Phy51c5 Letter5 8 302 (1993) 533-539 N0rth-H011and
PHY51C5 LE77ER5 8
Mea5urement 0fthe 5p1n-dependent 5tructure funct10n 91 (x) 0fthe deuter0n
5p1n Mu0n C011a60rat10n (5MC)
8. Adeva a, 5. Ahmad h, A. Arv1d50n c, 8.8ade1ek c•d, M.K. 8a111nt1jn c,e, 6 . 8ard1n f, 6 . 8 a u m 9, P. 8er91und h,1, L. 8etevJ, 1.6. 81rd f,1 , R. 81r5a k, P. 8j6rkh01m e, 8.E. 80nner h, N. de 80tt0n h,f, M. 80utemeur e~2, F. 8radamante k, A. 8re55an k, A. 8r1111 m, j. 8uchanan h, 5. 8111tmann 9, E. 8urt1n f, C. Cavata f, J.P. Chen n, j. C1ement 6, M. C10cch1att1 k, M.D. C0rc0ran 6, D. Cra66 n, J. Cran5haw h, 7. ~uhadar h,3, 5. Da11a 70rre k, R. van Dant219 e, D. Day n, 5. Dhawan e,
C. Du1ya 0, A. Dyr1n9 e, 5. E1ch61att 6, J.C. Fa1vre f, D. Fa5ch1n9 P, F. Fe1n5te1n h,4,
C. Fernande2 a,4, 8. Fr015 f, C. 6ara6at05 a•1 , J.A. 6ar20n a•4, L. 6at19n0n h, 7. 6au551ran h, M. 610r91 k, E. v0n 60e1er r, 1.A. 6010utv1n 5, A. 60me2 a,4, 6 . 6rac1a a,
M. 6r055e Perdekamp 0, W. 6r1161er t, D. v0n Harrach u, 7. Ha5e9awa v,5, p. Haut1e t,
N. Haya5h1 v, C.A. Heu5ch w, N. H0r1kawa v, V.W. Hu9he51, 6 . 190 0, 5. 15h1m0t0 v,6, 7. 1wata ~, M. de J0n9 u, E.M. Ka6u8 u, R. Ka15er m, A. Karev 5, H.J. Ke551er m, 7.J. Kete1 e, 1. K1ryu5h1n 5, A. K15h1 v, Yu. K155e1ev 5, L. K105termann e, W. Kn0p x, V. Kr1v0kh1j1ne 5, V. Kukht1n 5, J. Kyyn~1r~11nen 1, M. Lamanna k, U. Land9raf m, K. Lau 4, 7. Layda w, F. Lehar f,
A. de Le54uen f, J. L1chten5tadt Y, 7. L1nd4v15t c, M. L1tmaath e 5. L0pe2-P0nte a,4, M. L0we 6, A. Ma9n0n h,f, 6 . K . Ma110t h,u, F. Mar1e f, A. Mart1n k, J. Mart1n0 f, 8. Maye54, J.5. McCarthy n, 6 . van M1dde1k00p e, D. M111er p, J. M1tche11 n, K. M0r1 v, J. M0r0m15at0 r, 6.5. Mutch1er h, J. Na55a15k1 d, L. Naumann h, 8. Ne9an0v 5, 7 . 0 . N11n1k05k1 h, J.E.J. 06er5k1 e, 5. 0kum1 v, A. Pen20 k, 6 . Pere2 w,7, F. Perr0t-Kunne f, D. Pe5hekh0n0v 5, R. P1e9a1a h,8, L. P1n5ky 4, 5. P1atchk0v f, M. P10 a, D. P05e 5, H. P05tma e, 7. Pu551eux f, J. Pyr11k 4, J.M. R1eu61and h, A. R1j11art h, J.8. R06ert56, M. R0dr19ue2 a, E. R0nd10 d, L. R0pe1ew5k1 d, A. R05ad0J, 1. 5a60 Y, J.
