hep-ex/9610007 14 Oct 1996 Study NR Deep F Y P Mey P on  L Szalata Electrons Johnson W A LPC La Roblin Lom vieille ork supp orted b Stanford California Bosted Dietric er Univ Newbury An Cen wrence Souder bardNelsen National W thon INPCNRS Univ tre American Inelastic ersit ZE Old o o ds of Princeton h Y R Syracuse Stanford SE Ken y dEtudes Liv V Linear D ersit y Dominion T the Institute J Gearhart y Departmen Meziani of errien M t Breton ermore Ka Ro c Institute GG Dunne State J y RG California b Gaithersburg The Sp engos w Univ GifsurYv of Xu Accelerator y k Neutron all Univ Univ Univ J de Mic P Univ E Arnold Univ P Cedex AK of National etratos SH Marroncle t of Energy con Scattering ersit Univ Sacla GD ersit ersit R higan olarized ersit of CC T C R ec H ersit y Standards and Erbac Rokni Collab oration Thompson ersit Kepp el Blaise F Holmes hnology y y ette y y Cates W F Middleton Y Cen Syracuse Stanford rance Staley D y HR Princeton Ann MD ashington Lab oratory LBL oung y APNIASPhN her Ken tract DEA R F Spin Norfolk ter P T rance Arb or ascal G Band Pitthan P SE t Berk TE and Maruy EW asadena Stanford LM J G Shapiro OH He JL of CA NY CSF F Kuhn eley NJ T F DC Structure Zapalac SLA J Ch V ellbaum MI ec Liv Hughes ama A H Septem Stuart White P Morgenstern and hnology upp ermore CA CPUB R olarized CA Borel F CA T Prep ost Aubiere FS b er Smith RM the H W ZM CA M P JR E

