---

-gt J

___1

f

i I

A Measurement of the Gross-Llewellyn Smith Sum Rule

from the CCFR xF3 Structure Function

WCLeung PZQuintas 1 SRMishra 2 FSciulli

CArroyo KTBachmann 3 REBlair4 CFoudas 5 BJKing

WCLefmann EOltman 6 SARabinowitz WGSeligman MHShaevitz

Columbia University New York NY 10027

FSMerritt MJOreglia BASdnmun6

University of Chicago Chicago IL 60637

RHBernstein F Borcherding HEFisk MJLanun

WMarsh KWBMerritt HSchellman 7 DDYovanovitch

Fermilab Batavia IL 60510

ABodek HSBudd P de Barbaro WKSakwnoto

University of Rochester Rochester NY 14627

PHSandler WHSmith

University of WIScOnsin Madison WI 53 ROUTE TO middot ~~~~~~~--~--~JOCATOtJ ~-----

~~bull~_~~

(Nevis Preprint 1460 Jun1992) -~__ _ltgt_ =---I~-~--J

-~ f N- ~

t 1f - tmiddot_

j

lAddress after Jan 1992 Fermilab Batavia IL 60510 tgtmiddot~ 2Address after Aug 1991 Harvard University Cambridge MA 021~=~

3Present address NCAR Boulder CO 80307 ~ f r( ~

middotPresent address Argonne N ationa Laboratory Argonne IL 6043q~

5Present address University of Wisconsin Madison WI 53706

6Present address Lawrence Berkeley Laboratory Berkeley CA 9420

7Present address Northwestern University Evanston IL 60208 I ~I ltt ~

1

middot

We report a measurement of the Gross-Uewellyn Smith Smn Rule

Ja xF3(XQl =3 GeVl) =250plusmn 018( stat)plusmn 078( syst)

PACS mnnbers 1360Hb 1150Li 1238Qk 253Fj

The Gross-Uewellyn Smith (GLS) Swn Rule[l] predicts that the integral of xF

weighted by lx equals the nwnber of valence quarks inside a mcleon - three in

the naive quark parton 1I1Odel With next to leading order QCD corrections the

GLS sum rule can be written as

_ [1 dx _ [ 12 2 ] (1)SGLS = o xxf(xCf) - 3 1- (33 _ 2N)ln((JlA2) +0(([- )

where N is the number of quark flavors (=4) and A is the mass parameter of

QCD Higher twist effects of the order O(Q-2) are expected to be small laquo 1

of SGLS at x ~ 001)[2] Until now the most precise measurement of the GLS

Sum Rule has come from the Narrow Band Beam (NBB) neutrino data of the

CCFR collaboration[3] The factor of 18 increase in the v-induced charged current

(CC) sample of the new data compared to our earlier experiment provides a nmm more precise detennination of xF3 and an improved measurement of SGLS In an

accompanying letter we have reported a high statistics determination of F2(x (2)

and xF3(X Ql)[4]

Due to the lx weighting in Eql the small x region (x lt 01) is particularly

important Accurate measurements of the following ensure small systematic errors

(a) the nmon angle (01)[5] and (b) the relative vv flux Since xF3 is obtained from

2

middot

We report a measurement of the Gross-Uewellyn Smith Smn Rule

Ja xF3(XQl =3 GeVl) =250plusmn 018( stat)plusmn 078( syst)

PACS mnnbers 1360Hb 1150Li 1238Qk 253Fj

The Gross-Uewellyn Smith (GLS) Swn Rule[l] predicts that the integral of xF

weighted by lx equals the nwnber of valence quarks inside a mcleon - three in

the naive quark parton 1I1Odel With next to leading order QCD corrections the

GLS sum rule can be written as

_ [1 dx _ [ 12 2 ] (1)SGLS = o xxf(xCf) - 3 1- (33 _ 2N)ln((JlA2) +0(([- )

where N is the number of quark flavors (=4) and A is the mass parameter of

QCD Higher twist effects of the order O(Q-2) are expected to be small laquo 1

of SGLS at x ~ 001)[2] Until now the most precise measurement of the GLS

Sum Rule has come from the Narrow Band Beam (NBB) neutrino data of the

CCFR collaboration[3] The factor of 18 increase in the v-induced charged current

(CC) sample of the new data compared to our earlier experiment provides a nmm more precise detennination of xF3 and an improved measurement of SGLS In an

accompanying letter we have reported a high statistics determination of F2(x (2)

and xF3(X Ql)[4]

Due to the lx weighting in Eql the small x region (x lt 01) is particularly

important Accurate measurements of the following ensure small systematic errors

(a) the nmon angle (01)[5] and (b) the relative vv flux Since xF3 is obtained from

2

the difference of II and J7 aass-sections small relative normalization errors can beshy

come magnified by the Mighting in the integral The abolute normalization uses an

average of II-N cross-section measurements[4] Here e desaibe procedures for obshy

taining the relative flux ratios of neutrino flux from energy to energy and between

IiIJ and vIJ Two methods have been used in extracting the relative flux [tP(E)] the

fixed v-cut method and y-intercept method[6] The two teclmiques yielded consistent

lneasures of 4gt(E)

The fixed v-cut method uses the most general fonn for the differential cross

section for the V-A neutrino mcleon interaction (Eq of Ref[4]) which requires

that the number of events with v lt lin in a Ell bin N(v lt vo) is proportional to

the relative flux 4gt(Ell) at that bin up to corrections of order of O(voEll )

JI(VltVn = OIgt(E~)vo[A+(~)B+(~yC+O(~y] (2)

The parameter Vo was chosen to be 20 GeV to simultaneously optimize statistical

precision while keeping corrections small There are 426000 v- and 146000 Iishy

induced events in the fixed v-cut flux analysis

The y-intercept method comes from a simple helicity argument the differenshy

tial cross sections dody for v- and v-induced events should be equal for forward

scattering ie as y--+O

[ do] = [dJ] = Constant (3)E dy=o E dy =0

Thus in a plot of number of events versus y the y-intercept obtained from a fit

to the entire y-region is proportional to the relative flux The fixed v-cut and yshy

intercept methods of 4gt(E) determination typically agreed to about 15 with no

3

measureable systematic difference Asmoothing procedure WaS applied to minimize

the effects of point-to-point flux variations[7]

Structure functions were extracted from the CC data in the kinematic domain

EIuJd gt 10 GeV Q2 gt 1 GeV2 and E gt 30 GeV In this sample there were 1050000

11- and 180000 ii-induced events Accepted events ~e separated into twelve x bins

and sixteen Q2 bins from 1 to 600 GeV2 Integrating the 11-N differential cross-section

