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---
-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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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