98 Nuclear Physics B (Proc. Suppl.) 23B (1991) 98-107 North-Holland

STRANGEQUARKSIN THE PROTON

Marek KARLINER

School of Physics and Astronomy, Tel-Aviv University, Tel-Aviv, Israel

We discuss the recent developments related to the issue of presence of non-valence strange quark pairs in the proton: their large contribution to the polarized structure functions, cT-term and OZl violation in baryon-meson couplings, and their peaceful coexistence with deep inelastic scattering data and with the successes of non-relativistic quark model and QCD sum rules.

1. INTRODUCTION

In the context of QCD we think of the proton as built

from three light current valence quarks, two u-s and one

d, each surrounded by a cloud of virtual gluons and quark-

antiquark pairs. For many practical purposes it is conve-

nient to treat the proton as composed of just three rela-

tively heavy constituent quarks, each with a mass of about

330 MeV. This cloud of virtual quanta is responsible for

the difference in the properties of the current and con-

stituent quarks. The electric, color and isospin charges

of the constituent u and d quarks are the same as those

of the corresponding current quarks. These properties are

given by matrix elements of conserved currents. For a long

time it was assumed that the only differences are the mass

and the axial-vector charges. In the recent years, however,

there is growing of experimental and theoretical evidence

that the "vacuum polarization" in the proton has additional

observable consequences, some of them quite striking.

The first indication that something unexpected is hap-

pening was probably the analysis of the ~ - N ~-term, I-4

indicating that among the virtual quark-antiquark pairs

there is a substantial number of.~.~ pairs. This is usually

referred to as the relatively large "strangeness content" of

the proton. The analysis leads to the estimate (with large

uncertainties)

<pL~li,> ~ o.1 (1.1)

More recently, the surprising results of the EMC

measurement 5 of the polarized structure function g~(x)

and the theoretical analysis that followed 6' 7 have lead to a

0920-5632/91/$03.50 © 1991 - Elsevier Science Publishers B.V.

rather surprising conclusion that the valence and sea quarks

together carry only a small fraction of the proton's helic-

ity and that the strange quark polarization }ks is large and

negative, about 50% of Ad. It is responsible for sum of

quark helicities being very small, consistent with zero. 8

It is important to verify these phenomena experimen-

tally, and if they are true - to understand from the theory

how and why they happen. We are still far from the sec-

ond goal, but progress is being made. The following is an

attempt to describe some of this progress.

2. EFFECTIVE LAGRANGIANS

Given that at present we cannot obtain a satisfactory

description of proton structure in QCD, in the interim we

try to understand the experimentally observed phenomena

by studying models known to reproduce some of the rele-

vant properties of QCD. Both the question of proton spin 7

and the scalar density of strange current 9-11 have in the

past been discussed in the framework of the chiral soli-

ton models. These are low-energy effective lagrangians

containing only chiral bosonic fields. Baryons appear as

topological solitons, or skyrmions. 12' 13 We have many in-

dications that lagrangians of this type correctly describe

the long-wavelength limit of large-N c QCD. Borrowing the

terminology from the theory of critical phenomena, one can

say that they are in the same universality class. 14 Such la-

grangians are necessarily only a very rough approximation

to the full theory in four dimensions. For example, asymp-

totic freedom implies that the full bosonized lagrangian

should contain an infinite number of fields. 15 To the extent

All rights reserved.

M. Kadiner/Strange quarks in the proton 99

that the large-A~ QCD correctly represents the real world

with N~=3, there is a chance that chiral soliton models

will capture the essential physics as well. In four space-

time dimensions, with 5'U(3) flavor symmetry broken by

the strange quark mass it is quite difficult to make a re-

liable estimate of this quantity. The results obtained 9-11

in the Skyrme model in 3+1 dimensions should therefore

be taken as a qualitative, but not necessarily quantitative

description of the correct physics. The quark content of

a given flavor eli in a baryon state liT) is usually given in

terms of the normalized ratio:

<qq)B (2.1)

In the chiral l imit of QCD, i.e. with all current quark

masses taken to zero, for the proton we have 9

,3+1 } 13,+1 il (=~:3.+, 7 uuh' = 5 : <dd = ~ ; "s'%P = 5;(--~ (2.2)

and I I

,:~+1 7 . . . . :~+l 5 (2.3) SS]A = 2~: t's's/f~- = 1~

Instead of studying rough approximations to the full theory

in four dimensions, it is possible to solve exactly a two di-

mensional analogue of 0CD 16 in the strong-coupling limit.

