EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
4 Decemb er 1995
CERN{PPE/95{178
NUCLEON SPIN STRUCTURE FROM POLARIZED DEEP INELASTIC
MUON-NUCLEON SCATTERING AT CERN
Vernon W. Hughes
(On b ehalf of the Spin Muon Collab ora tio n)
Physics Department, Yale University, 260 Whitney Avenue, 465 J.W. Gibbs,
New Haven, CT 06520-8121 , USA
E-mail: [email protected]
Abstract
Polarized deep inelastic inclusivemuon-nucleon scattering has b een measured at
+
CERN by the Spin Muon Collab oration (SMC) with incident energies of 100
and 190 GeV and with p olarized proton and deuteron targets in an x interval of 0.003
2 2
to 0.7, with Q ranging from 1 to 60 GeV . The spin dep endent structure functions
g have b een determined for the proton, deuteron and neutron. The fundamental
1
Bjorken p olarization sum rule has b een con rmed, and the Ellis-Ja e sum rules have
b een found to b e invalid, with the consequences that the fraction of the nucleon
spin contributed by the quark spins is small and strange quarks have a net negative p olarization.
1 INTRODUCTION
The spin structure of the nucleon can b e studied from p olarized deep inelastic inclu-
sivemuon-nucleon scattering [1{5]. Spin structure functions have not yet b een calculated
from basic QCD, but are useful for testing nucleon mo dels. With their rst moments a
basic test of QCD is made and imp ortant information ab out the comp osition of nucleon
spin is obtained. The intrinsic nucleon spin angular momentum of 1/2 must equal the
sum of the spin contributions from the quark spins , from the gluon spins G, and
from the orbital angular momentum L of quarks and gluons, i.e.
1
+G+L =1=2 (1)
z
2
The quark contribution has b een obtained.
The kinematics and variables for p olarized inclusivemuon-proton scattering in the
2 2
single photon exchange approximation are given in Fig. 1. G (; Q ) and G (; Q ) are
1 2
spin dep endent structure functions. They are related in the scaling limit to the two spin
dep endent structure functions g (x) and g (x).
1 2
2 2
M G (; Q )= g (x)
1 1
2 2
M G (; Q )= g (x)
2 2
Spin dep endent structure functions are determined by measuring di erences or asymme-
tries in the di erential scattering cross sections for the antiparallel and parallel spin cases.
These determine the virtual photon-proton absorption asymmetry A .
1
The counting rate asymmetry is related to the intrinsic muon-proton scattering
cross-section asymmetry as shown in Fig. 2. A is a virtual photon-proton asymmetry
2
arising from the interference of longitudinal and transverse photon p olarizatio ns, and the
kinematic factor is small for longitudinal muon and proton p olarizations. The kine-
matic dep olarization factor D relates the muon b eam p olarizatio n to the virtual photon
p olarizatio n. A should scale, and p ositivity limits are indicated for A and A . The usual
1 1 2
+
expressions for F and g in the quark-parton mo del are given, in which q (x)[q (x)] is
1 1
i i
the probability that a quark of avour i has its spin parallel [antiparallel] to the proton
spin.
Spin p olarization sum rules are given in Fig. 3. The Bjorken p olarization sum rule
is a rigorous consequence of QCD in the scaling limit, indep endent of the mo del of the
nucleon [6]. Perturbative QCD corrections to the Bjorken sum rule are given [7]. This sum
rule assumes only that a general quark-parton picture of the nucleon applies and that the
weak interactions of quarks and leptons are the same.
The Ellis-Ja e sum rules for the rst moments of the proton and neutron structure
functions separately are mo del-dep endent and assume that strange quarks in the nucleon
sea are unp olarized and that SU(3) symmetry applies [8]. Perturbative QCD corrections
F
are given [9].
Formulae are given in Fig. 4 for the rst moments of the proton and neutron spin
structure functions based on the op erator pro duct expansion which is basically a p er-
2
turbative QCD approach excluding non-p erturbativelowQ e ects. Assuming isospin
invariance and SU(3) symmetry and using measured values for g =g from neutron b eta
F A V
decay and of F/D from hyp eron b eta decay, the fraction of the nucleon spin contributed
by the spins of all quarks, , can b e determined. Also the fractional angular momenta
due to u,d, and s quarks separately can b e evaluated. 1 k, sµ ′ Polarized k Scattered muon muon Virtual q photon P, S Px Hadron final state Polarized Wµν nucleon
Wµν (F1, F2, G1, G2)
Kinematic variables
(Lab oratory frame)
m muon rest mass
M proton rest mass
s electron spin-four-vector
S =(O; S ) proton-spin four-vector
k =(E; k) four-momentum of incidentmuon
0 0 0
k =(E ;k ) four-momentum of scattered muon
P =(M; O) four-momentum target proton
0
q = k k =(; q ) four-momentum transfer
2
2 2 0 2
Q = q =4EE sin (=2) {(invariant mass) of virtual photon
0
energy of the virtual photon in the lab oratory = P q=M = E E
scattering angle in the lab oratory
2
x = Q =2M Bjorken scaling variable
y = =E fractional energy loss of scattered electron
P four-momentum of hadronic nal state
x
0 1
"
2 2
2
B C
a cos
d F F
2 1
2 2 0
2
B C
= + 2 tan 2 tan (E + E cos )
@ A
0
d dE 2 M 2
2 4
4E sin
2
#
+(A)
0 2 2
MG 8EE tan sin G
1 2
2 2
(P )
2 2
d d
("#) ("")
0 2
MG (E + E cos ) Q G
0 0
1 2
d dE d dE
A =
2 2
F F
d d
l 2
+
("#)+ ("")
2
0 0
M
2 tan
d dE d dE
2 Virtual photon-proton absorption P γ
⇒ zÐaxis collision
P Y
J =+1=2 J =1
z z
" "
Y(J = +1); Y + P !
