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The electric neutron form factor and the strange quark content of the nucleon
Physics Letters B 274 (1992) 159-162 North-Holland
PHYSICS LETTERS B
The electric neutron form factor and the strange quark content of the nucleon M.F. G a r i a n d W. K r t i m p e l m a n n lnstitut fiir Theoretische Physik, Ruhr-Universitiit Bochum, W-4630 Bochum, FRG Received 29 August 1991; revised manuscript received 16 October 1991
We have reanalyzed the electromagnetic form factor data of the nucleon within the QCD-VM model with special emphasis on the electric neutron form factor. We show that the strange quark content of the nucleon is of especial importance. Although, due to the Zweig rule, the 0 does not couple to the nucleon directly and does not contribute to the asymptotic behaviour of the form factors, the strange quarks can give important contributions via two-step processes at intermediate momentum tranfers. The analysis shows that the strange quark contributions can reduce the electric form factor of the neutron at low Q2, but have little effect on the asymptotic behaviour or on the other form factors.
The electromagnetic probes of nucleons provide crucial information on the internal structure of baryons ~ [2]. The electromagnetic form factors of the nucleons are measured [ 3-12] within a wide range of momentum transfer and allow already a detailed study of different theoretical models for the nucleons. While in a theoretical description of the nucleon structure perturbative QCD can be applied only at large momentum transfer, the low Q2 region is governed by nonperturbative effects and therefore the low lying vector-meson resonances play an important role. In a semiphenomenological description of the nucleon form factors the Q C D - V M model [2] incorporates these basic features. Restricting to the vector-mesons P and to the model allows a rather accurate description of the data. There are essentially two shortcomings in the description ofref. [2 ] which are caused by (i) the unknown importance of the strange quark content of the nucleon, a problem which is connected with the coupling of the 0-meson to the nucleon, and (ii) the suppression of the Pauli form factor relative to the Dirac form factor due to quark helicity flip. There has been much work on the theoWork is supported by Deutsche Forchungsgemeinschaft (Ga 153/11-3 and Ga 153/13-1 ) and partially by COSY-KFA Jiilich (41140512) and BMFT (06BO7027). ~ For vector-meson dominance form factor models, see ref. [ 1 ].
retical u n d e r s t a n d i n g [ 1 2 ] ; h o w e v e r , t h e r e is n o t m u c h i n f o r m a t i o n w h i c h c o u l d b e u s e d in t h e des c r i p t i o n o f t h e f o r m factors. T h e s a m e is t r u e for t h e d e s c r i p t i o n o f t h e r a t i o P a u l i / D i r a c f o r m f a c t o r s at h i g h Q2. I n t h e p r e s e n t p a p e r we i n v e s t i g a t e b o t h effects o n t h e n u c l e o n f o r m f a c t o r s w i t h i n t h e Q C D VM model. T h e c o u p l i n g o f t h e 0 - m e s o n to t h e n u c l e o n is illust r a t e d i n fig. 1. D u e to t h e Z w e i g rule t h e s t r a n g e q u a r k s d o n o t c o n t r i b u t e to t h e D i r a c f o r m f a c t o r o f t h e n u c l e o n at low Q2. H o w e v e r , a t w o - s t e p p r o c e s s allows t h e c o u p l i n g to t h e n u c l e o n at i n t e r m e d i a t e m o m e n t u m t r a n s f e r s . T h i s is d i r e c t l y c o n n e c t e d w i t h the importance of the strange meson cloud of the nu-
g ( s
s)
Iol
{hi
>
(cl
Fig. 1. Illustration of a possible strange quark coupling to the nucleon. In the quark model the ~-meson is an almost pure sg-state, where s denotes the strange quark. At low Qz (a) the Zweig rule decouples ~-meson and nucleon. The two-step process (b) is allowed and contributes at intermediate momenta. At high Q2 (c) the transition to the nonstrange quarks is damped due to the smallness of the three-gluon phase-space.