(poundql of Rcf[4]) times the flux over each x and Q2 Din gives two equations for the

nwnber of neutrino and antineutrino events in the bin in terms of the structure

functions at the bin centers Xo and Q5

where a and b are known fWlctions of x y E and R(x Q2)[4] and cp(E) is the flux

The observed nwnbers of events N amp Ni were correCted with an iterative Monte

Carlo procedure for acceptance and resolution smearing

To solve these equations for F2 and xF3 certain known correCtions have to be

applied We assumed a parameterization of R(xCl) determined from the SLAC

measurements[8] and applied corrections for the 685 excess of neutrons over proshy

tons in iron We used the magnitude and the x-dependence of the strange sea

determined from our opposite-sign dinmon analysis [9] The threshold dependence of

charm quark production was corrected with the slow rescaling model[10] where the

relevant charm quark mass parameter me =134plusmn O31GeV was determined from

our data[9] Radiative corrections followed the calculation by De RUjula et al[ll]

and the cross-sections were corrected for the massive W-boson propagator The

4

charm-threshold strange sea and radiative corrections were largdy independent ci

Ql For F2 they ranged fran plusmn10 at =015 to plusmn3 at =0125 to ~~ at

= 065 over our Ql range For xF3 they ranged from ~ at =015 to ~i at

x = 0125 to ~ at x = 065 Resolution smearing was corrected using a Monte

Carlo calculation which incorporated the measured resolution functions from dedishy

cated test nul data[5] We have excluded the highest x-bin 07 x 10 due to its

susceptibility to Fenni motion (which was not included in the smearing correction)

To measure SGLS the values of xF3 were interpolated or extrapolated to Qt =3

GeV2 which is the mean Q2 of the data in the lowest x-bin which contributes mC13t

heavily to the integral Figure 1 shows the data and the qz-dependent fits used to

extract xF3(x qz =3) in three x-bins The resulting xF3 is then fit to a function

of the fonn f(x) = Axb(l- x)C (bgt 0) The best fit values are A = 5976 plusmn 0148

b =0766 plusmn 0010 and c =3101 plusmn 0036 The integral of the fit weighted by lx

gives SGLS Figure 2 shows the measured xF3(x) at Q2 =3 GeV2 as a function of

x the fits and their integr~ The measurement of the sum rule yields[12]

SGLS =J~ X3dx =250 plusmn 0018(stat)

Fitting different functional forms to our data[7] gives answers within plusmn15 of

the above We estimate plusmn0040 to be the systematic error on SGrs due to fitting

The dominant systematic error of the measurement comes from the uncertainty in

determining the absolute level of the flux which is 22 The other two systematic

errors are 15 from uncertainties in relative 1) to v flux measurement and 1 from

llllcertainties in Ep calibration[7 The systematic errors are detailed in Table 1 Our

5

value for SGrs is

1 xF38GLS = -dx =250 plusmn OOI8( stat) plusmn O078( syst) (5)

o x ~ The theoretical prediction of SGlS for the measured A = 210 plusmn 50 MeV from

the evolution of the non-singlet structure function[7] is 266 plusmn 004 (Eq1) The

prediction asswnes negligible contributions from higher twist effects target mass

corrections[13] and higher order QCD corrections 8 The WOrld status of 8GLS

measnfeInents is shown in Fig3

We thank the management and staff of Fenni1ab and aclmowledge the help of

many individuals at our home institutions This research was supported by the

National Science Foundation and the Department of Energy

8An next-to-next-to-Ieading order calculation predicts SGLS =263 plusmn 004[14]

6

References

[1] DJGrass and CHLlewyllyn Smith Nucl Phys B14 337(1969) WABardeen

et al Phys Rev D18 3998 (1978)

[2] BAIijima and RJaffe MIT Preprint CTP993 1983 RJaffe private cammlnishy

cation

[3] EOltman et al Accepted for publication in ZPhysC For a review of SGLSshy

measurement see SRMishra and FJSciulli Ann Rev Nucl Part Sci 39

259(1989)

[4] SRJAishra et al Nevis Preprint 1459 submitted for publication in Phys Rev

Lett

[5] Small x events have small angles The IIDlon angle resolution of the CCFR

detector is about 13mrad at the mean E of 100GeV for details see WKSakumoto

et al Nucl [nst Meth A294 179(1990)

[6] PAuchincloss et al ZPhys C48 411(1990) PZQujntas et ale in preparation

[7] WCLeung PhD thesis submitted to Columbia University 1991 PZQujntas

PhD thesis submitted to Colwnbia University 1991 PZQuintas et al Nevis

Preprint 1461 submitted to Phys Rev Lett

[8] SDasu et al Phys Rev Lett 61 1061 1988 LWWhitlow et al PhysLett

B250 193(1990)

[9] CFoudas et al Phys Rev Lett 641207 1990 MShaevitz review talk at

7

middot

Neutrino 00

[10] HGeorgi and HDPolitzer Phys Rev D14 1829 1976 RMBarnett Phys

Rev Lett 36 1163 1976

[11] ADe RUjula et aI Nucl Phys B154394 1979 We have estimated the effect

of using the more detailed radiative correction calculation by DYuBardin et al

JINR-E2-86-260 (1986) The difference between the two corrections was generally

very small except at the lowest (x =0015) and the highest (x = 065) x-bins

Our structure ftmction results would thus change by a few percent if the Bardins

instead of the De RUjulas calrulation were used In a future publication we shall

present our results with Bardins calculation

[12] Our present value of SGLS (250) is lower than the earlier preliminary presenshy

tations (266) [are SRMishra Thlk at Lepton-Photon 1991 Geneva] Two small

changes in the assumptions of the analysis lowered SGLS These changes We beshy

lieve are more accurate than those employed earlier See Ref[7]

[13] SRMishra Probing Nucleon Structure with v-N Experiment Nevis Preprint

1426 review talk presented at the Workshop on Hadron Structure FmctioIlS and

Parton Distributions Fennilah Batavia April(l990) World Scientific EdDGeesaman

et al

[14] SALarin and JAMVennaseren Phys Lett B259 345(1991)

[15] Measurements of SGLS a)CDHS JGHdeGroot et al Phys Lett B82

292(1979 bCHARM FBergsma et al Phys Lett B123 269(1983) c)CCFRR

8

DBMacFarlane et al ZPhys C26 1(1984) d)WA25 DAllasia et al PhysLett

BI35 231(1984) ibid ZPhys C28 321(1985)

9

Table 1 Error on the Gross-Llewellyn Smith sum rule The statistical and

systematic errors on SOLS are presented

I IEhor Variation

IStatistical I Systematic

Fit different fits plusmn040

aN ~vel plusmn21 1= 056

uN Le cl plusmn10 1=034

Energy Scale

v

plusmn eX)1

Rel Calibr

plusmn10

plusmn06 1= 010

Flux Shape smoothing onloff plusmn006

Total plusmn 078

Figure Captions

Figtne 1 Fits to Q2-dependence of xF3 in 3 x-bins (the 2 lowest x-bins and a middle

x-bin) xF3 at ~ =3 GeV2 (squares) is obtained by interpolation as in the 2 lowest

x-bin and shown by a dark symbol or by extrapolation as in the middle x-bin (dark

symbol)

