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Nuclear Physics A547 (1992) 17c-26c North-Holland, Amsterdam
N U C L E A R PHYSICS A
STRANGE AND UNUSUAL ASPECTS OF THE NUCLEON*
R. L. J affe
Center for Theoretical Physics, Laboratory for Nuclear Science and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 U.S.A.
At first sight it seems out of place to devote an entire talk to the nucleon at a conference on strange particles and hypernuclei. The nucleon has no net strangeness, and the simple and successful constituent quark model classifies the nucleon as a bound state of three non-strange quarks. Recently, however, several precise experiments have found that the nucleon conta:,ns a significant admixture of strange quark pairs. These results require further confirmation. In the meantime theorists have speculated on the changes in our picture of the nucleon required by these unexpected results. It is my intention in this talk briefly to summarize the subject.
Roughly the talk is organized as follows. First, I will briefly remind you why we ever believed strange quarks were unimportant in the nucleon in the first place. Second, I will explain why the question has arisen with urgency only recently. Third, I will summarize what is known and how precisely. And fourth, I will briefly discuss the "spin crisis" and its relation to the flavor structure of the nucleon. My talk is brief and many important points are left to the references.
1. S T R A N G E N E S S IN T H E N U C L E O N A N D T H E OZI R U L E
The strange quark mass, extracted from studies of chiral symmetry breaking, is of the same order as AQCD. It is therefore natural to suppose that the dynamical processes which lead to confinement and chiral symmetry breaking in QCD dress hadrons with pairs of strange (as well as up and down) quarks. [The charm and bottom quarks are much heavier and can be ignored or incorporated perturbatively in the small parameter AQcD/mq.] Contrary to some claims, SU(3)f symmetry alone makes no statement on the question of S S-pairs in the nucleon wavefunction. The constituent quark model which we teach our students classifies the proton as IUUD) and the neutron as IDDU). But it is easy to augment these wavefunctions in several distinct ways which preserve exact flavor symmetry (ignoring quark masses) and add SS-pairs. The simplest way is to include terms like I(VO + DD + SS)nUUD) m the so-called SU(3)j, symmetric sea. Note, however, that pairs can be added to the nucleon in a v j consistent with
* This work is supported in part by funds provided by the U. S. Department of Energy (D.O.E.) under contract #DE-AC02-76ER03069.
0375-9474/92/$05.00 © 1992 - Elsevier Science Publishers B.V. All rights reserved.
18c R.L. Jaffe / Strange and unusual aspects of the nucleon
SU(3)S but without including SS-pairs. An obvious way is to dress each quark with pairs of the same flavor:
v -~ vCV0)" D --, D ( D D ) "
s -~ s ( s $ ) " .
Another, intermediate possibility suggested by the 't Hooft resolution to the U(1) problem is a sea which is "off-diagonal" in flavor:
v --, U ( D b ) ( S $ )
D - , D(S$)(UO)
s - , S ( U O ) ( D b ) .
So the nucleon may or may not contain a significant admixture of pairs and the pairs may or may not include strange quarks even in the limit of exact SU(3) flavor symmetry.
The prejudice that the nucleon contains few SS-pairs is based on a qualitative se- lection rule abstracted from hadron scattering and decay processes long ago by Okubo, Zwieg and Iizuki (OZI). 1 The rule, simply stated is: 1) Hadrons contain only those quarks required by their quantum numbers; and 2) Quark pair creation is suppressed in hadron reactions. The nucleon contains no SS pairs because it contains no pairs at all. The theoretical support for this rule comes from the Nc -* o¢ limit of QCD in which diagrams which mix QQ pairs into hadron wavefunctions are suppressed by O(1]N¢) . 2 The experimental support for the OZI rule comes from selection rules in scattering and decay processes, especially those involving vector mesons. For example
~r N ---, p N w ~ 3 ~r ~rN --. ¢N >> 1 and ¢--, 37r >> 1
are neatly explained by the OZI rule.