0370-2693/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
159
Volume 274, number 2
PHYSICS LETTERS B
cleon. The sensitivity of the suppression of the Pauli form factor with respect to the Dirac form factor shows up directly in the electric form factor of the proton:
Q2 Gp =F p - 4M 2 F~. At high Q2 the Dirac and Pauli contributions are of about equal importance. This indicates that there can be a delicate cancellation between both contributions. In our earlier form factor analysis the data were not precise enough above 2-3 (GeV/c) 2 for a detailed understanding of the helicity flip region. It seems that the recent SLAC data have much improved, although the data are likely not to be conclusive. In the present paper we shall discuss three cases within the Q C D - V M model: (i) the form factors of ref. [2] (9 and m only), where the scale for the helicity flip was assumed to be connected with A2 (quark-gluon scale); (it) 9 and o contributions only, however, helicity flip scale A ~ (meson scale); (iii) corresponds to case (it) and includes in addition the contribution of the 0-nucleon coupling. The Q C D - V M description of the EM isovector F ~'Z.: and isoscalar F]~2 for factors can be summarized as follows: F~(Q2)-f~
m2+Q2F~(Q2)+
1-
F?(Q2),
gp m 2 ~CvF~(Q 2) =x~,,)cpm~ +Q2 F ~ ( Q 2) + (~c,. - ~'p~-°) F P (Q2) , go FitS(Q2)- fm
m2
m~o+Q2F~(Q2)
+go rn2Q2F,~(Q2)+(I_ ~ ) F ? ( Q 2 ) f, m~+ lqF,2S(Q2)=lc gm m~ i'm m2,+Q 2F~(Q2) +K,
m~+Q~F~(Q z)
+ ( Ks - K'°zg°'- t% ,~_,) gF p0(Q2) 160
(1)
9 January 1992
where F~, F~ and F? denote the meson-nucleon form factors. F D describes the nucleon nonresonant quark structure which is responsible for the asymptotic (Q2--+oo) behaviour. Eq. (1) embodies a onefield approximation for the vector mesons with the V-I, couplings given by f2/4g=2.12_+0.25, f~,/4g= 18.3 ___4.0,f~/47t= 14.3_+ 1.3; ~Cv=3.706 and tq= -0.12. Perturbative QCD [ 13 ] constrains the form factors at high Q2. A convenient ansatz is
A~ F]'~=P''(Q2)- d~ + 0
A~ 2 A~ Or-0 2 '
_{ A~ ~ F~=O"°(O2)-\A2 +02/I 2
~
A~ 2
A~+02,
\,u ~ 7/I~Ut-Q~J
(2)
with
O2=Q21og[(A~ +Q 2)lAhcD] ~ Iog(A2/A~cD) and c~= p, m, D. Note that the suppression of the tensor coupling with respect to the vector coupling by a power ofQ 2 is required from PQCD [ 14]. The form for the O form factor contribution is chosen in order to meet the constraints on the 0-nucleon coupling. Note that the asymptotic form for the 0-contribution is not exactly the one required from PQCD. The exact form is not very important as at high Q2 the direct term dominates over the mesonic ones due to the meson-propagator suppression at high Q2. We have fitted the Q C D - V M EM-nucleon form factors to the available data [3-11], including the most recent SLAC measurements [10]. Our results are summarized in figs. 2-4. The respective parameters are given in table 1. We realize that compared with our standard model (denoted by 1 ) differences occur in the electric proton form factor above 1 GeV/ c and in the electric neutron form factor at momentum transfers below 2 (GeV/c) 2. The large effects in the electric proton form factor arise from the sensitivity of G~ to the size of the Pauli form factor contribution. The SLAC data [ 10] show a rapid fall-off
Volume 274, number 2
PHYSICS LETTERS B
1 30 120
T
1 @
•
I
9 January 1992
010
008 Ij,.~
4"" CI
100
r~ i
090
~
T
-.
