-valence ss quarks. (b) A connected diagram contributing to the reaction pp-~ (0 or f' )Tt+r~- .
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PHYSICS LETTERS B
plings, there is another indication from I)p annihilation that baryons contain significant numbers of gs pairs. A backward peak has been observed [42] in the reaction p p - , K + K - at pp ~0.5 GeV. It is not present at lower momenta, where only a few direct channel partial waves contribute, and disappears at higher momenta where non-exotic t-channel exchanges are expected to dominate. The appearance of this backward peak is prima facie evidence of a direct p ~ K - coupling, which is forbidden in the NQM model, where p = luud), K = Isa), but is allowed if the proton wavefunction contains gs pairs, as seen in fig. 2a. This coupling is related by crossing to the exotic channel K+p--,Z *. Despite the recent appearance of two partial wave analyses [43] agreeing on the presence ofa P l3 r e s o n a n c e in K+p scattering, the Particle Data Group [44] does not recognize the evidence for any Z* resonance. Instead, it comments that "the results permit no definite conclusion - the same story heard for 15 years" and "the general prejudice against baryons not made of three quarks (...) make it likely that it will be another 15 years before the issue is decided". However, exotic states such as the Z* are predicted by the Skyrme model [45 ]. Since their existence goes against the general prejudice so well reflected by ref. [ 44 ], they have historically been regarded as rather embarrassing for the model. Perhaps the boot should now be on other foot. After this review of the experimental indications that the na'fve OZI rule is indeed inapplicable to baryons, we now make some quantitative estimates of OZl-evading meson-baryon couplings. O - + mesons. Their couplings to baryons are related by PCAC and the Goldberger-Treiman relation to the baryonic matrix elements of axial currents. We know from experiment [ 6 ] and the Skyrme [20] model that A s ¢ 0 (see eq. (3)) (a prima facie breach of the na]'ve OZI rule) and A u + A d + A s - ~ 0 (see eq. (8)). We therefore predict [20] that gnopp-~0 ,
(17)
where rlo
19 January 1989
can be estimated. Pseudoscalar meson loop corrections, which are of next-to-leading order in 1/Arc, do not alter the predictions that A u + A d + A s = 0 and gnovp = 0, but possible other 1/Arc corrections cannot be excluded at this time. Chiral symmetry breaking may explain why the physical pseudoscalar q and T1' are mixtures ofrls and rio with a mixing angle 0 of 10 ° to 20 °. Taking, for example, 0_~ 14 ° as suggested by a first-order analysis ofchiral symmetry breaking, we find [20] gn' op -
-
-~tan 0-~0.25,
(18)
gr]pp
which is not in conflict with experiment, but should not be taken as a very reliable estimate. l - mesons. These mesons' couplings are usually related to the zero-momentum-transfer (Q2 = 0) matrix elements of vector currents by the vector meson dominance (VMD) hypothesis [46 ]. We know that ( p ] gT~s]p ) = 0 at Q2 = 0, because it measures the net strangeness of the proton I
#(s)- #g-= fdx [s(x)-g(x)l=0,
(19)
0
(where s (x) and g(x) are patton densities for strange quarks and anti-quarks) which vanishes because of the proton's net quantum numbers. It follows from (19) and VMD that g, pp = O.
(20)
Therefore, exceptionally, the OZI rule works for this and other elastic 0-baryon couplings. However, naive VMD is not directly applicable to inelastic form factors and therefore in general one could expect that the inelastic coupling g0pN* ¢ 0
(21)
for any baryon resonance N *. The vanishing ofg0p p (20), whereas go,pp ¢ 0, indicates that the angular distribution of the 0 in pp-~0rc+~ - should not be peaked forward-backward in the same way as the o in pp-~0r~+~ - (as seen by experiment [251). However, since inelastic couplings (21) do not vanish in general, we would expect R g ~ c ~ ( p p - ~ t ~ + T r - ) / a(15p~0~+~- ) to be larger than the OZI expectation 177
Volume 217, number 1,2
PHYSICS LETTERSB
of a few × 10 -3 (as also seen by experiment (9), (11 ) [25-28]. A sample diagram enhancing Rg is shown in fig. 2b. The value of R~(~+~_),, should also be enhanced (as observed (15), (16) [ 41 ] ), whereas we would expect R~+~-),, to be given by the OZI rule for 0 mesons in the beam fragmentation region (as observed) [37 ] ), but larger in the target fragmentation region (for which data are not available). The nonzero inelastic vertices goON* may also explain why a ( x - p ~ ¢)n ) / a ( x - p--, con) is seen to exceed the OZl expectation at low energies [38,39]. On the other hand, since the 11o should not couple even inelastirally to baryons, we expect no such low energy enhancement for a ( ~ - p - ~ r l ' n ) / a ( x - p - ~ r l n ) (as seen by experiment [47,48 ] ). 0 + + m e s o n s . The NQM assignments of the known scalars are obscure, and the theoretical possibility exists of substantial mixing between ~lq, ¢tq~lq and gluonium states. In principle, by analogy with VMD, one can use scalar meson dominance (SMD) of the Q2= 0 matrix elements of gs, uu and dd densities between protons and the x-N o-term information (2) or the Skyrme model to infer that go +,~go + = 0.38
(o-term) ,
=7x/2/23-~0.43
(Skyrme),
(22)
where here and subsequently we denote the gs member of a meson nonet by a prime (0 + +', 1+ + ', etc. ) while the I = 0 non-strange member is unprimed. However, the above-mentioned phenomenological uncertainties seem to preclude any clear test of this potentially large deviation from the naive OZI rule. 1 + + mesons. The analogue of the previous PCAC, VMD and SMD hypotheses would be to suppose (AMD) that axial mesons dominate the Q : = 0 matrix elements of the transverse components of the corresponding axial currents. The previous analysis [ 20 ] of axial current matrix elements combined with AMD suggests that gl++,ffp=--xf2gl++pp
•
(23)
Even if this result is correct, its implications for the physical isoscalar D and E mesons are unclear, since their mixing pattern is not known. We quote below predictions based on (23) for different possible mixing patterns, 178
19 January 1989 0
(singlet/octet),
= - ~
(ideal mixing) ,
=-0.68
(ref. [ 4 9 ] ) .