The theory can then be bosonized in a closed form and

the semi-classical approximation can be employed. (The

bosonization technology is reviewed in detail in Ref. 17.) In

two space-time dimensions, thanks to the exact bosoniza-

tion we can obtain a precise answer in the flavor symmetry

limit, for any number of flavors :Vf and colors :\[.. QCD2 is

known 16 to exhibit many of the phenomena familiar from

strong interaction phenomenology and we hope that in this

case it also reproduces the essential physics.

In this case, like for skyrmions in 3+1 dimensions,

baryons also correspond to solitons of the bosonic La-

grangian. The wave functions of the allowed states with

B = 1 can be written down explicitly, yielding matrix ele-

ments of the various currents, i.e. quark bilinears. In par-

ticular, it is possible to compute the strange quark content

of non-strange baryons. 18

In order to mimic the real world as much as possible, we

focus on IVy-3 and N I - 3 . There is a substantial similarity

to the spectrum in 3+1 dimensions, but there are also im-

portant differences, the most important being that baryons

appear only in decuplet (10) representation of SU(3) ] and

there is no octet. Similarly, for SU(2) j there is only the

triplet and no doublet. 19 This is what we would expect

from na(ve quark model considerations. The total wave

function must be antisymmetric. Baryon is a color singlet,

so the wavefunction is antisymmetric in color and it must

be symmetric in all other degrees of freedom. There is no

spin, so the baryon must be in a totally symmetric represen-

tation of the flavor group, a 10 for three flavors. Therefore,

strictly speaking there is no state analogous to the proton.

On the other hand, there is a state which is the analogue

of the A +. The 10 is the lowest baryon multiplet in QCD>

For A +

1 1 < ) 1 (2.4)

Similarly, for LS ++

2 1 ] (2.5)

In the constituent quark picture / \++ contains just three

zt quarks. Both the d-quark and the s-quark content of

the A ++ come only from virtual quark pairs. Therefore

in the SU(3)-symmetric case <L~s>2`++ = <rid)2`++, and

("")2,+ = <:,~s)2`+÷, as expected.

From eq. 2.5 one can also read the results for ~ - , by

replacing u +-~ .~,

1 < > 1 - ,

In the general case of Ny flavors and N~ colors, one obtains

I <(qcl)~")B - N / + N~' (2.7)

where (qq),~ refers to the non-valence quarks in the baryon

B. Moreover, one can also compute flavor content of va-

lence quarks. Consider a baryon B containing/c quarks of

flavor ~,. The v-flavor content of such a baryon is

k + l <~-,v>~ - Ny + N~ (2.8)

This implies an "equipartit ion" for valence and sea, each

with a content of 1 / ( N j + N / ) . tt also follows that the total

100 M. Kadiner/ Strange quarks in the proton

sea content of N flavors is

Nj ?"J (2.9) q=l

which goes to zero for fixed A'f and .'~ -~ co, as expected.

It is interesting to compare these result with the

Skyrme model in 3+1 dimensions. The qualitative pic-

ture is similar, although the ss content in the non-strange

baryons is lower in i + i dimensions. One may speculate

that in i + i dimensions the effects of loops are smaller than

in 3+1 dimensions, since the theory is super-renormalizable

and there are only longitudinal gluons. In the SU(3)-

symmetric limit the strange quark content of baryons with

zero net strangeness is significant, albeit smaller than that

of either of the other two flavors. The situation obviously

is reversed for Q-.

In the real world the current mass of the strange quark

is much larger than the current masses of u and d quarks.

Since strange quarks pairs appear through quantum fluctu-

ations, the larger value of nz~ tends to decrease the strange

quark content from its value in the ,q'U(3)f symmetry limit.