/ ~ : / / v ~ 7,~.0,...,\I ~ ".
// I
o o6 T
zw {.9
-~
./
\ T T
~
•T
/
~t"~w 0 . 8 0 2
I
070
,5
0 60
I £
0.50 001
. . . . . . . .
' 01
. . . . . . . .
' 1
'
0.00 001 3
Fig. 2. The proton electric form factor within the QCD-VM model divided by the dipole form factor FD = 1/ ( Q 2+ 0.71 ) 2. ( 1 ): standard form of ref. [2], with a helicity flip scale corresponding to the quark-gluon scale (A2); (3): helicity flip scale equals meson scale (A~). In addition the strange quark contributions are taken into acount via the e-meson. The results of model (2) are not shown as they are very similar to case (3). Data are from ref. [ 10] (dots) and refs. [3-6].
o10 1
°----.
gp/f~ Xp
g,J.fo~ x,o
004
~,
T
w ~q
I
T 2~T
12
g,/f,
1
~%,#, A~ A~ A2
602
1 0.00
0 01
01
I
. . . . 10
Model 1
Model 2
Model 3
0.377 6.62 0.411 0.163 0.00 0.0, 0.0 0.795 0.795 2.270 0.29
0.631 3.3 0.658 0.40 0.00 0.0, 0.0 0.863 1.21 2.1 0.33
0.571 3.46 0.575 0.424 -- 1.59 0.54, 0.33 0.823 1.24 1.95 0.31
T
006
0 zuj 0
' I
Table 1 Coupling constants and parameters as obtained in the present analysis in comparison with our standard model. Model 1: corresponds to the standard model [2] (Pauli suppression scale: A2). Model 2: Pauli suppression scale: A~. Model 3: corresponds to model 2, with additional e-meson contributions. Note that the values for p/o~ coupling are close to the static SU(6) prediction as obtained by de Swart [ 16].g~ = ' v 3g v and gT = .ggp.3 T
• "
. . . . . . . .
Fig.4. Effect of the e-meson contribution in the electric neutron form factor of model ( 3 ).
008 ,/
' 01
a~[IG~v/aq
Q2 [[GeV/c) 2]
2
. . . . . . . .
1o
02[{O~V/c)q Fig. 3. As fig. 2 for the electric neutron form factor. Note that G~ is shown. Data points (dots) are as obtained from our analysis of the neutron/proton cross-section of refs. [7,8]. The points below 1 GeV/c are from ref. [ 15 ] and are obtained via an analysis of the deuteron electromagnetic form factors. They are strongly model dependent. o f t h e P a u l i f o r m f a c t o r c o m p a r e d to t h e D i r a c f o r m factor, i n d i c a t i n g t h a t t h e scale w h e r e t h e h e l i c i t y flip o c c u r s is r o u g h l y a r o u n d 1 G e V / c . N o t e t h a t t h e diff e r e n c e s b e t w e e n t h e cases w i t h a n d w i t h o u t {)-meson c o n t r i b u t i o n s are i m p o r t a n t o n l y in t h e e l e c t r i c n e u t r o n f o r m factor. It is also i n t e r e s t i n g to n o t e t h a t w i t h i n t h e S U ( 6 ) r e l a t i o n f o r t h e P a n d c0 c o u p l i n g s ,
AQCD
neglecting the strange quark contributions, one obt a i n s a l w a y s a s m a l l D i r a c f o r m f a c t o r for t h e n e u t r o n , a n d t h e r e f o r e a s m a l l G~ at low Q2. T h e electric n e u t r o n f o r m f a c t o r is d i s c u s s e d in figs. 3 a n d 4. It is s e e n t h a t t h e r e l a t i v e s u p p r e s s i o n o f t h e P a u l i f o r m f a c t o r l e a d s to a d e c r e a s e o f t h e electric n e u t r o n f o r m f a c t o r a r o u n d 1 ( G e V / c ) . T h i s is c a u s e d b y t h e d e c r e a s e d P a u l i c o n t r i b u t i o n as c o m p a r e d to case 1. T h e effect o f t h e s t r a n g e q u a r k s , i.e., t h e c o u p l i n g o f t h e 0 - m e s o n in t h e p r e s e n t d e s c r i p t i o n , c a n lead to a r e l a t i v e l y large s u p p r e s s i o n o f G~ u p t o Q 2 ~ 2 ( G e V / c ) 2. 161