5 a 6 0 r 1 d 0 a,6 . 5a1vat0 k, A. 5andaC2 d, D. 5ander54, 1. 5av1n 5, P. 5Ch1av0n k, P. 5Ch111er e~9, R. 5e9e1P, R. 5e1t2 u, 5. 5er9eev 5, F. 5ever e,1°, P. 5hanahan P, 6 . 5m1rn0v 5, A. 5taudeJ,
A. 5te1nmet2 u, H. 5tuhrmann x, K.M. 7e1ChertJ, F. 7e55ar0tt0 k, W. 7h1e19•11, 5. 7renta1an9e 0, Y. 72am0uran154~12, M. Ve1a5C0 p, J. V09tJ, R. V055 h, R. We1n5te1n 4, C. Wh1tten 0,
R. W1ndm01der52, W. W1511ck1 d, A. W1t2mann m, A. Ya5e2 a, N.1.2am1at1n 5 and A.M. 2anett1 k
a Un1ver51ty 0f5ant1a90, Department 0fPart1c1e Phy51c5, E-15706 5ant1a90 de C0mp05te1a, 5pa1n 13 6 R1ce Un1ver51ty, 80nner La60rat0ry, H0u5t0n, 7X 77251-1892, U5A 14
e Upp5a1a Un1ver51ty, Department 0f Rad1at10n 5c1ence5, 5- 75121 Upp5a1a, 5weden d War5aw Un1ver51ty and 501tan 1n5t1tutef0r Nuc1ear 5tud1e5, PL-00681 War5aw, P01and 15 e N1KHEF, F 0 M and Free Un1ver51ty, NL-1009 AJ Am5terdam, 7he Nether1and516 f DAPN1A, CEN 5ac1ay, F-91191 61f-5ur-Yvette, France
9 Un1ver51ty 0f81e1efe1d, Phy51c5 Department, W-4800 81e1efe1d 1, F R 6 17 h CERN, CH-1211 6eneva 23, 5w1t2er1and
1 He151nk1 Un1ver51ty 0f 7echn0109Y, L0w 7emperature La60rat0ry, 5F-02150 E5p00, F1n1and J Un1ver51ty 0fMun1ch, Phy51c5 Department, W-8000 Mun1ch, F R 6 17
k 1NFN 7r1e5te and Un1ver51ty 0f 7r1e5te, Department 0f Phy51c5, 1-34127 7r1e5te, 1ta1y Ya1e Un1ver51ty, Department 0f Phy51c5, New Haven, C7 06511, U5A 14
m Un1ver51ty 0f Fre16ur9, Phy51c5 Department, W- 7800 Fre16ur9, F R 6 17
n Un1ver51ty 0f V1r91n1a, Department 0fPhy51c5, Char10tte5v111e, VA 22901, U5A 18 0 Un1ver51ty 0f Ca11f0rn1a, Department 0f Phy51c5, L05 An9e1e5, CA 90024, U5A 14
V01ume 302, num6er 4 PHY51C5 LE77ER5 8 1 Apr11 1993 P N0rthwe5tern Un1ver51ty, Department 0fPhy51c5, Evan5t0n, 1L 60208, U5A 14,18
4 Un1ver51ty 0fH0u5t0n, Department 0fPhy51c5, H0u5t0n, 7X 77204-5504, U5A and 1n5t1tute f0r 8eam Part1c1e Dynam1c5, H0u5t0n, 7X 77204-5506, U5A 14,18 r N0rthea5tern Un1ver51ty, Department 0fPhy51c5, 805t0n, MA 02115, U5A 18 5 J1NR, La60rat0ry 0f 5uper H19h Ener9y Phy51c5, Du6na, Ru551an Federat10n t E7H, CH-8093 211r1ch, 5w1t2er1and
u Un1ver51ty 0fMa1n2, 1n5t1tutef0r Nuc1ear Phy51c5, W-6500 Ma1n2, F R 6 17
v Na90Ya Un1ver51ty, Department 0fPhy51c5, Fur0-Ch0, Ch1ku5a-Ku, 464 Na90ya, Japan t9 w Un1ver51ty 0f Ca11f0rn1a, 1n5t1tute 0f Part1c1e Phy51c5, 5anta Cru2, CA 95064, U5A x 6K55, W-2054 6ee5thacht, F R 6 17
Y 7e1Av1v Un1ver51ty, 5ch001 0fPhy51c5, 69978 7e1Av1v, 15rae12°
2 Un1ver51ty 0fM0n5, Facu1ty 0f5c1ence, 8-7000 M0n5, 8e191um Rece1ved 1 March 1993
We rep0rt 0n the f1r5t mea5urement 0f the 5p1n-dependent 5tructure funct10n 91 d 0f the deuter0n 1n the deep 1ne1a5t1c 5catter1n9 0f p01ar15ed mu0n5 0ff p01ar15ed deuter0n5, 1n the k1nemat1ca1 ran9e 0.006 < x < 0.6, 1 6eV 2 < Q2 < 30 6eV 2. 7he f1r5t m0ment, F1 d = f0 ~ 9tddx = 0.023 + 0.020 (5tat.) + 0.015 (5y5t.), 15 5ma11er than the pred1ct10n 0f the E1115-Jaffe 5um ru1e5. U51n9 ear11er mea5urement5 0f 9~, we 1nfer the f1r5t m0ment 0f the 5p1n-dependent neutr0n 5tructure funct10n 9~. 7he d1fference F~ - ~ = 0.20 + 0.05 (5tat.) • 0.04 (5y5t.) a9ree5 w1th the pred1ct10n 0f the 8j0rken 5um ru1e, F~ - ~ = 0.191 + 0.002.
1 Pre5ent addre55: CERN, CH-1211 6eneva 23, 5w1t2er1and.
2 Pre5ent addre55: Un1ver51ty 0f M0ntrea1, M0ntrea1, PQ,, Canada H3C 3J7.
3 Permanent addre55:809a21~1 Un1ver51ty, 8e6ek, 15tan- 6u1, 7urkey.
4 Permanent addre55: DAPN1A, CEN 5ac1ay, F-91191 61f-5ur-Yvette, France.
5 Permanent addre55: M1ya2ak1 Un1ver51ty, 88921 M1ya2ak1-5h1, Japan.
6 Permanent addre55: KEK, 305 16arak1-Ken, Japan.
7 Permanent addre55: Un1ver51ty 0f H0ndura5, Phy51c5 Department, 7e9uc19a1pa, H0ndura5.
5 Permanent addre55: Un1ver51ty 0f 8uen05 A1re5, Phy51c5 Department, 1428 8uen05 A1re5, Ar9ent1na.
9 Pre5ent addre55: 55C La60rat0ry, Da11a5, 75237 7X, U5A.
10 Pre5ent addre55: E5RF, F-38043 6ren061e, France.
11 Pre5ent addre55:Ph111p5 K0mmun1kat10n5-1ndu5tr1e A6, W-8500 N11rn6er9 10, FR6.
12 Pre5ent addre55: Un1ver51ty 0f V1r91n1a, Department 0f Phy51c5, Char10tte5v111e, VA 22901, U5A.
13 5upp0rted 6y C0m1510n 1nterm1n15ter1a1 de C1enc1a y 7ecn01091a.
