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The valon model and the low-x behavior of the EMC effect
Volume 187, number 3,4
PHYSICS LETTERS B
26 March 1987
THE VALON MODEL AND T H E LOW-x BEHAVIOR OF T H E EMC E F F E C T ~ Chao-hsi C H A N G Instttute of TheorettcalPhysws, Academia Sznlca, P.O Box 2735, Betjmg, P.R.Chtna and Wei Z H U Physws Department, East China Normal Umverstty, Shanghaz, P.R. Chma Received 8 October 1986; revised manuscript recewed 22 December 1986
New experimental results of the EMC effect are discussed. It ~sshown that the dlstortzon of the structure function of a nucleon bound in a nucleus may be understood by means of the valon picture.
Recently the E M C a n d B C D M S groups published their new results on the E M C effect at Q2> 10 ( G e V / c ) 2 for Cu a n d F e respectively [ 1 ], showing a quite clear b e h a v i o r in the low-x region. According to the new data, R = F A(X, Q2)/F°E(X, Q2) presents a decrease as x - , 0 a n d R crosses 1 near x_~0.3 (fig. 1 ). This tendency is precisely contrary to that o f the earliest results o f the E M C group [2] but roughly consistent with those o f the SLAC group [3] and neutrino experiments [4]. Therefore, we t h m k it-isnow time to consider the low-x b e h a v i o r o f the E M C effect seriously and it should be noted that these characteristics, the decrease o f R as x ~ 0 and R crossing 1 near x = 0.3, cannot be explained by either the rescaling m o d e l [5 ] or the meson enhancement m o d e l [ 6 ] (see fig. 1 ). It is obvious that the low-x b e h a v i o r o f the E M C effect is relevant to the p r o d u c t i o n m e c h a n i s m o f the sea quark in the nucleon [ 5 - 7 ] . Q 2 being very large, the decrease o f R as x--, 0 cannot be owed to the shadowing effect [ 8 ]. In this p a p e r we point out that if the valon m o d e l picture [ 9 ] is accepted as follows: the nucleon is regarded as consisting o f three dressed valence quark-valons, the valons having universal *
This work is supported in part by the Science Fund of the Chinese Academy of Sciences.
l.~- r
~
• BCDMS ~FeJ~lg86 • EMC. tC'~} I o ~LA~tFQ)
o,1
0
az
~
~6
o~
X
Fig. 1. R---FA(x, Q2)/FD(x, Q2) at Q 2= 10 (GeV/c) 2 --valon model (this work); - - - meson enhancement model [ 6 ], - . - rescahng model [ 5 ]. 405
Volume 187, number 3,4
PHYSICS LETTERS B
structure functions due to QCD processes, i.e. their structure functions are independent on nucleus but the valon distribution inside a nucleon is distorted due to nuclear medium as compared with that of a free nucleon, then a nice tendency of the EMC effect can be obtained which fits the expenmental data quite well. According to ref. [9 ], the structure function of a nucleon is 1
FN(x, 0 2) = . ~ J d y Gv(y)Fv(x/y,
a2),
(1 )
x
where Fvis the structure functmn ofvalon V, and Gv is the distribution of V reside N. The momentum distribution of the valons is independent of Q2, the probing value, however, the structure of a valon is Q2-dependent. The normalization of Gv is
inside a nucleon, bound in a nucleus A, has the form
G~.(y) = a y P ( 1
_y)2+~,
(5)
where a is a normalization constant, fl a constant related to the slope of the Regge trajectory, and 2 +A a number which may be related to that of the effective spectators according to the counting rule. (2) The mass factor: the effective mass of a nucleon inside a nucleus might be different from and less than that m vacuum, i.e. Meff= o~'MN
(6)
with a ' ~< 1, due to binding and color induction etc. Therefore we have the rescahng for y: y/a' instead of y, based on the definition o f y [ 11 ]. Accordingly, the normalization equation (2) becomes
fl
or'
dy ~ G¢(ym') = 1
1
fGv(y)
26 March 1987
dy= 1
(2)
0
(7)
0
and the momentum sum rule equation (3):
and ~t satisfies the m o m e n t u m sum rule
f dy Y-~ G~.(y/a',= 3 .
1
fGv(y)y
d y = 1/3 .
(3)
0
Concretely, as for a free nucleon we take [ 9 ]
Gv(y) = tr~y'/2( l _ y)2 .