gEpJgDpp=
(24)
It should be noted that the E meson first seen in I)P annihilation was identified as O - +, and can probably be identified with the t seen subsequently in radiative J/u] decay. The fact that the D meson has been seen in lbp annihilation but not the 1+ + E meson might be taken as evidence against ideal mixing, if the predictions (24) are to be believed. At least the possibility of apparently OZbviolating couplings to baryons should not be neglected in future D and E phenomenology. 2 + + m e s o n s . For these and higher-spin mesons we propose a weakened form of the previous meson dominance hypotheses, namely that the ratios of spinJ gs(J' ), I--0 (~tu + d d ) / x ~ (J) and I = 1 (uu - d d ) / ~ (Jr) meson couplings to baryons are equal to the ratios of the corresponding matrix elements of local spin-J operators at Q2=0, e.g. ( p [gT, D~s [p ) etc. for spin 2. These matrix elements are in turn related in the parton model to the ( J - 1 ) th moments of parton distributions in baryons:
gJ' pp : g.If~p :gJI pp I = f dXXJ-I[S(X)"}-(--1)Jg(x)] 0 1 : f dxxJ-~
0 ×{[u(x)+d(x)] + (- 1)J[o(x)+d(x)]}/x/2
: i d x xJ I 0
x { [ (u(x) - d ( x ) ] + ( - 1 ),'[~ (x) - a ( x ) ] } / ~ 2 . (25) This Ansatz enables us to calculate gf, pp/gfpp and appropriate set of deep inelastic structure functions. Table 1 shows values of g f ' p p / g c p p a n d gA2pp/gfpp calculated using the Duke and Owens [50] and Eichten, Hinchliffe, Lane and Quigg [ 51 ] parton distributions. We see that
gA2pp/gfPp, given an
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PHYSICS LETTERS B
Table 1 Values of~/.pp/~,,pp and gJIpp/gJpp for J = 2 and J=4, calculated using eq. (25) and the distributions of refs. [ 50,51 ] with Q 2= 6 GeV 2 and A=200 MeV. These numbers do not change qualitatively if Q2 is taken as 10 GeV z, or ifA is increased by between 100 and 200 MeV. Distribution DO [50] EHLQ [51]
gfpp
gA2pp
gt~p
gfpp
g4pp g4pp
g4,pp g41~p
0.145 0.057
0.249 0.391
0.027 0.010
0.451 0.557
gfPP 20.10_____0.05, grpp
gA2pp ~ 0 . 3 2 _ + 0 . 0 8
.
(26)
grpp
T h e s e p r e d i c t i o n s c o u l d be tested in OP a n n i h i l a t i o n , b a c k w a r d m e s o n p r o d u c t i o n in ~p collisions, and in pp collisions. B e c a u s e the elastic f'lSp c o u p l i n g does not vanish, u n l i k e the elastic OPP coupling, there m i g h t be f o r w a r d - b a c k w a r d p e a k i n g in I~P--" f' 7r+ 7r-, s i m i l a r to that e x p e c t e d for l~p~ f~+Tr - a n d that seen in 1Op-~c0~+r~ - ( b u t not f ) p - , ~ ) n + ~ - ) . C e r t a i n l y we e x p e c t R p to be larger t h a n e x p e c t e d f r o m the O Z I rule (as seen by e x p e r i m e n t [ 2 8 , 3 3 , 3 4 ] ). 3 - m e s o n s . A c c o r d i n g to the general f o r m u l a ( 2 5 ) , t h e i r c o u p l i n g s to b a r y o n s should be p r o p o r tional to the m o m e n t s f~ d x x 2 [ s ( x ) - g ( x ) ] etc .... It is n o r m a l l y a s s u m e d that the s a n d s d i s t r i b u t i o n s h a v e the s a m e shape, but there is no r i g o r o u s reason w h y this s h o u l d be so: all o n e k n o w s is that f~ cL~ s ( x ) = f~ cbc g ( x ) . In principle, a d i f f e r e n c e bet w e e n s ( x ) a n d g ( x ) c o u l d be seen in the n e u t r i n o p r o d u c t i o n o f c h a r m , but p r a c t i c e t h e y are difficult to d i s e n t a n g l e with sufficient a c c u r a c y f r o m the c o m peting d(x) [d(x) ] distributions. 4 ++ m e s o n s . P r e d i c t i o n s for t h e i r c o u p l i n g s to b a r y o n s are also g i v e n in table 1. H o w e v e r , since o n l y one I = 0 4 ++ m e s o n has b e e n i d e n t i f i e d so far, [44] n a m e l y the h ( 2 0 3 0 ) w h i c h is p r e s u m a b l y p r e d o m i n a n t l y non-strange, it is not yet possible to test the p r e d i c t e d m a g n i t u d e o f the O Z I - v i o l a t i n g 4 + + ' - b a r yon coupling. We c o n c l u d e this p a p e r w i t h a few c o m m e n t s on g l u o n i u m searches in processes with i n c i d e n t baryons. T h e fact that m e s o n c o u p l i n g s to b a r y o n s violate the O Z I rule m e a n s that the o b s e r v a t i o n o f a reso n a n c e in an O Z l - f o r b i d d e n c h a n n e l d o e s not necessarily m e a n that it is a g l u o n i u m state. It c o u l d
19 January 1989
be an excited gs state. T h i s c a u t i o n applies in particular to the Q0 r e s o n a n c e s r e p o r t e d in ref. [ 52 ]. We t h a n k Y. F r i s h m a n , H. Fritzsch, H. Harari, R. L a n d u a and L. M o n t a n e t for useful discussions. N o t e a d d e d . By analogy with the n o n - z e r o gs content o f the p r o t o n , we expect a n o n - z e r o flu a n d dd c o n t e n t in the f 2 - a n d its e x c i t e d states. We t h e r e f o r e expect that f2 c o u p l i n g s to n o n - s t r a n g e m e s o n s will also a p p e a r to v i o l a t e the O Z I rule. In particular, we w o u l d expect f ~ * - ~ f 2 - + p i o n s decays not to be O Z I suppressed by c o m p a r i s o n with f 2 - - , E K T r decays. T h e recent o b s e r v a t i o n [53] o f a state f 2 " - ( 2 . 4 7 G e V ) ~ f2 + ~ + ~ - with a n o r m a l h a d r o n i c w i d t h ~ 70 M e V is c o n s i s t e n t with o u r e x p e c t a t i o n s .
