- Email: [email protected]
The instanton based Chiral Quark Soliton Model: Form factors and (skewed) parton distributions
@ ELSEVIER
A Nuclear Physics A666&667 (2000) 18c-23c www.elsevier.nl/locate/npe
The instanton based Chiral Quark Soliton Model: Form factors and (skewed) parton distributions K. Goeke ~* ~Institute of Theoretical Physics , Ruhr-University of Bochum, D-44780 Bochum, Germany The Chiral Quark Soliton Model is presented and its applications to electromagnetic and axial form factors and to forward and non-forward parton distributions of the nucleon are reviewed. The model is an effective chiral field theory for interacting constituent quark fields. It has been derived by Diakonov and Petrov from the QCD assuming that the gluonic field of the QCD vacuum is dominated by instantons. The model fulfils automatically all requirements for the description of partonic distributions as e.g. sum rules, positivity of quark- and antiquark distributions etc. In this paper numerical results are shown for recently measured antiquark distributions d(x) - ~(x), Ad(x) - A~(z) and for the transversity distribution 8d(x) - 8~(x). Explicit calculations for the heavily discussed skewed (off-forward) parton distributions are presented. 1. I N T R O D U C T I O N There exist presently several theories (relativistic and non-relativistic) which are able to calculate static observables and form factors of the baryonic octet and decuplet. Only few of them, like e.g. the models of ref.[4-6] or [17] or [20], bear the possibility to calculate (at a low renormalization scale) parton distributions. Those distributions do not correspond to conserved currents, a feature, which makes their formulation in terms of bosonic fields ( e.g in the Skyrme-model or in the chiral perturbation theory) difficult if not impossible. However, most of the models, which are in principle able to calculate quark parton distributions, suffer from certain problems: Either they need heavy phenomenological input (like e.g. the patton distribution of the pion), or they cannot guarantee that (anti)quark distributions are positive definit, or they do not automatically fulfill momentum or axial sum rules [19]. A model, which does not exhibit these shortcomings, is the Chiral Quark Soliton Model (Instanton Model). This model has been derived by Diakonov and Petrov [3] from the QCD assuming that the gluon field of the vacuum can well be approximated by a weakly interacting dilute gas of instantons and anti-instantons. They integrated the out the instanton field and derived [2] in case of zero-mass current quarks an effective Lagrangean for the corresponding constituent quark fields. This Lagrangean, given below, has been extensively used in the *The results presented in this article have been worked out in collaboration with I. Boernig, B. Dressier, M. Penttinen, P. Pobylitsa, M. Polyakov,P. Schweitzer, D. Urbano and C. Weiss, from Bochum-University and Petersburg Nuclear Physics Institute (email: [email protected]) 0375-9474/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII S0375-9474(00)00003-8
K. Goeke/Nuclear Physics A666&667 (2000) 18c-23c
19c
last decade in order to describe static observables and form factors of the nucleon in SU(2) and SU(3). In general an agreement of 20% and better has been found between this theory and experiment. A review of those applications can be found in ref. [7]. Since the model provides a mapping of the light current quarks and gluonic instantons on constituent quarks with a residual interaction it can also be used to calculate gluonic properties of a baryon. In this case the mapping has to be done for a quark-gluon operator and not for the Lagrangean. It has been shown in ref.[9,11] that indeed higher twist quantities can be evaluated in this way. Actually in the last years the Chiral Quark soliton model has systematically been applied to the nucleon and the other members of the baryon octet and decuplet. The quantities calculated were electromagnetic and axial form factors, axial and tensorial charges, strange contributions to electric and magnetic form factors, semi-leptonic decays and electromagnetic nucleon-delta transitions. Most of the relevant references one can find in the review article [7] and in [21,22]. In recent time the model has been applied (see below for references and details) to parton distributions (unpolarized, polarized, transversity), skewed parton distributions (unpolarized, polarized), and higher twist effects in partonic distributions. 2. T H E C H I R A L Q U A R K S O L I T O N M O D E L The Chiral Quark Soliton Model (Instanton Model) is an effective relativistic field theory for constituent quark fields ¢. It is given by the Lagrangean
£ = ~(iTuO~, - MU)~b
U = exp [iTr~(x)T~'Ts]