z 3=2
# "
Y (J = 1); Y + P !
z
1=2
1=2 3=2
A =
1
+
1=2 3=2
Figure 1: Polarized muon-proton scattering: kinematics and asymmetries. 2
N("#) N ("")
= Counting rate asymmetry
N ("#)+("")
= P P fA
p
P = Muon b eam p olarization ' 0:8
P = Proton target p olarization ' 0:8
p
f =Fraction of p olarizable protons in target (dilution factor) ' 0:1
Hence
' 0:06 A
A = D (A + A )
1 2
A ' DA
1
2
1=2 3=2 TL
A = ; A =
1 2
+ +
1=2 3=2 1=2 3=2
D and are kinematic quantities
0 2
D = (E E ")=E (1 + "R)=y(2 y )=[y + 2(1 y )(1 + R)]
q q
0
2 2
= " Q =(E E ") = [2(1 y )=y (2 y )]( Q =E )
where
" #
1
2
Q
2 2
" = 1 + 2(1 + =Q ) tan
2
and
R = =
L T
Scaling relation Positivity relations
p
2
A (; Q ) ! A (x) jA j 1; jA j R
1 1 1 2
2
(; Q ) !1 ; x f ixed
A F
1 2
g = = A F
1 1 1
2x(1 + R)
X
1
2 +
F (x)= e [q (x)+q (x)]
1
i i i
2
i
X
1
2 +
g (x)= e [q (x) q (x)]
1 i
i i
2
i
Figure 2: Measurement and prop erties of spin-dep endent quantities. 3
Z
1
g 1
A
p p
n n
=0:210(1) (Bjorken) = (g g )dx =
1 1
1 1
6 g
0
V
3
With O ( ) p erturbative QCD corrections
S
2 3
! ! !
2 3
2 2 2
(Q ) (Q ) (Q) 1 g
S S S A
p
n
4 5
1+C = +C +C
1 2 3
1
1
6 g
V
2 2
= 0:187(3) at Q = 10 GeV
With C = 1; C = 3:58 ; C = 20:21 .
1 2 3
------
# "
g 5 3F=D 1 1
A
p
=0:185(3) (Ellis-Ja e) 1+ =
1
12 g 3 F=D +1
V
# "
1 g 5 3F=D 1
A
n
= =0:024(3) (Ellis-Ja e) 1+
1
12 g 3 F=D +1
V
3
With O ( ) p erturbative QCD corrections for the non-singlet co ecient C and with
NS
S
2
O ( ) for the singlet co ecient C .
SI
S
1 1 (3F D )
p(n)
= C (F + D )+ (3F D ) + C
NS SI
1
12 36 9
p
2
n 2
=0:170(5) = 0:017(4) Q = 10 GeV
1
1
------
g =g =1:2573(28) (Ratio of axial to vector weak coupling constant in neutron
A V
b eta decay.)
2
(M )=0:117(5); (10 GeV )= 0:24(2) (Strong coupling constant.) [25]
S z S
F=D =0:575(16) (Co ecients in hyp eron semileptonic decay.) [14]
Three quark avours
Figure 3: Spin p olarization sum rules. 4
Z
1
1 1 1
p(n)
+( ) g dx = C (F + D )+ (3F D ) + C
NS SI
1
12 36 9
0
3
With O ( ) p erturbative QCD corrections for the non-singlet co ecient C and with
NS
S
2
O ( ) for the singlet co ecient C , using three quark avours:
SI
S
2 3
p(n)
g
1 1
A
S S S
3:58 20:21 +( ) + = 1
S
1
g
12 36
V
2
1
3
S S
+ 1 0:33 0:55 + O ( )
S
9
g
A
=3F D =1:2573(28) Isospin invariance a =
3
g
V
a = 3F D =0:579(32) SU (3) symmetry
g
In the Quark Parton Mo del
Z
n o
1
+ +
q = [q (x) q (x)+q (x) q (x)] dx
0
a = (u +d+s)=
0
a = (u d)
3
a = (u +d 2s)
g
For the Ellis-Ja e sum rule, s = 0 and a = a =(u+d).