(4)
We now discuss a nucleon inside a nucleus. Since the size of a v a l o n is smaller than that of a nucleon, it is reasonable to assume that in deep-inelastic scattering the valon structure functions are not influenced by the nuclear medium very much, but the valon distribution inside the nucleon is. In order to obtain the EMC behavior, based on the points of ref. [ I 0 ], we consider two factors which may cause distortion of the distribution: (1) The counting rule factor: when a nucleon is bound in a nucleus, the nucleon might be smeared out due to color induction and/or some other effects so that, as for scattering processes, the valon inside a nucleus scattered through a nucleon has a different number of the effective spectators from that in a nucleon alone, namely, based on general considerations, the behavior of the distribution of the valons 406
(8,
0
Ignoring the Fermi motion but highhghting the lowx region and consxdering the above two factors, the structure function of a nucleon inside a nucleus should be o¢'
F~,x, Q 2 , : ~ f d y l G , ( y / a ' , F v ( x / y ,
Q2,.
(9,
x
Below Q2= 10 (GeV/c) 2 is taken as an illustrating example, and the valon structure functions are parametnzed by means of the method which is used to parametrize the nucleon by Buras and Gaemers [ 12 ], but from the starting point xV(x, Q2) =8(1 - x ) and X~(X, Q2)=xG(x, Q2)-=0, when Q2~/I2, i.e. one cannot probe the structure of avalon if Q2~ p2, where /z is a characteristic size scale of the valons in momentum, and V(x, Q2), ~(x, Q2) and G(x, Q2) are the valence, sea and gluon structure functions respectively. The structure functions of the valon for Q2= 10 (GeV/c) 2, which we use through this paper, are
xV(x, Q2) =0.914x o 8 6 2 ( 1
_ _ X ) 0 065
(10)
Volume 187, number 3,4
26 March 1987
PHYSICSLETTERSB
and x ~ ( x , Q2) =0.0815(1 - x ) 416
(11 )
(see refs. [9,13] for details). If we take a ' =0.98 and A = 0.4, then a = 10.3 and fl = 0.7 as determined from the normalization equations (7) and (8), and a nice fit is obtained (fig. 1 ). For comparison we also plot in fig. 1 the curves of the ~ meson enhancement and the rescaling models. Based on the same reason as the rescaling model, the behavior of R is not dependent on Q 2 very much, thus the feature of fig. 1 is a typical one for various Q 2 Here A=0.4 (A=0 for a free nucleon, see eq. (4)) which may be explained by counting rule, i.e. according to the counting rule the number of effective spectators of the scattered valon increases by a definite quantity when a nucleon is bound inside a nucleus. To understand this, let us accept confinement pictures and assume that, being color singlets, only 3quark and 6-quark clusters may exist inside a nucleus; in addition, the "effective spectator number" then is in the sense of average A = 0.4 which means a 6-quark component of about 10% is obtained from the counting rule directly. In fact, it is not a unique mechanism which results in A= 0.4, and we will discuss this further in ref. [ 14 ]. However we would like to note here that the fit on a ' and A might have a deeper meaning than that of the counting picture. It is easy to see that due to the universality of the valons and the behavior of the valon structure functions x V ( x , Q2) x~O,o
(12)
and x ~ ( x , Q2) x~°,A ° ,
(13)
namely F v ( x , Q2)
x~0
2
, ~ Q , Ao ,
(14)
where Ao is the coefficient of the sea quark structure function, and Q, the charge of the quarks inside the valon, we have the tendency R x~O 1 ,
(15)
which is shown by the latest experimental data (note: at very small x, when Q2--,0, the shadowing effect should be considered [10]. We also note that an increase of R in the region 0~
°'8O
O.Z
t~
0.6
X Fig. 2. R~-FA(x, QZ)/FD(x, Q2) at Q2= 10 (GeV/c) 2 - - R = R v, valence quark components only; - - - R=R s, sea quark components only.