14 5upp0rted 6y the Department 0f Ener9y.
15 5upp0rted 6y K8N.
16 5upp0rted 6y the Nat10na1 5c1ence F0undat10n 0f the Nether1and5.
17 5upp0rted 6y 8unde5m1n15ter1um f•f1r F0r5chun9 und 7echn01091e.
18 5upp0rted 6y the Nat10na1 5c1ence F0undat10n.
1n the pa5t 15 year5, tw0 exper1menta1 determ1na- t10n5 0f the 5p1n-dependent 5tructure funct10n 9~ ( x ) 0f the pr0t0n were made fr0m mea5urement5 0f cr055 5ect10n a5ymmetr1e5 1n deep 1ne1a5t1c 5catter1n9 0f 10n91tud1na11y p01ar15ed 1ept0n5 6y 10n91tud1na11y p0- 1ar15ed pr0t0n5. 7 h e f1r5t wa5 an exper1ment at 5LAC [ 1 ] 1n wh1ch p01ar15ed e1ectr0n5 w1th ener91e5 6etween 6 a n d 21 6 e V were u5ed a n d wh1ch c0vered the k1ne- mat1c ran9e 0.1 < x < 0.7, where x 15 the 8j0rken 5ca11n9 var1a61e. 7 h e 5ec0nd wa5 an exper1ment at CERN [2] 1n wh1ch p01ar15ed mu0n5 0f 100, 120 a n d 200 6 e V ener9y were u5ed, a n d wh1ch c0vered the x ran9e 0.01 < x < 0.7. 7 h e re5u1t 0f the5e exper1- ment5 d15a9ree5 w1th the pred1ct10n 0f the E1115-Jaffe 5um ru1e [3] f0r the pr0t0n a n d 1nd1cate5 that 1n the 4 u a r k - p a r t 0 n m0de1, the 5p1n5 0f 4uark5 a n d ant1- 4uark5 c0ntr16ute 11tt1e t0 the 5p1n 0f the pr0t0n. 1n a 1ar9e n u m 6 e r 0f paper5, a var1ety 0f the0ret1ca1 1dea5 were pr0p05ed t0 exp1a1n th15 unexpected re5u1t [4].
5evera1 exper1ment5 are pre5ent1y 6e1n9 carr1ed 0ut 0r prepared at CERN [5], 5LAC [6], a n d DE5Y [7]
t0 mea5ure the 5p1n 5tructure funct10n 0f the n e u t r 0 n
19 5Upp0rted 6y M0n6U5h0 1nternat10na1 5C1enCe Re5earCh Pr09ram.
20 5Upp0rted 6y the U5--15rae1 81nat10na1 5C1enCe F0unda- t10n, Jeru5a1em, 15rae1.
V01ume 302, num6er 4 PHY51C5 LE77ER5 8 1 Apr11 1993 and t0 repeat the pr0t0n mea5urement w1th 1mpr0ved
accuracy.
1n th15 paper, we pre5ent f1r5t re5u1t5 fr0m a mea- 5urement 0f the cr055 5ect10n a5ymmetry f0r the deuter0n,
A d • trr~ -- trr7
crr~ + tr77 " (1)
1n th15 expre5510n, tr r~ (tr 77 ) are the cr055 5ect10n5 f0r 1nc1u51ve deep 1ne1a5t1c 5catter1n9 0f 10n91tud1na11y p0- 1ar15ed mu0n5 0ff 10n91tud1na11y p01ar15ed deuter0n5, f0r ant1para11e1 (para11e1) 0r1entat10n 0f 6eam and tar- 9et p01ar15at10n5. F r 0 m th15 a5ymmetry, we eva1uate the 5p1n-dependent 5tructure funct10n 9~ (x), wh1ch we then u5e t0 te5t the pred1ct10n 0f the E1115-Jaffe 5um ru1e5 [3]. 1n c0m61nat10n w1th the ear11er re5u1t5 fr0m mea5urement5 w1th pr0t0n tar9et5, 0ur data a1- 10w u5 t0 eva1uate the f1r5t m 0 m e n t 0f the 5tructure funct10n 9~ (x) 0 f t h e neutr0n and t0 te5t the 8j0rken 5um ru1e [ 8 ].
7 h e exper1ment u5e5 a p01ar15ed m u 0 n 6eam, a p0- 1ar15ed deuter0n tar9et, a 5pectr0meter t0 mea5ure the 5cattered mu0n, and a 6eam p01ar1meter. 7 h e tar9et and the 5pectr0meter are 6a5ed 0n the apparatu5 6u11t 6y the EMC C011a60rat10n [2,9], 6ut have 6een up- 9raded t0 reduce 5y5temat1c uncerta1nt1e5 [5,10]. 7 h e p01ar1meter 15 new and w111 6e de5cr16ed 1n a f0rth- c0m1n9 pu611cat10n [ 11 ].