Temple University Philadelphia PA

University of Wisconsin Madison WI

Abstract

The neutron longitudinal and transverse asymme

n n

tries A and A have b een extracted from deep inelas

tic scattering of p olarized electrons by a p olarized He

target at incident energies of and

GeV The measurement allows for the determination

n

of the neutron spin structure functions g x Q and

n

g x Q over the range x at an average

Q of GeVc The data are used for the evaluation

of the EllisJae and Bjorken sum rules The neutron

n

x Q is small and negative spin structure function g

within the range of our measurement yielding an inte

R

n

xdx stat sy st g gral

n

Assuming Regge b ehavior at low x we extract

R

n

xdx stat sy st g

Combined with previous proton integral results from

p

n

SLAC exp eriment E we nd

in agreement with the Bjorken sum rule prediction

p

n

at a Q value of GeVc

evaluated using

s

Submitted to Physical Review D

Intro duction

During the past twenty ve years exp eriments measuring spin

averaged deep inelastic scattering of electrons muons and neu

trinos have provided a wealth of knowledge ab out the nature of

QCD and the structure of the nucleon in terms of quarks and

gluons Among the highlights are the determination of scaling

violations from structure functions as predicted by QCD

leading to a value of the strong coupling constant and the

s

test of the GrossLewellynSmith sum rule in which QCD ra

diative corrections are veried within exp erimental errors More

recently p olarized deep inelastic scattering exp eriments which

prob e the spin orientation of the nucleons constituents are pro

viding a new window on QCD and the structure of the nucleon

Pioneering exp eriments with p olarized electrons and

protons p erformed at SLAC in the late s and early s

in a limited x range revealed large spin dep endence in deep

inelastic ep scattering These large eects were predicted by

Bjorken and by simple SU quark mo dels More recently re

sults from the CERN EMC exp eriment over a wider x range

have sparked considerable interest in the eld b ecause the data

suggest surprisingly that quarks contribute relatively little to the

spin of the proton and that the strange sea quark p olarization

is signicant

A central motivation for these exp eriments is a pair of sum

rules The rst due to Bjorken is a QCD prediction that

invokes isospin symmetry to relate the spindep endent structure

functions to the neutron b etadecay axial coupling constant g

A

The exp erimental test of this sum rule requires data on b oth the

proton and the neutron Advances in technology for pro ducing

highly p olarized b eams and targets make p ossible increasingly

precise measurements A second sum rule due to Ellis and

Jae which has more theoretical uncertainty applies to the

proton and neutron separately Assuming SU symmetry data

from either the neutron or proton can b e used to determine the

contributions of each quark avor to the spin of the nucleon

It is the apparent disagreement of the EMC proton data with

the prediction of the EllisJae sum rule that led to the striking

conclusions mentioned ab ove This pap er rep orts on a precision

n

determination of the neutron spin structure function g using a

p olarized He target

In spindep endent deep inelastic scattering one measures

the quantity

A x Q

where is the absorption cross section for virtual photons

with total J for the nal state

z

In the case of a target of Dirac particles A is unity In

QCD the nucleon may b e describ ed in terms of a set of quark

momentum distributions q x Q where x is the fraction of

i

nucleon momentum carried by the struck quark and Q is the

squared fourmomentum transfer to the nucleon The index i

includes u d and s quarks and antiquarks Thus for the nucleon

A measures how the individual quarks weighted by the square

of their charges are aligned relative to the nucleon as a whole

The q x Q have b een evaluated from the measured val

i

ues of the spin averaged structure function F x Q for vari

ous leptons and nucleon targets However the determination of

A x Q requires that quark momentum distributions b e de

comp osed in terms of spin Thus q x Q q x Q give the

i i

probability that a quark of typ e i has a fraction x of the nu

cleons momentum with its spin parallel antiparallel to that of

the nucleon Then

q x Q q q q x Q q x Q x Q x Q

i

i i i i

and

P

g x Q e q x Q

i

i

A x Q

P

q x Q e q x Q F x Q

i

i i

th

where e is the charge of the i quark

i

The latter equation denes the spindep endent structure func

tion g x Q A more precise denition of g and the relevant

kinematics is given in Section b elow

In the nonrelativistic quark mo del the spins of the quarks

relative to the spin of the nucleon are given by the SU wave

p

n

and A This functions resulting in the predictions A

p

simple picture holds approximately at x At low x A

decreases due to the dominance of sea quarks which one might

naively exp ect to have small p olarization In this region Regge

theory suggests that A x with At large x

A according to p erturbative QCD arguments Nu

cleon mo dels have b een constructed incorp orating these general

features and yield reasonable ts to the data for the

proton

The Bjorken sum rule however applies to the integrals of

g

Z

pn pn

Q g x Q dx

pn

The goal of the exp eriments is to measure g over as wide a

pn

kinematic range as p ossible to extract a value for

The pap er is organized as follows Section denes the the

oretical framework used in p olarized deep inelastic scattering

and tests of the Bjorken and EllisJae sum rules Section

discusses the exp erimental metho d and data collection Section

describ es the analysis leading to the raw asymmetries used

to extract the physics asymmetries A and A and spin struc

ture functions g and g of He Section rep orts on dilution

factor studies and radiative corrections while section rep orts

on the He results and the nuclear corrections used to extract

n n

and the spin and A the virtual photonneutron asymmetries A

n n

Section describ es the physics and g structure functions g

implications of the results and conclusions are presented in Sec

tion

Theoretical framework

Bjorken Sum Rule

The Bjorken sum rule prediction which relates high energy elec

tromagnetic scattering to the low energy b eta decay of the neu

tron was derived in the high Q limit by Bjorken using current

algebra and later shown to b e a rigorous QCD prediction with

calculable radiative corrections for nite Q This

sum rule may b e derived in QCD by using the Op erator Pro d

uct Expansion OPE The OPE relates integrals of quark

momentum distributions q x Q to matrix elements of single

i

op erators such as

q

i

q q jn si hn sj s G

i

i

An

q

i

where jn si represents a neutron n with spin s The G

An

are constants indep endent of Q although they do dep end on

the choice of renormalization scale There are dierent G s

A

corresp onding to each combination of quarks and baryons in the

lowest o ctet They are related by isospin and SU symmetry

so that in the limit that SU is exact only three indep endent

quantities remain

u

G u

Ap

d

G d

Ap

s

G s

Ap

These are the matrix elements of the proton With the lat

ter notation one must b e very careful to distinguish q from

q x Q

Useful linear combinations of the matrix elements are

u d

a g G G

A

Ap Ap

u d s

a G G G

Ap Ap Ap

u d s

a G G G

Ap Ap Ap

Similar combinations for the quark momentum distributions are

q x Q ux Q dx Q

q x Q ux Q dx Q sx Q

q x Q ux Q dx Q sx Q

Here q x Q is the nonsinglet combination and q x Q

is the singlet combination An immediate advantage of this no

tation is that a and a are constants indep endent of the renor

malization scale on the other hand dep ends on the

scale and sp ecial care must b e used when interpreting this quan

tity Using the ab ove notations the main result of OPE gives

Z

q x Q dx

P P

Q

K

s n

m

C a

n m

n m

Q

The p erturbative QCD series in Q describ es high en

s

ergy or short distance eects and has b een recently evaluated

exactly up to third order in QCD The p ower series in Q in

Eq contains the higher twist terms These terms describ e

longdistance nonp erturbative b ehavior that involves among

other eects the details of the wavefunctions of the quarks in

the nucleon The calculation of some of these terms has b een

the sub ject of recent literature It is exp ected that the con

tributions of these terms are small for the Q range discussed in

this pap er

The spin dep endent structure function g x Q measures the

dierence in numb er of partons with helicity parallel versus anti

parallel to the helicity of the nucleon weighted by the square of

the parton charge Explicitly we have

X

pn

e q x Q x Q g

i

i

ux Q dx Q sx Q

The Bjorken sum rule follows from Eqs and

p

B j n

Q Q Q

Q Q Q

s s s

g

A

where the upp er lower numb ers are for three four quark a

vors and higher twist terms have b een neglected The numb er

of active quark avors is determined by the numb er of quarks

with m Q taking m GeV and m GeV For our

q c b

case we use three avors since the eects of charm are exp ected

to turn on slowly

B j

Measuring at dierent Q provides a sensitive test of

QCD and its radiative corrections It is one of two QCD sum

rules the GrossLlewellynSmith b eing the other where the

right hand side of the sum rule is accurately known With suf

ciently precise data one can extract based on the Bjorken

S

sum rule and compare with the determination of from other

S

pro cesses

The Nucleon Sum Rule

The sum rule for a single nucleon is

pn

Q

s s s

g a

A

s s

Q

where the upp er lower co ecients are for three four avors

To leading order this expression requires a new nucleon matrix

element a which can only b e estimated from nucleon

mo dels As p ointed out by M Gourdin a F D as

determined from baryon b eta decay if avor SU symmetry

is assumed Then may b e determined from the sum rule

is an imp ortant input for nucleon mo dels Much of the ex

citement in the eld arises from the unexp ected EMC result

that In the nonrelativistic quark mo del How

ever the motion of the quarks should give a suppression similar

to the suppression of g from to the exp erimental value of

A

yielding In addition gluons and orbital angular

momentum may make substantial contributions to the spin of

the proton The present world average of was not

anticipated by most authors prior to the measurements

In addition is also needed for predicting elastic scatter

ing cross sections Two examples of physical pro cesses involving

are neutrino scattering and the scattering of p ossible sup er

symmetric particles

Eq involves singlet op erators which in leading order of

QCD includes the AdlerBellJackiw ABJ anomaly b e

cause the relevant anomalous dimension is nonzero One result

is the scale dep endence of Any physical pro cess dep en

dent on must also involve other dep endent factors such

that the result is indep endent of For example part of the

neutrinoproton elastic scattering cross section arises from the

current

z s J

the weak charge of the proton This Here z

quantity is just in the SUU electroweak theory and

is scaledep endent The scale dep endencies of z and cancel

so that J is scaleindep endent and thus a measurable physical

quantity Moreover cho osing M helps minimize

Z

Strikingly it is with GeVc that is needed to

compute neutrino scattering at Q

For our results we have chosen to use the scale Q to

avoid passing over quark thresholds If exp eriments p erformed

at dierent Q are compared the scale of one or b oth of the

exp eriments should b e changed according to the formula

s s

s s

or Ideally one would cho ose a universal scale M

P

M however the rst option suers from the fact that M

s P

Z

is not well known and the second option requires running the

scale across several mass thresholds which yields even more com

plex expressions Another option commonly used is to dene a

quantity and use the formula

inv

pn

Q

s s s

g a

A

s s

inv

We will also quote for our data

inv

The individual quark contributions can b e extracted using

either Eq or Eq along with a F D

u a g

A

d a g

A

s a

The EllisJae Sum Rule

Prior to the establishment of QCD Ellis and Jae made a

numerical prediction for the nucleon sum rule by arguing that

s

s G This gives the additional relation

A

a

which when combined with the value for a extracted from hy

p eron decay provides values for all of the needed matrix ele

ments As p ointed out by Jae this relation is rather cu

rious in the context of QCD b ecause a is scale indep endent

and is scale dep endent Hence the prediction of the El

lis Jae sum rule dep ends up on the scale chosen Exp eriment

E has used GeVc A more common choice is to

n

and should set a The dierence is ab out in

inv

b e accounted for when comparing dierent exp eriments

A second issue with the EllisJae sum rule is that Eq

pn

implies a large contribution to in Eq coming from a

so that the error a b ecomes imp ortant The determination

s

s from the nucleon sum rule also suers from this of G

A

problem

Given the imp ortance of a it is worth going into some detail

ab out its origin By assuming avor SU for the nucleon o ctet

we have

V j si hn sj V jn si hn sj

or in terms of quark op erators

u sj si g ns hn sj

A

u s

hn sj u u s sjn si G G

An An

d s

d d s sjp si G G s hp sj

Ap Ap

Thus the axial matrix elements for decay can b e related to pro

ton matrix elements Similar results hold for the other hyp eron

decays To average over many hyp eron decay measurements

the following relation is used

u s u d s

F hG i hG i and D hG i hG i hG i

Ap Ap Ap Ap Ap

Jae and Manohar assign a generous error F D

while Ratclie quotes a range of values form

to based on various assumptions ab out SU breaking and

f

which decays to use For the purp ose of this pap er we will use

a F D which is the up dated central value of

Close and Rob erts but has the generous error of Jae and

Manohar The net result is that the prediction of the Ellis

n

Jae sum rule for Q GeVc is The

uncertainty on F D translates to a uncertainty on

s which is not negligible compared to typical world averages

of s

An alternative denition equivalent in the limit of exact

SU that is often used in the literature is F D g n

A

p Then hyp eron data are used to ob

tain F D The world average based on the analysis of Close

and Rob erts is F D This result yields

n

with a substantially smaller uncertainty

while the uncertainty on s changes from to

The ab ove two alternatives illustrate how the prediction of

the EllisJae sum rule is sensitive to the various assumptions

chosen

The E exp eriment

The exp eriment discussed in this pap er was p erformed to mea

sure for the rst time the virtual photonnucleon spin asym

n n

metries A and A in deep inelastic scattering of p olarized

electrons by p olarized He From these asymmetries the neu

n n

tron spin structure functions g and g are extracted The ex

p eriment relied on the pro duction and delivery of a high energy

p olarized electron b eam at the Stanford Linear Accelerator Cen

ter SLAC The p olarized incident electrons were delivered to

End Station A where they scattered o a p olarized He target

and were detected in magnetic sp ectrometers The exp eriment

named SLAC E collected data over a p erio d of six weeks in

Novemb er and Decemb er of An overview of the primary

technical achievements of the exp eriment are presented in Table

Details of the p olarized electron b eam p olarimetry p olarized

target and magnetic sp ectrometers are discussed in subsequent

sections

n

from this Previous results on the spin structure function g

exp eriment have b een published This pap er rep orts on a

more thorough analysis of the results leading to a change in the

n

Among the new informa previously published results for g

tion presented in the present pap er are results on the neutron

n

transverse spin structure function g and the results on the Q

dep endence of the neutron longitudinal spin structure function

n

g

The Polarized Electron Beam

The SLAC p olarized electron source using an AlGaAs pho

to catho de at a temp erature of C pro duced the p olarized elec

tron b eam for this exp eriment Polarized electrons were

pro duced by illuminating the photo catho de with circularly p o

larized light at a wavelength near the bandgap edge of the pho

to catho de material AlGaAs with Al rather than GaAs

was chosen as the photo catho de since the larger band gap of the

AlGaAs catho de was a b etter match to the available ashlamp

pump ed dye laser op erating at a wavelength of nm The

electron helicity was changed randomly pulse by pulse by con

trolling the circular p olarization of the excitation light Using

this catho de the p olarized source pro duced an electron b eam

p olarization of ab out

Electrons from the source were accelerated to energies rang

ing from to GeV and directed onto the p olarized He

target The SLAC accelerator op erated with pulses of approxi

mately sec duration at a rate of Hz The b eam current

was quite high op erating at typically electrons p er pulse

The sp ectrometers collected typically events p er pulse from the

p olarized He target yielding approximately million events