to a distortion of the valence quark distribution through that of the valons, but not due to that of the sea quark increasing as various models indicated. To see this we also calculated the ratio (R) of the distribution of the valence (sea) quarks inside a nucleon bound in a nucleus to that of a free one (fig. 2). In summary, the behavior of the EMC effect in the low and intermediate regions of x may be understood by means of the valon model picture, namely, the valon structure functions are universal but the valon distribution function inside a nucleon is distorted when the nucleon is bound into a nucleus. The authors would like to thank Professor Liu Liansou for providing up-to-date results from the 23rd International Conference on High Energy Physics at Berkeley, and the referee for helpful suggestion. One of them (C.H.C.) would like to thank the Theoretical Group of Fermilab, especially Professor C. Quigg and Professor W.A. Bardeen for warm hospitality, as the revision was completed there. 407
Volume 187, number 3,4
PHYSICS LETTERS B
References [ 1 ] E.L Gerger, Talk 23rd Intern. Conf on High energy physics (Berkeley, 1986). [2] J.J. Aubert et al., Phys. Lett. B 123 (1983) 123, 275. [3] A. Bodek et al., Phys. Rev. Lett 50 (1983) 1431, 51 (1983) 534, R G. Arnold et al., Phys. Rev. Lett. 52 (1984) 727 [4] R.C. Cooper et al., Phys. Lett. B 141 (1984) 143. [5] R L Jaffe, Phys Rev. Lett. 50 (1983) 228, F E Close, R.G Robems and G. Ross, Phys Lett. B 129 (1983) 246 [61 C H Llewellyn Smith, Phys Lett. B 128 (1983) 107; M Ericson and A W Thomas, Phys. Lett. B 128 (1983)
112; E L. Berger, F Coester and R.B. Wlnngh, Phys. Rev D 29 (1984) 398.
408
[7] [8] [9] [ 10]
26 March 1987
W Zhu, Kexue Tongbao (China) 30 (1985) 1139. A.H. Mueller, Columbia Prepnnt CU-232 (1982) R C. Hwa, Phys Rev D 22-(-1980) 1593 C. Chang and W. Chao, prepnnt AS-ITP-85-025, Commun. Theor Phys, to be pubhshed. [ 11 ] L.S Celenza, A. Rosenthal and C M Shalon, Phys Rev. Lett. 53 (1984) 892; R P Bnckerstaffand G A Miller, Phys. Lett B 168 (1986) 409; A V. Efremov, Phys. Lett. B 174 (1986) 219 [ 12] A.J. Buras and K J F. Gaemers, Nucl. Phys. B 132 (1978) 249 [13] W. Zhu, Nature J (China) 5 (1982) 874. [ 14] C H. Chang and W Zhu, m preparation
PHYSICS LETTERS B
26 March 1987
THE VALON MODEL AND T H E LOW-x BEHAVIOR OF T H E EMC E F F E C T ~ Chao-hsi C H A N G Instttute of TheorettcalPhysws, Academia Sznlca, P.O Box 2735, Betjmg, P.R.Chtna and Wei Z H U Physws Department, East China Normal Umverstty, Shanghaz, P.R. Chma Received 8 October 1986; revised manuscript recewed 22 December 1986
New experimental results of the EMC effect are discussed. It ~sshown that the dlstortzon of the structure function of a nucleon bound in a nucleus may be understood by means of the valon picture.
Recently the E M C a n d B C D M S groups published their new results on the E M C effect at Q2> 10 ( G e V / c ) 2 for Cu a n d F e respectively [ 1 ], showing a quite clear b e h a v i o r in the low-x region. According to the new data, R = F A(X, Q2)/F°E(X, Q2) presents a decrease as x - , 0 a n d R crosses 1 near x_~0.3 (fig. 1 ). This tendency is precisely contrary to that o f the earliest results o f the E M C group [2] but roughly consistent with those o f the SLAC group [3] and neutrino experiments [4]. Therefore, we t h m k it-isnow time to consider the low-x b e h a v i o r o f the E M C effect seriously and it should be noted that these characteristics, the decrease o f R as x ~ 0 and R crossing 1 near x = 0.3, cannot be explained by either the rescaling m o d e l [5 ] or the meson enhancement m o d e l [ 6 ] (see fig. 1 ). It is obvious that the low-x b e h a v i o r o f the E M C effect is relevant to the p r o d u c t i o n m e c h a n i s m o f the sea quark in the nucleon [ 5 - 7 ] . Q 2 being very large, the decrease o f R as x--, 0 cannot be owed to the shadowing effect [ 8 ]. In this p a p e r we point out that if the valon m o d e l picture [ 9 ] is accepted as follows: the nucleon is regarded as consisting o f three dressed valence quark-valons, the valons having universal *
This work is supported in part by the Science Fund of the Chinese Academy of Sciences.