The Lagrangean describes the minimally chiral invariant interaction of the constituent quarks ¢ with Goldstone bosons zr~(x). Even without noticing its derivation from QCD the above Lagrangean can also be understood as the simplest Lagrangean in terms of constituent quark fields which incorporates spontaneous chiral symmetry breaking. In fact it can be used also to calculate low energy coefficients of the effective chiral Lagrangean used e.g. in Chiral Perturbation Theory [10]. The observables of the system are basically calculated by standard field theoretical methods based on the stationary phase approximation of the partition function (for details see [7]). In the ideal case one fully follows the instanton approach to the above Lagrangean. In this case one has no free parameters because all quantities are given in terms of AQCD and the regularization is done automatically by the momentum-dependent constituent mass M(k). Since this procedure is technically very demanding in most of the real calculations one replaces M(k) by a constant constituent mass M and a properly chosen regularization scheme (Pauli-Villars or Proper-Time) with a cut-off parameter A~to/]. Both quantities, M and A~tof] are adjusted to the pion decay constant (mesonic sector) f . and the delta-nucleon mass splitting (baryonic sector). After finishing the selfconsistent iterative procedure in order to find the stationary field U~,tf one ends up with a soliton consisting of a bound single quark level and a continuum of single quark levels, which is the polarized Dirac sea. After that one has to extract from the resulting soliton the properties of particular baryons. To this end the soliton is rotated in flavour space and by this projected on the quantum numbers I, T, Y. Thus in
20c
K. Goeke/Nuclear Physics A666&667 (2000) 18c-23c
the end the ground states of the baryons in the octet and decuplet are described. Excited states cannot be described in the model, since the Lagrangean is lacking confinement. The success in calculating nucleon form factors [7] and the results of lattice calculations [1] indeed show that for low energy quantities the confinement is less important than the binding effects from the goldstone fields. 3. P A R T O N D I S T R I B U T I O N S In the Chiral Quark Soliton Model (Instanton Model) the quark parton distributions can be defined as in QCD. The formalism has been developed in ref. [4] and applied in ref. [4-6,8,23]. One obtains (apart of kinematical factors) e.g. for the unpolarized q(x):
q(x) = f ~d~ expi~x < p, ~ ( 0 ) ¢ + ( ~ ) p,~ > and similar expressions for the longitudinally polarized Aq(x) and for the transversely polarized 6q(x)( the n is a light cone vector). In refs. [4] it has been shown that the following important properties hold: Antiquark distributions are supported at negative x: e.g. -q(x) = - q ( - x ) . Quark and antiquark distributions are positive definite: q(x) > 0 and ~(x) > 0. Sum rules are fulfilled (momentum, isospin, baryon number, Bjorken). Numerical examples are given below:
1
'
'\'
0.8
\
'
I
'
i
,
,
I
'
'
'
'
I
'
'-
\ [d-u](x)
06 0.4 0.2 ......
0
,
0
,
,
,
I
,
,
,
,
0.1
I
0.2
,
,
,
.....
,
I
,
0.3
X
Above we show the anti-quark distribution d(x) - ~(x) [81 evolved to Q2 = 54GeV 2 as it is measured in the recent experiment FNAL E866. This is one of several examples. Others concern A~(z) -- Ad(x) and the helicity distribution 5~(x) - 53(x) [13] responsible for the tensor charge:
K. Goeke /Nuclear Physics A666&667 (2000) 18c-23c
Isovector
transversity
2lc
quark distribution
(Su--Sd)(x) 3.0
.
.
.
.
,
.
.
.
.
quad<8
2.0
1.0
0.0
--1.0
L
J
~"
0.0
J 0.5 Bjorken x
• .O
4. O F F - F O R W A R D P A R T O N D I S T R I B U T I O N S
Off-forward (non-forward, skewed) parton distributions [14-16] are defined as
p__+_ +
f dz-eizP+z-(P'l¢(-z/2)(nT)O(z/2)[P) z + =za. =0
= a(x, ~, A~)~(P')n-~u(P) + E(x, ~, A 2 ) ~ ( P ' ) i n ~ a ~ Z ~ y U ( P ) If we replace (n~) by (n7)75, we get/~ and/~ corresponding to polarized distributions. The skewed parton distributions show some interesting limiting cases, which all are fulfilled in the present Chiral Quark Soliton Model: The forward-limit (A --+ 0) yields ordinary parton distrib.:
H(x,~ = O, A 2 = 0 ) = q ( x ) and form factors are obtained by integration over x: F1 (Dirac), F2 (Pauli), GA(axial), G p (pseudoscalar):
f_~dx tt(x, ¢,/,~) = F~(A 2) 1 d~ H(~, ~, A ~) = a~(zX ~)
f 1/ dE(x,•~, A 2) = F~(~X2) /lldJCF-,(x,~,/k2):
Gp(n
2)
1
Note that the {-dependence drops out, and that the forward limit E(x, ~ = A 2 = O) does not appear in usual DIS The first calculations for off-forward distributions have been performed using the Chiral Quark Soliton model. The calculations concentrated on H ( x , { , A 2 ) , see [12]. Here we show for illustration the skewed (off-forward) patton distribution E(x, {, A2). One notices that a description only in terms of the bound level is not sufficient:
22c
K. Goeke/Nuclear Physics A666&667 (2000) 18c-23c
4
t
i
t
t tt i
E 3.5
~=0.3
A2=._O.SGo~
3
,
,~,
i
:7
1
i~
il'~\ i \
,
'.