0 8
Figure 4: Spin content of the nucleon.
2 THE SMC EXPERIMENT
The Spin Muon Collab orati on at CERN (see Fig. 5) has measured p olarized deep
inelastic muon-proton and muon-deuteron scattering with incidentmuon energy E =
190 GeV. (A small amount of early data was taken with E = 100 GeV). Most of the
data were obtained with b oth muon and target spins along the incidentmuon b eam
direction, but a relatively small amount of data was also obtained with b oth proton and
deuteron target spins p erp endicular to the muon b eam direction in order to measure the
p
d
asymmetries A and A . Data have b een taken in 1992, 1994 and 1995 with a deuteron
2
2
target and in 1993 with a proton target. The nal year of data-taking will b e 1996 with a
proton target. Pap ers have b een published giving our results on spin structure functions
[10{15] and also describing some of our instrumentation [16{18].
The muon sp ectrometer is shown in Fig. 6. It detects and identi es the muon scat-
tered from the p olarized target and measures its momentum and scattering angle. Muon
identi cation is accomplished with the streamer tub e (ST/67) and drift tub e (DT/67)
chamb ers downstream of the iron absorb er, and the momentum and scattering angle
measurement is obtained from the data of some 150 planes of the prop ortional , drift and
streamer tub e chamb ers. The momentum and muon scattering angle are determined with
accuracies of ab out 1% and =0:4 mr, resp ectively. 5
THE SPIN MUON COLLABORATION (SMC)
University of Bielefeld
G. Baum, S. Bultmann, D. Kramer
Bogazici University,C ekmece Nuclear Research Center,
Istanbul Technical University and Istanbul University
E. Arik, T. C uhadar, E. Gulmez, C. Ozb en, I. Reyhancan, G. Unel
University of California, Los Angeles
C. Dulya, B. Derro, M. Grosse-Perdekamp, G. Igo, C. Whitten
CERN
P. Hautle, W. Kroger, J. Kyynarainen, T.O. Niinikoski, A. Rijllart,
U. Stiegler, R. Voss
UniversityofFreiburg
H.J. Kessler, U. Landgraf, A. Witzmann
GKSS
H. Stuhrmann, R. Willumeit, J. Zhao
Helsinki UniversityofTechnology
P. Berglund
University of Houston
C. Fernandez, J.A. Garzon, A. Gomez, B. Mayas,
L. Pinsky, S. Lop ez-Ponte
JINR, Dubna
A. Karev, Yu. Kisselev, V. Krivokhijine, K. Medved, A. Naga jcev,
D. Peshekhonov,D.Pose, I. Savin, G. Smirnov
University of Mainz
D. von Harrach, E.M. Kabuss, G.K. Mallot, J. Pretz, A. Steinmetz
University of Mons
R. Windmolders
University of Munich
L. Betev, A. Staude, J. Vogt
Nagoya University
T. Hasegawa, N. Hayashi, N. Horikawa, S. Ishimoto, T. Iwata, A. Kishi, T. Matsuda, K. Mori, A. Ogawa,
NIKHEF, FOM and Free University, Amsterdam
R. van Dantzig, N. de Gro ot, T.J. Ketel, M. Litmaath, G. van Middelko op, J.E.J. Ob erski, H. Postma, E.P. Sichtermann
Northeastern University
E. von Go eler, J. Moromisato
Northwestern University
D. Fasching, D. Miller, R. Segel, M. Velasco
Rice University
B.E. Bonner, S. Eichblatt, T. Gaussiran, J.B. Rob erts
SaclayDAPNIA
E. Burtin, N. de Botton, F. Feinstein, B. Frois, J.-M. Le Go ,
F. Lehar, A. de Lesquen, A. Magnon, F. Marie, J. Martino, F. Perrot-Kunne, S. Platchkov
University of Santiago de Comp ostela
B. Adeva, G. Gracia, C.A. Perez, M. Plo, M. Ro driguez, J. Sab orido,
Tel Aviv University
J. Lichtenstadt, I. Sab o
UniversityofTrieste
R. Birsa, F. Bradamente, A. Bressan, M. Clo cchiatti, J. Cranshaw, S. Dalla Torre, M. Giorgi, M. Lamanna
A. Martin, A. Penzo, R. Puntaferro, P.Schiavon, F. Tessarotto, A.M. Zanetti
Uppsala University
A. Arvidson, P. Bjorkholm, A. Dyring, M. Ro driguez
University of Virginia
D. Crabb, J. McCarthy,
Warsaw University and Soltan Institute for Nuclear Studies
B. Badelek, J. Nassalski, E. Rondio, A. Sandacz, W. Wislicki
Yale University
A. Deshpande, S. Dhawan, V.W. Hughes, R. Piegaia,
Sp okesman: V.W. Hughes
Contactman: A. Magnon
Figure 5: Spin Muon Collab orati on (26 Institutes and 151 Physicists). 6 ST67 DT67 H3V/H H4H H1V/H V3 H2 FSM W2 W45 BHA BHB PV1 B8 W1 P45 µ+ V1 V1.5 V2.1 V2 PV2 B7 Q33 H5 H6 B9 100–200 GeV Pµ = –0.8 4.5 × 107 /2.7 s every 14.4 s V4 polarized BEAM MWPC target MWPC 15/16 P1 P2 P3 17/18 P0B P0C P0D P0E P0A ABS ABS ABS TARGET S1 H1’ S2 H3’ S3 H4’ S4 BEAM DEFINITION
-30 -20 -10 0 10 20 DISTANCE FROM FSM - CENTER (m) Momentum Chamber Veto Hodoscope Muon identification Pµ
Momentum measurement Pµ
Figure 6: SMC muon sp ectrometer, including ho doscop es, p olarized target, prop ortional
wire chamb ers, drift chamb ers, calorimeter (H2), streamer tub es, drift tub es and iron
absorb er.