Volume 274, number 2
PHYSICS LETTERS B
In fig. 4 we show the r e l a t i v e i m p o r t a n c e o f the strange q u a r k effects for D i r a c and P a u l i f o r m factor c o n t r i b u t i o n s . It is seen that the largest r e d u c t i o n is to be e x p e c t e d f r o m the Q-contribution to the D i r a c f o r m factor. It is to be n o t i c e d that there is presently no e x p e r i m e n t a l i n f o r m a t i o n on G~ at low Q2. T h e discussed effects o f strangeness in the n u c l e o n c o u l d e v e n be larger w i t h o u t c h a n g i n g the quality o f the description o f the e x p e r i m e n t a l nucleon data. T h e given " d a t a p o i n t s " at low Q2are those o b t a i n e d in ref. [ 15 ] f r o m an analysis o f the d e u t e r o n f o r m factors with a variety o f n u c l e o n - n u c l e o n potentials. O t h e r p o t e n tials like N i j m e g e n , or B o n n lead to larger electric n e u t r o n f o r m factors in such an analysis. N o t e , however, that a small G~ at low Q2 does not necessarily require also a small G~ at large Q2! Still at Q2 a b o v e 4 ( G e V / c ) 2, the n e u t r o n f o r m factor d o m i n a t e s the m a g n e t i c one. S u m m a r i z i n g o u r results we n o t e that the strange quarks can h a v e a large effect on the electric n e u t r o n f o r m factor w i t h o u t strongly affecting the o t h e r nucleon f o r m factors. Small electric n e u t r o n f o r m factors at low m o m e n t u m transfer w o u l d t h e r e f o r e indicate large strange q u a r k effects in the nucleon. P r e c i s i o n m e a s u r e m e n t s o f the n e u t r o n electric f o r m factor are t h e r e f o r e o f greatest i m p o r t a n c e for an und e r s t a n d i n g o f the n u c l e o n structure. C o n c e r n i n g the electric p r o t o n f o r m factor a d d i t i o n a l precise inform a t i o n a r o u n d or a b o v e 2 ( G e V / c ) 2 are o f e x t r e m e i m p o r t a n c e for the clarification o f the suppression o f the Pauli c o n t r i b u t i o n .
162
9 January 1992
References [1] F. lachello, A. Jackson and A. Lande, Phys. Lett. B 43 (1973) 191; S. Blatnik and N. Zovko, Acta Phys. Austriaca 39 (1974) 62; G. H6hler et al., Nucl. Phys. B 114 (1976) 505; J.G. K6rner and M. Kuroda, Phys. Rev. D 16 (1977) 2165; S, Furuichi and K. Watanabe, Prog. Theor. Phys. 82 (1989) 581. [2] M.F. Gari and W. Kriimpelmann, Z. Phys. A 322 (1985) 689; Phys, Len. B 173 (1986) 10. [3] G. H6hler et al., Nucl. Phys. B 114 (1976) 505. [4 ] F, Borkowski et al,, Z. Phys. A 275 (1975) 29; Nucl. Phys. B 93 (1975) 461. [ 5 ] G.G. Simon et al., Z. Naturforsch. 35 A (1980) 1. [6] P.N. Kirk et al., Phys. Rev. D 8 (1973) 63. [ 7 ] W. Albrecht et al., Phys. Len. B 26 ( 1968 ) 642. 