The present status of the nucleon spin structure functions

NUCLEAR PHYSICS A

Nuclear Physics A577 (1994) 313c-318c North-Holland, Amsterdam

T h e present status of the nucleon spin s t r u c t u r e functions N Honkawa Department of Physics, School of Scmnce, Nagoya Umverslty Furo-cho, Chlkusa-ku, 464-01 Nagoya, Japan On behalf of the SMC Group SMC is progressing a series of experiments to reveal the spin structure of nucleon at CERN The first experiment on deuteron has been performed m 1992 We will report here the data on deuteron and &scuss the present status of nucleon spin structure using all data including SMC and also E142(SLAC) data recently reported 1. I n t r o d u c t i o n EMC[1] reported the striking result several years ago It tells us (1) the naive quark model by Elhs-Jaffe differs largely from the e x p e n m e n t and (2) s-quark spin c o n t n b u t e s unexpectedly largely (..020%) to proton spin with opposite darectmn There were, of course, many claims to this conclusion In order to make clear the nucleon spin problems, SMC started its experimental program by polarized muon b e a m and polarized nucelon target This is the report on the first experiment on the p o l a n z e d deuteron target[2] and the d~scussmn about the results[3] 2. K i n e m a t i c s

and Sum Rules E~

The deep inelastic scattering(DIS) is shown schematically by fig 1 In the case of spin polarized DIS, we can measure the a s y m m e t r y A defined by the differential cross sections as follows, ~rTl _ aU A -

G n + ~TT

(1)

The first(second) arrow means the direction of the muon(target nucleon) spin If the b e a m and target have polarizations of Pu and PT, the A is obtained from the experimental a s y m m e t r y A.,~a, by the followlng expression,

Pol Muon J

40

X

quarks

~

(q + x

VirtualPhoton(q)

-~

Pol Nucleon w,th P and S

p)

- q ° = Q~" = - ( k -

k') ~" = 4EE'~m~'(O/2)

Fig 1 The spin polarized deep inelastic scattenng

A = A .... /(P~,PTf) 0375-9474/94/$07 00 © 1994 - Elsevier Scmnce B V All nghts reserved SSDI 0375-9474(94)00389-0

(2)

314c

N Hortkawa I The present status of the nucleon spm structure functtons

f is called the dllutmn factor A has a following relation with the spin dependent structure funchon(SDSF) gl(x) neglecting the small component, A F 2 ( x , Q2) gi(~)

-

(3)

2xD(1 + R)

D is depolanzaUon factor F2 and R are the unpolanzed structure function and crobs sectmn ratio between the longitudinally polarized virtual photon and transversally polarized one

The integral of SDSF in the region 0 < z < 1 gives the first moment ['1 whmh is compared with the theoretical prediction For proton and neutron, the r i Is written a~ follows, 1 1 Ff = g f ( x ) d x = ~ [ ~ A u + A d + ~As], ( 4 - 1)

~01

14

[ 121911Au r ~ = ~0 gi'(~)dz =

+

4Ad+~As]

(-t-2)

Here, Au, for example, is the spin up-down difference to the u and antl-u quarks, like /Xu = 10~[(ut + aT) _ (u~ + ~l)]dx This rx ,s rearranged u~mg the s u ( a ) smglet a0 and the octet elements aa and as of the axial vector current, ]

1

1

(5)

P~''~ = 4--~a3 + -~-~as + -~ao

Then, a0 = A u + A d + As, a3 = A u - A d = F + D and as = A u + A d - 2As = 3 F - D From these formula, the Bjorken sum rule(Bj-SR) to C9(~)[4] and Ell,s-Jaffe sum rule(EJSR)[5] on which we will &scuss later are derived

Bj - s R

rf-ri

1 = N1 I -gA- I ( x --- ~2a~ gv

1

EJ - SR

5

spin structure

func-

)2+

7r 1

Ff 'n = -t--i-~a3 + ~ a ~ = ~

The mm of the spin polarized DIS is to offer the rehable I'f '~'d 3. S M C d e u t e r o n tion

-a,(Q - 2)+ c~( ~ gA

5

[ --g. I (4-1 + 3

7c

(6)

3F - D.