References [ I ] J.J.J. Kokkedee, The quark model (Benjamin, New York, 1969). [2]T. Sloan, G. Smadja and R. Voss, Phys. Rep. 162 (1988) 45. [3] T.P. Cheng and R.F. Dashen, Phys, Rev. Lett. 26 (1971) 594; T.P. Cheng, Phys. Rev. D 13 (1976) 2161. [4]J. Gasser, H. Leutwyler, M.P, Locher, and M.E. Sainio, Bern-SIN preprint BUTP-88/13-BERN, SIN-PR-88-13; T.P. Cheng, IAS Princeton preprint IASSNS/HEP-88/22 (May 1988). [5]J.F. Donoghue and C.R. Nappi, Phys. Lett. B 168 (1986) 105; J.F. Donoghue, Invited talk 2nd Intern. Conf. on nN physics (Los Alamos, NM, August 1987). [6] EM Collab. J. Ashman et al., Phys. Lett. B 206 (1988) 364. [ 7] J. Ellis, R. Flores and S. Ritz, Phys. Len. B 198 ( 1987 ) 393; M. Gliick and E. Reya, Dortmund preprint DO-TH-87/14 (August 1987). [8] A.V. Efremov and O.V. Teryaev, Dubna preprint, JIN-E288-287, submitted to Miinich Conf. (1988). [9] G. Altarelli and G. Ross, Phys. Lett. B 212 (1988) 391. [10] R.D. Carlitz, J.C. Collins and A.H. Mueller, PittsburghIllinois-Tech-Columbia preprint (August 1988). [ 11 ] J. Ellis and M. Karliner, Phys. Lett. B 213 ( 1988 ) 73. [12] E. Witten, Nucl. Phys. B 223 (1983) 422, 433; G. Adkins, C. Nappi and E. Winen, Nucl. Phys. B 228 (1983) 433. [13] E. Guadagnini, Nucl. Phys. 236 (1984) 35; P.O. Mazur, M.A. Nowak and M. Praszotowicz, Phys. Lett. B 147 (1984) 137. [ 14] L. Maiani, G. Martinelli, M. Paciello and B. Taglienti, Nucl. Phys. B 293 (1987) 420. 179
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[ 15 ] S. Gtisken, K. Shilling, R. Sommer, K.-H. Mutter and A. Patel, CERN preprint CERN-TH-5027/88 (July 1988 ). [16]M.P. Locher and M.E. Sainio, Paul Scherrer Institute preprint PR-88-17. [ 17 ] J. Gasser and H. Leutwyler, Phys. Rep. 87 ( 1982 ) 77. [ 18] S. Narrison and E. De Rafael, Phys. Lett. B 103 ( 1981 ) 57; P. Pascual and R. Tarrach, Phys. Left. B 116 (1982) 443; B.L. Ioffe, Nucl. Phys. B 188 (1981) 317, B 191 (1981) 591; B.L. Ioffe and V.M. Belyaev, Sov. Phys. JETP 83 (1982) 876; L.J. Reinders, H.R. Rubinstein and S. Yazaki, Phys. Lett. B 120 (1983) 209. [ 19 ] E.V. Shuryak, Novosibirsk preprint IYF-88-49 (June 1988 ). [20] S. Brodsky, J. Ellis and M. Karliner, Phys. Lett. B 206 (1988) 309. [ 21 ] G. 't Hooft, Nucl. Phys. B 72 ( 1974 ) 461, B 75 (1974) 461, [22] G. Veneziano, Nucl, Phys. B 117 (1976) 519. [ 23 ] E. Witten, Nucl. Phys. B 160 ( 1979 ) 57. [24] S. Okubo, Phys. Lett. B 5 (1963) 165; G. Zweig, CERN Report No. 8419/TH412 (1964) unpublished; I. Iuzuka, Prog. Theor. Phys. Suppl. 37, 38 (1966) 21. [25 ] Bombay-CERN-College de France-Madrid Collab., A.M. Cooper et al., Nucl. Phys. B 146 ( 1978 ) 10. [26] R. Bizzari el al., Nucl. Phys. B 14 (1969) 169. [27] R.A. Donald et al., Phys. Lett. B 61 (1976) 210. [28] C.K. Chen et al., Nucl. Phys. B 130 (1977) 269. [29] C. Amsler, CERN preprint C E R N / E P 86-178 (November 1986); rapporteur's talk VIIlth European Symp. on Nucleon-nucleon interactions (Thessaloniki, Greece, September 1986). [30] L. Gray et al., Phys. Lett. 17 (1966) 901. [ 31 ] L. Montanet, private communication ( 1988 ). [32] R. Bizzarri et al., Phys. Rev. Lett. 25 (1970) 1385,
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[ 33 ] V. Vuillemin et al., Nuovo Cimento 33A (1976) 133. [34]Bombay-CERN-College de France-Pisa Collab., S.N. Ganguli et al., Nu¢l. Phys. B 183 (1981) 295. [35] D. Cohen et al., Phys. Rev. Lett. 38 (1977) 269. [36] R. Baldi et al., Phys. Lett B 68 (1977) 331. [37] The Omega Groups, P.L. Woodworth et al., Phys. Lett. B 65 (1976) 89. [38] R.H. Davies et al., Phys. Rev. D 2 (1970) 506; J.S. Dansburg et al., Phys. Rev. D 2 (1970) 2564. [39] D.S. Ayres, Phys. Rev. Lett. 32 (1974) 1463. [ 40 ] E.L. Berger and C. Sorensen, Phys. Lett. B 62 ( 1976 ) 303. [41 ] V. Blobel et al., Phys. Lett. B 59 (1975) 88. [42] T. Tanimori et al., Phys. Rev. Lett. 55 (1985) 1835. [43] K. Hashimoto, Phys. Rev. C 29 (1984) 1377; R.A. Arndt and L.D. Roper, Phys. Rev. D 31 ( 1985 ) 2230. [44] Particle Data Group, M. Aguilar-Benitez et al., Review of particle properties, Phys. Lett. B 170 (1986) 1. [45 ] M, Karliner and M. Mattis, Phys. Rev. D 34 (1986) 1991. [46 ] J.J. Sakurai, Currents and mesons (University of Chicago Press, Chicago, 1969 ). [47] N.R. Stanton et al., Phys. Lett. B 92 (1980) 353. [48] W.D. Apel et al., Phys. Left. B 40 (1972 ) 680; B 46 (1973) 459;B 83 (1979) 131. [49] A. Seiden, H.F.-W. Sadrozinski and H.E. Haber, Phys. Rev. D38 (1988) 824. [ 50 ] D.W. Duke and J.F. Owens, Phys. Rev. D 30 (1984) 49. [51 ] E. Eichten, I. Hincbliffe, K. Lane and C. Quigg, Rev. Mod. Phys. 56 (1984) 579. [ 52 ] A. Etkin et al., Phys. Rev. Lett. 49 ( 1982 ) 1620; Phys. Lett. B 165 (1985) 217; Brookhaven preprint BNL-40716 (December 1987); S.J. Lindenbaum and R.S. Longacre, Phys. Lett. B 165 (1985) 202: D. Aston et al., Phys. Lett. B 215 (1988) 799.