18 ] S. Rock et al., Phys. Rev. Lett. 49 ( 1982 ) 1139. [9] W. Barrel et al., Nucl. Phys. B 58 (1973) 429. [ 10 ] R,C. Walker et al., Phys. Lett. B 224 ( 1989 ) 353. [ 11 ] R, Arnold et al., Phys. Rev. Lett. 57 ( 1968 ) 174. [12] W. Barrel et al., Phys. Lett. B 39 (1972) 407; R.J. Budnitz et al., Phys. Rev. 173 (1968) 1357; E.B. Hughes et al., Phys. Rev. B 139 ( 1965 ) 458; J.R. Dunning et al., Phys. Rev. 141 (1989) 1286. [ 13] R.L. Jaffe, Phys. Lett. B 229 (1989) 275; D.B. Kaplan, Nucl. Phys. B 310 (1988) 527. [ 14] S.J. Brodsky and G.R. Farrar, Phys. Rev. D 11 (1975) 1309; S.J. Brodsky and G.P. Lepage, Phys. Scr. 23 ( 1981 ) 945; G.P. Lepage and S.J. Brodsky, Phys. Rev. D 22 (1980) 2157. [ 15] S. Platchkov et al., Nucl. Phys. A 510 (1990) 740. [ 16] J.J. de Swart, Rev. Mod. Phys. 35 (1963) 916; M.M. Nagets, T.A. Rijken and J.J, de Swart, Ann. Phys. (NY) 79 (1973) 338.
PHYSICS LETTERS B
The electric neutron form factor and the strange quark content of the nucleon M.F. G a r i a n d W. K r t i m p e l m a n n lnstitut fiir Theoretische Physik, Ruhr-Universitiit Bochum, W-4630 Bochum, FRG Received 29 August 1991; revised manuscript received 16 October 1991
We have reanalyzed the electromagnetic form factor data of the nucleon within the QCD-VM model with special emphasis on the electric neutron form factor. We show that the strange quark content of the nucleon is of especial importance. Although, due to the Zweig rule, the 0 does not couple to the nucleon directly and does not contribute to the asymptotic behaviour of the form factors, the strange quarks can give important contributions via two-step processes at intermediate momentum tranfers. The analysis shows that the strange quark contributions can reduce the electric form factor of the neutron at low Q2, but have little effect on the asymptotic behaviour or on the other form factors.
The electromagnetic probes of nucleons provide crucial information on the internal structure of baryons ~ [2]. The electromagnetic form factors of the nucleons are measured [ 3-12] within a wide range of momentum transfer and allow already a detailed study of different theoretical models for the nucleons. While in a theoretical description of the nucleon structure perturbative QCD can be applied only at large momentum transfer, the low Q2 region is governed by nonperturbative effects and therefore the low lying vector-meson resonances play an important role. In a semiphenomenological description of the nucleon form factors the Q C D - V M model [2] incorporates these basic features. Restricting to the vector-mesons P and to the model allows a rather accurate description of the data. There are essentially two shortcomings in the description ofref. [2 ] which are caused by (i) the unknown importance of the strange quark content of the nucleon, a problem which is connected with the coupling of the 0-meson to the nucleon, and (ii) the suppression of the Pauli form factor relative to the Dirac form factor due to quark helicity flip. There has been much work on the theoWork is supported by Deutsche Forchungsgemeinschaft (Ga 153/11-3 and Ga 153/13-1 ) and partially by COSY-KFA Jiilich (41140512) and BMFT (06BO7027). ~ For vector-meson dominance form factor models, see ref. [ 1 ].