We do not know the exact extent of this effect, but it is

likely that the strange content decreases by a factor which is

less than two. This estimate is based on both explicit com-

putation in the Skyrme model 10, 11 and what we know

from PCAC, 20 QCD sum-rules 21' 22 and instanton-liquid

calculations 23, namely that the analogous quark bilinear

expectation values in the vacuum are not dramatically dif-

ferent from their ~'U(3) symmetric values:

0.5 < (.~.s)~, < t (2.10)

3. OZl VIOLATION IN BARYON-MESON COUPLINGS

If the proton wave function contains ..~ pairs even at

large distances (low Q2) then .~ mesons can couple di-

rectly via connected diagrams to non-strange baryons, as

in Fig. la, thus evading 24 the na(ve form of the Okubo-

Zweig-lizuka (OZI) rule, 25 which implicitly assumes that

such couplings can only occur via disconnected diagrams,

as in Fig. ib, and are therefore strongly suppressed. (The

idea that the proton wave functions contains a nonpertur-

bative 9s component bears a certain similarity with the phe-

nomenon of "intrinsic charm". For a review see Ref. 26.)

e, f...

g . g U " ~ U

U ~" U d - d

(a)

I) I from---

U = ~ ~ " U

Ud :-- d u

(b)

Figure i. (a) A connected diagram coupling a ss meson (e.g. ~, f ' ) to a non-strange baryon via non-valence ss quarks, thereby evading the OZI rule. (b) A disconnected OZl-forbidden diagram contributing to the same vertex.

The traditional estimates of h-nucleon coupling are

based on the small departure from ideal mixing in the

and ~, mesons. In the limit of ideal mixing ~ is a pure

.s~ state. A deviation from ideal mixing adds a light-quark

component to the 9, through which it can couple to the

tz and d quarks in the nucleon. The deviation from the

ideal mixing is very small. It is usually estimated from a

meson mass formula with either quadratic or linear depen-

dence on the amount of the SU(3) breaking. Experimen-

tally, the OZI rule is known to work well for meson-meson

couplings, where it is theoretically justified by the I/Nc expansion.16, 27 However, as argued in Ref. 24, this justi-

fication does not extend to meson-nucleon couplings and,

as we will see, the data provide strong indications of OZl

violation in meson-nucleon couplings.

Most of the evidence for OZI evasion in meson-baryon

couplings comes from /~p annihilation both at rest and in

M. Kadiner / Strange quarks in the proton 101

flight. Several experiments have compared the rates for the

OZl-forbidden process pp --~ ¢ ~+Ir and the OZl-allowed

process/Sp ---* w 7r+~ --. The general conclusion has been

that R~p ~ ¢(w)Tr+z -] --= ~r(pp ~ ¢Tr+Tr-)/~r(pp---+

WTr%T-) is larger than the ratio (74-2) ×10 -3 rtl 5 +1"3~ L\ " - - 0 . 9 / X

10 -3 ] expected on the basis of the departure from ideal

mixing in the ¢ and ~ and a quadratic [linear] meson mass

formula. For example, ref. 28 finds that

R ~ p ---+ ¢(w) 7r+Tr -] = (19 + 5) × 10 -3

for pp = (0.70 to 0.76) GeV (3.1)

after making a phase-space correction. Ref. 28 finds an

amplitude ratio

V/22A(/~)- ~ ~ S+-:¥) 0 99 (3.2) 0.05 < A(]Sp ~ ~u(dd) + X) < " "

that apparently violates the OZI rule, with the precise value

of the ratio depending on the relative phase of the ampli-

tudes. Other measurements of R[pp --~ ¢(w) ~-+¢r ] give

(15 4- 3) x 10 -3 (Ref. 29)

(19t~) × 10 -3 (Ref. 30)

(30 4- 7 ) × 10 -3 (Ref. 31)

(12+~) x 10 -3 (Ref. 30) (3.3)

at p momenta of 0, 1.2, 2.3, 3.6 GeV, respectively, also

indicating that the OZI rule appears to be violated (see

also Ref. 32).

There is also evidence of substantial OZI violation in

the reaction pN --~ ¢(w) 7r at KEK 33 and at LEAR. 34 For

~p annihilation at rest Ref. 33 finds,

R [ p p - - ~ ¢ ( w ) z °] ~ 1/15

while ASTERIX 34 reports ~/~ ratios up to

R[p,~ ~ ¢ (~ ) ~-] ~ 1/8.5,

R[pp --, 6 (~) ~°] ~ z/15,

t~[pl)----+ ¢(u.,)p °] ~ 1/49

(3.4)

(3.5)

According to Ref. 34, ¢ production occurs mostly in S-

wave and increases with the momentum with which the ¢

is produced in/Sp annihilation at rest. This dependence on

¢ momentum and on the parity of the ~Sp system might be

related to the hypothesis discussed in Section 3 below.