F0r th15 exper1ment, we have u5ed a 6eam 0f p051- t1ve mu0n5 w1th an avera9e ener9y 0f 100 6 e V [ 12 ], a 5p111 t1me 0f 2.4 5 and a per10d 0f 14.4 5. 7 h e 6eam 1nten51ty wa5 4 × 107 mU0n5 per 5p111. 7 h e 1nC1dent m u 0 n m 0 m e n t u m 15 mea5ured 0n an event-6y-event 6a515.
7 h e p01ar15ed tar9et 1n the pre5ent exper1ment U5e5 the 5ame Cry09en1C C0mp0nent5 a5 the EMC tar9et
[2,13,14]. A 5UperC0nduCt1n9 501en01d pr0v1de5 a ma9net1C f1e1d 0f 2.5 7 para11e1 t0 the 6eam d1rec- t10n. A d11ut10n refr19erat0r c0015 the tar9et t0 a tem- perature 0f a60ut 500 m K dur1n9 p01ar15at10n, and t0 50 m K dur1n9 fr02en 5p1n 0perat10n. 7 h e tar9et 15 d1v1ded 1n tw0 ha1ve5, each 40 cm 10n9 and 5 cm 1n d1ameter, 5eparated 6y 20 cm. 7 h e 10n91tud1na1 p01ar15at10n5 1n the tw0 ha1ve5 are 0pp051te 1n 519n 50 that data can 6e rec0rded f0r 60th p01ar15at10n d1rect10n5 51mu1tane0u51y.
7 h e tar9et mater1a1 15 deuterated 6utan01 w1th an adm1xture 0f parama9net1c m01ecu1e5. Dynam1c Nu-
C1ear P01ar15at10n ( D N P ) 15 06ta1ned 6y app1y1n9 m1cr0wave5 at a fre4uency c105e t0 the re50nance 0f the parama9net1c e1ectr0n5. 7 h e typ1ca1 deuter0n p01ar15at10n wa5 a60ut 0.25 unt11 1t wa5 d15c0vered that a 5u65tant1a1 1ncrea5e 1n the p01ar15at10n can 6e 06ta1ned 6y m0du1at1n9 rap1d1y the m1cr0wave fre- 4uency 0ver a ran9e 0f 30 MH2 [ 15]. 1n th15 way, deuter0n p01ar15at10n5 1ar9er than 0.40 have 6een r0ut1ne1y 06ta1ned. 7 h e p01ar15at10n 15 mea5ured u5- 1n9 10 N M R c0115 em6edded 1n the tar9et mater1aL 7 h e 1nte9rated N M R a650rpt10n 519na15 were ca11- 6rated 1n therma1 e4u1116r1um at 1.1 K. 7h15 a110w5 u5 t0 mea5ure the p01ar15at10n t0 an accuracy 0f a60ut 0.02.
1n 0rder t0 m1n1m15e 5y5temat1c err0r5, we rever5ed the p01ar15at10n d1rect10n5 1n the tw0 tar9et ha1ve5 at re9u1ar t1me 1nterva15. F0r m05t 0f 0ur data the 5p1n5 were rever5ed every 8 h0ur5 6y r0tat1n9 the f1e1d d1rec- t10n u51n9 the 0.2 7 tran5ver5e f1e1d 0 f a new 5uperc0n- duct1n9 d1p01e c011 w0und 0n the m1cr0wave cav1ty.
1n add1t10n, the re1at1ve 0r1entat10n 0f the 501en01d f1e1d and the tar9et p01ar15at10n wa5 chan9ed at 1ea5t 0nce per week w1th DNP.
1n the f1r5t 5ta9e 0 f t h e m u 0 n 5pectr0meter, char9ed part1c1e5 are m 0 m e n t u m ana1y5ed w1th a c0nvent10na1 1ar9e-aperture d1p01e ma9net and 5evera1 5et5 0f pr0- p0rt10na1 and dr1ft cham6er5. Hadr0n5 are a650r6ed 1n an 1r0n wa11. D0wn5tream 0f th15 wa11 5treamer tu6e5, dr1ft tu6e5, pr0p0rt10na1 cham6er5 and 5c1nt11- 1at0r h0d05c0pe5 are u5ed f0r m u 0 n 1dent1f1cat10n and tr199er1n9.
7 h e 6eam p01ar15at10n 15 determ1ned fr0m the 5hape 0f the ener9y 5pectrum 0f the p051tr0n5 fr0m the de- cay #+ ~ e + v e ~ . D0wn5tream 0f the m u 0 n 5pec- tr0meter, a 30 m 10n9 m u 0 n decay path 15 def1ned 6e- tween a 5h0wer vet0 h0d05c0pe wh1ch 1dent1f1e5 the /t + and a d1p01e ma9net where the m 0 m e n t u m 0f the e + 15 mea5ured u51n9 mu1t1w1re pr0p0rt10na1 cham- 6er5. 1dent1f1cat10n 0f the decay p051tr0n5 15 d0ne u5- 1n9 the ener9y dep051ted 1n a 1ead 91a55 ca10r1meter.