Figtne 2 The GLS sum rule The squares are xF3(xQ2 =3) and the dashed line

is the fit to xF3(x Q2 =3) by Axb(l - x)c The solid line is the integral of the

fit J dxFa The diamonds are an approximation to the integral computed by a

weighted stun [S(Xj)] of x~ = xF3 (Xj Q2 =3) ie S(Xj) = r ~ixI1

10

middot Figure 3 GLS sum rule as measured by p-evious experiments and these data The

repounderenas for other measurements are CDHS[l~ CHARM[lSb) CCFRRtl5c)

WA25[l5d] and CCFR-NBB[3]

11

Fit

s to

xF

3(x

Q2)

0

20

x=

O0

10

0

15

010

00

5

t 0

00

x=O

02

5

C)

P

03

0gtlt

t 0

25

02

0

I I

I I II

I I

I0

8 -

~ I

II I

I

j0

15

I

I

07

06

05

04

t I

II I

r

1

Q2

(GeV

2)

c

GLS

Su

m R

ule

CC

FR D

ata

at

Q2

=

3

GeV

2

3 t-

-11

00

m

--l

it

bull

1lI

~z

m

07

5

~

shy2

~

bullgtlt

U

m

0

50

gtlt

C)

t-

rj

t)

tt

0 f

Fad

x

~

gtlt

~

1 0

xF

a

bull -

02

5

m

bull

bull

bullbull

bull

bull

bull

11

or--------------------------------------------------------------------------------------------~

f~ F

3dx

= 2

50

plusmn 0

01

8 plusmn

00

78

100

10

-3

10

-2

10

-1

x

measureable systematic difference Asmoothing procedure WaS applied to minimize

the effects of point-to-point flux variations[7]

Structure functions were extracted from the CC data in the kinematic domain

EIuJd gt 10 GeV Q2 gt 1 GeV2 and E gt 30 GeV In this sample there were 1050000

11- and 180000 ii-induced events Accepted events ~e separated into twelve x bins

and sixteen Q2 bins from 1 to 600 GeV2 Integrating the 11-N differential cross-section

(poundql of Rcf[4]) times the flux over each x and Q2 Din gives two equations for the

nwnber of neutrino and antineutrino events in the bin in terms of the structure

functions at the bin centers Xo and Q5

where a and b are known fWlctions of x y E and R(x Q2)[4] and cp(E) is the flux

The observed nwnbers of events N amp Ni were correCted with an iterative Monte

Carlo procedure for acceptance and resolution smearing

To solve these equations for F2 and xF3 certain known correCtions have to be

applied We assumed a parameterization of R(xCl) determined from the SLAC

measurements[8] and applied corrections for the 685 excess of neutrons over proshy

tons in iron We used the magnitude and the x-dependence of the strange sea

determined from our opposite-sign dinmon analysis [9] The threshold dependence of

charm quark production was corrected with the slow rescaling model[10] where the

relevant charm quark mass parameter me =134plusmn O31GeV was determined from

our data[9] Radiative corrections followed the calculation by De RUjula et al[ll]

and the cross-sections were corrected for the massive W-boson propagator The

4

charm-threshold strange sea and radiative corrections were largdy independent ci

Ql For F2 they ranged fran plusmn10 at =015 to plusmn3 at =0125 to ~~ at

= 065 over our Ql range For xF3 they ranged from ~ at =015 to ~i at

x = 0125 to ~ at x = 065 Resolution smearing was corrected using a Monte

Carlo calculation which incorporated the measured resolution functions from dedishy

cated test nul data[5] We have excluded the highest x-bin 07 x 10 due to its

susceptibility to Fenni motion (which was not included in the smearing correction)

To measure SGLS the values of xF3 were interpolated or extrapolated to Qt =3

GeV2 which is the mean Q2 of the data in the lowest x-bin which contributes mC13t

heavily to the integral Figure 1 shows the data and the qz-dependent fits used to

extract xF3(x qz =3) in three x-bins The resulting xF3 is then fit to a function

of the fonn f(x) = Axb(l- x)C (bgt 0) The best fit values are A = 5976 plusmn 0148

b =0766 plusmn 0010 and c =3101 plusmn 0036 The integral of the fit weighted by lx

gives SGLS Figure 2 shows the measured xF3(x) at Q2 =3 GeV2 as a function of

x the fits and their integr~ The measurement of the sum rule yields[12]

SGLS =J~ X3dx =250 plusmn 0018(stat)

Fitting different functional forms to our data[7] gives answers within plusmn15 of

the above We estimate plusmn0040 to be the systematic error on SGrs due to fitting

The dominant systematic error of the measurement comes from the uncertainty in

determining the absolute level of the flux which is 22 The other two systematic

errors are 15 from uncertainties in relative 1) to v flux measurement and 1 from

llllcertainties in Ep calibration[7 The systematic errors are detailed in Table 1 Our

5

value for SGrs is

1 xF38GLS = -dx =250 plusmn OOI8( stat) plusmn O078( syst) (5)

o x ~ The theoretical prediction of SGlS for the measured A = 210 plusmn 50 MeV from

the evolution of the non-singlet structure function[7] is 266 plusmn 004 (Eq1) The

prediction asswnes negligible contributions from higher twist effects target mass

corrections[13] and higher order QCD corrections 8 The WOrld status of 8GLS

measnfeInents is shown in Fig3

We thank the management and staff of Fenni1ab and aclmowledge the help of

many individuals at our home institutions This research was supported by the

National Science Foundation and the Department of Energy

8An next-to-next-to-Ieading order calculation predicts SGLS =263 plusmn 004[14]

6

References

[1] DJGrass and CHLlewyllyn Smith Nucl Phys B14 337(1969) WABardeen

et al Phys Rev D18 3998 (1978)

[2] BAIijima and RJaffe MIT Preprint CTP993 1983 RJaffe private cammlnishy

cation

[3] EOltman et al Accepted for publication in ZPhysC For a review of SGLSshy

measurement see SRMishra and FJSciulli Ann Rev Nucl Part Sci 39

259(1989)

[4] SRJAishra et al Nevis Preprint 1459 submitted for publication in Phys Rev

Lett

[5] Small x events have small angles The IIDlon angle resolution of the CCFR

detector is about 13mrad at the mean E of 100GeV for details see WKSakumoto

et al Nucl [nst Meth A294 179(1990)

[6] PAuchincloss et al ZPhys C48 411(1990) PZQujntas et ale in preparation

[7] WCLeung PhD thesis submitted to Columbia University 1991 PZQujntas

PhD thesis submitted to Colwnbia University 1991 PZQuintas et al Nevis

Preprint 1461 submitted to Phys Rev Lett

[8] SDasu et al Phys Rev Lett 61 1061 1988 LWWhitlow et al PhysLett

B250 193(1990)