,
..... J ' * ' ~ •F"
0.5 0
i
n i
. . . . . .
-0.5 -1
-0.8
-0.6
-0.4
-0.2
i - .......... .......
t t
I/ ;/ i
1.5
i Bo~ state Dirac sea Full
M ..~
l"l
2
i
:\
~...'/'
:l 11...
2.5
t
o/t~, ,/ i ;
",
i i
,, 0
-]~
]
02
,
,
04
06
, 0
8
2 9 E
.
.
.
.
.
A ,~ '
' ~ ~b.2o,v~-Z~ =.-0.SGeV~. ..........
/
S ~=0.3
it
Az ~ 0 . 8 GeV"Z . . . . . . .
7 6 5 4
m
M
n.
...," m'-.
i
...'"
J
...==°°
i'..,
3 2
.." ..."
1 0 -1
5. S U M M A R Y
,°"
...... > . - *
01.8
-0.6
-0.4
-0.2
i,.,
i
i
, i
,
".. ,,,
"..,
--..'-. ..... •
0 x
0.2
0,4
0.6
0.8
AND OUTLOOK
The Chiral Quark Soliton Model describes the baryonic ground states of the octet and decuplet. It is charakterized by the following features: • It is a field theory derived from the Instanton-Vacuum of QCD. • It includes the polarized Dirac sea. • It describes the system by constituent quarks interacting with the self-consistent Goldstone mean field. • It describes well static observables and electromagnetic and axial formfactors. • It describes quark parton and antiparton distributions at a low renormalization point (# ~ 6 0 0 M e V ) which fulfill automatically sum rules, positivity, etc. • It reproduces amongst several other parton distributions the d ( x ) - ~ ( x ) and A~(x)-Ad(x) (E866, HERMES, SMC) • It predicts transversity distribution 5u(x) - 5d(x) and tensor charges g(~). • It predicts skewed parton distributions H,H, E,/~ for all x, ~ and small A s.
K. Goeke/Nuclear Physics A666&667 (2000) 18c-23c
23c
REFERENCES
1. M. Chu, J. Grandy, S. Huang, J. Negele, Phys. Rev. Lett. 70 (1993) 225; Phys. Rev. D49 (1994) 6039 2. D.I. Diakonov, V.Yu. Petrov, and P.V. Pobylitsa, Nucl. Phys. B 306 (1988) 809. 3. D. Diakonov and V. Petrov, Nucl. Phys. B 245 (1984) 259; Nucl. Phys. B 272 (1986) 457. 4. D.Diakonov, V.Petrov, P.Pobylitsa, M.Polyakov and C.Weiss, Nucl. Phys. B480 (1996) 341; Phys. Rev. D56 (1997) 4069; Phys. Rev. D58 (1998) 038502. 5. P.V. Pobylitsa and M.V. Polyakov, Phys. Lett. B 389 (1996) 350. 6. P.V. Pobylitsa, M.V. Polyakov, K. Goeke, T. Watabe, C. Weiss, Phys. Rev. D 59 (1999) 034024. 7. Chr.V. Christov, A. Blotz, H.C. Kim, P. Pobylitsa, T. Watabe, Th. Meissner, E. Ruiz Arriola, K. Goeke, Prog. Part. Nucl. Phys. 37 (1996) 91. 8. B. Dressier, K. Goeke, P. Pobylitsa, M.V. Polyakov, T. Watabe, C. Weiss, Proceedings of the XI Conference "Problems of quantum field theory", Dubna, Russia, 13-17 July, 1998, hep-ph/9809487.. 9. D.Diakonov, M.V. Polyakov, C. Weiss, Nucl.Phys. B461 (1996) 539 10. C.Schueren, E. Ruiz Arriola, K. Goeke, Nucl. Phys. A547 (1992) 612 11. J. Balla, M.V. Polyakov, and C. Weiss, Nucl. Phys. BS10 (1998) 327. B. Dressier, M. Maul, and C. Weiss, Bochum University Report RUB-TP2-5/99, hepph/9906444. 12. V.Yu. Petrov, P.V. Pobylitsa, M.V. Polyakov, I. B6rnig, K. Goeke, and C. Weiss, Phys. Rev. D 57, 4325 (1998). 13. P. Schweitzer, K. Goeke, P. Pobylitsa, M.V. Polyakov, C. Weiss, in preparation. 14. X.-D. Ji, Phys. Rev. Lett. 78, 610 (1997); Phys. Rev. D 55, 7114 (1997). 15. A.V. Radyushkin, Phys. Rev. D 56 (1997) 5524; Phys. Rev. D 59, 014030 (1999). 16. J.C. Collins, L. Frankfurt and M. Strikman, Phys. Rev. D 56, 2982 (1997). 17. F.M. Steffens, W. Melnitchouk, and A.W. Thomas, hep-ph/9903441 and J.Speth, A.W. Thomas, Adv. Nucl. Phys. 24 (1997) 83. 18. D. Diakonov, M. Polyakov, and C. Weiss, Nucl. Phys. B461 (1996) 539 19. S. Scopetta, V. Vento, M. Traini, Phys. Lett. B421 (1998) 64, B442 (1998) 28 20. A. Szczurek, M. Ericson, H. Holtmann, J. Speth, Nucl.Phys.A596:397-414,1996 21. R. Alkofer, H. Reinhardt, H. Weigel, Phys. Rep. 265 (1994) 139 22. M. Wakamatsu, H. Yoshiki, Nucl. Phys. A524 (1991) 561 23. M. Wakamatsu, T. Kubota, Phys.Rev.D57:5755-5766,1998
A Nuclear Physics A666&667 (2000) 18c-23c www.elsevier.nl/locate/npe