2. P R O B E S OF L O C A L F L A V O R S I N G L E T M A T R I X E L E M E N T S
The recent interest in the flavor structure of the nucleon can be described as the failure of the OZI rule when probed quantitatively with local operators. If one wants to look for SS-pairs in the nucleon, the cleanest way to do it is to measure the nucleon expectation value of local operators of the form gFs where F is some matrix in Dirac space which may also include derivatives or coordinates. These belong to a set of operators of the form
r~(~2) = q~rq~ I (1) #2
where a = u, d, s, F is as before and #2 is a renormalization scale (if necessary). In the limit of exact SU(3)f these operators form the three diagonal members of an SU(3)f nonet: The singlet
r : - ' _
[qr¢l ~ = ~/~ (~r~ + drd + ~r~) (2)
R.L. Jaffe / Strange and unusual aspects of the nucleon 19c
the octet isoscalar
and the octet isovector,
[#rd -o = + drd-
I (ar= - ara) =
The OZI rule suggests the selection rule:
(3)
(4)
( N I rsI N ) - 0 , (5)
o r 3
Equations (5) and (6) clearly go beyond SU(3)! symmetry. It is easy to make models in which they are violated (e.g. the SU(3)! symmetric Skyrme modeP) and others in which they are satisfied (e.g. the constituent quark model). Unless the operator qrq is renormalization group invariant (or at least does not mix with other operators under renormalization), Eq. (6) can hold exactly only at one scale in QCD. The left- and right-hand sides evolve differently with mass scale so the relation can only be approximately satisfied at other scales. It is not so obvious whether Nature chooses to obey Eqs. (5) and (6) and, upon reflection, how to make the measurements necessary to test them. Until recently little was known about the singlet matrix dement in Eq. (6) and much of the recent revival of interest in the subject was triggered by measurements of the singlet.
Many different operators r are probed by weak and electromagnetic currents and by baryon mass differences. Electromagnetic currents probe 7 °, ~27° and ½~ x -~, corre- sponding to the charge, charge radius and magnetic moment, respectively. Semileptonie weak decays probe axial currents, 7.7s, and hadron mass differences can be related to the scalar operator r = 1. The matrix elements of the octet isoscalar, [qrq]S=o,_ are relatively easy to extract from experiment. The flavor singlet is much more elusive. Consider first the nucleon matrix elements of the electromagnetic current,
.em 2 1 - 1 3 . = ~ f t T . u - -~dT.d - " ~ 7 . s • (7)
" e l 3~ can be written as a linear combination of octet operators m the isovector, fiT.u - d'7.d, and the isoscalar aT.u + t iT .d - 2~7.s. So the baryon matrix elements of j~m give us no information about the singlet operator fiT.u + dT.d + .~7.s. [Notwithstanding heroic at tempts 5 to use SU(3)f violation to access a small singlet admixture.] This "accident of Nature" m that the sum of the charges of the three light quarks is zero
preventes us from learning quantitatively about the nucleon's flavor content from electromagnetic interactions.
Next, consider the axial currents measured in f~-decay. The AS = 0 charged current fiT.75d, and AS = 1 charged current, fiT.')'ss, are octet members. An SU(3)f rotation can - - to the accuracy of $U(3)! 8 __ yield the nucleon matrix elements of the octet, isosinglet axial current but yield no information on the flavor singlet.
20c R,L, Joffe / Strange and unusual aspects of the nucleon
Finally, consider the information coming from baryon mass differences. The flavor symmetry violating term in the QCD Hamiltonian is
6// = + rid) +
= ! + + + + 3
fit /Tt s + r i d -
3
(8)
(ignoring the u-d mass difference). The octet term can be extracted from baryon mass differences. The singlet term gets lost among other flavor singlet terms in the flavor symmetric part of the Hamiltonian.
