SLACPUB Septemb er Deep Inelastic Scattering of Polarized Electrons by Polarized He and the Study of the Neutron Spin Structure The E Collab oration PL Anthony RG Arnold HR Band H Borel PE Bosted V Breton GD Cates TE Chupp FS Dietrich J Dunne R Erbacher J Fellbaum H Fonvieille R Gearhart R Holmes EW Hughes JR Johnson D Kawall C Kepp el SE Kuhn RM LombardNelsen J Marroncle T Maruyama W Meyer ZE Meziani H Middleton J Morgenstern NR Newbury GG Petratos R Pitthan R Prep ost Y Roblin SE Ro ck SH Rokni G Shapiro T Smith PA Souder M Sp engos F Staley LM Stuart ZM Szalata Y Terrien AK Thompson JL White M Wo o ds J Xu CC Young G Zapalac American University Washington DC LPC INPCNRS Univ Blaise Pascal F Aubiere Cedex France University of California and LBL Berkeley CA California Institute of Technology Pasadena CA hep-ex/9610007 14 Oct 1996 Centre dEtudes de Saclay DAPNIASPhN F GifsurYvette France Kent State University Kent OH Lawrence Livermore National Lab oratory Livermore CA University of Michigan Ann Arb or MI National Institute of Standards and Technology Gaithersburg MD Old Dominion University Norfolk VA Princeton University Princeton NJ Stanford Linear Accelerator Center Stanford CA Stanford University Stanford CA Syracuse University Syracuse NY Work supp orted by Department of Energy contract DEACSF 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