[9] CFoudas et al Phys Rev Lett 641207 1990 MShaevitz review talk at

7

middot

Neutrino 00

[10] HGeorgi and HDPolitzer Phys Rev D14 1829 1976 RMBarnett Phys

Rev Lett 36 1163 1976

[11] ADe RUjula et aI Nucl Phys B154394 1979 We have estimated the effect

of using the more detailed radiative correction calculation by DYuBardin et al

JINR-E2-86-260 (1986) The difference between the two corrections was generally

very small except at the lowest (x =0015) and the highest (x = 065) x-bins

Our structure ftmction results would thus change by a few percent if the Bardins

instead of the De RUjulas calrulation were used In a future publication we shall

present our results with Bardins calculation

[12] Our present value of SGLS (250) is lower than the earlier preliminary presenshy

tations (266) [are SRMishra Thlk at Lepton-Photon 1991 Geneva] Two small

changes in the assumptions of the analysis lowered SGLS These changes We beshy

lieve are more accurate than those employed earlier See Ref[7]

[13] SRMishra Probing Nucleon Structure with v-N Experiment Nevis Preprint

1426 review talk presented at the Workshop on Hadron Structure FmctioIlS and

Parton Distributions Fennilah Batavia April(l990) World Scientific EdDGeesaman

et al

[14] SALarin and JAMVennaseren Phys Lett B259 345(1991)

[15] Measurements of SGLS a)CDHS JGHdeGroot et al Phys Lett B82

292(1979 bCHARM FBergsma et al Phys Lett B123 269(1983) c)CCFRR

8

DBMacFarlane et al ZPhys C26 1(1984) d)WA25 DAllasia et al PhysLett

BI35 231(1984) ibid ZPhys C28 321(1985)

9

Table 1 Error on the Gross-Llewellyn Smith sum rule The statistical and

systematic errors on SOLS are presented

I IEhor Variation

IStatistical I Systematic

Fit different fits plusmn040

aN ~vel plusmn21 1= 056

uN Le cl plusmn10 1=034

Energy Scale

v

plusmn eX)1

Rel Calibr

plusmn10

plusmn06 1= 010

Flux Shape smoothing onloff plusmn006

Total plusmn 078

Figure Captions

Figtne 1 Fits to Q2-dependence of xF3 in 3 x-bins (the 2 lowest x-bins and a middle

x-bin) xF3 at ~ =3 GeV2 (squares) is obtained by interpolation as in the 2 lowest

x-bin and shown by a dark symbol or by extrapolation as in the middle x-bin (dark

symbol)

Figtne 2 The GLS sum rule The squares are xF3(xQ2 =3) and the dashed line

is the fit to xF3(x Q2 =3) by Axb(l - x)c The solid line is the integral of the

fit J dxFa The diamonds are an approximation to the integral computed by a

weighted stun [S(Xj)] of x~ = xF3 (Xj Q2 =3) ie S(Xj) = r ~ixI1

10

middot Figure 3 GLS sum rule as measured by p-evious experiments and these data The

repounderenas for other measurements are CDHS[l~ CHARM[lSb) CCFRRtl5c)

WA25[l5d] and CCFR-NBB[3]

11

Fit

s to

xF

3(x

Q2)

0

20

x=

O0

10

0

15

010

00

5

t 0

00

x=O

02

5

C)

P

03

0gtlt

t 0

25

02

0

I I

I I II

I I

I0

8 -

~ I

II I

I

j0

15

I

I

07

06

05

04

t I

II I

r

1

Q2

(GeV

2)

c

GLS

Su

m R

ule

CC

FR D

ata

at

Q2

=

3

GeV

2

3 t-

-11

00

m

--l

it

bull

1lI

~z

m

07

5

~

shy2

~

bullgtlt

U

m

0

50

gtlt

C)

t-

rj

t)

tt

0 f

Fad

x

~

gtlt

~

1 0

xF

a

bull -

02

5

m

bull

bull

bullbull

bull

bull

bull

11

or--------------------------------------------------------------------------------------------~

f~ F

3dx

= 2

50

plusmn 0

01

8 plusmn

00

78

100

10

-3

10

-2

10

-1

x

charm-threshold strange sea and radiative corrections were largdy independent ci

Ql For F2 they ranged fran plusmn10 at =015 to plusmn3 at =0125 to ~~ at

= 065 over our Ql range For xF3 they ranged from ~ at =015 to ~i at

x = 0125 to ~ at x = 065 Resolution smearing was corrected using a Monte

Carlo calculation which incorporated the measured resolution functions from dedishy

cated test nul data[5] We have excluded the highest x-bin 07 x 10 due to its

susceptibility to Fenni motion (which was not included in the smearing correction)

To measure SGLS the values of xF3 were interpolated or extrapolated to Qt =3

GeV2 which is the mean Q2 of the data in the lowest x-bin which contributes mC13t

heavily to the integral Figure 1 shows the data and the qz-dependent fits used to

extract xF3(x qz =3) in three x-bins The resulting xF3 is then fit to a function

of the fonn f(x) = Axb(l- x)C (bgt 0) The best fit values are A = 5976 plusmn 0148

b =0766 plusmn 0010 and c =3101 plusmn 0036 The integral of the fit weighted by lx

gives SGLS Figure 2 shows the measured xF3(x) at Q2 =3 GeV2 as a function of

x the fits and their integr~ The measurement of the sum rule yields[12]

SGLS =J~ X3dx =250 plusmn 0018(stat)

Fitting different functional forms to our data[7] gives answers within plusmn15 of

the above We estimate plusmn0040 to be the systematic error on SGrs due to fitting

The dominant systematic error of the measurement comes from the uncertainty in

determining the absolute level of the flux which is 22 The other two systematic

errors are 15 from uncertainties in relative 1) to v flux measurement and 1 from

llllcertainties in Ep calibration[7 The systematic errors are detailed in Table 1 Our

5

value for SGrs is

1 xF38GLS = -dx =250 plusmn OOI8( stat) plusmn O078( syst) (5)

o x ~ The theoretical prediction of SGlS for the measured A = 210 plusmn 50 MeV from

the evolution of the non-singlet structure function[7] is 266 plusmn 004 (Eq1) The

prediction asswnes negligible contributions from higher twist effects target mass

corrections[13] and higher order QCD corrections 8 The WOrld status of 8GLS

measnfeInents is shown in Fig3

We thank the management and staff of Fenni1ab and aclmowledge the help of

many individuals at our home institutions This research was supported by the

National Science Foundation and the Department of Energy

8An next-to-next-to-Ieading order calculation predicts SGLS =263 plusmn 004[14]

6

References

[1] DJGrass and CHLlewyllyn Smith Nucl Phys B14 337(1969) WABardeen

et al Phys Rev D18 3998 (1978)

[2] BAIijima and RJaffe MIT Preprint CTP993 1983 RJaffe private cammlnishy

cation

[3] EOltman et al Accepted for publication in ZPhysC For a review of SGLSshy

measurement see SRMishra and FJSciulli Ann Rev Nucl Part Sci 39

259(1989)

[4] SRJAishra et al Nevis Preprint 1459 submitted for publication in Phys Rev

Lett

[5] Small x events have small angles The IIDlon angle resolution of the CCFR

detector is about 13mrad at the mean E of 100GeV for details see WKSakumoto

et al Nucl [nst Meth A294 179(1990)