Rad1at1ve c0rrect10n5 are taken 1nt0 acc0unt. F0r 100 6 e V p051t1ve mu0n5, the 6eam p01ar15at10n 15 f0und t0 6e P~ = - 0 . 8 2 -4- 0.06, 1n 900d a9reement w1th M0nte Car10 51mu1at10n5 0f the 6eam tran5p0rt [ 12 ].
0ff-11ne event rec0n5truct10n Pr09ram5 determ1ne the k1nemat1c5 0f the 1nc1dent and 5cattered m u 0 n and the vertex p051t10n. 5tart1n9 fr0m the 5cattered mu0n 1dent1f1ed d0wn5tream 0f the a650r6er wa11 1n
V01ume 302, num6er 4 PHY51C5 LE77ER5 8 1 Apr11 1993 the m u 0 n 5pectr0meter, the up5tream traject0ry 15 re-
c0n5tructed up t0 the 1nteract10n p01nt. 7 h e avera9e vertex re501ut10n 15 3 cm 1n the d1rect10n 0 f the 6eam and 0.3 m m 1n the tran5ver5e p1ane. 7h15 perm1t5 a 900d 1dent1f1cat10n 0f the event5 0r191nat1n9 fr0m the up5tream and d0wn5tream tar9et ce115.
A M0nte Car10 51mu1at10n wa5 deve10ped f0r 0ur exper1menta1 5et-up u51n9 the 6 E A N 7 pr09ram [ 16 ].
7 h e deta11ed de5cr1pt10n 0f the apparatu5 1nc1ude5 the re501ut10n5 and eff1c1enc1e5 0f a11 detect0r5. 7 h e 51mu1at10n u5e5 the d15tr16ut10n 0f 1nc1dent mu0n5 rec0rded dur1n9 the data tak1n9. 7 h e M0nte Car10 pr0- 9ram ha5 6een u5ed t0 te5t the event rec0n5truct10n, t0 determ1ne 5mear1n9 due t0 f1n1te re501ut10n and t0 e5t1mate 5y5temat1c err0r5.
We rep0rt here 0n data taken 1n 1992, c0ver1n9 the k1nemat1c ran9e 1 6 e V 2 < Q2 < 30 6 e V 2 and 0.006 <
x < 0.6. Cut5 were app11ed 0n k1nemat1c var1a61e5 1n 0rder t0 m1n1m15e 5mear1n9 effect5, t0 11m1t the 512e 0f rad1at1ve c0rrect10n5, and t0 reject mu0n5 0r191nat1n9 fr0m the decay 0f p10n5 pr0duced 1n the tar9et. After cut5, the data 5amp1e am0unt5 t0 3.2 × 106 event5 w1th an avera9e deuter0n p01ar15at10n Pr = 0.35.
7 h e mea5ured event y1e1d5 fr0m the tw0 tar9et ce115 can 6e expre55ed 1n term5 0f the cr055 5ect10n a5ym- metry Ad:
Nu = nu0au0"0 ( 1 - fPuPuA d), N0 = ndd0ad0"0 ( 1 - f PuPdA 0),
(2) (3) where the 5u65cr1pt5 u and d refer t0 the up5tream and d0wn5tream tar9et ce115, n 15 the num6er 0f tar- 9et nuc1e0n5, • the 6eam f1ux, a the apparatu5 accep- tance, tr0 the unp01ar15ed cr055 5ect10n, f the fract10n 0 f t h e event y1e1d fr0m the deuter0n51n the tar9et ma- ter1a1 (d11ut10n fact0r), and Pu and Pu,d are the 6eam and tar9et p01ar15at10n5. 7 h e 519n 0f the p01ar15at10n 0f 60th the tar9et and the 1nc1dent m u 0 n 15 def1ned t0 6e p051t1ve when para11e1 t0 the 6eam d1rect10n.
W1th th15 def1n1t10n, Pu 15 ne9at1ve f0r the/~+ 6eam, and Pu and Pd are 0f 0pp051te 519n. Cut5 are app11ed t0 en5ure that the 6eam f1ux • 15 the 5ame f0r 60th tar9et ce115. 7 h e d11ut10n fact0r 15 f "-~ 0.19, and the raw a5ymmetry fP~P.rA d 15 0f 0rder 10 -3.
7 h e 10n91tud1na1 v1rtua1 ph0t0n a5ymmetry A1 d 15 re1ated t0 the mu0n-deuter0n a5ymmetry A d 6y [ 17 ]
0.6
0.3
0
-0.3
-0.6
0.01 0.1
X
F19. 1.7he v1rtua1 ph0t0n-deuter0n cr055 5ect10n a5ymmetry A~ a5 a funct10n 0f the 8j0rken 5ca11n9 var1a61e x. 0n1y 5tat15t1ca1 err0r5 are 5h0wn w1th the data p01nt5. 7he 512e 0f the 5y5temat1c err0r5 15 1nd1cated 6y the 5haded area.