PHYSICS LETTERS B
19 January 1989
THE OZI RULE DOES NOT APPLY TO BARYONS John ELLIS CERN, CH- I 211 Geneva 23, Switzerland Erwin G A B A T H U L E R Physics Department, University of Liverpool, Liverpool L69 3BX, UK and Marek K A R L I N E R J,2 SLAC, Stanford, CA 94309, USA Received 28 October 1988
Determinations of the x-N a-term and the EMC measurement of deep inelastic polarized i.tp scattering and various theoretical arguments indicate that baryons contain a significant number of strange quark-antiquark pairs. Their presence gives rise to additional connected diagrams which evade the Okubo-Zweig-Iizuka (OZI) rule for meson-baryon couplings, and explain the apparent violation of the OZI rule seen in the reaction pp~0~+x - as well as the process pp~pp0 + pions, and the backward peak seen in pp~K+K -. We catalogue predictions, based on moments of deep inelastic structure functions, for the OZI-evadingcouplings to baryons of 0-+, 0+ +, and 2 + + and other mesons. Processes where these predictions can be tested include backward meson production in x-N scattering as well as pp annihilation and pp scattering.
According to the Naive Quark Model ( N Q M ) ~ the proton wave function contains just two u quarks and one d quark. This model gives a good general picture o f h a d r o n structure at large distances (small mom e n t u m transfers Q2), while probes of shorter distance (larger Q2) reveal more constituents, notably a sea of (tq ( q = u , d, s) pairs and gluons, qualitatively as expected on the basis of perturbative Q C D [2 ]. However, there are now two experimental indications that these non-na]'ve constituents are present already at large distances (small Q2). One indication comes from determinations of the ~ - N sigma term [31 ~2:
Work supported by the Department of Energy, contract DEAC03-76SF00515. 2 Address after 1 October 1988: School of Physics and Astronomy, Tel-AvivUniversity, 69978 Tel-Aviv,Israel. ~ Fora review see ref. [ 1]. ,2 Fora recent review see ref. [4]. 0 3 7 0 - 2 6 9 3 / 8 9 / $ 03.50 © Elsevier Science Publishers B.V. ( N o r t h - H o l l a n d Physics Publishing Division )
L"~N= ~(mu + m d ) ( P l ( ~ l u + d d ) ] p ) ,
(l)
which is a factor of about 2 larger than the value expected from the G e l l - M a n n - O k u b o mass formula and the assumption ( p [gslp) = 0 , motivated by the NQM. The value (1) of X ~N indicates instead that
[5] (Pl (gslp) (Pl ( ~ u + a d + g s ) l p )
~_0.21.
(2)
A second indication comes from the recent EMC m e a s u r e m e n t of deep inelastic polarized ~tp scattering [ 6 ], which indicates that [ 7 ] A s = --0.24_+0.07,
(3)
where (PIgYtYsslp) - 2 s / A s : As_=As- (c~s/2zc)AG [ 8 - 1 0 ] , where As is the fraction of the proton spin carried by strange quarks and antiquarks, and AG is 173
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the fraction of the proton spin carried by gluons ~3 In addition to these experimental facts, there are strong indications from lattice gauge theory ( L G T ) that quark loops are important in baryon physics. Hadron spectrum calculations done in an approximation where quark loops are neglected (the so-called "quenched" approximation) consistently obtain too big a ratio of m p / m o. More recently, attempts were made to compute the n - N sigma term in the quenched approximation [ 14,15 ]. These too, gave a value substantially smaller than the one obtained from n - N scattering~4. Given that quark loops, i.e. non-valence quarks, are important, we would like to know whether non-valence s quarks are roughly as important as the non-valence u and d. One might have expected some suppression of s quark loops relative to those of u and d, because rn~ >> mu,d. Phenomenologically, this suppression seems to be a moderate effect. Whenextracting ( m u + m a ) / m ~ f r o m m~mK 2 2 [17],it is usually assumed that the vacuum expectation values of all three flavors are roughly of the same magnitude,
(au)o~(ad)o~(gS)o.