3. A S U M M A R Y OF S T R A N G E Q U A R K M A T R I X E L E M E N T S
Slowly, over the past decade, evidence on the singlet matrix elements of quark bilinear operators has accumulated from a variety of sources. The present state of affairs is summarized in Table I. The information on the scalar density, qq, comes from low- energy, pion-nucleon scattering. T The information on the singlet axial charge, q%75q, comes from the deep inelastic spin sum rule. s The information on the "momentum sum role" operator, qT+D+q, comes from muon pair production in deep inelastic neutrino scattering. 9 There is still no experimental information on the nucleon's flavor singlet magnetic moment or charge radius, so I have filled those entries in the Table with some educated theoretical guesses based on dispersion theory. 1° Time does not permit me to treat all these entries in detail. For a fairly up-to-date review the reader can consult Ref. [8]. Instead, I will confine myself to a few comments on the problem of separating strange and non-strange quark matrix elements. The reader should not lose sight, however, of the basic result evident from Table I, that strange quark matrix elements in the nucleon appear to be significant.
C 0 1 ~ M E N T S
, Confirmation: The most controversial entry in Table I, the singlet axial charge, needs confirmation. SMC at CERN and E142 at SLAC are competing in the attempt to do this. LSND at LAMPF can measure the same quantity in an entirely different manner.
, Chiral non-linearities: The extraction of m~ (NI~sIN) has been complicated by the possibility of higher order (in m,) effects in chiral perturbation theory. The effect would be to reduce m, (NIgs[N) while preserving the relatively large value of the pion-nucleon sigma term. 7,11
® Z°-Nucleon C o u p l i n g s - A generic probe of strange quark content: The Z ° boson couples to the current
"z "3 3~, = Jl, n -- sin2 0wj~, m • (9)
The first term has the flavor structure u - d + c - s + t - b. The c, b and t can be ignored (see Ref. [12] for an estimate of their importance) leaving u - d - s. The combination u - d is measured elsewhere, so the Z ° probes the strange vector and axial currents of the nucleon. Several experiments are being planned to
R.L. Jaffe I Strange and unusual aspects of the nucleon 21c
TABLE I
S T R A N G E GOINGS ON IN THE P R O T O N
The Ensemble of Bilinear Quark Operators
Common Name
Vector Charge
Momentum Sum Rule
Axial Charge
Sigma term
N o n °
IOperator Scale Strange Quarks
qT~q D t 3
10 0.438 q%,D.q GeV 2 +0.002
10 0.31 q%75q GeV 2 +0.08
mqq t ~ 45 MeV
1.01" ½~ × q-'~q t +0.09
Strange Quarks
0.026 +0.006
Magnetic Moment
1.06 r2q+q __ t +0.06*
fm 2
Charge radius
-0.19 +0.06
~, 300 MeV
-0.31" +0.09
Comments
Pedagogical
Higher spin operators, too.
Note small errors from dimuons. Deep inelastic
spin asymmetry. Extraction problems.
Q2-dependence, vp ~ vp
Extraction problems?
Problems with chiral dynamics?
vp ~ vp Kaplan/Manohar
ep --~ ep ~I
0.16 ±0.06*
fm 2
Beck/McKeown
e12C --, e12C g
t Renormalization scale invariant. *"Theoretical" results relying on vector dominance.
exploit this probe: the LSND experiment at LAMPF will measure (NI~7~75s]N)
via elastic neutrino scattering. The SAMPLE experiment at Bates will measure (N I~F × ~ s I N) via parity -violating electron nucleon scattering. Several similar
experiments are being planned for CEBAF.
® Recently Kaplan is has pointed out that non-leptonic hyperon decays give us infor-
mation about nucleon matrix elements of four quark operators involving SS-pairs.
Once again, the matrix element is larger than expected on the basis of the OZI
rule. The effective Hamiltonian for non-leptonic hyperon decays scaled down to
--~: R,L, Jaffe ! Strange and unusual aspects of the nucleon
# ~ 1 GeV is given by
He&ff S= l
= - ~ s ~ c ~ G F {-0.51 (a¢,d,~) a (~t~u~) n + 1.26 (,~d~) a (a~tt,,),. + small terms}
(10) (here (~ and ~ are color indices and A~-~ -- 150 MeV, rat > 50 GeV, ~ -- 1 GeV have been taken). He'eft S=1 transforms as a superposition of an SU(3)/ {8} and {27}. The data on non-leptonic hyperon decay require {8} >> {27} - - the well- known &I = 1/2 rule. Kaplan shows that it is possible to construct a ~ Q ~ Q
r.r,~s=l The operator, O(s -) operator with an SS-pair and the same octet part as "'e~ • with odd parity, has the flavor structure q-Tsqgs:
0 (-) "-- 2 { - O . 5 3 ( C l a T 3 q a ) L ($j98,8)L -I" 1.25(qaTsq~)n (8BSOt)L 3 t- s m a l l terms} .