The instanton based Chiral Quark Soliton Model: Form factors and (skewed) parton distributions K. Goeke ~* ~Institute of Theoretical Physics , Ruhr-University of Bochum, D-44780 Bochum, Germany The Chiral Quark Soliton Model is presented and its applications to electromagnetic and axial form factors and to forward and non-forward parton distributions of the nucleon are reviewed. The model is an effective chiral field theory for interacting constituent quark fields. It has been derived by Diakonov and Petrov from the QCD assuming that the gluonic field of the QCD vacuum is dominated by instantons. The model fulfils automatically all requirements for the description of partonic distributions as e.g. sum rules, positivity of quark- and antiquark distributions etc. In this paper numerical results are shown for recently measured antiquark distributions d(x) - ~(x), Ad(x) - A~(z) and for the transversity distribution 8d(x) - 8~(x). Explicit calculations for the heavily discussed skewed (off-forward) parton distributions are presented. 1. I N T R O D U C T I O N There exist presently several theories (relativistic and non-relativistic) which are able to calculate static observables and form factors of the baryonic octet and decuplet. Only few of them, like e.g. the models of ref.[4-6] or [17] or [20], bear the possibility to calculate (at a low renormalization scale) parton distributions. Those distributions do not correspond to conserved currents, a feature, which makes their formulation in terms of bosonic fields ( e.g in the Skyrme-model or in the chiral perturbation theory) difficult if not impossible. However, most of the models, which are in principle able to calculate quark parton distributions, suffer from certain problems: Either they need heavy phenomenological input (like e.g. the patton distribution of the pion), or they cannot guarantee that (anti)quark distributions are positive definit, or they do not automatically fulfill momentum or axial sum rules [19]. A model, which does not exhibit these shortcomings, is the Chiral Quark Soliton Model (Instanton Model). This model has been derived by Diakonov and Petrov [3] from the QCD assuming that the gluon field of the vacuum can well be approximated by a weakly interacting dilute gas of instantons and anti-instantons. They integrated the out the instanton field and derived [2] in case of zero-mass current quarks an effective Lagrangean for the corresponding constituent quark fields. This Lagrangean, given below, has been extensively used in the *The results presented in this article have been worked out in collaboration with I. Boernig, B. Dressier, M. Penttinen, P. Pobylitsa, M. Polyakov,P. Schweitzer, D. Urbano and C. Weiss, from Bochum-University and Petersburg Nuclear Physics Institute (email: [email protected]) 0375-9474/00/$ - see front matter © 2000 Elsevier Science B.V. All rights reserved. PII S0375-9474(00)00003-8
K. Goeke/Nuclear Physics A666&667 (2000) 18c-23c
19c
last decade in order to describe static observables and form factors of the nucleon in SU(2) and SU(3). In general an agreement of 20% and better has been found between this theory and experiment. A review of those applications can be found in ref. [7]. Since the model provides a mapping of the light current quarks and gluonic instantons on constituent quarks with a residual interaction it can also be used to calculate gluonic properties of a baryon. In this case the mapping has to be done for a quark-gluon operator and not for the Lagrangean. It has been shown in ref.