The surprisingly large ratios 3.4 and 3.6 are consistent

with earlier results 35, 36 which have lead to the estimate 37, 24

R[pn ~ ¢(~) ~r-] ~ 0.13 (3.6)

There is also evidence for OZI violation in pp annihilation

to f'(1525) + pions, compared with f(1275) or A~(1275)

+ pions. Ref. 31 finds

Blimp ~ f'(f)~r+Tr -] = (29+~ 1) × 10 -~ (3.7)

to be compared with the (1 to 2)×10 -3 expected from the

ratio r ( f ' ~ 7r+Tr-)/F(f ~ 7r+Tr-). Other experiments

also find surprisingly many f ' final states:

R[pp ~ f ' ( f ) 7r+Tr -] ~ 0.43 (Ref. 38)

R[pp ---* f ' ( f + A2)Tr °] ~ 0,064 (Ref. 39)

Blimp ~ f'(A~)~r] ,-~ 8.6x10 -3 (Ref. 39)

(3.8)

indicating OZI violation also in couplings of tensor mesons

to baryons.

On the other hand, the ratio of forward

7r-p --+ ¢(w) n~- cross-sections, 40-42

R[Tr-p -~ ¢(w) nTr] ~ ( 3 + 9 ) × 10 -3 at p~ = 6 + 1 9

GeV is in agreement with the OZI rule and the expected

deviation from ideal mixing. Moreover, the natural spin-

parity exchange (NEX) amplitudes for ~T-p ~ CnTr and

~z/t,z have similar/-dependences, suggesting that the NEX

meson-meson-Reggeon vertices obey the OZl rule, as ex-

pected. However, at lower energies 43-45 there is a relative

enhancement of R[zc-p ~ ¢(w)n~-] since ¢ production

falls more rapidly with p~ and has a broader t-distribution

than the ~ production. These observations are consistent

with the appearance at lower energies of subleading pieces

in the amplitude which evade the OZI rule and could be

associated with baryonic vertices.

More evidence against the naTve OZI rule comes from

pp --~ pp~(~,')nTr reactions. One experiment at Pv = 24

GeV finds 46

= (19 4- 7) × 10 -3 (3.9)

102 M. Karliner / Strange quarks in the proton

while another experiment at pv=10 GeV finds 41

R ~ p --~ pp¢(w)] = (20 ± 9 ± 8) × 10 -3 (3.10)

The former experiment 46 indeed claims on the basis of

a comparison between the ratio 3.10 and the correspond-

ing ratio for incident pions that "... ¢ is produced also

from strange quarks in the incident particle, with protons

containing more 3s pairs than pions". If one assumes

that the observed violation of the OZI rule is due to the

presence of 3s pairs, then it is possible 24 to give quan-

titative estimates of OZI-evacling meson-baryon couplings.

S II S,

I~ ~ : u K,

Figure 2. A connected diagram contributing to a backward peak in the region pp --~ K - K + via non-valence ~s quarks.

In addition to the above pieces of evidence that the

na'fve OZl rule is violated in meson-baryon couplings, there

is another indication from pp annihilation that baryons con-

tain significant numbers of S~ pairs. A backward peak has

been observed 47 in the reaction pp -~ K + E - at p~ ~ 0.:3

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 L-channel exchanges

are expected to dominate. The appearance of this back-

ward peak is prima facie evidence of a direct p ~ / ( -

coupling, which is forbidden in the non-relativistic quark

model, where p = [uud), K = [s~), but is allowed if the

proton wavefunction contains ~s pairs, as seen in Fig. 2.

This coupling is related by crossing to the exotic channel

K + p - - ~ Z*. Despite the recent appearance of two partial

wave analyses 48 agreeing on the presence of a P13 reso-

nance in K + p scattering, the Particle Data Group does

not recognize the evidence for any Z* resonance. Instead,

in the 1986 edition 49 one can read that "the results per-

mit 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. 50 Since their existence goes against the general

prejudice so well reflected by ref. 49, they have historically

been regarded as rather embarrassing for the model. Per-

haps the issue ought to be re-examined.

The question of OZI violation in baryonic

physics 24'51-56 is an excellent probing ground for our

understanding of the nonperturbative phenomena in the

hadronic spectrum. The theorists have but a year or two

until the new data from LEAR settles the issue.