(4)
QCD sum rules [18] and instanton liquid calculations [ 19 ] give (gS)o 0.sz
(5)
These estimates are supported indirectly by the consistency of (mu + md)/ms with the values of mu.a.s deduced from elsewhere, for example from baryon masses. Since ( p Igs [p ) represents the perturbation of (gs)o in the neighborhood of the proton, one could expect ( P l ~ s l P ) ~ (p[fm, a d l p ) if (5) holds. Thus the proton wave function seems to contain a significant fraction of gs pairs, even when probed at large distances (small Q2). Although a surprise for
~3 From now on, we shall drop the tildes on As etc. We note in passing that AG_~ 0 in one interpretation [ 11 ] of the Skyrme model [ 12 ]. (For the three flavor extension of the model see ref. [13].) ~4 See however ref. [ 16] for a recent discussion of experimental uncertainties in determining the a-term.
174
19 January 1989
the NQM ~5, the indications (2), (3) of strange quarks in the proton are expected in models based on approximate chiral symmetry, i,e. light quarks: mu,d,s<< AQCD. The Skyrme model, [ 12,13 ] which correctly reproduces the low-energy behavior of the QCD lagrangian in the limit of chiral symmetry, mu,d.s--'O, and a large number of colors, Nc--.oe, predicts [5] 0.23 for the right-hand side ofeq. (2). In addition, there are other model-independent predictions for the strange content of the proton, given by all chiral soliton theories of which the Skyrme model is the simplest representative. One such model-independent prediction is [ 20 ] Aura 4 g A ,
Ad=
-
3 , ~gA
AS =
--
l • ~gA
(6)
With gA = 1.25 taken from experiment ~6, (6) yields Au=0.71,
Ad=--0.54,
As=--0.18,
(7)
to be compared with the values [ 6 ] Au=0.73 +-0.07, As= --0.24+_0.07,
Ad=--0.52+_0.07, (8)
extracted from experiment [ 6 ]. The usual 1/Nc argument indicating that non-valence dlq pairs are suppressed in mesons [ 21,22 ] does not carry over immediately to baryon wave functions [23 ]. Quark-antiquark pairs are visualized as being generated by the splitting of gluons. In the 1~No expansion, baryons contain Arc quarks in a first approximation, and therefore the number ofgluon exchange diagrams is enhanced by O(N~) relative to their number in flq mesons. Color matching reduces this enhancement to O(Nc), a factor which carries over to the number of~lq pairs relative to their abundance in mesons. Gluons are enhanced relative to qq pairs by O(Nc) in both mesons and baryons ~7, indicating that neglecting gluons may not be a good initial ap~5 In the NQM language this means that the constituent quarks are objects which contain a substantial admixture of gs pairs. The traditional successes of the NQM, such as mass and magnetic moment calculations, remain unaffected by this fact. As we point out, however, there are experimental phenomena where the presence of ss pairs does make a difference. ~ We take gA from experiment since while (6) is a model-independent prediction, the value of gA is in general modeldependent. ~7 The same is also true in the vacuum, but this does not prevent the non-zero value of ( q q ) o from being important!
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proximation to the baryon wave-function. Nevertheless, we still expect clq pairs to be O(Nc) more important in baryons than in mesons. The fact that the proton wave function contains gs pairs even at large distances (low Q2) implies that gs mesons can couple directly via connected diagrams to non-strange baryons, as in fig. 1a, thus evading the naYve form of the O k u b o - Z w e i g - I i z u k a ( O Z I ) rule [24], which implicitly assumes that such couplings can only occur via disconnected diagrams, as in fig. lb. Experimentally, the OZI rule is known to work well for m e s o n - m e s o n couplings, where it is theoreticallyj ustified by the 1/iV,, expansion. [21,22 ]. However, as argued above, this justification does not extend to meson-nucleon couplings and, as we will see, there are several published experimental claims to see violations of the OZI rule for m e s o n - n u c l e o n couplings. Most of the evidence for OZI evasion in m e s o n baryon couplings comes from lop annihilation both at rest and in flight. Several experiments have compared the rates for the OZI-forbidden process lop~ 0rt+rt and the OZI-allowed process lop-,o~Tt+:t -. The general conclusion has been that Rg-~r(lop--, 0n+~ )/cr(15p-,o~+~t - ) is larger than the ratio (7 _ 2 ) X 1 0 -3 [(1.5_+3:3×10 31 expected on the basis of the departure from ideal mixing in the 0 and co me-
19 January 1989
sons calculated using first-order SU (3) breaking in a quadratic (linear) mass formula. For example, ref. [25] finds that R g = ( 1 9 + _ 5 ) X l 0 -3 forpp = (0.70-0.76) GeV
(9)
after making a phas :-space correction. Ref. [ 25 ] also finds that the CM angle distribution of the 0 differs from that of the o, which has a small amount of forward-backward peaking ~s. Ref. [25] therefore claims that the OZI rule is violated in the reaction f)p--,07t+rt -, and finds an amplitude ratio < 0.05
~ A (pp~ss+X)__ A ( 1 5 p ~ u + X) + A (r)p-~dd+ X) <0.22
(10) that apparently violates the OZI rule, with the precise value of the ratio depending on the relative phase o f the amplitudes. Other measurements give R g = ( 1 5 _ + 3 ) X l 0 -3
(lla)
(ref. [26] ), Rg__ (19+v5)×10
3
(llb)
(ref. [27] ),
Rg= ( 3 0 +
7 ) × 10 --~
(1 lc)
(ref. [28 ] ),
Rg =
g u
g
,
u
m-
d
~
u
=
d
u
(a)
(I) f ' . . .