[6] PAuchincloss et al ZPhys C48 411(1990) PZQujntas et ale in preparation

[7] WCLeung PhD thesis submitted to Columbia University 1991 PZQujntas

PhD thesis submitted to Colwnbia University 1991 PZQuintas et al Nevis

Preprint 1461 submitted to Phys Rev Lett

[8] SDasu et al Phys Rev Lett 61 1061 1988 LWWhitlow et al PhysLett

B250 193(1990)

[9] CFoudas et al Phys Rev Lett 641207 1990 MShaevitz review talk at

7

middot

Neutrino 00

[10] HGeorgi and HDPolitzer Phys Rev D14 1829 1976 RMBarnett Phys

Rev Lett 36 1163 1976

[11] ADe RUjula et aI Nucl Phys B154394 1979 We have estimated the effect

of using the more detailed radiative correction calculation by DYuBardin et al

JINR-E2-86-260 (1986) The difference between the two corrections was generally

very small except at the lowest (x =0015) and the highest (x = 065) x-bins

Our structure ftmction results would thus change by a few percent if the Bardins

instead of the De RUjulas calrulation were used In a future publication we shall

present our results with Bardins calculation

[12] Our present value of SGLS (250) is lower than the earlier preliminary presenshy

tations (266) [are SRMishra Thlk at Lepton-Photon 1991 Geneva] Two small

changes in the assumptions of the analysis lowered SGLS These changes We beshy

lieve are more accurate than those employed earlier See Ref[7]

[13] SRMishra Probing Nucleon Structure with v-N Experiment Nevis Preprint

1426 review talk presented at the Workshop on Hadron Structure FmctioIlS and

Parton Distributions Fennilah Batavia April(l990) World Scientific EdDGeesaman

et al

[14] SALarin and JAMVennaseren Phys Lett B259 345(1991)

[15] Measurements of SGLS a)CDHS JGHdeGroot et al Phys Lett B82

292(1979 bCHARM FBergsma et al Phys Lett B123 269(1983) c)CCFRR

8

DBMacFarlane et al ZPhys C26 1(1984) d)WA25 DAllasia et al PhysLett

BI35 231(1984) ibid ZPhys C28 321(1985)

9

Table 1 Error on the Gross-Llewellyn Smith sum rule The statistical and

systematic errors on SOLS are presented

I IEhor Variation

IStatistical I Systematic

Fit different fits plusmn040

aN ~vel plusmn21 1= 056

uN Le cl plusmn10 1=034

Energy Scale

v

plusmn eX)1

Rel Calibr

plusmn10

plusmn06 1= 010

Flux Shape smoothing onloff plusmn006

Total plusmn 078

Figure Captions

Figtne 1 Fits to Q2-dependence of xF3 in 3 x-bins (the 2 lowest x-bins and a middle

x-bin) xF3 at ~ =3 GeV2 (squares) is obtained by interpolation as in the 2 lowest

x-bin and shown by a dark symbol or by extrapolation as in the middle x-bin (dark

symbol)

Figtne 2 The GLS sum rule The squares are xF3(xQ2 =3) and the dashed line

is the fit to xF3(x Q2 =3) by Axb(l - x)c The solid line is the integral of the

fit J dxFa The diamonds are an approximation to the integral computed by a

weighted stun [S(Xj)] of x~ = xF3 (Xj Q2 =3) ie S(Xj) = r ~ixI1

10

middot Figure 3 GLS sum rule as measured by p-evious experiments and these data The

repounderenas for other measurements are CDHS[l~ CHARM[lSb) CCFRRtl5c)

WA25[l5d] and CCFR-NBB[3]

11

Fit

s to

xF

3(x

Q2)

0

20

x=

O0

10

0

15

010

00

5

t 0

00

x=O

02

5

C)

P

03

0gtlt

t 0

25

02

0

I I

I I II

I I

I0

8 -

~ I

II I

I

j0

15

I

I

07

06

05

04

t I

II I

r

1

Q2

(GeV

2)

c

GLS

Su

m R

ule

CC

FR D

ata

at

Q2

=

3

GeV

2

3 t-

-11

00

m

--l

it

bull

1lI

~z

m

07

5

~

shy2

~

bullgtlt

U

m

0

50

gtlt

C)

t-

rj

t)

tt

0 f

Fad

x

~

gtlt

~

1 0

xF

a

bull -

02

5

m

bull

bull

bullbull

bull

bull

bull

11

or--------------------------------------------------------------------------------------------~

f~ F

3dx

= 2

50

plusmn 0

01

8 plusmn

00

78

100

10

-3

10

-2

10

-1

x

value for SGrs is

1 xF38GLS = -dx =250 plusmn OOI8( stat) plusmn O078( syst) (5)

o x ~ The theoretical prediction of SGlS for the measured A = 210 plusmn 50 MeV from

the evolution of the non-singlet structure function[7] is 266 plusmn 004 (Eq1) The

prediction asswnes negligible contributions from higher twist effects target mass

corrections[13] and higher order QCD corrections 8 The WOrld status of 8GLS

measnfeInents is shown in Fig3

We thank the management and staff of Fenni1ab and aclmowledge the help of

many individuals at our home institutions This research was supported by the

National Science Foundation and the Department of Energy

8An next-to-next-to-Ieading order calculation predicts SGLS =263 plusmn 004[14]

6

References

[1] DJGrass and CHLlewyllyn Smith Nucl Phys B14 337(1969) WABardeen

et al Phys Rev D18 3998 (1978)

[2] BAIijima and RJaffe MIT Preprint CTP993 1983 RJaffe private cammlnishy

cation

[3] EOltman et al Accepted for publication in ZPhysC For a review of SGLSshy

measurement see SRMishra and FJSciulli Ann Rev Nucl Part Sci 39

259(1989)

[4] SRJAishra et al Nevis Preprint 1459 submitted for publication in Phys Rev

Lett

[5] Small x events have small angles The IIDlon angle resolution of the CCFR

detector is about 13mrad at the mean E of 100GeV for details see WKSakumoto

et al Nucl [nst Meth A294 179(1990)

[6] PAuchincloss et al ZPhys C48 411(1990) PZQujntas et ale in preparation

[7] WCLeung PhD thesis submitted to Columbia University 1991 PZQujntas

PhD thesis submitted to Colwnbia University 1991 PZQuintas et al Nevis

Preprint 1461 submitted to Phys Rev Lett

[8] SDasu et al Phys Rev Lett 61 1061 1988 LWWhitlow et al PhysLett

B250 193(1990)

[9] CFoudas et al Phys Rev Lett 641207 1990 MShaevitz review talk at

7

middot

Neutrino 00

[10] HGeorgi and HDPolitzer Phys Rev D14 1829 1976 RMBarnett Phys

Rev Lett 36 1163 1976

[11] ADe RUjula et aI Nucl Phys B154394 1979 We have estimated the effect

of using the more detailed radiative correction calculation by DYuBardin et al

JINR-E2-86-260 (1986) The difference between the two corrections was generally

very small except at the lowest (x =0015) and the highest (x = 065) x-bins

Our structure ftmction results would thus change by a few percent if the Bardins

instead of the De RUjulas calrulation were used In a future publication we shall

present our results with Bardins calculation

[12] Our present value of SGLS (250) is lower than the earlier preliminary presenshy

tations (266) [are SRMishra Thlk at Lepton-Photon 1991 Geneva] Two small

changes in the assumptions of the analysis lowered SGLS These changes We beshy

lieve are more accurate than those employed earlier See Ref[7]