4. SO HOW MANY STRANGE QUARKS ARE THERE

IN THE PROTON ?

So far we have been discussing experimental data and

theoretical arguments which indicate that the proton con-

tains a substantial number of 3s pairs. This issue is now

subject to a vigorous discussion. 2-4,6-11,24,51-56,57"65

The main reason is that there are also some strong ar-

guments pointing in the opposite direction. I will review

them briefly and then describe a possible reconciliation.

The best-known argument in favor of a small number

of .~ pairs in the proton is the success of the non-relativistic

quark model, based on the hypothesis that proton is built

from tL and d quarks only. The recent discussion about the

proton strangeness has only added urgency to the need for

a justification of the quark model from QCD. 66-69 The hy-

pothesis about the absence of strange quarks has also been

successfully used in the framework of the QCD sum rule cal-

culations of the various static and dynamic nucleon param-

eters (mass, magnetic moments, form factors, etc. 21' 22).

Deep-inelastic scattering data provides yet another piece

of evidence in the same direction. The measured value of

the proton momentum fraction carried by strange quarks is

very small, much less than the fraction carried by u and d

quarks. 70 Yet, as discussed earlier, certain other physical

M. Karliner / Strange quarks in the proton 103

observables indicate that the proton contains a relatively

large number of $~ pairs. Roughly speaking, strange quark

vector and tensor currents have very small matrix ele-

ments in the proton, but scalar and axial vector currents

have relatively large matrix elements. In Ref. 71 we pro-

posed a likely resolution of this seeming contradiction. In

meson physics the mixing between the light quark ~q and

the gs states strongly depends on the spin and parity of the

multiplet. (Recall also the dependence of ~ production on

/3p parity and on 0 momentum, as reported in Ref. 34.) We

conjectured that this pattern of OZI violation in mesons

and the wide variation in the magnitude of strang'e quark

matrix elements in the proton are both caused by the

same nonperturbative mechanism. The following gives

the essence of our argument and of the proposed physical

pict u re.

The first thing one must realize is that the question

"how many strange quark pairs are there in the proton"

is not well defined until one specifies the operator which

one wishes to discuss. In afterthought, this should not

come as a surprise. In meson physics it is well known that

the question of strange quark content, or the degree to

which the OZ125 rule works, strongly depends on the spin

and parity of the meson multiplet. In the pseudoscalar

sector the physical ~/and q' mesons are close to the SU(3)

octet q8 ~ (~u + dd - 2s~)/,,/-6 and to the singlet r h

(gu + dd + ~s)/x/3, respectively. Both contain a strange

quarks admixture of order O(] ). In contrast, in the vector

multiplet the "ideal mixing" of the singlet and octet leads

to a physical 0 which is almost purely an s.~, while w

(£~u + dd)/v/2~. Similarly, in the spin-2 meson multiplet,

the mixing of f ' and f , results in f ' being an almost pure

~s. These facts cannot be explained by perturbative QCD

and must be of nonperturbative origin.

4.1. Instantonsand OZlviolation in mesons

An early attempt to explain this pattern of OZI vio-

lation in the context of nonperturbative QCD was made

in Ref. 72, It assumed that the nonperturbative effects

are due to instantons and can be treated in the dilute

gas approximation. These assumptions turn out to be

somewhat too optimistic, but still it is instructive to re-

view their physical consequences. In a typical OZl violat-

ing process the mixed polarization operator I](q~-~s) an-

nihilates (creates) a pair of light quarks (u or (/)and cre-

ates (annihilates) an ~s pair. Ref. 72 considered quarks

as moving not in "empty" vacuum, but rather in the

presence of an external instanton field, neglecting per-

turbative gluon exchange. In this case ]~(q~-~s) factor-

izes and may be represented by the diagram in Fig. 3.

°,O',

s u(d)

Figure 3. The diagram representing the mixed polarization operator in the instanton field. The instanton is depicted by the black point.