Our large p olarized target is based on the metho d of dynamic nuclear p olarization
with butanol and deuterated butanol as the target material. The target material is divided
into two cells each 65 cm in length and 5 cm in diameter. Figure 7 shows the magnet and
the dilution refrigerator. A sup erconducting solenoid provides a homogeneous magnetic
eld of 2.5 T and the dilution refrigerator achieves a temp erature of 40 mK in frozen spin
op eration. Two microwave frequencies of ab out 70 GHz allow p olarizing the target in either
direction with resp ect to the magnetic eld direction. Target p olarization is measured by
nuclear magnetic resonance with a relative accuracy of ab out 3%. Polarizations of 0.86
for protons and of 0.5 for deuterons were obtained. A sup erconducting dip ole magnet
with a 0.5 T eld p erp endicular to the solenoid eld is part of the magnet system. It is
used together with the solenoid to mo dulate the target spin direction by rotating the eld
direction, and also to provide a target p olarization p erp endicular to the b eam direction. 7 VACUUM VESSELS SUPERINSULATION He-3 PRECOOLER He-4 EVAPORATOR SEPARATOR AND SIPHON THERMAL RADIATION SHIELDS DILUTION REFRIGERATOR MICROWAVE CAVITY TARGET HOLDER TARGET MAGNET HELIUM BATH SUPERCONDUCTING COILS
MAGNET COIL FORMER
Figure 7: Sup erconducting magnet and dilution refrigerator for the SMC p olarized target.
The p olarization of the muon b eam, P , is determined bytwo metho ds. The rst
+ +
metho d measures the e energy sp ectrum from decay (Fig. 8) and values of P re-
p orted thus far have b een determined by this metho d with a relative accuracy of ab out
4%. The value of P is ' 0:8. The second metho d is based on measuring the spin dep en-
dent asymmetry in the elastic scattering of p olarized muons by p olarized electrons in a
magnetized iron target, and consistent results are b ecoming available from this metho d.
Aschematic diagram of the p olarimeter apparatus used for b oth metho ds is shown in
Fig. 9. 8 2.0 Pµ = -1
Pµ = 0
1.5 Pµ = +1
dN/dy 1.0
0.5
0 0 0.2 0.4 0.6 0.8 1.0 ÷ +
y = Ee /Eµ
+ +
Figure 8: Energy sp ectrum of p ositrons from muon decay, ! +e + + , for
e
longitudinal muon p olarizatio ns P = 1; 0; +1.
HMD PPC4
BVU BVD SVV MNP26 MAGNETIZED BEAM SVH B10 VACUUM PIPE TARGET PBC7 HMS
Pb B9 Q34 Q35 PBC1 PBC2 PBC3 PBC4 PBC6 PPC1 PBC5 PPC2 PPC3 VLG HLG Pb LG
30 40 50 60 70 80 DISTANCE FROM FSM - CENTER (m)
Chamber Veto Hodoscope
+
Figure 9: SMC muon p olarimeter, indicating apparatus for b oth the decay and the
+
;e scattering metho ds.
The kinematic range and the event distribution obtained for E = 190 GeV with a
2 2 2
proton target is shown in Fig. 10. Wehavechosen Q = 1 GeV as the low Q cuto for
DIS which corresp onds to x = 0.003. Note that there is a substantial b o dy of data with
2
2 4
< 1 GeV and x extending down to ab out 4 10 . In our analysis of DIS data we Q
0
take the cuts: y<0:9; > 20 GeV;P > 19 GeV and >13 mr.