[9,11] that indeed higher twist quantities can be evaluated in this way. Actually in the last years the Chiral Quark soliton model has systematically been applied to the nucleon and the other members of the baryon octet and decuplet. The quantities calculated were electromagnetic and axial form factors, axial and tensorial charges, strange contributions to electric and magnetic form factors, semi-leptonic decays and electromagnetic nucleon-delta transitions. Most of the relevant references one can find in the review article [7] and in [21,22]. In recent time the model has been applied (see below for references and details) to parton distributions (unpolarized, polarized, transversity), skewed parton distributions (unpolarized, polarized), and higher twist effects in partonic distributions. 2. T H E C H I R A L Q U A R K S O L I T O N M O D E L The Chiral Quark Soliton Model (Instanton Model) is an effective relativistic field theory for constituent quark fields ¢. It is given by the Lagrangean
£ = ~(iTuO~, - MU)~b
U = exp [iTr~(x)T~'Ts]
The Lagrangean describes the minimally chiral invariant interaction of the constituent quarks ¢ with Goldstone bosons zr~(x). Even without noticing its derivation from QCD the above Lagrangean can also be understood as the simplest Lagrangean in terms of constituent quark fields which incorporates spontaneous chiral symmetry breaking. In fact it can be used also to calculate low energy coefficients of the effective chiral Lagrangean used e.g. in Chiral Perturbation Theory [10]. The observables of the system are basically calculated by standard field theoretical methods based on the stationary phase approximation of the partition function (for details see [7]). In the ideal case one fully follows the instanton approach to the above Lagrangean. In this case one has no free parameters because all quantities are given in terms of AQCD and the regularization is done automatically by the momentum-dependent constituent mass M(k). Since this procedure is technically very demanding in most of the real calculations one replaces M(k) by a constant constituent mass M and a properly chosen regularization scheme (Pauli-Villars or Proper-Time) with a cut-off parameter A~to/]. Both quantities, M and A~tof] are adjusted to the pion decay constant (mesonic sector) f . and the delta-nucleon mass splitting (baryonic sector). After finishing the selfconsistent iterative procedure in order to find the stationary field U~,tf one ends up with a soliton consisting of a bound single quark level and a continuum of single quark levels, which is the polarized Dirac sea. After that one has to extract from the resulting soliton the properties of particular baryons. To this end the soliton is rotated in flavour space and by this projected on the quantum numbers I, T, Y. Thus in
20c
K. Goeke/Nuclear Physics A666&667 (2000) 18c-23c
the end the ground states of the baryons in the octet and decuplet are described. Excited states cannot be described in the model, since the Lagrangean is lacking confinement. The success in calculating nucleon form factors [7] and the results of lattice calculations [1] indeed show that for low energy quantities the confinement is less important than the binding effects from the goldstone fields. 3. P A R T O N D I S T R I B U T I O N S In the Chiral Quark Soliton Model (Instanton Model) the quark parton distributions can be defined as in QCD. The formalism has been developed in ref. [4] and applied in ref. [4-6,8,23]. One obtains (apart of kinematical factors) e.g. for the unpolarized q(x):
q(x) = f ~d~ expi~x < p, ~ ( 0 ) ¢ + ( ~ ) p,~ > and similar expressions for the longitudinally polarized Aq(x) and for the transversely polarized 6q(x)( the n is a light cone vector). In refs. [4] it has been shown that the following important properties hold: Antiquark distributions are supported at negative x: e.g. -q(x) = - q ( - x ) . Quark and antiquark distributions are positive definite: q(x) > 0 and ~(x) > 0. Sum rules are fulfilled (momentum, isospin, baryon number, Bjorken). Numerical examples are given below:
1
'
'\'
0.8
\
'
I
'
i
,
,
I
'
'
'
'
I
'
'-
\ [d-u](x)
06 0.4 0.2 ......