A d - - 0"1/2 -- 0"3/2 = --Ad -- 4A20, ( 4 )
0"1/2 + a3/2 D
where 1/2 and 3/2 are the t0ta1 5p1n pr0ject10n5 1n the d1rect10n 0f the v1rtua1 ph0t0n. 7 h e dep01ar15a- t10n fact0r D and r/depend 0n the event k1nemat1c5.
7 h e p055161e c0ntr16ut10n fr0m the tran5ver5e a5ym- metry A2 ° ha5 6een ne91ected; 1t 15 c0n5tra1ned 6y a p051t1v1ty 11m1t wh1ch 151nc1uded 1n the 5y5temat1c er- r0r. 7 h e c0ntr16ut10n fr0m the 4uadrup01e 5tructure funct10n 61 (x) 0 f t h e deuter0n 15 expected t0 6e 5ma11 1n the k1nemat1c ran9e 0f 0ur data [ 18 ], and ha5 6een ne91ected.
7 h e c0m61nat10n 0 f t w 0 data 5et5 taken 6ef0re and after a p01ar15at10n rever5a1 pr0v1de5 f0ur e4uat10n5 f0r the y1e1d5, fr0m wh1ch A~ can 6e extracted under the a55umpt10n that the acceptance rat10 r = au/ad 15 the 5ame f0r the tw0 data 5et5. 7 h e rad1at1ve c0rrec- t10n5 t0 A1 d have 6een eva1uated fr0m a deta11ed ca1cu- 1at10n 0f h19her 0rder effect5 0n 5p1n-dependent cr055 5ect10n5 [ 19 ]. W1th1n the 5y5temat1c uncerta1nty, they are 1n a9reement w1th the c0rrect10n5 06ta1ned fr0m the meth0d de5cr16ed 1n ref. [2], and are 5ma11 w1th re5pect t0 the 5tat15t1ca1 err0r5. A1 d 15 eva1uated 1n 61n5 0f x and Q2; h0wever, n0 Q2 dependence 0f A~ 15 065erved w1th1n the 5tat15t1ca1 err0r5. We theref0re pre5ent the avera9e A~ 1n each 61n 0f x (ta61e 1 and f19.1).
7 h e d0m1nant 5y5temat1c err0r 15 a p055161e t1me var1at10n 0f the acceptance rat10 r. 7 0 e5t1mate th15
V01ume 302, num6er 4 PHY51C5 LE77ER5 8 1 Apr11 1993 7a61e 1
Re5u1t5 0n the v1rtua1 ph0t0n a5ymmetry A10 and 0n the 5p1n 5tructure funct10n 90 0f the deuter0n. 7he f1r5t err0r 15 5tat15t1ca1, the 5ec0nd 0ne 15 5y5temat1c.
x ran9e (x) (Q2) A10 90
(6eV 2)
0.006-0.010 0.009 1.2 - 0.029 4- 0.071 4- 0.013 0.010-0.020 0.015 1.7 -0.046 • 0.046 -4- 0.015 0.020-0.030 0.025 2.5 -0.032 + 0.059 4- 0.018 0.030-0.040 0.035 3.1 -0.098 4- 0.073 4- 0.021 0.040-0.060 0.050 3.7 +0.096 + 0.067 4- 0.025
0.060-0.100 0.079 4.6 +0.013:1:0.070 + 0.030
0.100-0.150 0.123 5.6 +0.144 + 0.095 4- 0.037 0.150-0.200 0.173 6.9 +0.168 4- 0.143 4- 0.042 0.200-0.300 0.241 9.0 +0.245 4- 0.154 + 0.046 0.300-0.400 0.343 12.0 +0.170 + 0.286 + 0.050 0.400-0.600 0.470 15.5 + 0.031 4- 0.456 4- 0.054
-0.554 4- 1.347 + 0.251 -0.490 + 0.493 4- 0.155 -0.198 4- 0.360 4- 0.100 -0.417 4- 0.312 4- 0.078 +0.283 4- 0.197 + 0.060 +0.023 4- 0.127 4- 0.043 +0.162 4- 0.107 4- 0.031 +0.128 + 0.109 -1- 0.024 +0.122:1:0.077 4- 0.017 +0.047 4- 0.080 4- 0.010 +0.004 4- 0.059 + 0.005
uncerta1nty, we have carefu11y ana1y5ed the var1at10n5 0 f a11 detect0r eff1c1enc1e5 6etween pa1r5 0 f d a t a 5et5 preced1n9 a n d f0110w1n9 a p01ar15at10n rever5a1. 7 h e 1ar9e5t p055161e c0ntr16ut10n t0 the 5y5temat1c uncer- ta1nty wa5 then e5t1mated 6y a M0nte Car10 51mu1a- t10n u51n9 the 1ar9e5t eff1c1ency var1at10n5 065erved w1th1n the5e pa1r5. 1n a 5ec0nd m e t h 0 d the 5ame var1- at10n5 were art1f1c1a11y 1mp05ed 0n the exper1men- ta1 data. 7 h e acceptance chan9e5 06ta1ned w1th 60th meth0d5 are 1n 900d a9reement a n d 1ead t0 an u p p e r 11m1t
Ar/r
< 2 x 10 -3. 7 h e 5y5temat1c err0r 0n A1045 then 91ven 6yAA0 = 1 Ar
4fP~PrD r
(5)Add1t10na1 5y5temat1c err0r5 ar15e fr0m the uncer- ta1nt1e5 0n the 6 e a m a n d tar9et p01ar15at10n5, the d11u- t10n fact0r, the rad1at1ve c0rrect10n5, the m 0 m e n t u m mea5urement, the dep01ar15at10n fact0r D, a n d fr0m a 5ma11 c0ntam1nat10n 0 f pr0t0n5 1n the tar9et. 7 h e 1nd1v1dua1 5y5temat1c err0r5 are c0m61ned 1n 4 u a d r a - ture (ta61e 1 ).