Its matrix elements are then zero for vector and tensor cur-

rents and nonzero for axial vector, pseudoscalar and scalar

currents. For vector current this follows simply from an

analogue of G-parity, with SU(2) isospin global symmetry

replaced by an SU(2) subgroup of the SU(3)c local sym-

metry group of QCD. For tensor mesons one also needs to

assume that the quark energy-momentum tensor 0~ acts

as their source. 72 In contrast, for axial vector j~ = (J'Y~'75q,

pseudoscalar j~ ~ a~j~, and scalar currents the mixed po-

larization operators do not vanish in general. In such a

way a qualitative explanation of the OZl rule for mesons

can be achieved, with the simplifying assumptions above.

A quantitative description 73, 74 is also possible but the

results are necessarily model-dependent.

Regardless of the details of any particular model, this

type of OZI violating mechanism is characterized by the

strong momentum dependence of R(q~-*s), since it re-

sults from long-wave, nonperturbative gauge-field config-

urations. For the axial-vector case at large Q2

Q~Q~ n(q~)~ Q~ (4.z)

in the dilute instanton gas approximation. This property

is also very desirable from the phenomenological point of

view: it explains the disappearance of nonperturbative el-

104 M. Kadiner/ Strange quarks in the proton

fects in the charmonium region (e.g. the narrow r/c decay

width into light hadrons).

The results obtained in the dilute instanton gas approx-

imation should be taken as no more than an indication of

what kind of phenomena can be expected from nonpertur-

bative gauge field configurations. One can only hope that

some features of the instanton model of the QCD vacuum,

like the selection rules (vanishing of matrix elements of

some operators) and the strong Q2 dependence correctly

capture the essential physics.

belief that perturbative effects are small even at i GeV. An

analogous conclusion can be obtained for nucleon magnetic

moments and electromagnetic form factors.

4.3. Proton Structure Functions

The matrix element (p[ g%75s [P) is extremely impor-

tant in the analysis of the EMC polarized structure function

data. 5 It is proportional to the integral

Jo 1 As -- dx [s+(x) - s_(x)] (4.2)

4.2. Quark Operator Mixing in the Proton

We now turn back to the problem of strange

quarks in the proton. Here perturbative effects are

also negligible, so the relatively large values of some

strange quark bilinear operators must be due to a

some kind of nonperturbative mixing between the s

and u or d quark bilinears, as indicated in Fig. 4.

,,',.' u~ ',,

Figure 4. The diagram representing the non- perturbative mixing of .s,~ and ~u+(Id in the proton.

We conjecture that on the qualitative level the same non-

perturbative mechanism is responsible for the flavor

mixingin both the proton and in the mesons. In the ten-

sor mesons there is practically no mixing between strange

and light quarks, so nonperturbative flavor mixing for tensor

currents is small. It follows from our hypothesis that non-

perturbative effects do not contribute to (pl 0~ Ip). Since

the fraction of proton momentum carried by strange quarks

is given by (p [O~ [p), it must be due to perturbative ef-

fects only and ought to be small, if one adopts the common

where s+(x), s_(x) are the strange quark distributions

with helicities +½(-½), respectively. In the framework

of our hypothesis (p[ ~7,%s [P) oc As is nonzero due to

nonperturbative effects. (Interested reader is referred to

Refs. 75, and 76 where instanton contributions to the spin-

dependent proton structure are discussed in some detail.)

Even though in this case we cannot perform an explicit

calculation, it is enough to point out that the nonpertur-

bative gauge-field configurations of instanton type lead to

the mixing of ss and ~ u + d d pairs in pseudoscalar meson

nonet and to the formation of r/and r/~ states. In general, if

(Pl g%%s [P) ~Z 0 is due to some nonperturbative mecha-

nism then the s-quark contribution to the nonperturbative

component of the proton axial form factor has a very strong

Q2 dependence, G'~(Q 2) ~ ( I /Q2) ~. In the dilute instan-

ton gas approximation n _> 5. The large-Q 2 behavior of the

form factor is connected with the x --+ I behavior of the

corresponding structure functions through the Drell-Yan

relation: (1/Q2) 'r~ --+ (1 - x) p, p = 2n - 1. Therefore for

x -~ ] we expect that s+(x) - s_(x ) ~ ( l - x) p, p ~, 10.