retical u n d e r s t a n d i n g [ 1 2 ] ; h o w e v e r , t h e r e is n o t m u c h i n f o r m a t i o n w h i c h c o u l d b e u s e d in t h e des c r i p t i o n o f t h e f o r m factors. T h e s a m e is t r u e for t h e d e s c r i p t i o n o f t h e r a t i o P a u l i / D i r a c f o r m f a c t o r s at h i g h Q2. I n t h e p r e s e n t p a p e r we i n v e s t i g a t e b o t h effects o n t h e n u c l e o n f o r m f a c t o r s w i t h i n t h e Q C D VM model. T h e c o u p l i n g o f t h e 0 - m e s o n to t h e n u c l e o n is illust r a t e d i n fig. 1. D u e to t h e Z w e i g rule t h e s t r a n g e q u a r k s d o n o t c o n t r i b u t e to t h e D i r a c f o r m f a c t o r o f t h e n u c l e o n at low Q2. H o w e v e r , a t w o - s t e p p r o c e s s allows t h e c o u p l i n g to t h e n u c l e o n at i n t e r m e d i a t e m o m e n t u m t r a n s f e r s . T h i s is d i r e c t l y c o n n e c t e d w i t h the importance of the strange meson cloud of the nu-
g ( s
s)
Iol
{hi
>
(cl
Fig. 1. Illustration of a possible strange quark coupling to the nucleon. In the quark model the ~-meson is an almost pure sg-state, where s denotes the strange quark. At low Qz (a) the Zweig rule decouples ~-meson and nucleon. The two-step process (b) is allowed and contributes at intermediate momenta. At high Q2 (c) the transition to the nonstrange quarks is damped due to the smallness of the three-gluon phase-space.
0370-2693/92/$ 05.00 © 1992 Elsevier Science Publishers B.V. All rights reserved.
159
Volume 274, number 2
PHYSICS LETTERS B
cleon. The sensitivity of the suppression of the Pauli form factor with respect to the Dirac form factor shows up directly in the electric form factor of the proton:
Q2 Gp =F p - 4M 2 F~. At high Q2 the Dirac and Pauli contributions are of about equal importance. This indicates that there can be a delicate cancellation between both contributions. In our earlier form factor analysis the data were not precise enough above 2-3 (GeV/c) 2 for a detailed understanding of the helicity flip region. It seems that the recent SLAC data have much improved, although the data are likely not to be conclusive. In the present paper we shall discuss three cases within the Q C D - V M model: (i) the form factors of ref. [2] (9 and m only), where the scale for the helicity flip was assumed to be connected with A2 (quark-gluon scale); (it) 9 and o contributions only, however, helicity flip scale A ~ (meson scale); (iii) corresponds to case (it) and includes in addition the contribution of the 0-nucleon coupling. The Q C D - V M description of the EM isovector F ~'Z.: and isoscalar F]~2 for factors can be summarized as follows: F~(Q2)-f~
m2+Q2F~(Q2)+
1-
F?(Q2),
gp m 2 ~CvF~(Q 2) =x~,,)cpm~ +Q2 F ~ ( Q 2) + (~c,. - ~'p~-°) F P (Q2) , go FitS(Q2)- fm
m2
m~o+Q2F~(Q2)
+go rn2Q2F,~(Q2)+(I_ ~ ) F ? ( Q 2 ) f, m~+ lqF,2S(Q2)=lc gm m~ i'm m2,+Q 2F~(Q2) +K,
m~+Q~F~(Q z)
+ ( Ks - K'°zg°'- t% ,~_,) gF p0(Q2) 160
(1)
9 January 1992