1n 0rder t0 check the c0n515tency 0 f 0ur data, we d1v1ded t h e m 1nt0 d1fferent 5u65et5 acc0rd1n9 t0 a va- r1ety 0 f cr1ter1a (e.9. d a t a tak1n9 per10d5, rad1a1 ver- tex p051t10n, event5 rec0n5tructed 1n d1fferent part5 0 f the 5pectr0meter). 7 h e a5ymmetr1e5 fr0m 5uch 5u6- 5et5 were 1n a9reement w1th each 0ther.
7 h e 10n91tud1na1 5p1n 5tructure funct10n 90 ( x ) 15 06ta1ned fr0m the a5ymmetry A~ 6y the re1at10n
0.08 0.04 e~0 0 - 0.04 - 0.08
r "1
0.01 0.1
X
F19. 2. 7he 5p1n-dependent 5tructure funet10n
x90 (x)
a5 a funct10n 0f the 8j0rken 5ca11n9 var1a61e x. 0n1y 5tat15t1ca1 err0r5 are 5h0wn. w1th the data p01nt5. 7he 512e 0f the 5y5- temat1c err0r5 15 1nd1cated 6y the 5haded area.A~(x)F2a(x, Q 2)
90(x)
= 2 x [ 1 +R(x, Q2)] "
(6)W e a d 0 p t here the c0nvent10n that 90 a n d F2 a are the avera9e 5tructure funct10n5 0 f the nuc1e0n 1n the deuter0n. W e have taken F2 a (x, Q2 ) a n d R (x, Q2 ) at the avera9e Q2 0 f t h e data, Q2 = 4.6 6 e V 2. 7 h e va1ue5 0 f F2 a (x, Q2 ) were taken fr0m the N M C parametr15a- t10n [20] and th05e 0 f R fr0m a 9106a1 f1t 0 f t h e 5LAC d a t a [21 ]. Uncerta1nt1e5 1n F2 a n d R are 1nc1uded 1n the 5y5temat1c err0r. 7 h e re5u1t5 are 5h0wn 1n f19. 2 and are a150 91ven 1n ta61e 1 . 7 h e d a t a 1nd1cate that f0r x < 0.04, 90 6ec0me5 ne9at1ve.
7 h e 1nte9ra1 0f 90 0ver the mea5ured ran9e 0 f x 15
V01ume 302, num6er 4 PHY51C5 LE77ER5 8 1 Apr11 1993
~2
0.08
0.04
1 1 1 r 1 1 1 [
:%)
1 1 1 1 1 1 1 1 [ 1 9 1 ~ 1 1 1 1
a) 7he0ry - 6) 7h15 exp.
1 1 1 1 1111 1
0.01
11
1 1 1 1 1 1 1 1 1 , , , , •,
0.1 Xm
3. 7he 1nte9ra1 f~1
9d1(x ) dx
a5 a funct10n 0fthe 10wer F19.1nte9rat10n 11m1t
xra.
7he err0r 6ar5 are 5tat15t1ca1 0n1y. 7he 0pen p01nt repre5ent5 the extrap01at10n t0 1ar9e x. 7he 5um ru1e pred1ct10n 15 d15cu55ed 1n the text.0 . 6
f 9~(x)dx
0 . 0 0 6
= 0 . 0 2 4 + 0 . 0 2 0 (5tat.):k 0.014 (5y5t.). (7) 7 0 e5t1mate the 1nte9ra1 1n the unmea5ured re910n at 5ma11 x, we f1t the 10we5t three data p01nt5 1n x a55um1n9 a 6ehav10ur
9~(x) cx x-%
w1th - 0 . 5 <a < 0 [22]. 7h15 c0ntr16ut10n am0unt5 t0 - 0 . 0 0 3 -4- 0.003. 7 0 e5t1mate the 1nte9ra1 at x > 0.6, we u5e a parametr15at10n wh1ch 15 c0n5tra1ned t0 9~ ( x ) = 0 at x = 1 . 7 0 e5t1mate the uncerta1nty 1n th15 extrap- 01at10n, we u5e the 6 0 u n d [A1[ ~< 1. 7h15 c0ntr16u- t10n am0unt5 t0 0.002 • 0.004. 7 h e re5u1t f0r the f1r5t m 0 m e n t 0f
9~(x)
15 thu5 (f19. 3)= f 9 ,x)
dx0
= 0.023 • 0.020 (5tat.) :1:0.015 (5y5t.). (8) 7 h e 5y5temat1c err0r5 0n ~ are deta11ed 1n ta61e 2.