9
Figure 10: Kinematic distribution of p scattering events.
The approach used to extract the virtual photon-proton asymmetry A from the
1
measurements of the total scattered muon counts from the upstream and downstream
target halves with b oth target p olarizatio n directions is shown in Fig. 11.
p
2
All the DIS data available on A (x; Q ) from SLAC [19{21], EMC [22] and SMC
1
p
2
exp eriments are shown in Fig. 12. Analysis of these data concludes that A (x; Q )is
1
p
2
indep endentofQ within the statistical errors. All the available data on A (x) are plotted
1
in Fig. 13.
2
2
The data cover the x range from x = 0.003 to x = 0.75 with Q varying from 1 GeV
2
2
at the lowest x to Q = 60 GeV at high x. The electron data from SLAChave small
statistical errors whereas the muon data from CERN extend to smaller x and have higher
2
Q . Systematic errors are comparable for the electron and muon data. Data from the
electron and muon exp eriments are in go o d agreement.
p p
The values of the spin structure function g (x), obtained from A as indicated in
1 1
2
Fig. 2, are plotted for all available data in Fig. 14 at the Q values of the data. The F
2
values are taken from NMC results [23] and R values from the SLAC parametrization
p
[24]. Figure 15 shows g (x)values taken from Fig. 14 normalized to the common value of
1
2 2
2 2 2
Q for SMC data. F and R values for Q = 10 GeV = 10 GeV , which is the mean Q
2
0
p
2
. were used but A was taken to b e indep endentof Q
1 10 Φσ η N = na 0 [1Ðf Pµ PDt (A1 + A 2 )] { ↑↓ ↑↑ σ Ð σ A = ↑↓ ↑↑ σ + σ
Up Down µ+ → Nu a→u N→ d ad
Reversed Polarization
N→ «u a«u Nd « a«→d
0 0 0
N N a =a
d
u u d
(1 + 4fP P DA + :::) =
t 1
0
N N a =a
u u d
d
n; ; CANCEL
0
ONLYACCEPTANCE RATIO MUST BE CONTROLLED
3 2
`Raw asymmetry' 10 to 10
Figure 11: Extraction of the asymmetry A from the measurements. The subscripts u and
1
d refer to the upstream and downstream target cells, n is the numb er of target nucleons,
the b eam ux, a the apparatus acceptance, the unp olarized cross section, f the fraction
0
of the event yield from the protons in the target material (dilution factor), and P and
P are the b eam and target p olarizations.
u;d 11 SMC EMC Proton SLAC
10 p 1 p 1
A x= 0.049 A x= 0.467 (+ 4.0) 4 (+ 8.45)
8 x= 0.035 (+ 3.2) 3 x= 0.342 (+ 6.34)
x= 0.025 6 (+ 2.4)
2 x= 0.243 x= 0.014 4 (+ 4.24) (+ 1.6)
x= 0.173
1 (+ 2.66) x= 0.008 (+ 0.8) 2 x= 0.123
(+ 1.34) x= 0.005 0 (+ 0.0) x= 0.078 0 (+ 0.0) 2 1 10 1 10 10 22
Q (GeV/c) Q 22 (GeV/c)
p
2
Figure 12: A for the proton as a function of Q for di erentvalues of x. The maximum x
1
value for each bin is shown. The numb ers in parentheses corresp ond to the vertical scale
o set of each data set.
1 p A1 E80/E130 (1983) 0.8 EMC (1988) SMC (1993) E143 (1994) 0.6
0.4
0.2
0
-2 -1
10 10 x 1
p
Figure 13: The virtual photon-proton cross-section asymmetry A as a function of x. Only
1
statistical errors are shown with the data p oints. The size of the systematic errors for the
SMC p oints are indicated by the shaded area. 12 2.5 p g1(x) Yale-SLAC (1983) 2 EMC (1983) SMC (1993) E143 (1994) 1.5
1
0.5
0
-0.5 -2 -1
10 10 x 1
p
2
Figure 14: The spin-dep endent structure function g (x) at the average Q of each x bin.
1
Only statistical errors are shown with the data p oints. The size of the systematic errors
for the SMC data is indicated by the shaded area.
3 p g1 2.5 2 2 Q0 = 10 GeV Yale-SLAC (1983) 2 EMC (1983) SMC (1993) 1.5 E143 (1994)
1
0.5
0
-0.5 -2 -1
10 10 x 1
Figure 15: The spin-dep endent structure function g (x) taken from Fig. 14 and normalized
1
p
2
2 2 2
to Q = 10 GeV using exp erimental values for F (x; Q ) and R(x; Q ) and assuming A
2
1
0
2
is indep endentofQ .