0
,
0
,
,
,
I
,
,
,
,
0.1
I
0.2
,
,
,
.....
,
I
,
0.3
X
Above we show the anti-quark distribution d(x) - ~(x) [81 evolved to Q2 = 54GeV 2 as it is measured in the recent experiment FNAL E866. This is one of several examples. Others concern A~(z) -- Ad(x) and the helicity distribution 5~(x) - 53(x) [13] responsible for the tensor charge:
K. Goeke /Nuclear Physics A666&667 (2000) 18c-23c
Isovector
transversity
2lc
quark distribution
(Su--Sd)(x) 3.0
.
.
.
.
,
.
.
.
.
quad<8
2.0
1.0
0.0
--1.0
L
J
~"
0.0
J 0.5 Bjorken x
• .O
4. O F F - F O R W A R D P A R T O N D I S T R I B U T I O N S
Off-forward (non-forward, skewed) parton distributions [14-16] are defined as
p__+_ +
f dz-eizP+z-(P'l¢(-z/2)(nT)O(z/2)[P) z + =za. =0
= a(x, ~, A~)~(P')n-~u(P) + E(x, ~, A 2 ) ~ ( P ' ) i n ~ a ~ Z ~ y U ( P ) If we replace (n~) by (n7)75, we get/~ and/~ corresponding to polarized distributions. The skewed parton distributions show some interesting limiting cases, which all are fulfilled in the present Chiral Quark Soliton Model: The forward-limit (A --+ 0) yields ordinary parton distrib.:
H(x,~ = O, A 2 = 0 ) = q ( x ) and form factors are obtained by integration over x: F1 (Dirac), F2 (Pauli), GA(axial), G p (pseudoscalar):
f_~dx tt(x, ¢,/,~) = F~(A 2) 1 d~ H(~, ~, A ~) = a~(zX ~)
f 1/ dE(x,•~, A 2) = F~(~X2) /lldJCF-,(x,~,/k2):
Gp(n
2)
1
Note that the {-dependence drops out, and that the forward limit E(x, ~ = A 2 = O) does not appear in usual DIS The first calculations for off-forward distributions have been performed using the Chiral Quark Soliton model. The calculations concentrated on H ( x , { , A 2 ) , see [12]. Here we show for illustration the skewed (off-forward) patton distribution E(x, {, A2). One notices that a description only in terms of the bound level is not sufficient:
22c
K. Goeke/Nuclear Physics A666&667 (2000) 18c-23c
4
t
i
t
t tt i
E 3.5
~=0.3
A2=._O.SGo~
3
,
,~,
i
:7
1
i~
il'~\ i \
,
'.
,
..... J ' * ' ~ •F"
0.5 0
i
n i
. . . . . .
-0.5 -1
-0.8
-0.6
-0.4
-0.2
i - .......... .......
t t
I/ ;/ i
1.5
i Bo~ state Dirac sea Full
M ..~
l"l
2
i
:\
~...'/'
:l 11...
2.5
t
o/t~, ,/ i ;
",
i i
,, 0
-]~
]
02
,
,
04
06
, 0
8
2 9 E
.
.
.
.
.
A ,~ '
' ~ ~b.2o,v~-Z~ =.-0.SGeV~. ..........
/
S ~=0.3
it
Az ~ 0 . 8 GeV"Z . . . . . . .
7 6 5 4
m
M
n.
...," m'-.
i
...'"
J
...==°°
i'..,
3 2
.." ..."