for the exp eriment

The exp eriment collected data at three discrete energies of

GeV with an energy acceptance of typically

Since the primary b eam undergo es a b end b efore

reaching the exp erimental target the electron spin precesses

more than the momentum by an amount

g E

e

m

where E is the b eam energy m is the electron mass g is the

e

electron gyromagnetic ratio and is the angle b etween the

electron spin and momentum at the target When is an integer

multiple of the electron spin is longitudinal at the target

The energies and GeV satisfy this condition exactly

while the energy corresp onds to of the maximum

available p olarization This latter energy was the maximum

energy that the b eam line magnets could supp ort at the time

The b eam sp ot size was typically to mm at the target

Studies of the sp ot p osition and radius near the target as mea

sured by a wire array found no dep endence on b eam helicity at

the level of b etter than mm From mo dels of the variation

of the target window thicknesses it was determined that this im

plied that false asymmetries due to a p ossible helicitydep endent

motion of the electron b eam p osition would b e signicantly less

than

The electron b eam p olarization was determined using single

arm Mller p olarimetry The high p eak b eam currents precluded

the detection of double arm coincidences The cross section for

spin dep endent elastic electronelectron scattering is given by

X

j

i

P A P d d d d

ij

T B

ij

j

i

are the comp onents of the b eam p olarization and P where P

T B

are the comp onents of the target p olarization The z axis is

along the b eam direction and the y axis is chosen normal to

the scattering plane The cross section is given by the unp olar

ized cross section d d and the asymmetry terms A If P

ij T

is indep endently known the ab ove expression may b e used to

determine the b eam p olarization P

B

To lowest order the fully relativistic unp olarized lab oratory

cross section is given by

cos cos

CM CM

d d

L

m sin

CM

For the measurement of longitudinal p olarization with a lon

gitudinally p olarized target foil the only relevant asymmetry

term is A given by

z z

cos sin

CM CM

A

z z

cos

CM

Here is the centerofmass scattering angle m is the elec

CM

tron mass and is the ne structure constant The asymmetry

maximum is at where the unp olarized lab oratory

CM

cross section is bsr and A

z z

Most if not all Mller p olarimeters utilize thin ferromagnetic

foils as the p olarized electron target The distinction b etween

the free target electrons of the previous formulae and the b ound

atomic electrons of the physical target was ignored until re

cently when Levchuk p ointed out that the analyzing p ower

of Mller p olarimeters may have signicant corrections due to

the electron orbital motion of the target foil electrons Atomic

electrons have momentum distributions which are dierent for

dierent atomic shells Electrons in the outer shells have small

momenta but those from the inner shells have momenta up to

keV Although small compared to a b eam energy of

GeV these momenta are not small compared to the electron

rest mass and can alter the center of mass energy and thus the

scattering angle in the lab frame by up to The relative

angular smearing correction for p olarized and unp olarized elec

trons is shown in Fig The eect causes dierent line shap es

for scatters from dierent shells Since the p olarized target elec

trons are only in the d M shell the fraction of signal from the

p olarized target electrons and thus the exp ected Mller asym

metry varies over the Mller scattering elastic p eak Inclusion

of this eect has b een shown to mo dify the analyzing p ower

of Mller p olarimeters by up to dep ending on

the exact geometry of the p olarimeter Inclusion of this eect

mo dies the analyzing p ower of the E Mller p olarimeter by

The E Mller p olarimeter shown in Fig consisted of a

scattering target chamb er containing several magnetized foils a

collimator to dene the scattering angle and angular acceptance

a magnet to measure the momentum of the scattered electrons a

segmented detector array to detect the scattered electrons and

a data acquisition system

The magnetized target foils were made of Vacoux an

alloy of Co Fe and Va by weight The foils were

cm wide by cm long and were mounted at a angle with

resp ect to the b eam Three foils of approximate thickness

and m were installed Nearly all the Mller data were

taken with the two thinner foils The foils were magnetized by

Helmholtz coils providing a G eld along the b eam direction

The p olarity of the coils was typically reversed b etween Mller

data runs to alternate the sign of the foil p olarization and to

minimize systematic errors

The p olarization P of the target electrons was determined

T

from the relation

g g M

e

P

T

n g g

e B e

where M is the bulk magnetization in the foil n is the elec

e

tron density g is the free electron gyromagnetic

e

ratio and Gcm is the Bohr magneton

B

The factor involving the magnetomechanical ratio g includes

the correction for the orbital contribution to the magnetization

Interp olating b etween the measured g values of Fe and Co the

g of Vacoux was calculated to b e Substituting

into the ab ove equation yields

M

P

T

n

e B

The magnetization M was determined by direct ux measure

ments using a precise integrating voltmeter IVM connected to

a pickup coil placed around the foils From Faradays law as

the external H eld is swept b etween H and H the integral

of the induced voltage over time can b e related to the B and H

elds and hence the magnetization M through

R R

V dt V dt

in out

M B H

N A

T f oil

where in and out refer to ux measurements with the foil in and

out and A is the crosssection area of the foil Recognizing

f oil

that the foil density can b e determined from the measured mass

of the foil length and area A the foil p olarization P can b e

f oil T

determined from Eq and Eq

A radiation length thick tungsten mask lo cated me

ter from the Mller target restricted the scattering angles of the

particles entering the p olarimeter detector to

mrad The azimuthal acceptance of the rectangular mask op en

ing dep ended on the scattering angle and varied from to

rad with resp ect to the horizontal plane The scattered

particles next passed through a mm thick Mylar vacuum

window and entered a large ap erture sp ectrometer magnet The

R

meter long magnet was typically run at a B dl

kGm for the GeV data The sp ectrometer setting se

lects Mller scattered electrons at GeVc corresp onding to

a center of mass scattering angle of The eld integral was

adjusted during the exp eriment to p osition the Mller p eak in

the detector to comp ensate for dierent b eam energies and to

maximize signal and reduce background

The main b eam passed through a mm round hole in the

mask and continued down the E b eam line The b eam

exiting the central hole in the mask contained large numb ers

of low energy bremsstrahlung electrons pro duced by the target

foil Large magnetic elds would b end these particles out of the

b eamline generating unacceptable backgrounds in the detector

To reduce the eld along the b eamline a cm by cm soft

iron septum with a cm by cm hole for the b eam was inserted

in the magnet gap The septum reduced the B eld seen by the

R

b eam by ab out a factor of reducing B dl to approximately

Gm

After exiting the magnet the Mller scattered electrons trav

eled through a He bag to the detector lo cated meters from

the target The detector consisted of gas prop ortional tub es

emb edded in lead Each mm diameter brass tub e contained

a micron wire strung through the center The tub es were

placed in two parallel rows mm apart The rst row was b e

hind mm of lead The second row was mm b ehind the

front row and oset by mm giving an eective segmentation

of mm in the horizontal scattering plane The lead ab

sorb ed soft photon backgrounds and amplied the Mller signal

Since the momenta and scattering angle of the Mller scatters

are correlated the scatters fall in a tilted strip e at the detector

The detector was oriented so that the tub es were parallel to the

Mller strip e The active detector length of cm corresp onded

to a momentum acceptance of The entire detector package

was mounted on a vertical mover allowing dierent momenta to

b e selected

The signal in each tub e was integrated over the sec long

b eam pulse by a charge integrating preamplier The data to

gether with the sign of the b eam p olarization were recorded by

a p eak sensing analog to digital converter ADC system The

b eam p olarization was randomly reversed b etween pulses to re

duce systematic errors The numb er of Mller electrons detected

p er pulse varied with current and target thickness but was typ

ically p er pulse A typical Mller run lasted seconds and

contained a million Mller electron scatters

Beam Polarization Analysis

For each Mller run an average pulse height for each detector

channel was calculated for b oth right R and left L handed

incident b eam The pulse to pulse variance of the ADC val

ues was used to estimate the error in the average pulse height

These averages and errors were recorded with relevant b eam

currents detector and target p ositions and magnet settings

Typical measured distributions for RL and RL are shown

in Fig The RL distribution Fig a shows an elastic

scattering p eak with a radiative tail on top of an unp olarized

background The signal to background ratio varied with shield

ing conditions and b eam parameters from at the b eginning

of the exp eriment to after shielding improvements made

during the exp eriment The RL distribution Fig b is to a

go o d approximation pure Mller electron scattering and shows

only a radiative tail with no background

The b eam p olarization was determined by tting the ob

served elastic scattering and asymmetry distributions to line

shap es based on Mller scattering plus a background comp o

nent Although several techniques were used as cross checks

the full data sets were analyzed with a technique which derived

the Mller comp onent of the line shap es from the measured R

L distributions and used this shap e together with a quadratic

background comp onent to t the observed scattering distribu

tions In this technique all of the observed RL line shap e is

attributed to Mller scattered electrons and the background is

assumed to b e unp olarized

The analysis technique used the observed RL lineshap e and

the angular smearing functions shown in Fig to generate a

predicted RL lineshap e for Mller scatters For zero target

momenta the RL lineshap e and the RL lineshap es are iden

tical except for backgrounds The trial RL line shap e was gen

erated from the observed RL lineshap e by rst correcting for

the angular smearing due to the p olarized target electrons and

then convoluting the result with the smearing correction for all

p olarized and unp olarized target electrons Additional correc

tions were made for the variation of the cross section and change

of azimuthal acceptance with scattering angle and for the vari

ation in the value of the Mller scattering asymmetry over the

angular acceptance of the detector The observed RL distri

bution was then t by the predicted lineshap e plus a quadratic

background The solid line is Fig a shows the resultant tted

line shap e for the typical runs

The measured longitudinal b eam p olarization P is shown

B

in Fig for Mller p olarimeter data runs covering the last

weeks of the exp eriment Only runs with the Mller p eak well

centered and with statistical errors less than are displayed

The lower p olarization of the GeV data is evident showing

the eect of the nonoptimal b eam energy Correcting for the

b eam energy an average b eam p olarization was calculated for

each of the target foils averaging over the dierent b eam ener

gies The average b eam p olarization determined from the m

foil data was and from the m foil data was

where the errors are statistical only The foil aver

ages dier by within the systematic error on the foil

p olarization The b eam p olarization did not exhibit any time

dep endence over the duration of the exp eriment

In addition to the systematic error in the foil p olarization

there is a contribution to the overall systematic error from the

uncertainty in the mo deling of the scattering kinematics line

shap es asymmetries detector linearity and preampADC lin

earity The various contributions to the systematic error are

summarized in Table Adding the systematic uncertainties in

quadrature yields an overall systematic error of relative

The resulting longitudinal b eam p olarization averaged over the

E GeV

target foils is then P cos

B

The Polarized He Target

The exp eriment used a p olarized He target to extract the neu

tron spin structure function The p olarized He target relies

on the technique of spinexchange optical pumping

Spinexchange optical pumping refers to a two step pro cess in

which rubidium Rb atoms are p olarized by optical pump

ing and the electronic p olarization of the Rb atoms is trans

ferred to the nuclei of the He atoms by spinexchange collisions

The optical pumping is accomplished by driving transitions from

the Rb S ground state to the P rst excited state us

ing circularly p olarized light from lasers The wavelength of

this transition often referred to as the Rb D line is nm

Within a timescale of milliseconds one of the two substates of

the ground state is selectively dep opulated resulting in very

high atomic p olarization The spin exchange takes place

when the p olarized Rb atoms undergo binary collisions with the

He atoms The He electrons b eing paired in the S ground

state do not participate in the collision from a spin p oint of

view The spin He nucleus however interacts with the Rb

valence electron through hyp erne interactions which can re

sult in a mutual spin ip As long as the Rb vap or is continu

ally b eing p olarized this results in a gradual transfer of angular

momentum to the He nuclei

The time evolution of the He p olarization assuming the He

p olarization P at t is given by

He

SE

t

SE R

e P t hP i

He Rb

SE R

where is the spinexchange rate p er He atom b etween the

SE

Rb and He is the relaxation rate of the He nuclear p olar

R

ization through all channels other than spin exchange with Rb

and hP i is the average p olarization of a Rb atom The spin

Rb

exchange rate is dened by

SE

h iRb

SE SE A

where h i cm sec is the velo cityaveraged spin

SE

exchange cross section for Rb He collisions and Rb

A

is the average Rb numb er density seen by a He atom We op

erated at Rb numb er densities such that the spinexchange time

was typically to hrs and the time constant constant

SE

for buildup of He nuclear p olarization ranged

SE R

from ab out to hours A typical spinup p olarization curve

is shown in Fig

In order to achieve the highest He p olarization we attempted

to maximize and minimize From Eq maximizing

SE R

implies increasing the alkalimetal numb er density which in

SE

turn requires more laser p ower For a xed volume of

p olarized Rb the numb er of photons needed p er second must

comp ensate for the numb er of Rb spins destroyed p er second

In total we used ve lasers which collectively provided ab out

W and achieved a value of hours

SE

There are several pro cesses which contribute to the He relax

ation rate An imp ortant example is relaxation that o ccurs

R

during He He collisions due to the dip ole interaction b etween

the two He nuclei Dip ole induced relaxation provides a

lower b ound to and has b een calculated to b e

R

He

dip olar

hours

C where He is the numb er density of He in amagats an at

amagat is a unit of density corresp onding to atm at C

The relaxation rate varies with temp erature implying a maxi

mum relaxation time constant of hours for the He densi

ties and temp eratures found in our target Another imp ortant

contribution to is relaxation that o ccurs during wall colli

R

sions a relaxation rate we will designate Both and

wall dip olar

are intrinsic to a given target cell making it useful to dene

wall

the quantity

cell dip olar wall

that accounts for all relaxation mechanisms that are asso ciated

with a sp ecic cell For the three cells actually used in our

varied b etween and hours exp eriment

cell

In addition to there are interactions not inherent to the

cell

target cell which further increase the nuclear relaxation rate

Inhomogeneities in the magnetic eld that provides an alignment

axis for the He nuclear p olarization induce relaxation according

to

jrB j jrB j

x y

A

D

rB

B

where D is the diusion constant of the He in the target B

is the magnitude of the alignment eld assumed to lie along

the zaxis and B and B are the comp onents of the magnetic

x y

eld transverse to B This eect was very small and we

z

hours in our target calculated

rB

During the exp eriment nuclear relaxation was also induced

by the presence of ionizing radiation from the electron b eam

a phenomenon which is well understo o d b oth theoretically

and exp erimentally When a He atom is ionized the hyp er

ne interaction couples the nuclear spin to the unpaired electron

spin which can in general b e dep olarizing Furthermore elec