F - + L~ )

(7)

Table 1 Experimental c o n d m o n l~,tmmng tlm~ E,, I,.mematlcal Range

(1) Experimental set-up SMC aimed at the measurement of Ff and pulling out the quark spin content of the neutron The experiment has been performed m 1992 The experimental condltmns are summarized in table 1 The whole set-up xs shown m fig 2 The p o l a n m e t e r is constructed just downstream of the spectrometer The polarimeter measured the decayed positron spectrum through the/~+ --, e+z~7,

C3(~,(Q2) )%

da~s 100 Ge\ 00l
220

4xlO' Muon Flu,, Re( onstruLtlble Flux 22 × 1012tt (80 :k 4)% Beam Polanz~tlon 19 x 106 E~ent. Total Nt D~uterated Butanol Pol j = (40 4- 1 2)~ Polarized Targets

Butanol(C~HgOH)

Pol ~ = (80 4- 2 4)%/ ~t&tlStlC Elrors _xr~ _xF? .x(r~ - r ? )

o 009 0 006(1/2 of EMC) o o11 o o15

~

315c

N Hortkawa / The present status of the nucleon spm structurefuncuons

The polarization was deterrmned comparing the measured s p e c t r u m with Monte Carlo slmulatmn to the positron s p e c t r u m The obtained s p e c t r u m and the calculated one are shown m fig 3

V)

W4~ P4~

PV2

H)V~I

H2

w2Hi V/H

ST/DT61

V2 TARGET J llll I

| !

I, . : l ~

!

l l[lll .....

BFIB

ABS

ABSORBER

I,o

,B,

Fig 2 SMC spectrometer

1~coaI

F \ z

!

Ftg 3 Calculated positron s p e c t r u m for muon polarization(left) and measured spectrum(right)

~cai

1

0

I

L

l

,

~PL : -,I ~

~ ,

I Efllt!

05

The polarized target consists of a pair of 5cmCx4Ocmlong target material which are I uP made of small frozen d e u t e r a t e d - b u t a n o l beads packed in the capsule and Installed in 2 5T magnetic field and 50mK t e m p e r a t u r e by dilution refrigerator Two capsules are set on the b e a m hne in series and polarized reversely each other, in parallel or anti-parallel along the b e a m axis The polarization was reversed regularly every 8 hours The vertex position was well reproduced ms shown in fig 4 The events from the tar . . . . . . . . . . . . . . . . get and the surrounding walls are clearly projected

]

Fig 4 Reconstlucted vertex position

(2) Results The events amounted 3 2 x 106 ovel the x and Q"%range, 0 003 < x < 0 6 and 1 <

316c

N Hortkawa / The present status of the nucleon spm structure functtons

The I':' = - 0 0224-0 0074-0 009 by E142 has a discrepancy with the I'~ of S M C ( + E M C ) F:'(E142) can reproduce the EJ-SR very well and give the quark spin sum A E -= 0 57 40 11 But, the agreement to the Bj-SR is found to be poor when it was combined with EMC I'~ The results by both groups seem inducing the more confused state to the understanding of the nucleon spin However, this disagreement may be solved by considering the O 2 dependence of the data, the probable extrapolation to x = 0 and x = 1, the contributions of higher order QCD, twist effect and the role of gluon etc [2][8] We will discuss the consistency of all d a t a and its physical conclusions (a)The evaluation of SDSF of proton, neutron and deuteron All F~'"'a d a t a are reevaluated at the common Q~ = 5GeV 2, taking the effects of the extrapolation of x to x = 0 and x = 1 into account In this procedure, the most recent values of FI(x, Q2)[9] and R(x, Q2)[10] are used The results are t a b u l a t e d in table 2 Comparing the evolved values of A~, it has been found that the values measured by SMC and E 1 4 2 + E M C agree well within the errors The value F~' obtained from all experiments has taken a large negative value comparing with E142 This is caused by the e x t r a p o l a t i o n from x = 0 03 to x = 0 006 where the emsting SMC d a t a are added to the E142 d a t a The large erior reflects the SMC d a t a inclusmn Table 2 Evolved SDSFs to Q2 = 5 1st Experimental Evolved Moment values value F~ + 0 126 4- 0 018 +0 1264-0 018 rd + 0 023 4- 0 025 +0 0234-0 025 Y:' - 0 022 4- 0 011 - 0 0284-0 012 F~' - 0 0554-0 025

GeV 2 and estimated spin contents AE As Experiments +0 +0 +0 +0

14-t-0 09-t-0 574-0 244-0

17 25 11 23

-0 -0 -0 -0

154-0 16-t-0 014-0 11+0

06 08 06 08

EMC SMC E142+EMC all d a t a

(b) The test of Bj-SR The Bj-SR is checked by the evolved SDSFs The value theoretically predicted gives 0 185 4- 0 004 at Q2 = 5 GeV 2, tat~ng the higher order QCD correction up to 3rd order in c~ into account On the other hand, the experimental Bj-SR is calculated by the first three F~'n'd listed in table 2 It gives 0 1524-0 020 which does not agree with the prediction But, if we take the values of F~(EMC) and r~' for all data, we can get F~ - F~' = 0 181 4- 0 032 This agrees well with the prediction (c) Spin content of nucleon To evaluate the sum of the quark spins AE, we take the values for the combination of F and D as follows, F + D = 1 257 4- 0 003 and 3 F - D = 0 675 4- 0 038 which are almost same values with adopted in [8] The results are summarized also In table 2, corresponding to the first moments to proton, deuteron and neutron The value to the all d a t a decreases nearly one half of the E142+EMC, but it is fmrly larger than the estnnation based on the FT(EMC) or F~(SMC) The strange quark contribution is estimated in the same order among three d a t a sets(lst, 2nd and 4th-hne In table 2) and negative But, the E142 result does not agree