7 h e 5um 0f the f1r5t m0ment5 0f the 5p1n 5tructure funct10n5 91 ( x ) 0 f the pr0t0n a n d the n e u t r 0 n can 6e c0mputed fr0m the mea5ured 1~t u51n9 the re1at10n F1 p + ~ ~ 21~1/(1 - 1.5t00), where c0D 15 the pr06a- 6111ty 0f the deuter0n t0 6e 1n a D-5tate. U51n9 t0D = 0.058 [23], we f1nd F~ + ~ = 0.049• 0.044 (5tat.) • 0.032 (5y5t.). 7 h e E1115-Jaffe 5um ru1e5 [3] pred1ct F~ + F~ = 0.187 + 0.010 f0r 5 = 0.26. 7h15 15 m0re than 2 5tandard dev1at10n5 a60ve the mea5ured va1ue.
7a61e 2
C0ntr16ut10n5 t0 the err0r 0 n F. d. 1
50urce 0f the err0r A1-~1 acceptance var1at10n Ar 0.0130
ne91ect 0f A 2 0.0041
extrap01at10n at h19h x 0.0040 extrap01at10n at 10w x 0.0030 6eam p01ar15at10n 0.0015 uncerta1nty 0n F 2 0.0012 tar9et p01ar15at10n 0.0010
d11ut10n fact0r 0.0010
rad1at1ve c0rrect10n5 0.0009 k1nemat1c re501ut10n 0.0008 m0mentum mea5urement 0.0005
uncerta1nty 0n R 0.0005
pr0t0n 6ack9r0und 0.0005 t0ta1 5y5temat1c err0r 0.0148
5tat15t1c5 0.0200
7 h e va1ue 0f F~ + F~ can 6e expre55ed 1n term5 0 f t h e 5 U ( 3 ) matr1x e1ement5 a8 a n d a0 0f the ax1a1 vect0r current5 [2]. U51n9
a8
= (1/x/3) ( 3 F - D) = 0.397 + 0.020 a5 der1ved fr0m hyper0n decay [24,2], we 06ta1na0 = 0.05 + 0.16 (5tat.) + 0.12 (5y5t.), (9) 1n a9reement w1th the re5u1t fr0m the mea5urement 0fF~: a0 -- 0.098 • 0.076 (5tat.) + 0.113 (5y5t.) [2], U51n9 a m0re recent ana1y515 0f hyper0n decay data [25], we 06ta1n a 51m11ar re5u1t 0n a0. 1n the 4 u a r k - part0n m0de1, a0 15 pr0p0rt10na1 t0 the 5um 0f the 4uark 5p1n c0ntr16ut10n5 2 t0 the nuc1e0n 5p1n. 0 u r re5u1t c0rre5p0nd5 t0
Y . = A u + A d + A 5
= 0.06 + 0.20 (5tat.) • 0.15 (5y5t.). (10) C0m61n1n9 0ur re5u1t 0n ~ w1th F1 v = 0.126 + 0.010 (5tat.) -1-0.015 (5y5t.) fr0m ref. [2], we can de- term1ne the f1r5t m 0 m e n t 0f the n e u t r 0 n 5p1n 5truc- ture funct10n:
F~ = - 0 . 0 8 5 : 0 . 0 4 ( 5 t a t . ) + 0 . 0 4 (5y5t.), (11) wh11e the E1115-Jaffe 5um ru1e pred1ct5 F~ = - 0 . 0 0 2 + 0.005.7h15 a110w5 u5 t0 te5t the 5um ru1e f0r the d1f- ference F1 v - F~ that wa5 0r191na11y f0und 6y 8 j 0 r k e n
V01ume 302, num6er 4 PHY51C5 LE77ER5 8 1 Apr11 1993 [8] and 1ater der1ved a5 a r190r0u5 Q C D pred1ct10n
[26]:
1~1-1~1 = - ~ 9 a ( 1 0 5 ( Q 2 ) ) = 0 • 1 9 1 - 1 - 0 • 0 0 2 ( 1 2 ) n at Q2 = 4.6 6 e V 2. F r 0 m th15 exper1ment, we f1nd:
F ~ - F ~ = 0 . 2 0 + 0 . 0 5 (5tat.) 5: 0.04 (5y5t.), (13) 1n a9reement w1th the pred1ct10n 0 f the 8 j 0 r k e n 5um ru1e.
1n c0nc1u510n, we have p e r f 0 r m e d the f1r5t mea- 5urement 0f the 5p1n-dependent 5tructure funct10n 9t d 0f the deuter0n. 7 h e f1r5t m 0 m e n t 0 f 9d ( x ) 15 5ma11er than the pred1ct10n 06ta1ned fr0m the E1115- Jaffe 5um ru1e5 a n d 1nd1cate5 that the c0ntr16ut10n 0 f 4uark 5p1n5 t0 the nuc1e0n 5p1n 15 c0mpat161e w1th 2er0. 7h15 15 51m11ar t0 the 065ervat10n that the EMC m a d e f0r the pr0t0n. U51n9 the EMC data, we have 1nferred the 1nte9ra1 0 f the 5tructure funct10n 9~ ( x ) 0 f the neutr0n. 7 h e d1fference 0 f the f1r5t m0ment5 0 f the 5p1n 5tructure funct10n5 91 0 f the pr0t0n a n d the neutr0n 15 1n 900d a9reement w1th the pred1ct10n 0 f the fundamenta1 8 j 0 r k e n 5um ru1e.
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