trons from other He atoms can b e transferred to the original

ion creating the p otential for dep olarizing other atoms The

dep olarization rate therefore dep ends on the ionization

b eam

rate of the He and the average numb er of He nuclear dep o

larizations p er He ion created The relaxation time for

b eam

our exp eriment inferred from the relative drop in He

p olarization at our maximum b eam current of A is

hours consistent with the predicted time constant of

hours

When all the relaxation mechanisms are included the total

He nuclear relaxation rate is given by

R cell b eam rB

was in the range From the previous discussion we see that

R

of ab out hours With hours equation predicts

SE

that the maximum p olarization given by is ab out

SE SE R

A schematic of the target system is shown in Fig The cen

tral feature of the p olarized He target is the glass cell containing

atm of He as measured at C several milligrams of Rb

metal and Torr of N The N aids in the optical pump

ing by causing radiationless quenching of the Rb atoms when

they are in the excited state The target cells were based

on a double chamb er design comprising an upp er pump

ing chamb er in which the optical pumping and spin exchange

to ok place and a lower target chamb er through which the

electron b eam passed The Rb was contained almost entirely in

the upp er pumping chamb er which was the only chamb er that

was heated to achieve the desired Rb numb er density when

the target was in op eration The upp er and lower chamb ers had

roughly the same volume cm and cm resp ectively for a

total volume of ab out cm and were connected by a mm

long mm inside diameter transfer tub e The target chamb er

had a length of ab out cm a diameter that was roughly cm

and thinned rounded convex end windows The average window

thickness for the cells used in the exp eriment was m p er

window

The pumping chamb er was enclosed by an oven with heating

supplied by owing hot air the temp erature of which determined

the Rb numb er density The oven and all other items which

were near the target cell were made of nonmagnetic materials

so as not to interfere with the NMR p olarimetry The oven was

made of a high temp erature plastic called Nylatron GS and was

op erated at temp eratures of ab out to C which corre

sp onds to a Rb numb er density of atomscm

It was found that higher temp eratures resulted in leaks form

ing in the oven The colder target chamb er at C had

a Rb density that was ab out three orders of magnitude lower

The quantity Rb that was referred to earlier is the volume

A

weighted average of the Rb numb er density over b oth cham

b ers For the temp eratures at which we op erated the pressure

in the cell was atmospheres and the density in the target

chamb er was ab out Amagats

The optical pumping was accomplished using ve titanium

sapphire lasers pump ed by ve argon ion lasers The b eams were

passed through plates to achieve circular p olarization and

were arranged to get a reasonable lling of the pumping cham

b ers cross section The laser system was housed in a protective

laser hut in a high radiation area near the target Access for

laser tuning during the exp eriment was limited but was gener

ally necessary only once every few days

A set of m diameter Helmholtz coils coaxial with the

electron b eam pro duced a to G alignment eld for the

He nuclear p olarization The eld strength was chosen to b e

large enough to suppress the eects of ambient magnetic

eld inhomogeneities and to facilitate a nuclear magnetic

resonance NMR measurement of the Boltzmann equilibrium

p olarization of protons in water for p olarimetry purp oses The

He nuclear p olarization was measured using the NMR tech

nique of adiabatic fast passage AFP The AFP system

used in addition to the main eld coils a set of cm diam

eter Helmholtz rf drive coils and an orthogonal set of smaller

pickup coils b oth of which are pictured in Fig A second

set of Helmholtz coils transverse to the electron b eam axis was

used to rotate the target p olarization and for op eration with a

p olarization transverse to the b eam

The glass target cell the oven the rf coils the pickup coils

and other assorted target comp onents were lo cated inside a vac

uum chamb er in order to reduce the background event rates from

nontarget materials Small co oling jets of He were directed at

the thin entrance and exit windows of the target chamb er as

a precaution against the thin glass breaking due to excessive

heating from the electron b eam

The pro duction of target cells with long intrinsic relaxation

proved to b e a challenging task The cells were made times

cell

out of aluminosilicate glass Corning since such glass is

known to have favorable spinrelaxation prop erties The

use of aluminosilicate glass however was not sucient for ob

s We found it necessary for instance to re taining long

cell

size tubing b efore incorp orating the tubing into the nal cell

construction In this pro cess tubing of some initial diameter is

brought to a molten state and blown to a new diameter while

b eing turned on a glass lathe It is our b elief that this pro

cess results in a more pristine surface presumably with fewer

contaminants and defects

For lling with He gas the cells were attached to a high

vacuum system to Torr and given long bakeouts

under vacuum for to days at C The Rb was distilled

into the cell with a handheld torch from a side arm of the vac

uum system During the distillation the cells remained op en to

the vacuum pumps so that any material outgassed due to the

heat of the torch was pump ed away Next a small amount of

nitrogen pure was frozen into the cell Finally the

initially chemically pure He was intro duced into the

cell through a trap at liquid He temp erature This cryogenic

trap further puries the He by condensing out any contami

nants The cells were co oled with liquid He during lling in

order to achieve a high density of He while maintaining a pres

sure of less than one atmosphere The cryogenic lling technique

ensures that when the tub e through which the cell is lled is

heated the glass will collapse on itself thereby sealing the cell

Out of ten cells pro duced with the techniques describ ed ab ove

was carefully characterized in ve In these cases was

cell cell

always in excess of hours and for the cells used in the exp er

iment was in the range of to hours at ro om temp er

cell

ature These numb ers compared to the hour upp er limit on

at C imply that most of the relaxation was caused

dip olar

by the unavoidable He He dip ole interaction although some

improvement in is still p ossible

cell

Polarimetry was accomplished by comparing the AFP sig

nals of the He with the AFP signals from water samples The

AFP scans involved applying rf at kHz using the drive coils

while simultaneously sweeping the main magnetic eld through

the resonance condition When passing through the resonance

the nuclear spins reverse their direction creating a measureable

NMR signal in the pickup coils Two resonance curves were ob

tained during each AFP measurement one as the eld was

swept up and the other as the eld was swept down Examples

of resonance curves for b oth He and water are shown in Fig

In the case of the water signal the average of scans is shown

Target p olarization losses during a measurement were typically

less than relative

When studying water some care needs to b e taken to inter

pret the AFP signals prop erly The average proton p olarization

that o ccurs during the two AFP p eaks can b e written

h

P tanh

p

k T

B

where h is Plancks constant kHz is the frequency of the

applied rf k is Boltzmanns constant and T is the temp erature

B

of the sample Basically P is the thermal equilibrium Boltz

p

mann p olarization that is exp ected at the eld corresp onding to

the p oint at which resonance o ccurs There is a caveat however

in that the proton spins relax toward the eective magnetic eld

exp erienced in the rotating frame of the rf which on resonance

is given by the magnitude of the applied rf in our case ab out

mG much less than the applied static eld This eect is

accounted for by the parameter which we have calculated to

b e If the longitudinal relaxation time T for the

protons were innite would b e equal to one As it is how

ever the measured proton signal corresp onds to a slightly lower

p olarization than one would naively exp ect

Through a careful comparison with water signals we deter

mined a calibration of p olarization p er mV of

signal As Fig shows the He signals were extremely clean

The uncertainty in the p olarimetery was thus dominated by the

uncertainty in the calibration constant The largest contribu

tion was from the determination of the magnitude of the water

signals which were ab out V The error here was dominated

by a systematic shift in the base line of the NMR signal b efore

and after passing through resonance an eect that is clearly

visible in Fig The interpretation of the water signal that is

the calculation of was another imp ortant contribution Elec

tronic gains the comparison of the exact shap es of the dierent

He and water cells and knowledge of the exact density of the

He were also imp ortant contributions Finally the lo ckin am

plier that was used in the NMR setup had a time constant

that gave a small distortion to the AFP resonance shap e for

which a small correction had to b e applied The various errors

are summarized in Table

During the exp erimental run the He p olarization was mea

sured roughly every four hours The results of these measure

ments are shown in Fig The average He p olarization over

the entire exp eriment was ab out During the rst three

weeks of the exp eriment there were a few precipitous drops in

the p olarization due to a variety of problems as indicated in

Fig Later however the target p olarization was very stable

running for three weeks with only slow drifts Toward the end of

the exp eriment the slight drop in p olarization that is evident in

Fig is due to an increase in the b eam current from an average

of A to A

The Electron Sp ectrometers

Electrons scattered from the He target were detected in two

singlearm sp ectrometers The sp ectrometers were centered at

and with resp ect to the b eam line in order to maximize

the kinematic coverage for an electron b eam energy of GeV

and an event selection criteria of Q GeV c The mo

mentum acceptance ranged from to GeVc for b oth arms

A schematic of the two systems is shown in Fig Both arms

used magnetic elements from the existing SLAC and GeVc

sp ectrometers

The design of the sp ectrometer was driven by several require

ments The cross sections to b e measured were known to b e

small typically of the order of cm srGeV The raw

counting ratio asymmetry of the two dierent spin orientations

was also predicted to b e small of the order of to In or

der to minimize b eam running time the spin structure function

measurements required sp ectrometers with the largest p ossible

solid angle over a momentum acceptance range extending from

to GeVc Such a momentum acceptance gives a rather

wide coverage over x with Q GeVc see Fig

In addition these small scattering angle sp ectrometers were

designed to suppress an exp ected large photon background com

ing from the target due to bremsstrahlung radiative Mller scat

tering and the decay of photopro duced mesons Background

rate calculations indicated the need for at least a twob ounce

system the conguration of the sp ectrometer should allow a

photon to reach the detectors only after scattering at least twice

on the magnet p oles or vacuum walls in order to keep this back

ground at a tolerable level

The energy resolution of the sp ectrometers was dened solely

by the required x resolution The cross section asymmetries were

not exp ected to exhibit any sizable dep endence on momentum

transfer The energy resolution ranged from at E GeV

to at E GeV for each sp ectrometer The resulting

resolution in xx ranged from at low x up to at

the highest x covered by each sp ectrometer x in the

sp ectrometer and x in the sp ectrometer

The sp ectrometer design used two dip oles b ending in op

p osite directions providing a large solid angle acceptance which

remains constant over a very large momentum interval The

solid angle of the reverseb end dip ole doublet conguration

when integrated over the to GeVc momentum interval

is twice that of previous conventional designs with the two

dip oles b ending in the same direction The maximum solid an

gle of the two sp ectrometers is shown as a function of momen

tum in Fig The reverse b end also fullls the twob ounce

requirement by optimizing the deecting angles and the separa

tion of the two dip oles In the sp ectrometer the distance

b etween the two dip oles was m and the two vertical deection

angles were down for the front dip ole and up for the

rear dip ole for GeV particles This combination makes the

sp ectrometer atwo b ounce system for photons and at the same

time provides sucient disp ersion for determining the scattered

particle momenta In the arm the deection angles of the

dip oles are the same as for the arm but their separation is

m resulting also in a twob ounce system

Another advantage of the reverse b end conguration is that

the detector package is lo cated at approximately the primary

b eam height This convenient elevation makes the concrete

structure required for shielding the detectors from ro om back

ground considerably less massive compared to the conventional

design with b oth dip oles b ending up The reduced mechanical

complexity translates to signicant economic b enets as b oth

the setup time and apparatus costs are minimized

In the arm the b end plane p osition of the scattered parti

cles at the detectors dep ends weakly on their momenta as shown

in Fig The particle momenta are correlated with the diver

gence of their tra jectory at the exit of the sp ectrometer This

results in a loss in momentum resolution not critical to the ex

p eriment but spreads out the pion background which is highly

p eaked at GeVc onto a large detector area allowing mea

surements at a fairly large pion rate

The purp ose of the quadrup ole in the sp ectrometer was

to increase the angular magnication in the nonb end plane

and spread the scattered particles onto a larger detector area

in this direction as can b e seen in Fig In the b end plane

the quadrup ole fo cusing improves the momentum resolution of

the system as b oth the p osition and divergence of the scattered

particles at the exit of the sp ectrometer are correlated with mo

mentum The intro duction of the quadrup ole reduces the highly

p eaked solid angle in the range of to GeVc and relaxes the

instantaneous counting rates in the detectors allowing accumu

lation of data in parallel and at ab out the same rate with the

sp ectrometer

Each sp ectrometer was instrumented with a pair of gas thresh

old Cerenkov detectors a segmented leadglass calorimeter of

radiation lengths in a ys eye arrangement six planes of

segmented scintillation counters group ed into two ho doscop es

front and rear and two planes of lucite trigger counters The

electrons were distinguished from the large pion background us

ing the pair of Cerenkov counters in coincidence The scattered

electron energies were measured by two metho ds The rst used

the track information from the scintillator ho doscop es and the

known optical prop erties of the magnetic sp ectrometer The sec

ond one relied on energy dep osition in the leadglass calorimeter

The two Cerenkov counters of each sp ectrometer em

ployed N radiator gas with an eective length of and meters

resp ectively Two spherical mirrors in each of the twometer

tanks and three mirrors in each of the fourmeter tanks col

lected Cerenkov radiation over the active area of light emission

Each set of mirrors fo cused the Cerenkov light on one R

Hamamatsu photomultiplier p er tank The glass mirrors were

manufactured at CERN by slumping a mm thick mm di

ameter disk of oat glass into a stainless steel mold The glass

was cut to the appropriate dimensions cleaned and then coated

with nm of Al followed by a protective coating of nm of

MgF which is transparent down to nm The measure

ment of the reectivities for all ten mirrors used in the detectors

yielded an average of at nm and at nm To

enhance the electron detection eciency each of the photomul

tiplier UV glass surfaces was coated with nm of Pterphenyl

wavelength shifter followed by a protective coating of nm of

MgF The uorescence maximum of pterphenyl of ab out

nm matched well the region of high quantum eciency

of the photomultipliers Moreover the short ns decay time

of this emission enabled us to retain accurate timing information

from the Cerenkovs The m Cerenkov counters op erated at a

threshold for pions of GeVc and the m Cerenkov counters

at a threshold of GeVc The measured numb er of photo elec

trons p er incident electron was resulting in a detection

eciency of over

The two scintillator ho doscop es provided data for an eval

uation of p ossible systematic errors in the leadglass and Cerenkov

counter data They were used to identify backgrounds and to

measure the pion asymmetry in order to subtract contamina