(11) O (-} contains terms beyond the octet, but the assumption of octet dominance allows one to relate the matrix elements of O~ -) to non-leptonic hyperon decay. The result - -
is unexpectedly l a r g e - more evidence for S S content in the nucleon.
4. T H E S P I N CRISIS A N D T H E S T R A N G E N E S S C O N T E N T OF T H E N U C L E O N
There has been much attention given recently to the "spin crisis" in spin-dependent deep inelastic scattering. 14 The "crisis" originated in the EMC 15 experimental evalua- tion of the axial charge sum rule for deep inelastic electron proton scattering: s,16
dx gl 7r ?r 2
1 ,(1 A 2 ')) (13)
Here gl ) is the spin-dependent structure function measured at leading twist in ep scattering, and F and D are the SU(3)I invariant matrix elements of the axial charge measured in hyperon and nucleon E-decay. E(Q 2) is the proton expectation value of the quark spin operator,
a=n,d,8 D 2
where Ig is renormalization scale (/~2) dependent because of the axial anomaly. 16 Equa- tion (13) contains higher-order ,,erturbative corrections and alludes to higher-twist corrections of order A2 / Q2.
R.L. Jaffe ! Strange and unusual aspects of the nucleon 23c
In the naive, non-relativistic quark model E = 1. The OZI rule embodied in Eqs. (5) and (6) allows one to predict E,
EozI = 3F - D = 0.60 4- 0.12
where the errors reflect uncertainties in hyperon ~-decay data and in the SU(3)! rota- tion necessary to obtain the isoscalar octet current from the flavor changing currents measured in ~-decay. s [Note EozI disagrees with the naive quark model result E = 1.] The EMC result 15 disagrees with EozI:
EEMC(10 MeV 2) = 0.120 4- 0.094 4- 0.138 .
Several brief caveats and comments are in order:
1. The disagreement between EEMC and EOZl is only ~, 2 - 3 a.
2. EEMC is small because g~P(x, Q2) measured by EMC is small in four bins with x < 0.05. These experimental points need confirmation.
3. The data do not seem to be contaminated by higher-twist effects, 15 the speculations of Anselmino, Ioffe and Leader 17 notwithstanding.
4. ~EMC can be increased by assuming an unconventional extrapolation of gleP(x, Q2) to x = 0, is but the extrapolation looks contrived.
5. E is renormalization scale-dependent, so in principle it could be ~ 0.60 at some low constituent quark scale where the OZI rule (ss) = 0 applies and then evolve to
0.12 at Q2 = 10 GeV 2 where EMC measures it. 1° This "explanation" requires a rapid and otherwise unmotivated evolution of E is in a regime where it cannot be measured.
The EMC result contradicts no basic theorems; there are plenty of other sources for the nuclear spin: quark orbital angular momentum, gluon spin and gluon orbital angular momentum. It can be recast as a measurement of the strangeness axial charge:
d ga( , - ( 9 F - D + 6zXS) (15)
(suppressing all Q2-dependence and QCD radiative corrections), where
Aq(p2)sc, -- (palqTa',/5 q Ips) (16) #2
for each quark flavor. So the "spin crisis" is equivalently the "flavor crisis": the "naive" expectation As -~ 0 is not borne out by experiment, instead A$EMC "- --0.190 4-0.032=I= 0.046. The information on all flavor axial charges is summarized in Table II.