[13] SRMishra Probing Nucleon Structure with v-N Experiment Nevis Preprint

1426 review talk presented at the Workshop on Hadron Structure FmctioIlS and

Parton Distributions Fennilah Batavia April(l990) World Scientific EdDGeesaman

et al

[14] SALarin and JAMVennaseren Phys Lett B259 345(1991)

[15] Measurements of SGLS a)CDHS JGHdeGroot et al Phys Lett B82

292(1979 bCHARM FBergsma et al Phys Lett B123 269(1983) c)CCFRR

8

DBMacFarlane et al ZPhys C26 1(1984) d)WA25 DAllasia et al PhysLett

BI35 231(1984) ibid ZPhys C28 321(1985)

9

Table 1 Error on the Gross-Llewellyn Smith sum rule The statistical and

systematic errors on SOLS are presented

I IEhor Variation

IStatistical I Systematic

Fit different fits plusmn040

aN ~vel plusmn21 1= 056

uN Le cl plusmn10 1=034

Energy Scale

v

plusmn eX)1

Rel Calibr

plusmn10

plusmn06 1= 010

Flux Shape smoothing onloff plusmn006

Total plusmn 078

Figure Captions

Figtne 1 Fits to Q2-dependence of xF3 in 3 x-bins (the 2 lowest x-bins and a middle

x-bin) xF3 at ~ =3 GeV2 (squares) is obtained by interpolation as in the 2 lowest

x-bin and shown by a dark symbol or by extrapolation as in the middle x-bin (dark

symbol)

Figtne 2 The GLS sum rule The squares are xF3(xQ2 =3) and the dashed line

is the fit to xF3(x Q2 =3) by Axb(l - x)c The solid line is the integral of the

fit J dxFa The diamonds are an approximation to the integral computed by a

weighted stun [S(Xj)] of x~ = xF3 (Xj Q2 =3) ie S(Xj) = r ~ixI1

10

middot Figure 3 GLS sum rule as measured by p-evious experiments and these data The

repounderenas for other measurements are CDHS[l~ CHARM[lSb) CCFRRtl5c)

WA25[l5d] and CCFR-NBB[3]

11

Fit

s to

xF

3(x

Q2)

0

20

x=

O0

10

0

15

010

00

5

t 0

00

x=O

02

5

C)

P

03

0gtlt

t 0

25

02

0

I I

I I II

I I

I0

8 -

~ I

II I

I

j0

15

I

I

07

06

05

04

t I

II I

r

1

Q2

(GeV

2)

c

GLS

Su

m R

ule

CC

FR D

ata

at

Q2

=

3

GeV

2

3 t-

-11

00

m

--l

it

bull

1lI

~z

m

07

5

~

shy2

~

bullgtlt

U

m

0

50

gtlt

C)

t-

rj

t)

tt

0 f

Fad

x

~

gtlt

~

1 0

xF

a

bull -

02

5

m

bull

bull

bullbull

bull

bull

bull

11

or--------------------------------------------------------------------------------------------~

f~ F

3dx

= 2

50

plusmn 0

01

8 plusmn

00

78

100

10

-3

10

-2

10

-1

x

References

[1] DJGrass and CHLlewyllyn Smith Nucl Phys B14 337(1969) WABardeen

et al Phys Rev D18 3998 (1978)

[2] BAIijima and RJaffe MIT Preprint CTP993 1983 RJaffe private cammlnishy

cation

[3] EOltman et al Accepted for publication in ZPhysC For a review of SGLSshy

measurement see SRMishra and FJSciulli Ann Rev Nucl Part Sci 39

259(1989)

[4] SRJAishra et al Nevis Preprint 1459 submitted for publication in Phys Rev

Lett

[5] Small x events have small angles The IIDlon angle resolution of the CCFR

detector is about 13mrad at the mean E of 100GeV for details see WKSakumoto

et al Nucl [nst Meth A294 179(1990)

[6] PAuchincloss et al ZPhys C48 411(1990) PZQujntas et ale in preparation

[7] WCLeung PhD thesis submitted to Columbia University 1991 PZQujntas

PhD thesis submitted to Colwnbia University 1991 PZQuintas et al Nevis

Preprint 1461 submitted to Phys Rev Lett

[8] SDasu et al Phys Rev Lett 61 1061 1988 LWWhitlow et al PhysLett

B250 193(1990)

[9] CFoudas et al Phys Rev Lett 641207 1990 MShaevitz review talk at

7

middot

Neutrino 00

[10] HGeorgi and HDPolitzer Phys Rev D14 1829 1976 RMBarnett Phys

Rev Lett 36 1163 1976

[11] ADe RUjula et aI Nucl Phys B154394 1979 We have estimated the effect

of using the more detailed radiative correction calculation by DYuBardin et al

JINR-E2-86-260 (1986) The difference between the two corrections was generally

very small except at the lowest (x =0015) and the highest (x = 065) x-bins

Our structure ftmction results would thus change by a few percent if the Bardins

instead of the De RUjulas calrulation were used In a future publication we shall

present our results with Bardins calculation

[12] Our present value of SGLS (250) is lower than the earlier preliminary presenshy

tations (266) [are SRMishra Thlk at Lepton-Photon 1991 Geneva] Two small

changes in the assumptions of the analysis lowered SGLS These changes We beshy

lieve are more accurate than those employed earlier See Ref[7]

[13] SRMishra Probing Nucleon Structure with v-N Experiment Nevis Preprint

1426 review talk presented at the Workshop on Hadron Structure FmctioIlS and

Parton Distributions Fennilah Batavia April(l990) World Scientific EdDGeesaman

et al

[14] SALarin and JAMVennaseren Phys Lett B259 345(1991)

[15] Measurements of SGLS a)CDHS JGHdeGroot et al Phys Lett B82

292(1979 bCHARM FBergsma et al Phys Lett B123 269(1983) c)CCFRR

8

DBMacFarlane et al ZPhys C26 1(1984) d)WA25 DAllasia et al PhysLett

BI35 231(1984) ibid ZPhys C28 321(1985)

9

Table 1 Error on the Gross-Llewellyn Smith sum rule The statistical and

systematic errors on SOLS are presented

I IEhor Variation

IStatistical I Systematic

Fit different fits plusmn040

aN ~vel plusmn21 1= 056

uN Le cl plusmn10 1=034

Energy Scale

v

plusmn eX)1

Rel Calibr

plusmn10

plusmn06 1= 010

Flux Shape smoothing onloff plusmn006

Total plusmn 078

Figure Captions

Figtne 1 Fits to Q2-dependence of xF3 in 3 x-bins (the 2 lowest x-bins and a middle

x-bin) xF3 at ~ =3 GeV2 (squares) is obtained by interpolation as in the 2 lowest

x-bin and shown by a dark symbol or by extrapolation as in the middle x-bin (dark

symbol)