U
ud
---
J~ d
="=
U
(b)
Fig. 1. (a) A connected diagram coupling a gs meson (e.g. 0, f' ) to a non-strange baryon via non-valence ss quarks, thereby evading the OZI rule. (b) A disconnected OZI-forbidden diagram contributing to the same vertex.
(12_+~) × 10 -3
( 1ld)
(ref. [27] ), at 15 momenta of 0, 1.2, 2.3, 3.6 GeV, respectively, also indicating that the OZI rule appears to be violated (see also ref. [29 ] ). Although fewer data are available, there is also evidence of an apparent violation of the OZI rule in the reaction 1 5 n ~ 0 ( o ) + r t - . The data o f ref. [30] correspond to [ 31 ] P (15N--, 9~ - ) = ( 8.8 _+2.2 ) × 10- 4, whilst those o f ref. [32] correspond [31] to P ( p N _ , c 0 7 z - ) = ( 6 . 6 + l . 1 ) × l 0 3, leading to the estimate
R~ n - O'(0~-) a(ort- )
0.13.
(12)
This surprisingly large ratio should be checked and the related reactions !0p--, 0(c0)r~ ° also measured, to ~8 Later we will give a qualitative explanation of this feature. 175
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confirm the apparently large deviation ( 12 ) from the OZI rule. There is also evidence for a deviation from the naive form of the OZI rule in 15p annihilation to f ' ( 1 5 2 5 ) + p i o n s , compared with f(1275) or A2(1275) +pions. Ref. [28 ] finds R~
a(f'rc+rt-) - ( 2 9 _ + { ' ) × 1 0 -3
a(flt+~-)
(13)
to be compared with the ( 1 - 2 ) × 10-3 which would be expected from the ratio F ( f ' - , T t + T t - ) / F ( f ---, n + r t - ) . Other experiments also find surprisingly many f' final states, a(PP--*f'rt+rt- ) ~ 0.43 a(pp~flt+Tt )
14a)
(ref. [33] ), a(13P~ f'r~°) ~0.064 a (f)p--, ( f + A2)X ° )
14b)
(ref. [34] ), a(13P--+f'r~°) ~ 8 . 6 X 10 -3 a(pp-~A~ 7t-+)
(14c)
(ref. [ 34 ] ), indicating that the naWe OZI rule is also inapplicable to tensor meson couplings to baryons, possibly even to a greater extent than for vector mesons. On the other hand, the ratio of forward 7 z - p - , V n cross-sections, R; = a(Tt-p--,0n)/a(=-p--+mn) = (3.2+_0.4)X10 -3 at p = = 6 GeV [35], is in agreement with the OZ! rule and the expected deviation from ideal mixing ~9. Moreover, the natural spin-parity exchange ( N E X ) amplitudes for r t - p - , 0 n and mn have similar t-dependences, suggesting that the N E X m e s o n - m e s o n - r e g g e o n vertices obey the OZI rule, as expected. However, at lower energies [ 38-40] there is a relative enhancement of R~ since a(n-p--+Qn) falls more rapidly with p= than does a(rt-p--+t0n), and production has a broader t-distribution than does production. These observations are consistent with the appearance at lower energies o f subleading pieces ~gThere are also measurements of R~,=-a(n-p-*nOp)/ a(n-p-~nop)=(6_+3_+2)×10 -3 at p~=10 GeV, [36] and R'~.o~- a(n-p---}n+n-n-gp)/a(n p~n+~-n-cop) =5+_~X 10 - 3 at p== 19 GeV [37], which are also in agreement with the OZI rule. 176
19 January 1989
in the amplitude which evade the OZI rule and could be associated with baryonic vertices. More evidence against the naive OZI rule comes from p p - , p p ( 0 or m)nrt reactions. One experiment at p v = 2 4 GeV finds [41 ]
P a(pP-*pPg, ppO(~+rc- ), ppO ( ~ % z - ) 2 ) a(pp--,ppo, ppm (~+rt - ), ppm(n+rt - )2) =(19+7)X10
-3 ,
(15)
while another experiment at pp = 10 GeV finds [ 36 ] O )) = ( 2 0 +-9 + 8 ) X 1 0 R ~ = aa (( pP pP ~~ pP pPm
-3
(16)
The former experiment [41 ] indeed claims on the basis of a comparison between the ratio ( 16 ) and the corresponding ratio for incident pions that "... ~ is produced also from strange quarks in the incident particle, with protons containing more ~s pairs than pions". In addition to the above pieces of evidence that the naive OZI rule is violated in m e s o n - b a r y o n cou-
$ p
d,
.
K"
~'
~s= ,%
tl K"
(a)
~ d
ig-- O, (,... d
(hi Fig. 2. (a) A connected diagram contributing to a backward peak in the region 0p-+K-K + via non-valence ss quarks. (b) A connected diagram contributing to the reaction pp-~ (0 or f' )Tt+r~- .