tions in the electron sample The ne ho doscop e segmentation

scintillator elements p er sp ectrometer was chosen to tol

erate the large exp ected photon and neutron backgrounds and to

reconstruct with sucient resolution the pro duction co ordinates

of the scattered particles Both horizontal and vertical planes

consist of scintillator elements of cm width with a over

lap resulting in a bin width of cm

The separation of the two ho doscop es was m in the

arm and m in the arm The angular tracking resolu

tion of the ho doscop es was mrad for the sp ectrometer

and mrad for the sp ectrometer the p osition tracking

resolution was cm for b oth sp ectrometers The angular

resolutions in the nonb end plane were mr for b oth

sp ectrometers whereas for the b end plane it was mr

for the arm and mr for the arm

The momentum resolution dep ends on the absolute value of

momentum and varied from to for the sp ec

trometer and from to for the sp ectrometer

as can b e seen in Fig The gure also displays the energy

resolution of the shower counter

The initial at the target pro duction co ordinates x y

and and the momentum of the particles transp orted through

the sp ectrometers were reconstructed by means of reverseorder

TRANSPORT matrix elements using the nal at the rear

ho doscop e lo cation co ordinates x y and of the detected

f f f f

particles The very large momentum bites of the sp ectrometers

required using a fourthorder reverse TRANSPORT expansion

in y and for reconstructing the particle momenta

f f

The shower counter calorimeter for each sp ectrometer was

assembled from a selected subset of rows of blo cks

lead glass bars from a previous exp eriment Each bar con

sisted of Schott typ e F refractive index of lead glass with

dimension cm providing for radiation lengths

along the direction of the detected electrons The blo cks were

arranged in a ys eye conguration stacked up on each other

with a segmentation that allowed for an accumulation of data

at a maximum e ratio of ab out With the two Cerenkov

counters in the trigger the contamination of the shower signals

by pions was small on the order of a few p ercent

The shower counter resolution for electrons was measured in

a test b eam at CERN to b e

p

E E

The counters were calibrated with a sample of scattered elec

trons of GeV energy in a sp ecial elastic electronproton scat

tering run using a gaseous hydrogen target Extrap olation of

the calibration algorithm to higher energies was p erformed us

ing the scintillator ho doscop es and the known optical prop erties

of the sp ectrometers The detailed study of the p erformance of

the detector is describ ed elsewhere

The sp ectrometer setup and detector packages proved to b e

robust All Cerenkov counters ran with an acceptable average

photo electron yield typically greater than six photo electrons

The simple ho doscop e tracking system was able to reconstruct

tracks with an eciency of greater than Subsequent sec

tions describ e in some detail the analysis and sp ectrometer p er

formance

The Electron Trigger

The main electron trigger for each sp ectrometer con

sisted of a triple coincidence b etween the two Cerenkovs and

the sum of the shower counter signals This trigger was

ecient for electron events and had a contamination of of

nonelectrons events Secondary triggers prescaled to reduce

the rates consisted of various combinations of the detector ele

ments designed to measure eciencies and pion backgrounds

Up to four triggers were allowed p er sp ectrometer p er b eam

spill There was a ns deadtime after each trigger Each trig

ger gated a separate set of ADCs Lecroy system for

the shower counter Each shower counter signal was sent to four

ADCs corresp onding to the four p ossible triggers making a to

tal of over ADC channels p er sp ectrometer The ho doscop e

signals along with the selected elements of the trigger went to

multihit TDCs LRS system which had a ns dead

time To reduce the load on the data aquisition the signals to

the ho doscop e TDCs had a ns gate provided by the trigger

system Thus each electron candidate had a ns window of

activity in the detector The deadtime correction to the asym

metry was determined from a Monte Carlo mo del of the trigger

and instantaneous b eam intensity The average cor

rection was ab out in the sp ectrometer and less than

in the sp ectrometer

Analysis

Data analysis was directed at extracting the electron scattering

asymmetries and structure functions with a high rate sp ectrom

eter The highest rates o ccurred in the degree sp ectrometer

arm ranging from to electron triggers p er pulse on aver

age The rate was typically less than electron trigger p er pulse

in the arm Since the SLAC linac delivers pulses at a rate of

Hz the exp eriment recorded a large sample of deep inelastic

scattering electron events In total approximately million

electron events were collected of which million were used to

determine the asymmetries and spin structure functions

The analysis fo cused on identifying electrons and determin

ing their momentum in a high rate environment Charged pions

were the main source of background The electron trigger con

sisted of a triple coincidence in the signals coming from the two

Cerenkov counters and summed shower counter p er sp ectrome

ter arm This metho d served to reject the ma jority of charged

pions which typically enter the sp ectrometer out of time com

pared to the Cerenkov signal

The remaining pion background originated from either very

high momentum pions typically greater than GeV or from

pions that enter the sp ectrometer in time with an electron

Backgrounds from pion contamination within the trigger were

studied by comparing the energy and momentum determination

of the event from the measurements in the shower counter and

ho doscop e resp ectively Overall the contamination from high

energy pion events was less than since the crosssection for

this pro cess is low whereas backgrounds from events with an

electron and pion in coincidence was also relatively small since

the electron energy cluster would typically dep osit more energy

than the pions and only the highest energy cluster p er trigger

was kept for the analysis Backgrounds from neutral particles

were minimal since the sp ectrometer was designed to accept

only charged particles

Electron events were selected if they triggered b oth Cerenkov

counters with an ADC signal greater than one and a half pho

to electrons and dep osited a minimum energy typically greater

than GeV as a cluster of x blo cks in the segmented

shower counter An algorithm based on articial intelligence

techniques cellular automaton was develop ed to cluster hit

blo cks b elonging to the same shower Events with a shower

contained entirely in one blo ck were rejected This singleblo ck

event cut served to reject a large fraction of pion events as deter

mined b oth from a GEANT simulation and from studying

results from the energy versus momentum comparison A trig

ger from the Cerenkov counters op ened a nsec gate during

the sec spill and the pulse heights from the lead glass blo cks

and from the phototub es of the Cerenkovs were recorded us

ing zerosuppressing LeCroy ADCs Only clusters with

the maximum energy in the nsec gate were accepted in the

analysis The ability to reject pions is studied by comparing

the energy and momentum determinations of an event Typ

ically pion events registered a higher momentum than energy

since the pion shower energy is usually not entirely visible in the

electromagnetic calorimeter

For extracting the asymmetries once an electron event was

selected the shower counter was used b oth to identify its energy

and to determine the scattering angle from the centroid p osi

tion of the shower in the calorimeter The p osition determina

tion of the shower centroid was accurate to approximately

mm signicantly b etter than needed for sucient x resolution

The ho doscop e tracking system was develop ed to calibrate the

shower counter p erform systematic studies of the backgrounds

and to monitor the shower counter and Cerenkov eciencies

throughout the exp eriment Typically ho doscop e tracking e

ciencies varied from to dep ending on the trigger rate

Noise sources from random hits due to photon background with

the asso ciated electronic deadtime were the main cause of ho

doscop e ineciency For this reason the shower counter was the

primary detector used for the analysis

Calibration of the shower counter energy was p erformed us

ing two metho ds First knowledge of the magnetic eld and

spatial p ositions of the sp ectrometer magnets allowed for the

determination of the particles momenta via tracking Tracking

with pristine events was used to calibrate the shower counter

The primary uncertainty in this metho d comes from the nite

width of the ho doscop e ngers and the knowledge of the p osi

tion of these ngers relative to the sp ectrometer magnets The

uncertainty in the momentum measurement is energy dep endent

and estimated to b e b elow over the range of energies de

tected Fig The second metho d employed a sp ecial test run

p erformed ahead of the exp eriment and used a GeV electron

b eam scattering o a hydrogen target H to observe the elas

tic p eak The lo cation of the p eak in b oth the ho doscop e and

the shower counter checked the absolute energy scale to as

determined from magnetic measurements

In order to investigate p ossible ineciencies in the detector

package some sp ecial low rate runs were p erformed to measure

the total cross section Although the sp ectrometer was not de

signed for cross section measurements such a check was useful

for systematic studies Extraction of the total cross section re

quires detailed knowledge of the sp ectrometer acceptance cen

tral momentum deadtime and target thickness Fig present

a comparison of the results on the total cross section for the

and sp ectrometer resp ectively Systematic errors on

the measurement are large typically The data are es

p ecially sensitive to the knowledge of the radiative corrections

which can change the shap e signicantly Within systematic

uncertainties there is reasonable agreement b etween the data

and the Monte Carlo determination which uses cross section

measurements from previous SLAC exp eriments

After event selection contamination of the electron event

samples was relatively small Fig presents distributions of

events comparing the energy measured in the shower counters

E compared to the momentum p measured by tracking us

ing the ho doscop es Lowenergy tails E p come largely

from pion contamination whereas highenergy tails E p

come from overlapping events with typically either two electron

interactions or an electron and pion interactions A neural net

work analysis was develop ed to study pion rejection using only

the calorimeter information but was not used in the nal

asymmetry analysis The pion contamination of the electron

event sample at low energy E GeV was found to b e ap

proximately and decreasing at higher energies to less than

Corrections to the electron asymmetries from pion contami

nation are p erformed assuming zero asymmetry coming from the

pions with an uncertainty of A sp ecial study using out

of time pion events within the trigger gate revealed no evidence

for a signicant pion asymmetry as shown in Fig The nal

eect due to pion contamination is small

An additional source of contamination to the deep inelastic

scattering electron event sample arises from hadron decays pro

ducing secondary electrons For example if a neutral pion is

pro duced in the nal state of an interaction it will decay into

two photons which themselves can scatter and pro duce an elec

tron which enters the sp ectrometer and simulates a true deep

inelastic scattering event Contamination due to this pro cess is

measured by reversing the p olarity of the sp ectrometer magnets

and collecting dedicated data on the p ositron rates The mea

surement serves as a valid subtraction as long as the hadronic de

cay pro cess is charge symmetric We found that approximately

of the low x events were contaminated from such a pro cess

The eect decreases rapidly as x increases The b ehavior is sim

ilar to the pion contamination with a larger contamination at

low E and dying o quickly at higher E The asymmetry in

the p ositron rates is measured to b e zero with large uncertainties

The largest systematic uncertainty in the lowest x

bin comes from this eect see Tables

For the asymmetry analysis electron events which passed the

event selection cuts were divided into bins of scattered energy

E scattering angle and relative target and b eam helicities

N E From these counts normalized by incident charge

N raw asymmetries are formed

e

N N N N

e e

r aw

A

k

N N N N

e e

and for data collected with transverse target p olarization

N N N N

e e

r aw

A

N N N N

e e

On these measured raw asymmetries corrections for the b eam

p olarization P target p olarization P dilution factor f elec

b t H e

tronic dead time radiative corrections and kinematics

dt RC

are p erformed to extract the He parallel and transverse asym

metries

r aw

A

dt

k

k

A

k

RC

P P f

b t H e

r aw

A

dt

A

RC

P P f

b t H e

From these asymmetries the virtual photon He asymmetries

H e H e

A x Q and A x Q are found as a function of x and

Q

A

k

A A D dA A

k

D

A d D A A

k

H e H e

x Q x Q and g Furthermore the spin structure functions g

are extracted using the asymmetries given ab ove

F

g A A

x R

F

A A g

xR

0

y

E E cos

F A sin A

0 0

k

xD R sin E

Here Rx Q is the ratio of the longitudinal to trans

L T

verse cross sections and F x Q is the unp olarized deep in

elastic structure function Both are functions of x and Q The

other kinematic variables are related to the incoming and out

going scattered electron energy E and E resp ectively via

E E

y E

E E

D

E R

y

D

y R

and

v

u

u

t

d D

The factors and are found via

p

Q

E E

p

Q

where characterizes the virtual photon p olarization

Q tan

The ab ove relations Eqs are valid for scattering o

any spin ob ject and therefore are used for a free nucleon as

well as He

Corrections and Systematic Uncertainties

Although statistical errors typically dominate any particular x

and Q bin for evaluating sum rules the systematic uncertain

ties play an imp ortant role The most imp ortant of these are

the b eam p olarization P the target p olarization P and the

b t

dilution factor f The relationship b etween the raw asymme

H e

try and the extracted physics asymmetries are given in Eq

Any uncertainty in P P or f will aect all the asymmetries

t b

together over the entire kinematic range Similarly this will

n

translate into a comparable uncertainty over the integrals of g

and therefore the sum rule The systematic uncertainties as

so ciated with P and P have b een discussed in the b eam and

b t

target sections and resp ectively Corrections due to

hadronic contaminations have b een discussed in the previous

section Here we discuss the dilution correction the radiative

corrections and their asso ciated systematic uncertainties

Dilution Factor

The largest systematic uncertainty in the exp eriment b esides

the low x extrap olation came from the determination of the

dilution factor f This factor corresp onds to the fraction of

H e

events originating from He scattering versus scattering from the

rest of the target and is measurable

The p olarized He target consisted of a mixture of He gas N

gas and glass windows The target cell contained approximately

atmospheres of He Torr of N and glass windows with a

thickness of approximately microns each The relative pro

p ortion of electron events originating from the He versus the N

versus the glass was in the ratio of approximately to to

The He nucleus itself consists of primarily a p olarized neutron

plus two unp olarized protons Further dilution is accounted for

to extract the p olarized neutron result from He as describ ed in

section

In order to determine the dilution factor f for the three

H e

targets used in the exp eriment we relied on two indep endent

techniques First we measured the amount of material in the

target and calculate f using known cross sections Table

H e

presents a breakdown of the material in the three cells used in

the exp eriment The dilution factor is dep endent on x and Q

and takes the form

n x Q

H e H e

f x Q

H e

n x Q n x Q n x Q

H e H e N N g g

where n is the total numb er of nucleons found in sp ecies i He

i

N or g for glass and is the average exp erimental cross section

i

p er nucleon expressed as

ND

P x

i

Z x Q A Z x Q x Q

i p i i n i

A

i

ND

where P accounts for the nuclear dep endence correction EMC

i

eect using the parameterization given by Gomez et al

and A is the atomic mass numb er of sp ecies i The target cell

i

glass Corning has the comp osition SiO Al

MgO CaO B O and Na yielding within

the same numb er of protons and neutrons Assuming that the

ratio R is the same for the proton and the neutron

L T

we can express the dilution factor as

f x Q

H e

ND

ND

np

P

P

n n RC RC R

g N g N

g

N

ND ND

np

R P RC n P RC n

H e H e H e H e

H e H e

where RC x Q is a radiative correction factor which relates

the Born cross section to the exp erimental cross section for dif