where F~, F~ and F? denote the meson-nucleon form factors. F D describes the nucleon nonresonant quark structure which is responsible for the asymptotic (Q2--+oo) behaviour. Eq. (1) embodies a onefield approximation for the vector mesons with the V-I, couplings given by f2/4g=2.12_+0.25, f~,/4g= 18.3 ___4.0,f~/47t= 14.3_+ 1.3; ~Cv=3.706 and tq= -0.12. Perturbative QCD [ 13 ] constrains the form factors at high Q2. A convenient ansatz is
A~ F]'~=P''(Q2)- d~ + 0
A~ 2 A~ Or-0 2 '
_{ A~ ~ F~=O"°(O2)-\A2 +02/I 2
~
A~ 2
A~+02,
\,u ~ 7/I~Ut-Q~J
(2)
with
O2=Q21og[(A~ +Q 2)lAhcD] ~ Iog(A2/A~cD) and c~= p, m, D. Note that the suppression of the tensor coupling with respect to the vector coupling by a power ofQ 2 is required from PQCD [ 14]. The form for the O form factor contribution is chosen in order to meet the constraints on the 0-nucleon coupling. Note that the asymptotic form for the 0-contribution is not exactly the one required from PQCD. The exact form is not very important as at high Q2 the direct term dominates over the mesonic ones due to the meson-propagator suppression at high Q2. We have fitted the Q C D - V M EM-nucleon form factors to the available data [3-11], including the most recent SLAC measurements [10]. Our results are summarized in figs. 2-4. The respective parameters are given in table 1. We realize that compared with our standard model (denoted by 1 ) differences occur in the electric proton form factor above 1 GeV/ c and in the electric neutron form factor at momentum transfers below 2 (GeV/c) 2. The large effects in the electric proton form factor arise from the sensitivity of G~ to the size of the Pauli form factor contribution. The SLAC data [ 10] show a rapid fall-off
Volume 274, number 2
PHYSICS LETTERS B
1 30 120
T
1 @
•
I
9 January 1992
010
008 Ij,.~
4"" CI
100
r~ i
090
~
T
-.
/ ~ : / / v ~ 7,~.0,...,\I ~ ".
// I
o o6 T
zw {.9
-~
./
\ T T
~
•T
/
~t"~w 0 . 8 0 2
I
070
,5
0 60
I £
0.50 001
. . . . . . . .
' 01
. . . . . . . .
' 1
'
0.00 001 3
Fig. 2. The proton electric form factor within the QCD-VM model divided by the dipole form factor FD = 1/ ( Q 2+ 0.71 ) 2. ( 1 ): standard form of ref. [2], with a helicity flip scale corresponding to the quark-gluon scale (A2); (3): helicity flip scale equals meson scale (A~). In addition the strange quark contributions are taken into acount via the e-meson. The results of model (2) are not shown as they are very similar to case (3). Data are from ref. [ 10] (dots) and refs. [3-6].
o10 1
°----.
gp/f~ Xp
g,J.fo~ x,o
004
~,
T
w ~q
I
T 2~T
12
g,/f,
1
~%,#, A~ A~ A2
602
1 0.00
0 01
01
I
. . . . 10
Model 1
Model 2
Model 3
0.377 6.62 0.411 0.163 0.00 0.0, 0.0 0.795 0.795 2.270 0.29
0.631 3.3 0.658 0.40 0.00 0.0, 0.0 0.863 1.21 2.1 0.33
0.571 3.46 0.575 0.424 -- 1.59 0.54, 0.33 0.823 1.24 1.95 0.31
T
006
0 zuj 0
' I
Table 1 Coupling constants and parameters as obtained in the present analysis in comparison with our standard model. Model 1: corresponds to the standard model [2] (Pauli suppression scale: A2). Model 2: Pauli suppression scale: A~. Model 3: corresponds to model 2, with additional e-meson contributions. Note that the values for p/o~ coupling are close to the static SU(6) prediction as obtained by de Swart [ 16].g~ = ' v 3g v and gT = .ggp.3 T
• "
. . . . . . . .
Fig.4. Effect of the e-meson contribution in the electric neutron form factor of model ( 3 ).
008 ,/
' 01
a~[IG~v/aq
Q2 [[GeV/c) 2]
2
. . . . . . . .