Figtne 2 The GLS sum rule The squares are xF3(xQ2 =3) and the dashed line

is the fit to xF3(x Q2 =3) by Axb(l - x)c The solid line is the integral of the

fit J dxFa The diamonds are an approximation to the integral computed by a

weighted stun [S(Xj)] of x~ = xF3 (Xj Q2 =3) ie S(Xj) = r ~ixI1

10

middot Figure 3 GLS sum rule as measured by p-evious experiments and these data The

repounderenas for other measurements are CDHS[l~ CHARM[lSb) CCFRRtl5c)

WA25[l5d] and CCFR-NBB[3]

11

Fit

s to

xF

3(x

Q2)

0

20

x=

O0

10

0

15

010

00

5

t 0

00

x=O

02

5

C)

P

03

0gtlt

t 0

25

02

0

I I

I I II

I I

I0

8 -

~ I

II I

I

j0

15

I

I

07

06

05

04

t I

II I

r

1

Q2

(GeV

2)

c

GLS

Su

m R

ule

CC

FR D

ata

at

Q2

=

3

GeV

2

3 t-

-11

00

m

--l

it

bull

1lI

~z

m

07

5

~

shy2

~

bullgtlt

U

m

0

50

gtlt

C)

t-

rj

t)

tt

0 f

Fad

x

~

gtlt

~

1 0

xF

a

bull -

02

5

m

bull

bull

bullbull

bull

bull

bull

11

or--------------------------------------------------------------------------------------------~

f~ F

3dx

= 2

50

plusmn 0

01

8 plusmn

00

78

100

10

-3

10

-2

10

-1

x

middot

Neutrino 00

[10] HGeorgi and HDPolitzer Phys Rev D14 1829 1976 RMBarnett Phys

Rev Lett 36 1163 1976

[11] ADe RUjula et aI Nucl Phys B154394 1979 We have estimated the effect

of using the more detailed radiative correction calculation by DYuBardin et al

JINR-E2-86-260 (1986) The difference between the two corrections was generally

very small except at the lowest (x =0015) and the highest (x = 065) x-bins

Our structure ftmction results would thus change by a few percent if the Bardins

instead of the De RUjulas calrulation were used In a future publication we shall

present our results with Bardins calculation

[12] Our present value of SGLS (250) is lower than the earlier preliminary presenshy

tations (266) [are SRMishra Thlk at Lepton-Photon 1991 Geneva] Two small

changes in the assumptions of the analysis lowered SGLS These changes We beshy

lieve are more accurate than those employed earlier See Ref[7]

[13] SRMishra Probing Nucleon Structure with v-N Experiment Nevis Preprint

1426 review talk presented at the Workshop on Hadron Structure FmctioIlS and

Parton Distributions Fennilah Batavia April(l990) World Scientific EdDGeesaman

et al

[14] SALarin and JAMVennaseren Phys Lett B259 345(1991)

[15] Measurements of SGLS a)CDHS JGHdeGroot et al Phys Lett B82

292(1979 bCHARM FBergsma et al Phys Lett B123 269(1983) c)CCFRR

8

DBMacFarlane et al ZPhys C26 1(1984) d)WA25 DAllasia et al PhysLett

BI35 231(1984) ibid ZPhys C28 321(1985)

9

Table 1 Error on the Gross-Llewellyn Smith sum rule The statistical and

systematic errors on SOLS are presented

I IEhor Variation

IStatistical I Systematic

Fit different fits plusmn040

aN ~vel plusmn21 1= 056

uN Le cl plusmn10 1=034

Energy Scale

v

plusmn eX)1

Rel Calibr

plusmn10

plusmn06 1= 010

Flux Shape smoothing onloff plusmn006

Total plusmn 078

Figure Captions

Figtne 1 Fits to Q2-dependence of xF3 in 3 x-bins (the 2 lowest x-bins and a middle

x-bin) xF3 at ~ =3 GeV2 (squares) is obtained by interpolation as in the 2 lowest

x-bin and shown by a dark symbol or by extrapolation as in the middle x-bin (dark

symbol)

Figtne 2 The GLS sum rule The squares are xF3(xQ2 =3) and the dashed line

is the fit to xF3(x Q2 =3) by Axb(l - x)c The solid line is the integral of the

fit J dxFa The diamonds are an approximation to the integral computed by a

weighted stun [S(Xj)] of x~ = xF3 (Xj Q2 =3) ie S(Xj) = r ~ixI1

10

middot Figure 3 GLS sum rule as measured by p-evious experiments and these data The

repounderenas for other measurements are CDHS[l~ CHARM[lSb) CCFRRtl5c)

WA25[l5d] and CCFR-NBB[3]

11

Fit

s to

xF

3(x

Q2)

0

20

x=

O0

10

0

15

010

00

5

t 0

00

x=O

02

5

C)

P

03

0gtlt

t 0

25

02

0

I I

I I II

I I

I0

8 -

~ I

II I

I

j0

15

I

I

07

06

05

04

t I

II I

r

1

Q2

(GeV

2)

c

GLS

Su

m R

ule

CC

FR D

ata

at

Q2

=

3

GeV

2

3 t-

-11

00

m

--l

it

bull

1lI

~z

m

07

5

~

shy2

~

bullgtlt

U

m

0

50

gtlt

C)

t-

rj

t)

tt

0 f

Fad

x

~

gtlt

~

1 0

xF

a

bull -

02

5

m

bull

bull

bullbull

bull

bull

bull

11

or--------------------------------------------------------------------------------------------~

f~ F

3dx

= 2

50

plusmn 0

01

8 plusmn

00

78

100

10

-3

10

-2

10

-1

x

DBMacFarlane et al ZPhys C26 1(1984) d)WA25 DAllasia et al PhysLett

BI35 231(1984) ibid ZPhys C28 321(1985)

9

Table 1 Error on the Gross-Llewellyn Smith sum rule The statistical and

systematic errors on SOLS are presented

I IEhor Variation

IStatistical I Systematic

Fit different fits plusmn040

aN ~vel plusmn21 1= 056

uN Le cl plusmn10 1=034

Energy Scale

v

plusmn eX)1

Rel Calibr

plusmn10

plusmn06 1= 010

Flux Shape smoothing onloff plusmn006

Total plusmn 078

Figure Captions

Figtne 1 Fits to Q2-dependence of xF3 in 3 x-bins (the 2 lowest x-bins and a middle

x-bin) xF3 at ~ =3 GeV2 (squares) is obtained by interpolation as in the 2 lowest

x-bin and shown by a dark symbol or by extrapolation as in the middle x-bin (dark

symbol)

Figtne 2 The GLS sum rule The squares are xF3(xQ2 =3) and the dashed line

is the fit to xF3(x Q2 =3) by Axb(l - x)c The solid line is the integral of the

fit J dxFa The diamonds are an approximation to the integral computed by a

weighted stun [S(Xj)] of x~ = xF3 (Xj Q2 =3) ie S(Xj) = r ~ixI1

10

middot Figure 3 GLS sum rule as measured by p-evious experiments and these data The

repounderenas for other measurements are CDHS[l~ CHARM[lSb) CCFRRtl5c)