l.~- r
~
• BCDMS ~FeJ~lg86 • EMC. tC'~} I o ~LA~tFQ)
o,1
0
az
~
~6
o~
X
Fig. 1. R---FA(x, Q2)/FD(x, Q2) at Q 2= 10 (GeV/c) 2 --valon model (this work); - - - meson enhancement model [ 6 ], - . - rescahng model [ 5 ]. 405
Volume 187, number 3,4
PHYSICS LETTERS B
structure functions due to QCD processes, i.e. their structure functions are independent on nucleus but the valon distribution inside a nucleon is distorted due to nuclear medium as compared with that of a free nucleon, then a nice tendency of the EMC effect can be obtained which fits the expenmental data quite well. According to ref. [9 ], the structure function of a nucleon is 1
FN(x, 0 2) = . ~ J d y Gv(y)Fv(x/y,
a2),
(1 )
x
where Fvis the structure functmn ofvalon V, and Gv is the distribution of V reside N. The momentum distribution of the valons is independent of Q2, the probing value, however, the structure of a valon is Q2-dependent. The normalization of Gv is
inside a nucleon, bound in a nucleus A, has the form
G~.(y) = a y P ( 1
_y)2+~,
(5)
where a is a normalization constant, fl a constant related to the slope of the Regge trajectory, and 2 +A a number which may be related to that of the effective spectators according to the counting rule. (2) The mass factor: the effective mass of a nucleon inside a nucleus might be different from and less than that m vacuum, i.e. Meff= o~'MN
(6)
with a ' ~< 1, due to binding and color induction etc. Therefore we have the rescahng for y: y/a' instead of y, based on the definition o f y [ 11 ]. Accordingly, the normalization equation (2) becomes
fl
or'
dy ~ G¢(ym') = 1
1
fGv(y)
26 March 1987
dy= 1
(2)
0
(7)
0
and the momentum sum rule equation (3):
and ~t satisfies the m o m e n t u m sum rule
f dy Y-~ G~.(y/a',= 3 .
1
fGv(y)y
d y = 1/3 .
(3)
0
Concretely, as for a free nucleon we take [ 9 ]
Gv(y) = tr~y'/2( l _ y)2 .
(4)
We now discuss a nucleon inside a nucleus. Since the size of a v a l o n is smaller than that of a nucleon, it is reasonable to assume that in deep-inelastic scattering the valon structure functions are not influenced by the nuclear medium very much, but the valon distribution inside the nucleon is. In order to obtain the EMC behavior, based on the points of ref. [ I 0 ], we consider two factors which may cause distortion of the distribution: (1) The counting rule factor: when a nucleon is bound in a nucleus, the nucleon might be smeared out due to color induction and/or some other effects so that, as for scattering processes, the valon inside a nucleus scattered through a nucleon has a different number of the effective spectators from that in a nucleon alone, namely, based on general considerations, the behavior of the distribution of the valons 406
(8,
0
Ignoring the Fermi motion but highhghting the lowx region and consxdering the above two factors, the structure function of a nucleon inside a nucleus should be o¢'
F~,x, Q 2 , : ~ f d y l G , ( y / a ' , F v ( x / y ,
Q2,.