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PHYSICS LETTERS B
plings, there is another indication from I)p annihilation that baryons contain significant numbers of gs pairs. A backward peak has been observed [42] in the reaction p p - , K + K - at pp ~0.5 GeV. It is not present at lower momenta, where only a few direct channel partial waves contribute, and disappears at higher momenta where non-exotic t-channel exchanges are expected to dominate. The appearance of this backward peak is prima facie evidence of a direct p ~ K - coupling, which is forbidden in the NQM model, where p = luud), K = Isa), but is allowed if the proton wavefunction contains gs pairs, as seen in fig. 2a. This coupling is related by crossing to the exotic channel K+p--,Z *. Despite the recent appearance of two partial wave analyses [43] agreeing on the presence ofa P l3 r e s o n a n c e in K+p scattering, the Particle Data Group [44] does not recognize the evidence for any Z* resonance. Instead, it comments that "the results permit no definite conclusion - the same story heard for 15 years" and "the general prejudice against baryons not made of three quarks (...) make it likely that it will be another 15 years before the issue is decided". However, exotic states such as the Z* are predicted by the Skyrme model [45 ]. Since their existence goes against the general prejudice so well reflected by ref. [ 44 ], they have historically been regarded as rather embarrassing for the model. Perhaps the boot should now be on other foot. After this review of the experimental indications that the na'fve OZI rule is indeed inapplicable to baryons, we now make some quantitative estimates of OZl-evading meson-baryon couplings. O - + mesons. Their couplings to baryons are related by PCAC and the Goldberger-Treiman relation to the baryonic matrix elements of axial currents. We know from experiment [ 6 ] and the Skyrme [20] model that A s ¢ 0 (see eq. (3)) (a prima facie breach of the na]'ve OZI rule) and A u + A d + A s - ~ 0 (see eq. (8)). We therefore predict [20] that gnopp-~0 ,
(17)
where rlo
19 January 1989
can be estimated. Pseudoscalar meson loop corrections, which are of next-to-leading order in 1/Arc, do not alter the predictions that A u + A d + A s = 0 and gnovp = 0, but possible other 1/Arc corrections cannot be excluded at this time. Chiral symmetry breaking may explain why the physical pseudoscalar q and T1' are mixtures ofrls and rio with a mixing angle 0 of 10 ° to 20 °. Taking, for example, 0_~ 14 ° as suggested by a first-order analysis ofchiral symmetry breaking, we find [20] gn' op -
-
-~tan 0-~0.25,
(18)
gr]pp
which is not in conflict with experiment, but should not be taken as a very reliable estimate. l - mesons. These mesons' couplings are usually related to the zero-momentum-transfer (Q2 = 0) matrix elements of vector currents by the vector meson dominance (VMD) hypothesis [46 ]. We know that ( p ] gT~s]p ) = 0 at Q2 = 0, because it measures the net strangeness of the proton I
#(s)- #g-= fdx [s(x)-g(x)l=0,
(19)
0
(where s (x) and g(x) are patton densities for strange quarks and anti-quarks) which vanishes because of the proton's net quantum numbers. It follows from (19) and VMD that g, pp = O.
(20)
Therefore, exceptionally, the OZI rule works for this and other elastic 0-baryon couplings. However, naive VMD is not directly applicable to inelastic form factors and therefore in general one could expect that the inelastic coupling g0pN* ¢ 0
(21)
for any baryon resonance N *. The vanishing ofg0p p (20), whereas go,pp ¢ 0, indicates that the angular distribution of the 0 in pp-~0rc+~ - should not be peaked forward-backward in the same way as the o in pp-~0r~+~ - (as seen by experiment [251). However, since inelastic couplings (21) do not vanish in general, we would expect R g ~ c ~ ( p p - ~ t ~ + T r - ) / a(15p~0~+~- ) to be larger than the OZI expectation 177
Volume 217, number 1,2
PHYSICS LETTERSB
of a few × 10 -3 (as also seen by experiment (9), (11 ) [25-28]. A sample diagram enhancing Rg is shown in fig. 2b. The value of R~(~+~_),, should also be enhanced (as observed (15), (16) [ 41 ] ), whereas we would expect R~+~-),, to be given by the OZI rule for 0 mesons in the beam fragmentation region (as observed) [37 ] ), but larger in the target fragmentation region (for which data are not available). The nonzero inelastic vertices goON* may also explain why a ( x - p ~ ¢)n ) / a ( x - p--, con) is seen to exceed the OZl expectation at low energies [38,39]. On the other hand, since the 11o should not couple even inelastirally to baryons, we expect no such low energy enhancement for a ( ~ - p - ~ r l ' n ) / a ( x - p - ~ r l n ) (as seen by experiment [47,48 ] ). 0 + + m e s o n s . The NQM assignments of the known scalars are obscure, and the theoretical possibility exists of substantial mixing between ~lq, ¢tq~lq and gluonium states. In principle, by analogy with VMD, one can use scalar meson dominance (SMD) of the Q2= 0 matrix elements of gs, uu and dd densities between protons and the x-N o-term information (2) or the Skyrme model to infer that go +,~go + = 0.38
(o-term) ,
=7x/2/23-~0.43
(Skyrme),
(22)
where here and subsequently we denote the gs member of a meson nonet by a prime (0 + +', 1+ + ', etc. ) while the I = 0 non-strange member is unprimed. However, the above-mentioned phenomenological uncertainties seem to preclude any clear test of this potentially large deviation from the naive OZI rule. 1 + + mesons. The analogue of the previous PCAC, VMD and SMD hypotheses would be to suppose (AMD) that axial mesons dominate the Q : = 0 matrix elements of the transverse components of the corresponding axial currents. The previous analysis [ 20 ] of axial current matrix elements combined with AMD suggests that gl++,ffp=--xf2gl++pp
•
(23)
Even if this result is correct, its implications for the physical isoscalar D and E mesons are unclear, since their mixing pattern is not known. We quote below predictions based on (23) for different possible mixing patterns, 178
19 January 1989 0
(singlet/octet),
= - ~
(ideal mixing) ,
=-0.68
(ref. [ 4 9 ] ) .