An exploratory measurementwas made with the proton target p olarizatio n direction
p
transverse to the incidentmuon b eam direction. The A values obtained are shown in
2
Fig. 16. They are consistent with zero and hence much smaller than the p ositivity limit
p
R , given in Fig. 2. of A <
2 13 0.8 SMC A2 0.6
0.4
0.2
0
-0.2 -3 -2 -1 10 10 10 1
X
p
Figure 16: The asymmetry A as a function of x. The solid line shows R from the SLAC
2
parametrization. The error bars represent statistical errors only. The dashed line is a term
2
obtained from g (x; Q ) alone [13].
1
3 INTERPRETATION AND CONCLUSIONS
Some of the most imp ortant conclusions asso ciated with the nucleon spin dep endent
p
structure functions come from their rst moments. Values of xg (x) and of the integral
1
R
p p
1
g (x)dx are plotted in Fig. 17 as well as the extrap olated exp erimental value for
1 1
x
m
and the theoretical value as predicted by Ellis and Ja e. The statistical and systematic
p
errors asso ciated with are shown in Fig. 18. 1
0.20
Ellis-Jaffe 0.08 0.15
(x) (x)
1 p
0.10 g (x) dx
x p 1 1 g m
x 0.04
0.05
0 0 10Ð2 10Ð1 1
x
p
Figure 17: The solid circles (right-hand axis) show the structure function xg as a function
1
2
2
of the Bjorken scaling variable x, at Q = 10 GeV : The op en b oxes (left-hand axis) show
0
R
p
1
(x)dx, where x is the value of x at the lower edge of each bin. Only statistical errors g
m
1
x
m
R
p
1
are shown. The solid square shows our result g (x)dx, with statistical and systematic
1
o
errors combined in quadrature. Also shown is the theoretical prediction by Ellis and Ja e. 14
Beam p olarizatio n 0.0057
Uncertaintyon F 0.0052
2
Extrap olation at low x 0.0040
Target p olarization 0.0039
Dilution factor 0.0034
Acceptance variation r 0.0030
Radiative corrections 0.0023
Neglect of A 0.0017
2
Momentum measurement 0.0020
Uncertaintyon R 0.0018
Kinematic resolution 0.0010
Extrap olation at high x 0.0007
Total systematic error 0.0113
Statistics 0.0114
p
Figure 18: Contributions to the error on .
1
p
It is clear that the exp erimental value for disagrees with the Ellis-Ja e value.
1
p
The several measured values of and the theoretically predicted value of Ellis and
1
2
Ja e, which dep ends on Q , are shown in Fig. 19. All exp erimental values are in clear
disagreement with the theoretical predictions.
Γp 2 1(Qo) 0.2
0.18 Ellis-Jaffe prediction
0.16
0.14 SMC
0.12 WORLD
0.1 E143 EMC/SLAC
0.08
0.06
0.04 246810122 2
Qo(GeV )
p
2
Figure 19: Measured values of (Q ) and the Ellis-Ja e prediction, in which the uncer-
1
0
tainty given by the shaded area arises principally from the exp erimental error in F/D.
d
For the deuteron the values for A from the SLAC and SMC measurements are
1
d
plotted in Fig. 20 and are seen to b e in go o d agreement. Figure 21 shows the values of g
1
2
2 d 2
and with at Q = 5 GeV obtained under the assumption that A do es not dep end on Q
0 1
d d d
values of F from other exp eriments. Values of and R disagree with the Ellis-Ja e
2 1
prediction (Fig. 22). 15 d A1 0.6 0.5 SMC E143 0.4
0.3
0.2
0.1
0
Ð0.1
Ð0.2 Ð2 Ð1
10 10 x 1
d
Figure 20: The virtual-photon deuteron cross section asymmetry A as a function of the
1
2
scaling variable x at the average Q of each x bin. Only statistical errors are shown on the
data p oints. The size of the systematic errors is indicated by the shaded areas. Results
from the SLAC E143 exp eriment are shown for comparison.
1 d g1 0.5
0
-0.5 2 2 Q0 = 5 GeV -1 SMC E143 -1.5
-2
10 10-1 X 1
d
Figure 21: The spin-dep endent structure function g (x) as a function of the scaling variable
1
2
2
xevaluated at a common Q = 5 GeV . Only statistical errors are shown on the data
0
p oints. Results from the SLAC E143 exp eriment are shown for comparison. The size of
the systematic errors is indicated by the shaded areas.
n
Several exp eriments have determined A for the neutron. Perhaps the most direct
1
3 n
He target. A is the SLAC exp eriment E142 which used a p olarized has also b een deter-
1
mined by SMC from their deuteron and proton data by subtracting the proton asymmetry
from the deuteron asymmetry, taking into account the D state admixture in the deuteron 16
wavefunction. Similarly SLAC E143 which used p olarized deuteron and proton targets has
n n
also determined A . The data are shown in Fig. 23 with the values of A from the various
1 1
2
n 2
exp eriments in go o d agreement. Values of g are shown for Q = 5 GeV in Fig. 24, where
1 0
n
the rather large negativevalues at low x are apparent. Values of obtained from the
1
n
exp eriments and predicted by Ellis-Ja e are shown in Fig. 25. The values from SMC
1
n
and E143 disagree with the Ellis-Ja e prediction whereas from E142 is in reasonable
1
n
agreement. We b elieve that this di erence is due to the negativevalues of g at x values
1
b elow those measured in E142 and the asso ciated diculty with their extrap olation to x=0.