Theory has yet to shed much light on the "spin crisis." For two contrasting reviews of the attempts theorists have made, the reader should consult Ross' talk at the Stanford Lepton Photon Symposium and Manohar's talk at the Penn State Workshop 19 later the same year. I will not attempt to review the subject here - - my opinions are summarized in Ref. [8] and reflected to some extent in Ref. [19]. Let me add only that I do not believe there is any simple theoretical "quick fix" which resolves the "spin crises" or the emerging flavor problem for that matter. Either the experiment is wrong, or we shall have to live with a nucleon whose flavor structure is more complex than we had supposed. In either case there is a rich program of experiment and interpretation to be pursued in the next several years.
24c R,L. Jaffe I Strange and unusual aspects of the nucleon
5Q
1.
Au
Ad
As
TABLE II Expectation* Experiment**
0.92 4- 0.05
-0.32 4- 0.05
0.782 4- 0.032 4- 0.046
-0.471 4- 0.032 4- 0.046
-0.190 4- 0.032 4- 0.046
E 0.60 4- 0.12 0.120 4- 0.094 4- 0.138
*Hyperon ~-decay, SU(3)1 symmetry and/ks = 0 **Hyperon E-decay, SU(3)y symmetry and EMC.
R E F E R E N C E S
S. Okubo, Phys. Left. 5 (1963) 165; Go Zweig, CERN preprints 401, 402 (1964) (unpublished); J. Iizuki, Suppl. Prog. Theor. Phys. 37 (1966) 21.
2. G. 't Hooft, Nucl. Phys. B72 (1974) 461.
3. To my knowledge this relation was first proposed for the operator q%,'ysq in J. Ellis and R. L. Jaffe, Phys. Rev. D9 (1974) 1444, and for qq by T. P. Cheng.
4. See, for example, J. Brodsky, J. Ellis and M. Karliner, Phys. Rev. D13 (1976) 2161; Phys. Left. B206 (1988) 309.
5. See, for example, G. Karl, Guelph preprint GWP2-PP-91-02 (July 1991).
6. For a recent evaluation, see F. E. Close, in Proceedings of the XXIV International Conference in High Energy Physics (World Scientific, Singapore, 1990).
7. For a recent review see J. Gasser, H. Leutwyler and M. E. Sainio, Phys. Left. B253 (1991) 252, and references therein.
8. J. D. Bjorken,Phys. Rev. 148 (1966) 1467; J. Ellis and R. L. Jaffe, Ref. [3]. For a review, see R. L. Jaffe and A. Manohar, Nucl. Phys. B337 (1990) 509.
9. For a review, see S. R. Mishra in, Proceeding8 of the Workshop on Hadron Structure Functions and Patton Distributions, D. F. Geeseman et al., eds. (World Scientific, Singapore, !990), p: 84=
10. R. L. Jaffe, Phys. Left. B229 (1989) 275.
11. R. L. Jaffe, Phys. Rev. D21 (1980) 3215; E. Jenkins and A. Manohar, USCD preprint UCSD/PTH 91-31 (November lao1~
12. D. Kaplan and A. Manohar, Nucl. Phys. B310 (1988) 527.
13. D. Kaplan, UCSD preprint UCSD/PTH 91-25 (October 1991).
14. For a review, see the last entry in Ref. [8] and G. G. Ross in Proceedings of the Stanford Lepton - Photon Symposium (Stanford, 1989).
15. 3. Ashman et al., Nucl. Phys. B206 (188)364; Nucl. Phys. B328 (1989) 1.
R.L. Jaffe / Strange and unusual aspects of the nucleon
16. J. Kodaira, Nucl. Phys. B165 (1979) 129; J. Kodaira et el., Phys. Rer. D20 (1979) 627; Nucl. Phys. B159 (1979) 99; R. L. Jaffe, Phys. Left. B193 (1987) 101.
17. M. Anselmino, B. L. Ioffe and E. Leader, Soy. J. Nucl. Phys. 49 (1989) 136.
18. F. E. Close and R. G. Roberts, Phys. Rev. I, ett. 66 (1988) 1471.
19. A. Manohar, in Proceedings of the Polarized CoUider Workshop, J. Collins, S. Heppelman and R. Robinett, eds. (AIP, New York, 1990), p. 90.