1 0 -1
5. S U M M A R Y
,°"
...... > . - *
01.8
-0.6
-0.4
-0.2
i,.,
i
i
, i
,
".. ,,,
"..,
--..'-. ..... •
0 x
0.2
0,4
0.6
0.8
AND OUTLOOK
The Chiral Quark Soliton Model describes the baryonic ground states of the octet and decuplet. It is charakterized by the following features: • It is a field theory derived from the Instanton-Vacuum of QCD. • It includes the polarized Dirac sea. • It describes the system by constituent quarks interacting with the self-consistent Goldstone mean field. • It describes well static observables and electromagnetic and axial formfactors. • It describes quark parton and antiparton distributions at a low renormalization point (# ~ 6 0 0 M e V ) which fulfill automatically sum rules, positivity, etc. • It reproduces amongst several other parton distributions the d ( x ) - ~ ( x ) and A~(x)-Ad(x) (E866, HERMES, SMC) • It predicts transversity distribution 5u(x) - 5d(x) and tensor charges g(~). • It predicts skewed parton distributions H,H, E,/~ for all x, ~ and small A s.
K. Goeke/Nuclear Physics A666&667 (2000) 18c-23c
23c
REFERENCES
1. M. Chu, J. Grandy, S. Huang, J. Negele, Phys. Rev. Lett. 70 (1993) 225; Phys. Rev. D49 (1994) 6039 2. D.I. Diakonov, V.Yu. Petrov, and P.V. Pobylitsa, Nucl. Phys. B 306 (1988) 809. 3. D. Diakonov and V. Petrov, Nucl. Phys. B 245 (1984) 259; Nucl. Phys. B 272 (1986) 457. 4. D.Diakonov, V.Petrov, P.Pobylitsa, M.Polyakov and C.Weiss, Nucl. Phys. B480 (1996) 341; Phys. Rev. D56 (1997) 4069; Phys. Rev. D58 (1998) 038502. 5. P.V. Pobylitsa and M.V. Polyakov, Phys. Lett. B 389 (1996) 350. 6. P.V. Pobylitsa, M.V. Polyakov, K. Goeke, T. Watabe, C. Weiss, Phys. Rev. D 59 (1999) 034024. 7. Chr.V. Christov, A. Blotz, H.C. Kim, P. Pobylitsa, T. Watabe, Th. Meissner, E. Ruiz Arriola, K. Goeke, Prog. Part. Nucl. Phys. 37 (1996) 91. 8. B. Dressier, K. Goeke, P. Pobylitsa, M.V. Polyakov, T. Watabe, C. Weiss, Proceedings of the XI Conference "Problems of quantum field theory", Dubna, Russia, 13-17 July, 1998, hep-ph/9809487.. 9. D.Diakonov, M.V. Polyakov, C. Weiss, Nucl.Phys. B461 (1996) 539 10. C.Schueren, E. Ruiz Arriola, K. Goeke, Nucl. Phys. A547 (1992) 612 11. J. Balla, M.V. Polyakov, and C. Weiss, Nucl. Phys. BS10 (1998) 327. B. Dressier, M. Maul, and C. Weiss, Bochum University Report RUB-TP2-5/99, hepph/9906444. 12. V.Yu. Petrov, P.V. Pobylitsa, M.V. Polyakov, I. B6rnig, K. Goeke, and C. Weiss, Phys. Rev. D 57, 4325 (1998). 13. P. Schweitzer, K. Goeke, P. Pobylitsa, M.V. Polyakov, C. Weiss, in preparation. 14. X.-D. Ji, Phys. Rev. Lett. 78, 610 (1997); Phys. Rev. D 55, 7114 (1997). 15. A.V. Radyushkin, Phys. Rev. D 56 (1997) 5524; Phys. Rev. D 59, 014030 (1999). 16. J.C. Collins, L. Frankfurt and M. Strikman, Phys. Rev. D 56, 2982 (1997). 17. F.M. Steffens, W. Melnitchouk, and A.W. Thomas, hep-ph/9903441 and J.Speth, A.W. Thomas, Adv. Nucl. Phys. 24 (1997) 83. 18. D. Diakonov, M. Polyakov, and C. Weiss, Nucl. Phys. B461 (1996) 539 19. S. Scopetta, V. Vento, M. Traini, Phys. Lett. B421 (1998) 64, B442 (1998) 28 20. A. Szczurek, M. Ericson, H. Holtmann, J. Speth, Nucl.Phys.A596:397-414,1996 21. R. Alkofer, H. Reinhardt, H. Weigel, Phys. Rep. 265 (1994) 139 22. M. Wakamatsu, H. Yoshiki, Nucl. Phys. A524 (1991) 561 23. M. Wakamatsu, T. Kubota, Phys.Rev.D57:5755-5766,1998