Γd 2 1(Qo) 0.09
0.08 Ellis-Jaffe prediction
0.07 0.06
0.05
0.04 E143 SMC (92+94) 0.03
0.02 WORLD
0.01
0 246810122 2
Qo(GeV )
d 2
(Q ) and the Ellis-Ja e prediction, in which the uncer- Figure 22: Measured values of
1 0
tainty given by the shaded area arises principally from the exp erimental error in F/D. 17 n A1 0.6 SMC 0.4 E143 E142 0.2
0
-0.2
-0.4
-0.6
-2 -1
10 10 x 1
n
Figure 23: The virtual photon deuteron cross-section asymmetry A as a function of the
1
2
scaling variable x at the average Q of each x bin. Only statistical errors are shown on the
data p oints. The size of the systematic errors is indicated by the shaded areas. Results
from the SLAC E143 exp eriment are shown for comparison.
n g1 0
-1
-2
Q2 = 5 GeV2 -3 0 SMC E143 -4 E142
-2 -1
10 10 x 1
n
Figure 24: The Spin-dep endent structure function g (x) as a function of the scaling vari-
1
2
2
able x evaluated at a common Q = 5 GeV . Only statistical errors are shown on the data
0
p oints. Results from the SLAC E142 and E143 exp eriments are shown for comparison.
The size of the systematic errors is indicated by the shaded areas. 18 Γn 2 1(Qo)
0 Ellis-Jaffe prediction
-0.02
-0.04 E142 E143
-0.06 SMC
-0.08
-0.1 246810122 2
Qo(GeV )
n 2
Figure 25: Measured values of (Q ) and the Ellis-Ja e prediction, in which the uncer-
1 0
tainty given by the shaded area arises principally from the exp erimental error in F/D.
The contribution of the quark spins to the nucleon spin can b e evaluated as
indicated in Fig. 4. Figure 26 plots the values of , the fraction of the nucleon spin
of 1/2 due to all the quark spins and of s due to the strange quarks. This evaluation
has assumed that the contribution G from p olarized gluons is zero. The result from
SMC data alone is = 0:22 0:09; u =0:80 0:03; d = 0:46 0:03 and s =
2
2
0:12 0:03 at Q = 10 GeV . These results are in agreement with the average values
from all exp eriments. Hence quark spins contribute only a small fraction of the nucleon
spin and thus the gluon spin and orbital angular momenta must contribute the remainder.
0.7 Q2 = 5 GeV2 ∆Σ E142 neutron o 0.6 E143 proton E143 deuteron SMC deuteron 0.5 SMC proton World average 0.4 Ellis-Jaffe prediction
0.3
0.2
0.1
0 -0.175 -0.15 -0.125 -0.1 -0.075 -0.05 -0.025 0 0.025
∆S
Figure 26: Exp erimental results on the total () and strange (s) quark contributions
2
2
to the nucleon spin at Q = 5 GeV .
The test of the fundamental Bjorken p olarization sum rule provided from SMC data
alone is shown in Fig. 27. The width asso ciated with the theoretical prediction is due to
uncertainty in the strong coupling constant . Theoretical and exp erimental values agree
S
within the one standard deviation exp erimental error of ab out 19%. Combining results
from all SLAC and CERN exp eriments yields a con rmation at the 10% level. 19 n 2 ∫ g dx Q = 10 GeV 2 1 o
0.1
Bjorken Sum Rule
∫ p -0.1 0 0.1 0.2 g1 dx 0
-0.1
SMC (d) -0.2
SMC (p)
Figure 27: Con rmation of the Bjorken p olarizatio n sum rule, based on SMC data alone.
Figure 28 lists the completed exp eriment on spin dep endent structure functions.
SMC has completed a 1995 run with a p olarized deuterated butanol target and plans a
1996 run with NH .