p

np n

ferent sp ecies The quantity R F F is the ratio of un

p olarized structure functions for neutrons and protons We de

p

D n

F F termined the neutron structure function using F

where the proton and deuteron structure functions p er nucleon

are taken from the NMC ts to the SLAC BCDMS

and NMC data Because no uncertainties are included in the

NMC t we used the relative p ointtop oint uncertainties to

the SLAC data which is at similar kinematics as the present

exp eriment We also included a normalization uncertainty from

p

D

Furthermore and for F the SLAC data of for F

we included a uncertainty for the proton and for the

deuteron arising from the maximum deviation of the SLAC and

NMC ts in the range x For x where

there is very little SLAC data a error is placed on the NMC

structure functions dening the maximum deviation b etween the

NMC data and the NMC t For R we used the central

L T

values and errors given by a SLAC global analysis

For this section and throughout this pap er the spinindep endent

He structure function in the deep inelastic region is evaluated

as follows

p

ND D H e

x Q F x Q P xF F x Q

ND

where P x is an estimate of the nuclear dep endence eect in

He from reference and diers from unity by less than in

our kinematic range We have assigned an additional uncer

H e

due to the nuclear dep endence eect The overall tainty to F

systematic uncertainty from this metho d is dominated by the

knowledge of the thickness of the glass windows The windows

of the target cells were measured using a precision to oling gauge

with an accuracy of Uncertainties in the measurement due

to variations of the glass thicknesses are included in estimating

this uncertainty Other contributions to the uncertainty from

the nuclear dep endence eect and F are negligible

A limitation of the metho d describ ed ab ove is that events

originating from b eam halo interactions with the cm long side

walls of the cm radius target cell are not taken into account

The electron b eam was centered on the target cell Primary

electrons from the b eam passing cm from the center could in

teract with the target glass walls pro ducing additional scattered

electrons

During the exp eriment several dedicated runs were p erformed

in which the b eam was steered away from the target center Fig

presents the average event rate p er pulse in the sp ectrometer

as a function of the central b eam p osition An increase in the

event rate is evident as the b eam is moved more than mm

from its nominal p osition The variation in event rate is well

describ ed by a quadratic function and is attributed to the b eam

passing through an increasingly thick part of the target endcaps

During the data taking the target was p ositioned at the event

rate minimum From such studies we concluded that as long

as the b eam p osition was stable at the center of the target the

b eam halo eect on the dilution factor should b e small except

for the p ossibility of at tails If the b eam halo has long at

tails then if the b eam is moved o center the event rate may not

change but a constant background of unp olarized events may

b e present from interactions with the glass side walls

A second indep endent metho d for determining the dilution

factor was p erformed Perio dically throughout the exp eriment

data were collected in which a reference cell was placed in the

electron b eam The cell consisted of the same glass typ e and

had the same dimensions as the p olarized target cells The cell

was lled with He gas at various controlled pressures

At zero pressure the events are due to the glass endcaps

but as the cell is lled to dierent pressures the event rate in

creases The event rate r x Q normalized to incident charge

is expressed as a function of pressure as follows

N LP

r

x Q r x Q C n x Q

H e g g

RT

where C is a prop ortionality constant R the He gas constant

T the temp erature of the gas N is Avogadros numb er L the

length and P the pressure of the reference cell resp ectively

r

When the pressure in the reference cell P equals that of the

r

target cell P the numb er density n N LP RT matches

TC H e r

that of Eq The rates were corrected for ratedep endent

electron detection eciencies and changes in the external unp o

larized radiative corrections as a function of helium pressure

Fig presents an example of a sequence of the reference cell

runs where the slop e can b e interpreted as n x Q P

H e H e TC

and intercept as C n x Q The dilution factor is extracted

g g

as

P

TC

f x Q

H e

P

TC

Since the He pressure was directly measured and the ref

erence cell glass window thicknesses known to b etter than

this measurement could b e compared directly to the rst metho d

describ ed ab ove Fig The direct measurement of the di

lution factor from these sp ecial runs would naturally take into

account any p ossible b eam halo eects From these studies we

conclude that there was no observation of any large b eam halo

eects on the dilution factor The nal systematic uncertainty

on the dilution factor is taken to b e where the dominant un

certainty comes from the knowledge of the window thicknesses

needed for the rst metho d describ ed ab ove

Radiative Corrections

Due to the real and virtual radiation of electrons during the scat

tering pro cess the longitudinal and transverse measured asym

metries A A need further corrections known as the elec

k

tromagnetic radiative corrections The latter are p erformed to

extract the structure functions g x Q and photonnucleon

asymmetries A x Q as dened in the Born approximation

where the scattering pro cess is describ ed by the exchange of a

single virtual photon These corrections are cast into two cat

egories internal and external The internal eects are those

o ccurring at the nucleus resp onsible for the deep inelastic scat

tering under investigation and therefore need to b e p erformed

even for an innitely thin target The external eects are those

which mo dify the energy of the incident and scattered electron

via bremsstrahlung and ionization losses from interactions with

other atoms b efore and after the deep inelastic pro cess has o c

curred The external corrections dep end on target thickness

While the formalism for the spinindep endent deep inelastic

scattering was develop ed by Mo and Tsai that of the

spindep endent formalism was develop ed by Kuchto Shumeiko

and Akushevich and implemented in their co de POL

RAD The internally radiated helicitydep endent deep inelastic

scattering cross section can b e decomp osed into its comp onents

following reference

IR l h r B

x y x y

v er t

R v ac v ac

q el

F el

x y x y x y

in

r

is the internally radiated helicitydep endent dieren where

tial cross section d dxdy and refers to the helicity of

B

the electron relative to that of the target and is the helicity

dep endent Born cross section of interest The quantities

v er t

IR l h

and are the electron vertex contribution the soft

R vac vac

photon emission the electron vacuum p olarization and hadronic

vacuum p olarization contributions resp ectively The quantity

F

is the infrared divergencefree part of the inelastic radiative

in

qel

el

tail and and are the quasielastic and elastic radiative

tail contributions resp ectively

The internal corrections were calculated using the program

POLRAD version which uses the new iterative metho d

In this metho d the b est t to the exp erimental asymmetry

H e H e

A x is used to build the p olarized structure functions g x

The cross sections for sp ecic states of p olarizations are then

constructed and used to evaluate all the contributions of Eq

Here all quantities refer to H e From this result a new A is

pro duced and used as an input to the next iteration step by

H e

constructing a new mo del for g

F x Q

k k

measur ed

A A g g

x Rx Q

where k is the iteration index

The pro cess is then rep eated until convergence is reached

which o ccurs within three to four iterations POLRAD was rst

checked against a program we develop ed based on the work by

Kuchto and Shumeiko and also against the Tsai formal

ism for the unp olarized case Similar results to POLRAD were

found with b oth checks as exp ected

The nuclear coherent elastic tail is evaluated using dierent

b est ts to the elastic form factors of He and found to b e small

This leaves only three physical regions of signicant contribution

to the total internal radiative correction to b e considered the

quasielastic region which starts a few MeV after the elastic p eak

since no nuclear excited states are b ound in He the resonance

region which partially overlaps the quasielastic tail and nally

the deep inelastic region which we have assumed to start at W

GeVc In Eq resonance and inelastic contributions

F

are b oth included in The internal and external radiative

in

corrections require the knowledge of the spin indep endent struc

H e H e

Q and spin dep endent x Q and F ture functions F

H e H e

structure functions g x Q and g x Q over the canonical

triangle region The lowest x bin in this measurement

x determines the largest kinematic range of Q and x

over which the structure functions have to b e known It extends

in the range Q GeVc and x

The variables of integration which dene the canonical triangle

are given by M and t in the range M m M W and

x n x

t t t t Q Here M is the invariant mass of all

min max x

p ossible contributing scattering and W the invariant mass of the

scattering of interest

The H e spinindep endent structure functions used in the

quasielastic region were those of de Forest and Walecka

These structure functions allow for a convenient parameteriza

tion in the evaluation of the unp olarized radiative tail In the

resonance region we chose the spin indep endent structure func

tions obtained by tting the data in the resonance region given

in reference while for the deep inelastic region we used the

same mo dels for the proton and deuteron structure functions as

describ ed in subsection to build the spinindep endent struc

ture functions of He see Eq

The spin dep endent structure functions used in the resonance

region were obtained from the AO program which is based

on an analysis of electromagnetic transition amplitudes in that

region In the deep inelastic region as describ ed previously

H e

a t to the extracted A from this exp eriment was used to

build the rst spindep endent structure functions input to the

iterative metho d

The external corrections were p erformed by extending the

pro cedure develop ed by Mo and Tsai for the unp olarized

scattering cross sections to that of the helicity dep endent scat

tering cross sections It used an iterative unfolding pro cedure

on the internal and external corrections together until conver

gence is reached The pro cedure requires the knowledge of the

internallyradiated Born helicitydep endent cross sections The

m

is expressed as the convolution of the measured cross section

internally radiated Born cross section with the radiation eect

due to the nite thickness of the target

m

E E

s p

max

R R

E

E

p

r

s

dE dE I E E t E E I E E t

min

s in p out

E

s p s s p p

E

p

s

where E E are the incident and detected electron energies and

s p

I E E t is the probability that an electron of energy E

in out in

will have an energy E due to bremsstrahlung emission after

out

having passed through t radiation lengths rl of material For

the p olarized case this probability function is spinindep endent

for a thin target b ecause it is dominated by forward charge

scattering o target atoms All kinematics parameters and the

function I are welldescrib ed and discussed in The entrance

glass window plus half of the He thickness accounts for t

in

rl For t the electrons exit the target through four

out

discrete sections in which the amount of material the electrons

traverses after scattering is dierent see Table These four

contributions to t from each region are summed Note that

out

t is much larger than t esp ecially in the region where the

out in

scattered electrons passed through the NMR pickup coils

The pro cedure is applied for each helicity case separately

H e

similar to the unp olarized case and then the asymmetry A

is formed from the result of each helicity case

B B

H e

A

B or n

B B

D

m m

ext int

RC RC

m m

D

The statistical uncertainty of the radiative corrections at each

measured kinematics p oint follows from the statistical uncer

tainty of the measured rate at that p oint and the assumption of

exact knowledge of the radiative background Using Eq we

can generalize this expression to the full radiative corrections

where internal and external radiative eects are convoluted In

order to evaluate the total statistical error for each corrected

kinematics p oint during the correction pro cedure a table of

fractions f of absolute background contributions to the to

i

tal cross sections due to the radiative elastic quasielastic and

deep inelastic tails was stored These fractions include photon

tails from the internal corrections as well as those of external

contributions However they do not include vertex and vacuum

p olarization terms which are considered as nonphysical back

ground contributions

The systematic errors in the radiative corrections are esti

mated by changing the input mo del for the asymmetries and

unp olarized cross sections in the unmeasured kinematics dened

by the canonical triangle in POLRAD The unmeasured re

gion for example includes the resonance region at low Q In

order to estimate the sensitivity of the corrections to these mo d

els we tested our results assuming a at asymmetry input for

H e

our raw A data and compare the results to a quadratic t

input to the same data with weak constraints at the low and

high x regions From the variation of the results we estimate

a relative uncertainty in the internal and external radia

tive corrections for the sp ectrometer data and for the

internal corrections to the sp ectrometer data The external

corrections to the were particularly sensitive to the cross

section shap e at high x This correction is assigned a rela

tive uncertainty

In Table we present the radiative corrections to the data as

well as the fractions necessary to evaluate the changes in statis

tical uncertainty on the results while Fig shows the eect of

the internal and external electromagnetic radiative corrections

H e

on the measured asymmetry A needed to obtain the Born

asymmetry One sees that the corrections are quite small typi

cally shifting the data by the size of the statistical error

Exp erimental Results

Measured He Results

H e H e H e H e

Results on A A g and g versus x are given in Ta

H e

is determined using Eq ble and The asymmetry A

H e

are Within our limited statistical precison the values of A

d

and consistent with zero Exp eriment E measured A

p

n

is consistent with zero with and found that the dierence A A

H e

small uncertainties For the rest of the analysis we extract A

H e H e

and g using Eq and Eq with A set to b e identically

zero with a systematic uncertainty equivalent to our measured

statistical uncertainties shown in Table or the p ositivity con

p

n

R whichever is smaller The uncertainty pro straint A

p

vided by the measurement of A was smaller than the R limit

except for the results in the two x bins x and x

H e

Within our precision there is no obvious Q dep endence of A

H e

at xed x The Q averaged A are given in Table From

H e H e

the asymmetry results of A the spin structure function g

H e

namely is obtained assuming A

H e

x Q F

H e H e

A x Q g x Q

x Rx Q

Extracting the Neutron Result from He

A p olarized He target can b e used to extract information on

p olarized neutrons The main reason is that in the naive approx

imation the He nucleus is considered to b e a system of three

nucleons in a spatially symmetric Sstate The Pauli principle

constrains the overall wavefunction to b e antisymmetric and

therefore the spinisospin wavefunction must then b e antisym

metric Exchanging the two protons must yield a symmetric

wavefunction implying that the two protons are paired anti

symmetrically in a spin singlet state In this picture the two

proton spins line up antiparallel to one another resulting in a

cancellation of spindep endent eects coming from the protons

Naturally the He nucleus is not exactly a system of nucleons in

a spatially pure Sstate and corrections due to the other states

must b e implemented in order to extract the result for a pure

neutron Fairly extensive work on the He wavefunctions has

b een p erformed and these wavefunctions are used to estimate

magnetic moments and to extract the degree of p olarization of

the neutron in He Furthermore the determination of the

neutron spin structure function from a measurement on He re

lies on an understanding of the reaction mechanism for the vir

tual photon absorption combined with the use of a realistic He

wavefunction Detailed investigations of the He inelastic spin

resp onse functions versus that of a free neutron have b een car

ried out by three groups They examined the eect

of the Fermi motion of nucleons and their binding in He along

with the study of the electromagnetic vertex using the most re