(9,
x
Below Q2= 10 (GeV/c) 2 is taken as an illustrating example, and the valon structure functions are parametnzed by means of the method which is used to parametrize the nucleon by Buras and Gaemers [ 12 ], but from the starting point xV(x, Q2) =8(1 - x ) and X~(X, Q2)=xG(x, Q2)-=0, when Q2~/I2, i.e. one cannot probe the structure of avalon if Q2~ p2, where /z is a characteristic size scale of the valons in momentum, and V(x, Q2), ~(x, Q2) and G(x, Q2) are the valence, sea and gluon structure functions respectively. The structure functions of the valon for Q2= 10 (GeV/c) 2, which we use through this paper, are
xV(x, Q2) =0.914x o 8 6 2 ( 1
_ _ X ) 0 065
(10)
Volume 187, number 3,4
26 March 1987
PHYSICSLETTERSB
and x ~ ( x , Q2) =0.0815(1 - x ) 416
(11 )
(see refs. [9,13] for details). If we take a ' =0.98 and A = 0.4, then a = 10.3 and fl = 0.7 as determined from the normalization equations (7) and (8), and a nice fit is obtained (fig. 1 ). For comparison we also plot in fig. 1 the curves of the ~ meson enhancement and the rescaling models. Based on the same reason as the rescaling model, the behavior of R is not dependent on Q 2 very much, thus the feature of fig. 1 is a typical one for various Q 2 Here A=0.4 (A=0 for a free nucleon, see eq. (4)) which may be explained by counting rule, i.e. according to the counting rule the number of effective spectators of the scattered valon increases by a definite quantity when a nucleon is bound inside a nucleus. To understand this, let us accept confinement pictures and assume that, being color singlets, only 3quark and 6-quark clusters may exist inside a nucleus; in addition, the "effective spectator number" then is in the sense of average A = 0.4 which means a 6-quark component of about 10% is obtained from the counting rule directly. In fact, it is not a unique mechanism which results in A= 0.4, and we will discuss this further in ref. [ 14 ]. However we would like to note here that the fit on a ' and A might have a deeper meaning than that of the counting picture. It is easy to see that due to the universality of the valons and the behavior of the valon structure functions x V ( x , Q2) x~O,o
(12)
and x ~ ( x , Q2) x~°,A ° ,
(13)
namely F v ( x , Q2)
x~0
2
, ~ Q , Ao ,
(14)
where Ao is the coefficient of the sea quark structure function, and Q, the charge of the quarks inside the valon, we have the tendency R x~O 1 ,
(15)
which is shown by the latest experimental data (note: at very small x, when Q2--,0, the shadowing effect should be considered [10]. We also note that an increase of R in the region 0~
°'8O
O.Z
t~
0.6
X Fig. 2. R~-FA(x, QZ)/FD(x, Q2) at Q2= 10 (GeV/c) 2 - - R = R v, valence quark components only; - - - R=R s, sea quark components only.
to a distortion of the valence quark distribution through that of the valons, but not due to that of the sea quark increasing as various models indicated. To see this we also calculated the ratio (R) of the distribution of the valence (sea) quarks inside a nucleon bound in a nucleus to that of a free one (fig. 2). In summary, the behavior of the EMC effect in the low and intermediate regions of x may be understood by means of the valon model picture, namely, the valon structure functions are universal but the valon distribution function inside a nucleon is distorted when the nucleon is bound into a nucleus. The authors would like to thank Professor Liu Liansou for providing up-to-date results from the 23rd International Conference on High Energy Physics at Berkeley, and the referee for helpful suggestion. One of them (C.H.C.) would like to thank the Theoretical Group of Fermilab, especially Professor C. Quigg and Professor W.A. Bardeen for warm hospitality, as the revision was completed there. 407
Volume 187, number 3,4
PHYSICS LETTERS B
References [ 1 ] E.L Gerger, Talk 23rd Intern. Conf on High energy physics (Berkeley, 1986). [2] J.J. Aubert et al., Phys. Lett. B 123 (1983) 123, 275. [3] A. Bodek et al., Phys. Rev. Lett 50 (1983) 1431, 51 (1983) 534, R G. Arnold et al., Phys. Rev. Lett. 52 (1984) 727 [4] R.C. Cooper et al., Phys. Lett. B 141 (1984) 143. [5] R L Jaffe, Phys Rev. Lett. 50 (1983) 228, F E Close, R.G Robems and G. Ross, Phys Lett. B 129 (1983) 246 [61 C H Llewellyn Smith, Phys Lett. B 128 (1983) 107; M Ericson and A W Thomas, Phys. Lett. B 128 (1983)
112; E L. Berger, F Coester and R.B. Wlnngh, Phys. Rev D 29 (1984) 398.
408
[7] [8] [9] [ 10]
26 March 1987
W Zhu, Kexue Tongbao (China) 30 (1985) 1139. A.H. Mueller, Columbia Prepnnt CU-232 (1982) R C. Hwa, Phys Rev D 22-(-1980) 1593 C. Chang and W. Chao, prepnnt AS-ITP-85-025, Commun. Theor Phys, to be pubhshed. [ 11 ] L.S Celenza, A. Rosenthal and C M Shalon, Phys Rev. Lett. 53 (1984) 892; R P Bnckerstaffand G A Miller, Phys. Lett B 168 (1986) 409; A V. Efremov, Phys. Lett. B 174 (1986) 219 [ 12] A.J. Buras and K J F. Gaemers, Nucl. Phys. B 132 (1978) 249 [13] W. Zhu, Nature J (China) 5 (1982) 874. [ 14] C H. Chang and W Zhu, m preparation