3
Exp eriment Beam Energy Target x range First moment
R
1
2
2 2 2
(GeV) (Q > 1 GeV ) = g (x)dx at [Q in GeV ]
1 1
0
0
E-80/E-130; 1976, 83 e 10{23 p (butanol) 0:1 x 0:7
+ 1)
EMC; 1988, 89 100{200 p (NH ) 0:01 x 0:7 0:126 0:010 0:015 [10.7]
3
+
SMC; 1993 100 d (butanol) 0:006 x 0:6 0:023 0:020 0:015 [4.6]
3
E-142; 1993 e 19{23 n( He) 0:03 x 0:6 0:022 0:011 [2]
+
SMC; 1994 190 p (butanol) 0:003 x 0:7 0:136 0:011 0:011 [10]
E-143; 1995 e 10,16,29 p (NH ) 0:03 x 0:8 0:127 0:004 0:010 [3]
3
2)
e 29 d (ND ) 0:03 x 0:8 0:041 0:003 0:004 [3]
3
+ 2)
SMC 190 d (butanol) 0:003 x 0:7 0:033 0:009 0:005 [10]
1)
Combined result of E-80, E-130 and EMC data
2)
Preliminary, unpublished
Figure 28: Completed exp eriments on nucleon spin structure functions.
In the overall eld of nucleon spin structure the ma jor exp erimental problems are
2
to measure the Q dep endence of A , the low x b ehaviour of g , and g . The contribu-
1 1 2
tion of gluon p olarization to the nucleon spin is of particular currentinterest. Several
di erent exp eriments are b eing considered. These include studies of exclusive p olarized
deep inelastic scattering and the use of two p ossible new ma jor facilities for the study of 20
nucleon spin structure: p olarized protons in the relativistic heavy ion collider (RHIC at
Bro okhaven) and p olarized protons at high energy in the HERA ring (DESY) [26, 27].
ACKNOWLEDGEMENTS
Research supp orted in part by the U.S. Department of Energy. 21
References
[1] V.W. Hughes and J. Kuti, Ann. Rev. Nucl. Sci. 33 (1983) 611.
[2] V.W. Hughes and C. Cavata, eds. Internal Spin Structure of the Nucleon (World
Scienti c, Singap ore, 1995).
[3] R. Voss, in Lepton and Photon Interactions, eds. P. Drell and D. Rubin (AIP, New
York, 1994), p. 144.
[4] R. Voss Experiments on PolarizedDeep Inelastic Scattering in Deep Inelastic Scat-
tering and QCD, eds. J.-F. Lap orte and Y. Sirois (Edition du Bicentenaire, Ecole
Polytechnique, France, 1995) to b e published.
[5] M. Anselmino, A. Efremov and E. Leader, CERN{TH.7216/94.
[6] J.D. Bjorken, Phys. Rev. 148 (1966) 1467; Phys. Rev. D1 (1970) 1376.
[7] S.A. Larin and J.A.M. Vermaseren, Phys. Lett. B259 (1991) 345.
[8] J. Ellis and R.L. Ja e, Phys. Rev. D9 (1974) 1444; D10 (1974) 1669.
[9] S.A. Larin, Phys. Lett. B334 (1994) 192.
[10] SMC, B. Adeva et al., Phys. Lett. B302 (1993) 533.
[11] SMC, B. Adeva et al., Phys. Lett. B320 (1994) 400.
[12] SMC, D. Adams et al., Phys. Lett. B329 (1994) 399; Errata Phys. Lett. B339 (1994)
332.
[13] SMC, D. Adams et al., Phys. Lett. B336 (1994) 125.
[14] SMC, D. Adams et al., Phys. Lett. B357 (1995) 248.
[15] V.W. Hughes, in Deep Inelastic Scattering and Related Subjects, ed. A. Levy (World
Scienti c, Singap ore, 1994), p. 237.
[16] SMC, B. Adeva et al., Nucl. Instr. and Meth. A343 (1994) 363.
[17] SMC, B. Adeva et al., Nucl. Instr. and Meth. 349 (1994) 334.
[18] SMC, B. Adeva et al., Enhancement of Nuclear Polarization with Frequency Modu-
lated Microwaves, to b e published in Nucl. Instr. and Meth.
[19] E142, P.L. Anthony et al., Phys. Rev. Lett. 71 (1993) 959.
[20] E143, K. Ab e et al., Phys. Rev. Lett. 74 (1995) 346.
[21] E143, K. Ab e et al., SLAC PUB, preprint 6997 (1995).
[22] EMC, J. Ashman et al. Nucl. Phys. B328 (1989) 1.
[23] NMC, P. Amaudruz et al., Phys. Lett. B295 (1992) 159 and preprint CERN-PPE/92-
124 (July 1992); Errata Oct. 26 (1992) and Apr. 19 (1993).
[24] L.W. Whitlow et al., Phys. Lett. B250 (1990) 193. We use the parametrization
published in L.W. Whitlow, PhD thesis, Stanford University, 1990.
[25] Review of Particle Properties Phys. Rev. D50 (1994) Part 1.
[26] Workshop on Prospects of Spin Physics at HERA (DESY-ZEUTHEN, August, 1995),
to b e published.
[27] Deep Inelastic Scattering and QCD, eds. J.-F. Lap orte and Y. Sirois (Edition du
Bicentenaire, Ecole Polytechnique, France, 1995), to b e published. 22