alistic He wavefunction Consistent ndings have b een reached

among these groups and we summarize here those relevant to

our exp eriment

In the deep inelastic region a neutron spin structure resp onse

and asymmetry can b e extracted from that of He using a pro

cedure in which S S and D states of the He wavefunction are

included but no Fermi motion or binding eects are intro duced

p

H e n

g g g

p

n

p

H e

F F

p

H e n

A A A

p

n

H e

F

F

n

p

n H e

where g g and g are the spin structure functions of an

eective free neutron a free proton and He resp ectively Simi

p

n H e

larly A A and A are the photontarget asymmetries for

an eective free neutron a free proton and He resp ectively

The studies yield and for

n p

the p olarizations of the neutron and proton in He due to the S

S and D states of the wavefunction The calculations

using the exact He wave function including the full treatment

of Fermi motion and binding eects show negligible dierences

with the ab ove approximation in the deep inelastic region A

precise proton measurement is imp ortant to minimize the error

on the correction We p oint out that our measurements have a

lower limit in missing mass W of GeV already b eyond the

quasielastic and resonance region which were found to b e more

sensitive to nuclear eects

In this analysis we have used Eqs and to extract

n

and spin dep endent structure func the neutron asymmetry A

p

n

tion g where the proton asymmetry A and spindep endent

p

structure function g used are those measured in exp eriment

E The uncertainties in the measured proton results are

n

The relative taken into account in extracting the results on g

impact on the overall error bars is small for all x bins

No further corrections due to p ossible nalstate eects have

b een incorp orated Nevertheless placing limits on p ossible con

taminations from nal state nuclear eects has b een one of the

signicant motivations for measuring the neutron spin structure

function with dierent nuclear targets ie p olarized deuterium

and He

n n n n

Results on A g A and g are presented in Tables and

n

In Table the values of g are also given at constant Q

GeVc Table and Table present the detailed contri

bution of every correction parameter to the overall systematic

n n

uncertainty on A and g at each x p oint In order to extract

n

at one unique value of Q we assumed that the the values of g

n

asymmetry A is Q indep endent and used A consistent

with the study of the Q dep endence of our data From the two

sp ectrometers and the three b eam energies used in this exp eri

n

at six dierent values of Q Over this ment we extracted A

mo dest range of Q and within the statistical errors we nd

n

that A is consistent with b eing indep endent of Q as seen in

Fig and enumerated in Table This trend is conrmed by

the recent precision E results on the proton and neutron

in the equivalent Q range Fig and Fig show the com

n n

piled results on A x and xg x Fig presents the results

n

x for A

Neutron First Moment and Physics Impli

cations

n

over the measured range of x at a xed x Q Integrating g

value of Q GeVc one obtains

Z

X

n n

g x Q dx g x Q x

i i

i

stat sy s

n

where x are the bin widths and the g x Q are evaluated

i i

using Eq The rst error is statistical and the second is sys

tematic The total systematic error is evaluated by adding all

contributions in quadrature assuming they come from uncorre

lated sources Table lists the dominant contributions to the

total systematic error of the integral in Eq

Since the data are only measured over part of the interval

x we must extrap olate in order to evaluate the integral

R

n n

dx over the full x range x Q g Q GeVc

There are two regions to consider large x x and

small x x For large x within a three constituent

quark description of the nucleon the assumption of single a

vor dominance at high x and Q leads to the prediction that

A as x This phenomenological result has also b een

derived from arguments based on p erturbative QCD and a non

p erturbative wavefunction describing the nucleon

In order to evaluate this integral we assumed that for x

n n

A and used the F results from SLAC rather

than NMC since it is based on data closer in kinematic range

to the present exp eriment The error assigned to A was chosen

n

to cover all p ossible b ehaviors of A in this region including that

n n

of g suggested by the quark counting rules g x x

We nd for Q GeV

Z

n

g xdx

For small x one must rely heavily up on theory esp ecially

R

noting that if A as x g dx We assume

the Regge theory prediction for the b ehavior of the nucleon g

where the Regge intercept can vary namely g x x

in the range although there are no strong

theoretical grounds for these limits In this region dominated by

the sea and gluon contributions to the nucleon structure it is

thought that no dierence should exist b etween the proton and

neutron b ehavior Therefore we used the same value of as

the previous proton spin structure function exp eriments

The low x contribution to the spin structure function

integral b ecomes

Z

x

n n

g xdx x g x

Here we assumed a Regge b ehavior up to x and used

n

to the lowest three x bins to reduce the sta a weighted t of g

tistical uncertainties The low x extrap olation yields the result

at Q GeVc

Z

n

g xdx

in which we assign a uncertainty to the extrap olation

n

If one uses an alternative low x b ehavior of g namely

n

g a log x and p erform the extrap olation using only the

R

n

lowest x bin data p oint one obtains g xdx The

assigned error encompasses this result statistical errors on the

low x p oints and the result obtained using the other b oundary

n

is also consistent of the Regge intercept Our t of g

with the low x results from SMC over the measured

range within the statistical uncertainties

The total neutron integral at Q GeVc b ecomes the

sum of the three integrals Eqs

Z

n n

g xdx stat sy s

A comparison of the E data with those of E and

SMC shows no signicant disagreement though there is

n

some interesting b ehavior Fig presents a comparison of xg

versus x for E and E The data from b oth exp eriments are

in reasonable agreement over the measured range The integrals

n n

stat sy s for E are over x of g

n

at Q GeVc and stat sy s

for E Q GeVc Fig compares the spin structure

n

extracted from SMC at Q GeVc and from function xg

E When the SMC and E neutron results are combined

the shap e of the structure function is interesting with small

n

over the range in x covered by E fol negative results for g

lowed by relatively large negative values at low x measured by

SMC just b elow the kinematic range accessible to E The

b ehavior is a strong motivator for future measurements at low

n

over the mid x range common to E x The integrals of g

and SMC dier however by approximately two standard devia

R

n

tions We extract g xdx stat sy s

from the E data over the x range from to where

the statistical error bars are relatively small We compare this

R

n

result to the SMC result over the same range g xdx

stat Systematic errors are neglected from the

SMC data since they are exp ected to b e small compared to the

statistical uncertainty We do not assign any sp ecial signicance

to the dierence but p oint out that it should not b e ignored and

needs to b e monitored in future measurements where the Q of

the measured data is investigated

In order to test the Bjorken sum rule the proton and the

p

n

neutron rst moments and are evaluated at the same Q

The available exp erimental proton data span a dierent range

of Q making it necessary to evolve the proton or the neutron

data to a common value of Q

Since our neutron results and the E proton results

are at similar Q we combine the two to test the Bjorken sum

p

rule The E proton results reads at Q

GeVc while evolving the E neutron result to Q

n

GeVc we nd These results lead

p

n B

j

where to the Bjorken integral

exp

correlations b etween the two exp eriments primarily from the

b eam p olarization determination have b een taken into account

There is agreement with the Bjorken sum rule prediction

B

j

using Eq from Section assum

th

ing three avors and cho osing Q GeV c

s

Fig shows tests of the Bjorken sum rule from

dierent exp eriments The present determination is the most

accurate test of the Bjorken sum rule to date

We can rewrite the Bjorken sum rule including the higher

twist contributions and extract a value for

s

B j

Q Q Q

C

s s s

HT

g

A

Q

where C is the higher twist contribution to the Bjorken sum

HT

rule Recent estimates of C show that it is very mo del de

HT

p endent For example using QCD sum rules metho ds sev

eral authors have evaluated C and found it to b e C

HT HT

in one case or C in

HT

another The sensitivity of the result can b e describ ed by the

change in sign in C found when the estimate is made using

HT

a bag mo del Therefore an additional theoretical uncer

tainty equal in magnitude to the present size of the higher twist

correction should b e included in the theoretical estimate of

s

We use the Bjorken sum rule with p erturbative QCD correc

tions up to third order in without higher twist term correc

s

tions to extract a value of at Q GeVc for p olarized

s

deep inelastic scattering

Q GeVc

s

B j

If we consider the higher twist corrections to and cho ose an

average value and error of C from the QCD sum rules that

HT

is C we nd

HT

Q GeVc

s

Both results with or without a higher twist correction for

s

are in agreement with the world average

For the EllisJae sum rule test we compare at the average

Q of the exp eriment namely Q GeVc From Eq

and using and F D we obtain

s

n

the theoretical value of where the error on

the result is dominated by the error on the quantity F D

We see that the EllisJae sum rule is one standard deviation

away from the exp erimental result and the exp erimental result

is consistent with the results of E and SMC

Higher order p erturbative QCD corrections to this sum rule

have had a signicant impact on the interpretation of the ex

p erimental results For the Q at which the SLAC exp eriment

E is p erformed these corrections are quite large At this

time these corrections have b een given up to third order in the

expansion of Q For example at the average Q of the

s

E exp eriment GeVc the corrections change the Ellis

Jae sum rule prediction for the neutron from without

corrections to with corrections assuming a value of

s

n

exp erimental results and the same values for g Using

A

and F D as earlier one can extract a value for the total

quark spin contribution to the nucleon using the E results

GeVc and similarly we can extract the

fraction of p olarized strange sea contribution s GeVc

We also nd with the cor

inv

resp onding fraction of p olarized strange sea contribution s

inv

Table gives the total quark avors contribu

tions to the nucleons spin using Eq in one case and Eq

in the other assuming a conservative uncertainty on F D The

uncertainty on the determination of s is still large even when

we take a more optimistic uncertainty on the value of F D For

F D as quoted by Close and Rob erts and

using Eq we nd s while the uncertainty

on the other quark avors contributions remains the same see

Table

Including the higher order p erturbative QCD corrections this

result is in agreement with the extraction of from the E

and SMC ex

inv inv

p eriments Care must b e taken when comparing these

numb ers since dierent authors make dierent assumption in ex

tracting from their data In addition the go o d agreement

do es dep end on the validity of the p erturbative QCD corrections

in the low Q region and the estimated small size of the higher

twist corrections

Conclusions

We rep ort nal results on the rst determination of the neutron

spin structure function using a p olarized He nucleus Over

the kinematic range accessible to the exp eriment we nd small

negative asymmetries similar to the predictions from the quark

parton mo del Within the statistics of the exp eriment

we are not able to distinguish any clear shap e as a function of

x to the neutron spin asymmetries although signicant devia

tions are exp ected particularly at low and high x For example

n

as x approaches unity the neutron asymmetry A is predicted

n

should approach to approach unity As x approaches zero A

zero The results are in agreement with an extraction of the neu

tron spin structure function from the deuteron as p erformed by

SLAC exp eriment E We see no dep endence on Q within the

limited precision of the data sample In addition we present re

n

sults on A x which are compatible with zero and signicantly

p

R in the range from x b etter than the unitarity limit given by

n

x results however are less precise of to x of The A

than what one could extract from the E proton and deuteron

data

From our measurement we pro ceed to extract the rst mo

R

n n

ment of g namely g xdx Since our asymmetries over the

R

n

measured region are small g xdx is small We pro ceed to use

the results for the neutron integral to extract the quark avor

distributions u d s and with some caveats In our

n

extraction of the g integral we assume that one can do a Regge

theory extrap olation of the contribution to the integral b etween

x of and the lowest values of x measured in the exp eriment

The implications of this t are that the integral contribution

at low x is itself small On the other hand recent data from

the SMC collab oration app ears to indicate that there may b e a

large negative contribution to the neutron integral in the x range

b elow where we measure If this is true then the assumption

of Regge b ehavior up to x of approximately underestimates

the neutron contribution at low x A ma jor motivator for fu

ture measurements of spin structure functions at either higher

energies or with higher precision comes from studying the spin

structure functions at lower x With the Regge theory assump

tion we extract a value of the total quark contribution

to the nucleons spin of approximately We note that this

result has a sensitive dep endence on higher order p erturbative

and nonp erturbative QCD corrections In addition the result

dep ends on the scale at which is evaluated and the numb er

of quark avors used in the evaluation typically three or four

We can tune for dierent values of ranging from of

to of with dierent theoretical assumptions

We combine the proton results from exp eriment E with

the neutron results from this exp eriment to test the Bjorken

sum rule Ignoring the unlikely p ossibility for large nonsinglet

contributions to the proton and neutron integrals at low x this

comparison still stands as the most precise test of the Bjorken

sum rule to date We nd that the sum rule is satised at the

level

Future measurements of the proton and neutron spin struc

ture functions will increase the kinematic coverage particularly

at low x SLAC exp eriments E and E will ex

tract the proton and neutron spin structure functions using a

higher energy GeV p olarized electron b eam These two exp er

iments aim to measure the spin structure functions at a higher

average Q and will extract data at lower values of x with higher

statistical precision Additional measurements from the CERN

SMC program will continue to increase the statistical precision

needed to draw decisive conclusions at low x A collider ex

p eriment like HERA with a p olarized electron and a p olarized

proton b eam would in principle b e ideal for reaching very low

x to extract the proton spin structure function In ad

dition precision measurements of the proton and neutron spin

structure functions at high x x are useful for testing

Quark Parton Mo del predictions The rising b ehavior of the

n

neutron asymmetry A at high x still needs to b e conrmed

Exp eriments at HERMES and TJNAF are likely to

b e the b est grounds for these tests along with future precision

measurements of g

We conclude by noting that this rst measurement of the

neutron spin structure function do es not complete the study but

instead has help ed pave the way for future measurements with

higher precision and investigations with an increasing attention

to detail

Acknowledgements

We are indebted to G S Bicknell G Bradford R Boyce B

Brau J Davis S Dyer R Eisele C Fertig J Hrica C Hud

sp eth M Jimenez G Jones J Mark J McDonald W Nichols

M Racine B Smith M Sousa R Vogelsang and J White for

their exceptional eorts in the prepartion of this exp eriment

to the SLAC Accelerator Op erations Group for delivering the

p olarized b eam and to the technical sta of CESaclay and

LPCClermont We also would like to thank NM Shumeiko

for providing us with the latest version of POLRAD to p erform

the electromagnetic internal radiative corrections This work

was supp orted by Department of Energy contracts DEAC

SF LBL WEng LLNL DEFGER

Princeton DEACSF SLAC DEFGER

Stanford DEFGER Syracuse DEFGER

Temple DEACER Wisconsin National Science

Foundation grants American

Michigan and the Bundesministerium fuer Forschung und Tech

nologie W Meyer the Centre National de la Recherche Scien

tique LPCClermontFerrand and the Commissariata lEnergie

Atomique Saclay

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Table Table of parameters for the E exp eriment