At small x, s+ - s_ is dominated by the A1 exchange, the

intercept of the A1 Regge trajectory being close to zero. 60

Disregarding the perturbative contribution to s + ( x ) - s _ ( x )

can be parametrized

s+(x) - s_(x) = B(1 - x) p (4.3)

The unpolarized strange quark distribution s(x) = s+(x )+

s_(x) can also be parametrized

s+(x) + s_(x) : A(1 - x) k + C(x) (4.4) X

M. Karliner/ Strange quarks in the proton 105

The 1/x factor comes from pomeron exchange at small

x, the factor ( i - x) k, k ~ 5 corresponds to the quark-

counting rule at x --* i . The term C(x) represents the

nonperturbativecontribution to s+ + s . Assuming that

the nonperturbative contribution to (Pl 0~,. IPl vanishes, we

must require that

L ' x c(~)&~ = ( 4 . 5 ) 0

Under the above assumptions the relatively large value of

/ks _~ -0 .2 proposed in Refs. 5,6,7 as an explanation for

the "spin crisis" can be reconciled 71 with the smallness of

proton momentum fraction carried by the strange quarks 70

/: V~= x[s+(x)+.~_(x)]dx=O.0264-O.O06 (4.6)

For example, for p = i0 and k = 5, we have i_~I _< SI~

and there is no contradiction between /ks ~ -0 .2 and 172"

in 4.6.

4.4. Physical Consequences and Tests of the Pro-

posed Picture

Our hypothesis can be directly tested by measuring

strange particle production in polarized muon (or electron)

scattering on a polarized proton. Because of 4.3, we expect

a very strong g-dependence in such an experiment, .s+ -

s_ ~ ( 1 - x ) ~ ,p~lO. Another possibility is the observation of inclusive charm

production in

P, + _N --* if+ + charm + .~:'.

This experiment measures the distribution 3+(x)+.s_(x) =

s+(x)-Fs_(x) and one can attempt to measure the nonper-

turbative component C(x) in 4.4. The recently published

data of the CCFR collaboration 77 on charm production in

neutrino experiment give some indications in favor of our

hypothesis. This experiment measured the ~(x) distribu-

tion and found that it falls with increasing x faster than the

cjdistribution. The authors parametrize the sea distribu-

tions by x3(x) = %(1 - x ) j3", xq(:r) = aq(1 - x ) ~', and find

fl, = 10.8 4- 1.0 4- 0.7, to be compared with /3,1 6.978.

From our point of view such a parametrization is not suit-

able. We can fit the data 77 using the parametrization 4.4

with

C ( x ) = c l ( 1 - b x ) ( 1 - x ) p', p ' ~ p ~ 1 2 , k=5 ,

(4.7)

the same of the s and the q sea. The factor 1 - bx in 4.7

is introduced so that eq. 4.5 will be fulfilled. The constant

C is constrained by the positivity of s+(x) and s_(x).

The nonperturbative mechanism contributing to the

sea-quark distribution can also contribute to the gluon dis-

tribution. For the time being, however, we have no good

ideas how one could observe such a nonperturbative com-

ponent of the gluon distribution.

The third possibility 60, 79 is the measurement of the

axial form factor in elastic ~,p scattering. (See however

ref. 63 for a caveat emptor on this point.) This involves

taking the difference dcr~l(~p) -daez(z~p). In this form fac-

tor we expect two structures: the usual one, which must

coincide 80 with the vector form factor at large Q2 and a

nonperturbative one, rapidly decreasing with Q2. Therefore

we expect that the proton axial form factor behaves differ-

ently from the electric or magnetic (Sachs) proton form fac-

tors. The latter two are well described by a dipole l i t in the

region of low and intermediate Q2 up to Q2 ~ 10 GeV 2. In

contrast, we expect that such a fit of the axial form factor

with just one axial meson mass will not reproduce the ex-

perimental data, and that some deviations from the dipole

fit must be found.

A neutrino experiment to do the necessary measure-

ments at LAMPF has been proposed. If the EMC polarized

structure functions data are corroborated by this experi-

ment and by the new deep inelastic scattering experiments

now in the planning stage, we will have a very compelling

experimental picture. It is a challenge for the theorists to

provide a quantitative explanation from QCD.

ACKNOWLEDGEMENTS

The original work described here resulted from col-

laborations with Stan Brodsky, John Ellis, Yitzhak Frish-

man, Erwin Gabathuler, Boris Ioffe, Jeff Manclula and Chris

Sachrajda. I am indebted to them for what I have learned.

I would also like to thank the conference organizers for

making this very fruitful meeting possible.

106 M. Karliner/ Strange quarks in the proton

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