WA25[l5d] and CCFR-NBB[3]

11

Fit

s to

xF

3(x

Q2)

0

20

x=

O0

10

0

15

010

00

5

t 0

00

x=O

02

5

C)

P

03

0gtlt

t 0

25

02

0

I I

I I II

I I

I0

8 -

~ I

II I

I

j0

15

I

I

07

06

05

04

t I

II I

r

1

Q2

(GeV

2)

c

GLS

Su

m R

ule

CC

FR D

ata

at

Q2

=

3

GeV

2

3 t-

-11

00

m

--l

it

bull

1lI

~z

m

07

5

~

shy2

~

bullgtlt

U

m

0

50

gtlt

C)

t-

rj

t)

tt

0 f

Fad

x

~

gtlt

~

1 0

xF

a

bull -

02

5

m

bull

bull

bullbull

bull

bull

bull

11

or--------------------------------------------------------------------------------------------~

f~ F

3dx

= 2

50

plusmn 0

01

8 plusmn

00

78

100

10

-3

10

-2

10

-1

x

Table 1 Error on the Gross-Llewellyn Smith sum rule The statistical and

systematic errors on SOLS are presented

I IEhor Variation

IStatistical I Systematic

Fit different fits plusmn040

aN ~vel plusmn21 1= 056

uN Le cl plusmn10 1=034

Energy Scale

v

plusmn eX)1

Rel Calibr

plusmn10

plusmn06 1= 010

Flux Shape smoothing onloff plusmn006

Total plusmn 078

Figure Captions

Figtne 1 Fits to Q2-dependence of xF3 in 3 x-bins (the 2 lowest x-bins and a middle

x-bin) xF3 at ~ =3 GeV2 (squares) is obtained by interpolation as in the 2 lowest

x-bin and shown by a dark symbol or by extrapolation as in the middle x-bin (dark

symbol)

Figtne 2 The GLS sum rule The squares are xF3(xQ2 =3) and the dashed line

is the fit to xF3(x Q2 =3) by Axb(l - x)c The solid line is the integral of the

fit J dxFa The diamonds are an approximation to the integral computed by a

weighted stun [S(Xj)] of x~ = xF3 (Xj Q2 =3) ie S(Xj) = r ~ixI1

10

middot Figure 3 GLS sum rule as measured by p-evious experiments and these data The

repounderenas for other measurements are CDHS[l~ CHARM[lSb) CCFRRtl5c)

WA25[l5d] and CCFR-NBB[3]

11

Fit

s to

xF

3(x

Q2)

0

20

x=

O0

10

0

15

010

00

5

t 0

00

x=O

02

5

C)

P

03

0gtlt

t 0

25

02

0

I I

I I II

I I

I0

8 -

~ I

II I

I

j0

15

I

I

07

06

05

04

t I

II I

r

1

Q2

(GeV

2)

c

GLS

Su

m R

ule

CC

FR D

ata

at

Q2

=

3

GeV

2

3 t-

-11

00

m

--l

it

bull

1lI

~z

m

07

5

~

shy2

~

bullgtlt

U

m

0

50

gtlt

C)

t-

rj

t)

tt

0 f

Fad

x

~

gtlt

~

1 0

xF

a

bull -

02

5

m

bull

bull

bullbull

bull

bull

bull

11

or--------------------------------------------------------------------------------------------~

f~ F

3dx

= 2

50

plusmn 0

01

8 plusmn

00

78

100

10

-3

10

-2

10

-1

x

middot Figure 3 GLS sum rule as measured by p-evious experiments and these data The

repounderenas for other measurements are CDHS[l~ CHARM[lSb) CCFRRtl5c)

WA25[l5d] and CCFR-NBB[3]

11

Fit

s to

xF

3(x

Q2)

0

20

x=

O0

10

0

15

010

00

5

t 0

00

x=O

02

5

C)

P

03

0gtlt

t 0

25

02

0

I I

I I II

I I

I0

8 -

~ I

II I

I

j0

15

I

I

07

06

05

04

t I

II I

r

1

Q2

(GeV

2)

c

GLS

Su

m R

ule

CC

FR D

ata

at

Q2

=

3

GeV

2

3 t-

-11

00

m

--l

it

bull

1lI

~z

m

07

5

~

shy2

~

bullgtlt

U

m

0

50

gtlt

C)

t-

rj

t)

tt

0 f

Fad

x

~

gtlt

~

1 0

xF

a

bull -

02

5

m

bull

bull

bullbull

bull

bull

bull

11

or--------------------------------------------------------------------------------------------~

f~ F

3dx

= 2

50

plusmn 0

01

8 plusmn

00

78

100

10

-3

10

-2

10

-1

x

Fit

s to

xF

3(x

Q2)

0

20

x=

O0

10

0

15

010

00

5

t 0

00

x=O

02

5

C)

P

03

0gtlt

t 0

25

02

0

I I

I I II

I I

I0

8 -

~ I

II I

I

j0

15

I

I

07

06

05

04

t I

II I

r

1

Q2

(GeV

2)

c

GLS

Su

m R

ule

CC

FR D

ata

at

Q2

=

3

GeV

2

3 t-

-11

00

m

--l

it

bull

1lI

~z

m

07

5

~

shy2

~

bullgtlt

U

m

0

50

gtlt

C)

t-

rj

t)

tt

0 f

Fad

x

~

gtlt

~

1 0

xF

a

bull -

02

5

m

bull

bull

bullbull

bull

bull

bull

11

or--------------------------------------------------------------------------------------------~

f~ F

3dx

= 2

50

plusmn 0

01

8 plusmn

00

78

100

10

-3

10

-2

10

-1

x

c

GLS

Su

m R

ule

CC

FR D

ata

at

Q2

=

3

GeV

2

3 t-

-11

00

m

--l

it

bull

1lI

~z

m

07

5

~

shy2

~

bullgtlt

U

m

0

50

gtlt

C)

t-

rj

t)

tt

0 f

Fad

x

~

gtlt

~

1 0

xF

a

bull -

02

5

m

bull

bull

bullbull

bull

bull

bull

11

or--------------------------------------------------------------------------------------------~

f~ F

3dx

= 2

50

plusmn 0

01

8 plusmn

00

78

100

10

-3

10

-2

10

-1

x

t t

i

2 2

5 3

3

5

4 II

I

I I I

I I

I

I I

I

I I

I I

bull C

DH

S

32

0 plusmn

05

bull C

HA

RM

2

56

plusmn

04

2

t bull

I C

CFR

R

28

3 plusmn

02

0

bull W

A25

2

70

plusmn 0

40

~

CC

FR

(NB

B)

27

8 plusmn

0

15

CC

FR(Q

TB)

25

0 plusmn

0

08

The

Sta

tus

of S

Gts

M

easu

rem

ent