Description

Average b eam p olarization using a AlGaAs source

Average current A

3

High density p olarized He target Pressure atm Vol cc Pol

Thin windows to minimize the dilution factor mwindow

High counting rate due to low sp ectrometer angle and

Large statistics with p olarized b eam on p olarized target million events

Target windows co oling in vacuum No explosions due to glass radiation damage

Table Systematic uncertainties contributing

to the b eam p olarization measurement

Value

Foil Magnetization

Kinematic Acceptance

Mo del Dep endence

Gain and Nonlinearity Correction

Fit Range

TOTAL

Table Target p olarimetry systematicuncertainties

Proton signal magnitude

Proton p olarization

Electronic gain

Cell geometry

Lo ckin time constant correction

3

He density

Total

Table Polarized Target parameters used in calculating the dilution factor

A run corresp onds typically to one or two hours of data taking

Target

Runs used

Length mm

Front window m

Rear window m

2

Glass density gcm

3

He density amagats

N density amagats

2

3 3 20 20 20

He density cm

3 18 18 18

N density cm

2

Table Radiation lengths t seen by electrons exiting the target

out

Sp ectrometer Fraction of Events Radiation Lengths t

out

3

H e 2

Table The radiative corrections to A x at the average Q of each x

1

bin are tabulated here with the corrections to the sp ectrometer given

rst then those of the The s are the additive correction to b e made

to the asymmetry for internal int external ext and f are the fractions

i

of events in a particular bin coming from quasielastic and inelastic tails in

cluding internal and external radiative eects The elastic contribution is

small

ext int

f f f x

q uel inel ext

RC RC

3 3

H e H e

Table Results for A and g

1 1

3 3

H e H e 2

stat sys stat sys g x range h x i h Q i A

1 1

2

GeV c

3 3

H e H e

Table Results for A and g Note that the systematic uncertainties

2 2

are small compared to the statistical uncertainties

3 3

H e H e 2

x range h x i h Q i A stat sys g stat sys

2 2

2

GeV c

n n 2 n

Table Results on A and g at the measured average Q along with g

1 1 1

2 2 n 2

evaluated at Q GeVc assuming that A do es not dep end on Q

1

2 n n n

x range h x i h Q i A stat sys g stat sys g stat sys

1 1 1

2 2

Q GeVc

n n

Table Results on A and g Note that the systematic uncertainties are

2 2

small compared to the statistical uncertainties

2 n n

x range h x i h Q i A stat sys g stat sys

2 2

2

GeV c

n

for each x p oint Table Table of systematic uncertainties on A

1

Parameter x x x x x x x x

P

b

P

t

f

dt

RC

R

F

2

n

p

A

1

p

A

A

+

e

A

3

He corr

Total

n

Table Table of systematic uncertainties on g for each x p oint

1

Parameter x x x x x x x x

P

b

P

t

f

dt

RC

R

F

2

n

p

A

1

p

A

A

+

e

A

3

He corr

Total

n 2

Table Results on A vs Q Systematic uncertainties are small and have

1

b een neglected See Table IX for other values of x

2 n

x range h x i h Q i A stat

1

2

GeV c

n n

Table Systematic uncertainties on The total uncertainty on com

1 1

ing from systematics is

p

3

P P f R F A A He corr

b t RC 2 p

1

Table Total quark avor contributions to the nucleons spin using a

conservative uncertainty on F D as describ ed in the text

2 2

u d s Q GeVc

u d s Invariant quantities

inv

Table Total quark avor contributions to the nucleons spin using an

uncertainty as quoted by Close and Rob erts see text

u d s Invariant quantities

inv

0.10

0.08

0.06

0 lab θ

P θ 0.04

0.02

0 0.90 0.95 1.00 1.05 1.10 θ lab 7-95 θ

0 7995A1

Figure The calculated probability distribution P for lab oratory

lab 0

scattering angles due to atomic electron motion The horizontal axis is the

lab oratory scattering angle in units of the central scattering angle

lab 0

The dashed curve is for M shell p olarized target electrons The solid curve

is an average for all target electrons 20 Detector

Magnet

10.5 mrad 10 7.5 Target 5.0

0 Mask 20 z (m) x (cm) Septum Beampipe –10

(a) –20

20 Beampipe Target Septum 0 Mask 20 z (m) y (cm) –20 14.6 GeV/cShielding 10 Magnet 6.6 –40

–60 (b) Detector 7-95

7995A2

Figure Top a and side b views of the E Mller Polarimeter The

mask selects Mller scattered electrons near the horizontal plane which are

then disp ersed vertically by the magnet The detector uses gas prop ortional

tub es emb edded in lead to sample the Mller signal over a sp ecic momentum

range and to measure the scattering angle a is the tted RL line shap e and the dotted line is the tted bac Mller runs at E GeVc with a Figure RL a and RL

7995A3 7-95 Relative Counts Relative Counts 1000 1500 500 10 20 30 40 0 0 b scattering distributions for an a 10 02 30 20 10 R –L R +L Channel m thic 030 20 k target (b) (a) This solid line in v erage of kground 60

E=19.42 GeV 40

20 25.51 GeV 0

–20 22.66 GeV

Beam Polarization (%) –40

–60 300 400 500 600 700

8-95 Moller Run 7995A4

Figure The measured longitudinal b eam p olarization P versus Mller

B

p olarimeter run numb er for runs passing the cuts describ ed in the text The

sign is relative to the p olarization direction at the source 50

40

30

20 Polarization (%) 10

0 0 50 100 150 200

2-96 Time (hours) 8126A5

3

Figure Typical p olarization spinup curve for the longitudinal He p olar

ization in one of the target cells used in the exp eriment Ti: Sapphire λ – 4

Main Coils

Oven e– Cell Beam Pickup Coils

RF Drive Coils

9-94

7759A1 Vacuum Chamber

3

Figure Schematic of the E He target system 200 3He Signal (a)2.5 Water (b) Signal

150 V) µ 2.0

100 1.5

50 NMR Signal (mV) NMR Signal ( 1.0

0 0.5 5 6 7 8 9 10 –6.0 –5.5 –5.0

9-94 DAC Voltage (V) 7759A4

3

Figure a He NMRAFP signal obtained using one sweep of the main

holding eld b Water NMRAFP average signal obtained using twenty ve

sweeps of the main holding eld Note the dierence in scale b etween the

two signals The curve corresp onds to a Lorentzian t to the data 50

Target Polarization (%) 40

30

20

10 Run Number Target Helicity 0 Nov. 7 Dec. 22 –10 1200 1400 1600 1800 3-96

8126A8 Run Number

3

Figure He target p olarization versus time SLAC E142 Spectrometers TOP VIEW Dipole Magnets Hodoscope

Quadrupole 4.5° 3He e' Target Cerenkov e Beam e' 7° Dipole Magnets Hodoscope Pb-glass Shower SIDE VIEW (7°) Counter

3 He 5.6° 9.6° Target

e Beam 2.1 m Floor 0 5 10 15 20 25 30 10-93

meter 7552A4

Figure Layout of the magnets and detectors used in E exp eriment 10

8 ] 2 6 7.0° Spectrometer [(GeV/c)

2 4 Q

2 4.5° Spectrometer

0 0.01 0.05 0.1 0.5 1 2-96 x 8126A10

2

Figure Q versus x range covered by the exp eriment for E

GeV This range is dened by the b eam incident energy scattering angle and

sp ectrometers momentum and angular acceptances The density of p oints

corresp onds to the relative electron scattering rates 0.8 (a) SLAC 8 GeV/c (b) 0.2 Spectrometer 0.6 E142 DQD E142 DD 4.5° Spectrometer 7° Spectrometer 0.4 0.1 SLAC 20 GeV/c E130 DD Spectrometer Spectrometer 0.2 SOLID ANGLE (msr)

0 0 5 10 15 20 5 10 15 20 2-96

8126A11 MOMENTUM (GeV/c) MOMENTUM (GeV/c)

Figure Momentum acceptance of a the and b the sp ectrom

eter Acceptances for the SLAC GeV a the GeV b and the E

sp ectrometers are presented for comparison 7 GeV/c 13 GeV/c 10 GeV/c 19 GeV/c –60

(a)

–40 B81 B202 Pb –16 mr –20

0 y (cm) 20 +16 mr

40

B202 Pb B81 60 05 10 15 20 30

(b) B81 20 B202 Pb

+10 mr 10

0 x (cm) –10 –10 mr

–20 Pb B81 B202 –30 05 10 15 20

10-91 z (m) 7032A4

Figure Bend plane a and nonb end plane b raytrace for the

sp ectrometer for rays of dierent momenta originating from the center of the

p olarized target All rays are drawn with resp ect to the central tra jectory of

the system a mr b mr and p GeVc Also shown

0 0 0

are the iron magnet p oles and lead collimators 7.5 GeV/c 8.5 GeV/c 13 GeV/c 10 GeV/c 19 GeV/c –60 (a)

–40 B82 B204

Q203 Pb –20 –12 mr

0 y (cm)

20 +16 mr

40 Pb B82 Q203 B204

60 0 10 20 30 30 (b)

B82 Pb 20 Q203

B204 +5 mr 10

0 x (cm)

–10 –5 mr

–20

B204 Pb B82 Q203 –30 0 10 20 30

5–96 z (m) 7032A5

Figure Bend plane a and nonb end plane b raytrace for the

sp ectrometer for rays of dierent momenta originating from the center of the

p olarized target All rays are drawn with resp ect to the central tra jectory of

the system a mr b mr and p GeVc Also shown

0 0 0

are the iron magnet p oles and lead collimators 0.08 7° Spectrometer 4.5° Spectrometer

0.06 ° Hodo + LG (7 ) ° Hodo + LG (4.6 ) 0.04 Lead Glass (E/P) σ °) Hodo (7 °) 0.02 Hodo (4.5

0 0 5 10 15 20 25

2-96 E (GeV) 8126A12

Figure Data for the resolution of the ratio of energy in the shower counter

divided by momentum from tracking E P versus E for each sp ectrom

eter Exp ected contributions from tracking ho doscop e from energy de

p osition in the lead glass LG and from b oth combined ho doscop e lead

glass calorimeter are also shown by the curves 30 ° 250 (a) 4.5° (b) 7

200 20 150 dE' (nb/sr GeV)

Ω 100

/d 10 σ d 50

0 0 10 15 20 10 15 20 3-96

8126A13 Scattered Electron Energy (GeV) Scattered Electron Energy (GeV)

Figure Comparison b etween measured solid circles and Monte Carlo

simulated highlighted band deep inelastic cross sections for the sp ec

trometer a and for the sp ectrometer b The data error bars are dom

inated by uncertainties in the sp ectrometer solid angle The exp ected cross

section is based on a mo del which relies on previous SLAC and CERN mea

surements The width of the band is due to uncertainty in the target density 4000 ° ° 4000 (a) 4.5 (c) 4.5 3000 3000 2000 2000 Counts 1000 1000

0 0 ° ° 4000 (b) 7 (d) 7 2000 3000

2000

Counts 1000 1000 0 0 0 1 2 0 1 2

3-96 E/P E/P 8126A15

Figure Plots a and b represent the ratio of energy determined by the

calorimeter to the momentum determined by the ho doscop es of events

detected in the and sp ectrometers The electrons are identied by

the p eak centered around E P whereas the pions which dep osit less

energy in the calorimeters are in the region E P Plots c and d

show events with the highest energy cluster for a given trigger and requiring

an electron hardware trigger These events dene greater than pure

electrons sample and are those used in the physics analysis 0.4

II 0.2 π

0

Pion Asymmetry A –0.2

–0.4

0.010.05 0.1 0.5

2-96 x 8126A19

Figure Inclusive pion asymmetry A versus x The results are consistent

k

2

with zero df 12

10 4.5° Spectrometer

8

6 Count (arb. units) 7° Spectrometer 4

2 2 4 6 8 10

2-96 Target Position (mm) 8126A16

Figure Sp ectrometer electron event rates as the target is swept vertically

through the b eam mm is the normal p osition The solid curves are quadratic ts 2.5 – e 6

2.0 Event Rate/10

1.5 0 50 100 150

2-96 Pressure (psia) 8126A17

Figure Event rate at x in the arm versus pressure for a

sequence of reference cell runs used to measure the dilution factor 0.5

(a) 4.5" Spectrometer (b) 7" Spectrometer 0.4

0.3

0.2 Method Method He Dilution Factor 3 I I 0.1 II II

0 0.01 0.050.1 0.5 0.1 0.20.3 0.4 0.5 0.6 10–96 x x 8126A18

Figure Material metho d I and reference cell metho d I I results for the

dilution factor of the reference cell as measured using the arm a and

3

the arm b for a He gas pressure of psi 0.02 without r.c. with Internal r.c. with Internal + External r.c. 3He 0 A1

–0.02

–0.04

–0.06 00.1 0.2 0.3 0.4 0.5

10–96 x 8126A20

3

H e

Figure Change in the asymmetry A averaged over E and as the

1

radiative corrections rc are added Only the statistical error on the nal

results are shown for comparison The x values of each data set are the same

but they have b een shifted for clarity x =0.08 0

–0.4

0.125 0

–0.4 0.175 0 n A1 –0.4 0.25 0

–0.4 0.4 0.35 0

–0.4 1 10 2-96 2 2

8126A26 Q [(GeV/c) ]

n 2

Figure The asymmetry A is plotted versus Q for ve dierent values

1

n 2

of x The results are consistent with A b eing indep endent of Q The data

1

comes from the two sp ectrometer arms and three b eam energies 0.2

0.1

0 n A1

–0.1

–0.2

–0.3 10–2 10–1 100 2-96 x 8126A24

n

Figure The neutron asymmetry A versus x The error bars are sta

1

tistical with the enclosed region at the b ottom representing the size of the systematic errors 0.02

E142 Q2=2 (GeV/c)2

0

x) ( 1 n xg

–0.02

–0.04 0.01 0.1 1

8126A29

10–96 x

n 2

Figure The spin structure function xg evaluated at xed Q

1 0

2

GeVc The error bars are statistical while the band at the b ottom rep

resents the size of the systematic uncertainties 2

1 + R

n 0 A2

– R –1

–2 0.05 0.1 0.5

10–96 x 8126A30

n

Figure A versus x averaged over b oth sp ectrometers is shown The error

2

bars are statistical only systematic errors are small in comparison 0.02

E142 Q2=2 (GeV/c)2 E143 Q2=3 (GeV/c)2 0

x) ( 1 n xg –0.02

–0.04 0.01 0.1 1

8126A31

10–96 x

n

Figure Comparison of xg b etween E and E 1 0.06

E142 Q2=2 (GeV/c)2 0.04 SMC Q2=2 (GeV/c)2

0.02

x) ( 1 n 0 xg

–0.02

–0.04

– 0.06 0.001 0.01 0.1 1

10–96 x 8126A27

n

Figure Comparison of xg b etween E and SMC 1 0.3

3rd order PQCD No corrections corrections

0.2

) 2 Q ( p–n Γ 0.1 E143 (p, d) SMC (p, d) E142 (He), E143 (p) EMC (p), EMC (d)

0 2 4 6 8 10 2 2

9–96 Q (GeV/c) 8126A28

p

n

Figure Comparison of data for using dierent exp eriments com

1

1

r d

pared to the Bjorken sum rule with order QCD corrections and no higher

2 2

twist corrections The E results are at Q GeVc but have b een

shifted for clarity