gEpJgDpp=
(24)
It should be noted that the E meson first seen in I)P annihilation was identified as O - +, and can probably be identified with the t seen subsequently in radiative J/u] decay. The fact that the D meson has been seen in lbp annihilation but not the 1+ + E meson might be taken as evidence against ideal mixing, if the predictions (24) are to be believed. At least the possibility of apparently OZbviolating couplings to baryons should not be neglected in future D and E phenomenology. 2 + + m e s o n s . For these and higher-spin mesons we propose a weakened form of the previous meson dominance hypotheses, namely that the ratios of spinJ gs(J' ), I--0 (~tu + d d ) / x ~ (J) and I = 1 (uu - d d ) / ~ (Jr) meson couplings to baryons are equal to the ratios of the corresponding matrix elements of local spin-J operators at Q2=0, e.g. ( p [gT, D~s [p ) etc. for spin 2. These matrix elements are in turn related in the parton model to the ( J - 1 ) th moments of parton distributions in baryons:
gJ' pp : g.If~p :gJI pp I = f dXXJ-I[S(X)"}-(--1)Jg(x)] 0 1 : f dxxJ-~
0 ×{[u(x)+d(x)] + (- 1)J[o(x)+d(x)]}/x/2
: i d x xJ I 0
x { [ (u(x) - d ( x ) ] + ( - 1 ),'[~ (x) - a ( x ) ] } / ~ 2 . (25) This Ansatz enables us to calculate gf, pp/gfpp and appropriate set of deep inelastic structure functions. Table 1 shows values of g f ' p p / g c p p a n d gA2pp/gfpp calculated using the Duke and Owens [50] and Eichten, Hinchliffe, Lane and Quigg [ 51 ] parton distributions. We see that
gA2pp/gfPp, given an
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PHYSICS LETTERS B
Table 1 Values of~/.pp/~,,pp and gJIpp/gJpp for J = 2 and J=4, calculated using eq. (25) and the distributions of refs. [ 50,51 ] with Q 2= 6 GeV 2 and A=200 MeV. These numbers do not change qualitatively if Q2 is taken as 10 GeV z, or ifA is increased by between 100 and 200 MeV. Distribution DO [50] EHLQ [51]
gfpp
gA2pp
gt~p
gfpp
g4pp g4pp
g4,pp g41~p
0.145 0.057
0.249 0.391
0.027 0.010
0.451 0.557
gfPP 20.10_____0.05, grpp
gA2pp ~ 0 . 3 2 _ + 0 . 0 8
.
(26)
grpp
T h e s e p r e d i c t i o n s c o u l d be tested in OP a n n i h i l a t i o n , b a c k w a r d m e s o n p r o d u c t i o n in ~p collisions, and in pp collisions. B e c a u s e the elastic f'lSp c o u p l i n g does not vanish, u n l i k e the elastic OPP coupling, there m i g h t be f o r w a r d - b a c k w a r d p e a k i n g in I~P--" f' 7r+ 7r-, s i m i l a r to that e x p e c t e d for l~p~ f~+Tr - a n d that seen in 1Op-~c0~+r~ - ( b u t not f ) p - , ~ ) n + ~ - ) . C e r t a i n l y we e x p e c t R p to be larger t h a n e x p e c t e d f r o m the O Z I rule (as seen by e x p e r i m e n t [ 2 8 , 3 3 , 3 4 ] ). 3 - m e s o n s . A c c o r d i n g to the general f o r m u l a ( 2 5 ) , t h e i r c o u p l i n g s to b a r y o n s should be p r o p o r tional to the m o m e n t s f~ d x x 2 [ s ( x ) - g ( x ) ] etc .... It is n o r m a l l y a s s u m e d that the s a n d s d i s t r i b u t i o n s h a v e the s a m e shape, but there is no r i g o r o u s reason w h y this s h o u l d be so: all o n e k n o w s is that f~ cL~ s ( x ) = f~ cbc g ( x ) . In principle, a d i f f e r e n c e bet w e e n s ( x ) a n d g ( x ) c o u l d be seen in the n e u t r i n o p r o d u c t i o n o f c h a r m , but p r a c t i c e t h e y are difficult to d i s e n t a n g l e with sufficient a c c u r a c y f r o m the c o m peting d(x) [d(x) ] distributions. 4 ++ m e s o n s . P r e d i c t i o n s for t h e i r c o u p l i n g s to b a r y o n s are also g i v e n in table 1. H o w e v e r , since o n l y one I = 0 4 ++ m e s o n has b e e n i d e n t i f i e d so far, [44] n a m e l y the h ( 2 0 3 0 ) w h i c h is p r e s u m a b l y p r e d o m i n a n t l y non-strange, it is not yet possible to test the p r e d i c t e d m a g n i t u d e o f the O Z I - v i o l a t i n g 4 + + ' - b a r yon coupling. We c o n c l u d e this p a p e r w i t h a few c o m m e n t s on g l u o n i u m searches in processes with i n c i d e n t baryons. T h e fact that m e s o n c o u p l i n g s to b a r y o n s violate the O Z I rule m e a n s that the o b s e r v a t i o n o f a reso n a n c e in an O Z l - f o r b i d d e n c h a n n e l d o e s not necessarily m e a n that it is a g l u o n i u m state. It c o u l d
19 January 1989
be an excited gs state. T h i s c a u t i o n applies in particular to the Q0 r e s o n a n c e s r e p o r t e d in ref. [ 52 ]. We t h a n k Y. F r i s h m a n , H. Fritzsch, H. Harari, R. L a n d u a and L. M o n t a n e t for useful discussions. N o t e a d d e d . By analogy with the n o n - z e r o gs content o f the p r o t o n , we expect a n o n - z e r o flu a n d dd c o n t e n t in the f 2 - a n d its e x c i t e d states. We t h e r e f o r e expect that f2 c o u p l i n g s to n o n - s t r a n g e m e s o n s will also a p p e a r to v i o l a t e the O Z I rule. In particular, we w o u l d expect f ~ * - ~ f 2 - + p i o n s decays not to be O Z I suppressed by c o m p a r i s o n with f 2 - - , E K T r decays. T h e recent o b s e r v a t i o n [53] o f a state f 2 " - ( 2 . 4 7 G e V ) ~ f2 + ~ + ~ - with a n o r m a l h a d r o n i c w i d t h ~ 70 M e V is c o n s i s t e n t with o u r e x p e c t a t i o n s .
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