1o
02[{O~V/c)q Fig. 3. As fig. 2 for the electric neutron form factor. Note that G~ is shown. Data points (dots) are as obtained from our analysis of the neutron/proton cross-section of refs. [7,8]. The points below 1 GeV/c are from ref. [ 15 ] and are obtained via an analysis of the deuteron electromagnetic form factors. They are strongly model dependent. o f t h e P a u l i f o r m f a c t o r c o m p a r e d to t h e D i r a c f o r m factor, i n d i c a t i n g t h a t t h e scale w h e r e t h e h e l i c i t y flip o c c u r s is r o u g h l y a r o u n d 1 G e V / c . N o t e t h a t t h e diff e r e n c e s b e t w e e n t h e cases w i t h a n d w i t h o u t {)-meson c o n t r i b u t i o n s are i m p o r t a n t o n l y in t h e e l e c t r i c n e u t r o n f o r m factor. It is also i n t e r e s t i n g to n o t e t h a t w i t h i n t h e S U ( 6 ) r e l a t i o n f o r t h e P a n d c0 c o u p l i n g s ,
AQCD
neglecting the strange quark contributions, one obt a i n s a l w a y s a s m a l l D i r a c f o r m f a c t o r for t h e n e u t r o n , a n d t h e r e f o r e a s m a l l G~ at low Q2. T h e electric n e u t r o n f o r m f a c t o r is d i s c u s s e d in figs. 3 a n d 4. It is s e e n t h a t t h e r e l a t i v e s u p p r e s s i o n o f t h e P a u l i f o r m f a c t o r l e a d s to a d e c r e a s e o f t h e electric n e u t r o n f o r m f a c t o r a r o u n d 1 ( G e V / c ) . T h i s is c a u s e d b y t h e d e c r e a s e d P a u l i c o n t r i b u t i o n as c o m p a r e d to case 1. T h e effect o f t h e s t r a n g e q u a r k s , i.e., t h e c o u p l i n g o f t h e 0 - m e s o n in t h e p r e s e n t d e s c r i p t i o n , c a n lead to a r e l a t i v e l y large s u p p r e s s i o n o f G~ u p t o Q 2 ~ 2 ( G e V / c ) 2. 161
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In fig. 4 we show the r e l a t i v e i m p o r t a n c e o f the strange q u a r k effects for D i r a c and P a u l i f o r m factor c o n t r i b u t i o n s . It is seen that the largest r e d u c t i o n is to be e x p e c t e d f r o m the Q-contribution to the D i r a c f o r m factor. It is to be n o t i c e d that there is presently no e x p e r i m e n t a l i n f o r m a t i o n on G~ at low Q2. T h e discussed effects o f strangeness in the n u c l e o n c o u l d e v e n be larger w i t h o u t c h a n g i n g the quality o f the description o f the e x p e r i m e n t a l nucleon data. T h e given " d a t a p o i n t s " at low Q2are those o b t a i n e d in ref. [ 15 ] f r o m an analysis o f the d e u t e r o n f o r m factors with a variety o f n u c l e o n - n u c l e o n potentials. O t h e r p o t e n tials like N i j m e g e n , or B o n n lead to larger electric n e u t r o n f o r m factors in such an analysis. N o t e , however, that a small G~ at low Q2 does not necessarily require also a small G~ at large Q2! Still at Q2 a b o v e 4 ( G e V / c ) 2, the n e u t r o n f o r m factor d o m i n a t e s the m a g n e t i c one. S u m m a r i z i n g o u r results we n o t e that the strange quarks can h a v e a large effect on the electric n e u t r o n f o r m factor w i t h o u t strongly affecting the o t h e r nucleon f o r m factors. Small electric n e u t r o n f o r m factors at low m o m e n t u m transfer w o u l d t h e r e f o r e indicate large strange q u a r k effects in the nucleon. P r e c i s i o n m e a s u r e m e n t s o f the n e u t r o n electric f o r m factor are t h e r e f o r e o f greatest i m p o r t a n c e for an und e r s t a n d i n g o f the n u c l e o n structure. C o n c e r n i n g the electric p r o t o n f o r m factor a d d i t i o n a l precise inform a t i o n a r o u n d or a b o v e 2 ( G e V / c ) 2 are o f e x t r e m e i m p o r t a n c e for the clarification o f the suppression o f the Pauli c o n t r i b u t i o n .
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