N Hortkawa / The present status of the nucleon spin structurefuncttons

317c

Q2 <_ 30 GeV 2, respectively The obtmned results are shown m fig 5 The m m n part of the systematic error comes from the acceptance v a n a t m n The first moment I'~ to the deuteron was derived extrapolating the data to z = 0 and x = 1 under the proper assumptions, I'd = 0 023 4- 0 020(star) 4- 0 O15(syst) 06

,,,,L, I

008 ~-a~ 03

b} This e~p j

/

o

-'----~E

l

~-b)

-03 i

i ~llt!

00t -0~

01

1

\m

001

01 X

Fig 5 The obtmned data A d and pd

4. D i s c u s s i o n s (1) Dmcussmns on SMC results The following e s h m a t m n s have been avadable by the obtmned F1d (a) The first moment of the neutron can be calculated by the formula,

(8) WD means the D-state ratio m deutelon and takes WD = 0 058 here, then, we can get F~(SMC) = --0 0S 4- 0 04 4- 0 04 with SLAC[6]-EMC r~(Hereafter, SLAC-EMC is written as EMC) (b) The value (P~ + P~)SMC = 0 049 4- 0 044 + 4-0 032 has a big discrepancy with (P~ + PT)Ej_sn = 0 187 4- 0 010 at c~ = 0 26 P and FI(SMC) " The experimental value (c) Bj-SR is also checked directly by FI(EMC) P n (PI(EMC) -- PI(SMC) ) = 0 20 4- 0 05 4- 0 04 agrees very well with the theoretical prediction (r~ - Fl~(B3_sn)) = 0 191 4- 0 002 (d) The derived a0 = 0 05 4- 0 16 4- 0 12 is compatible with the value reported by EMC The sum of quark spins A E m the nucleon gives the value AE = A u + A d + As = 0 06 + 0 02 + 0 15 This means the contribution of quark spins IS very little and follows the conclusion of EMC (2) Dmcusslons on whole data A little bit later, E142(SLAC)[7] reported the F~' measured by polarized electron beam(E~ = 19 - 26 GeV, P~ = 38 8%) and polarized 3He gas target(P(3g~ ) = 30 -40%, T(th,~) = 30cm with a density of 2 3x 102°atoms/cm a) over the x-range, 0 03 < x < 0 6, at an average Q2 of 2 GeV 2 with less stahstlc error

318c

N Hortkawa / The present status of the nucleon spin structure funcnons

The distribution of the values, EJ-SR, Bj-SR and the experiments are shown in fig 6 As a summary, we can deduce the following conclusions from the exastlng data (1) tha data A1a agrees consistently In the measured region, (2) 1st moment of the neutron I~ evolved to 5 GeV 2 for all data takes about twice larger value than E142 data only, (3) the Bj-SR derived from r e for all data agrees very well with theoretical prediction, (4) the sum of all quark spins contrlbute~ very little to the nucleon spin and has a sizable contribution to the nucleon spin with negative sign

+0

I

•--[ .

Q2= 5 GeV2

~

÷-'.

0 . _ -

F?

~

-.

I

°'I

02 01

0

i

+01

i

+02

F? Fig 6 Overlapping of measured r~ 'n and sum rules

The disagreement between SMC and E142 seems to be not caused by the lmcompatlblhty between data The effects of the extrapolation of data, higher QCD correction, higher twist, gluon polarization etc should be checked carefully SMC has measured the SDSF of ploton in 1993 as the second step The prehmlnary result will be reported In this Symposium by another reporter

References [1] J Ashman et al, Phys Lett B206(1988)364, Nucl Phys B328(1989)1 [2] B Adeva et al, Phys Lett B302(1993)533 [3] B Adeva et al, Phys Lett B320(1994)400 [4] J D Bjorken, Phys Rev 148(1966)1467, Phys Rev D1(1970)1376, S A Larin and J A M Vermaseren, Phys Lett B259(1991)345 [5] J Ellis and R L Jaffe, Phys Rev D9(1974)1444, D10(1974)1669 [6] M J nlguard et al, Phys Rev Lett 37(1976)1261, 41(1978)70, G Baum et al Phys Rev Lett 51(1983)1135 [7] D L Anthony et al, Phys Rev Lett 71(1993)959 [8] J Ellis and M Kalllner, Phys Lett B313(1993)131 , F E Close and R G Roberts, Phys Lett B316(1993)165 , G Altarelh, P Nason and G Rldolfi, Phys Left B320(1994) 152 [9] P Amaudruz et al, Phys Lett B295(1992)159 [10] L W Whitlow et al, Phys Lett B250(1990)193