meson cloud and nucleon strangeness: an update f.s. n., f. carvalho, m. nielsen university of são...
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Meson cloud and nucleon strangeness: an update
F.S. N., F. Carvalho, M. Nielsen
University of São Paulo
Brazil
H. Forkel, F. Navarra, M. Nielsen, PRC 61, 055206 (2000)
F. Carvalho, F. Navarra, M. Nielsen, PRC 72, 068202 (2005)
New data: A4 (2004); SAMPLE (2004); HAPPEX (2005); G0 (2005)
F. Carvalho, F. Navarra, M. Nielsen, (2006), in progress
Strange sea quarks in the nucleon:
theory : pQCD
theory : lattice QCD, CHPT, models
Strange meson loops: “the meson cloud”
p
High Q2
experiment: deep inelastic scattering
Low Q2
experiment: parity violating e- scattering at TJNAF
pK
K
s
s
Assumptions:
Convergence of Fock-state expansion: lighter states dominate
Multiloop contributions are suppressed
Motivation
New data: SAMPLE(04), HAPPEX(05), MAMI(05), G0(05)
arbitrary cut-off parameter
functional formRegularization with form factors:
New strange meson: E791 (2001) m = 800 MeV
Meson Loops
M =
B =
seagull terms
~ 30 diagrams
Ward – Takahashi identity
Decuplet baryons neglected
Malheiro Melnitchouk (1997)
Calculation
)()(´)()(||´)( 2 puQpupNsspN
)( 2Q
Feynman rules: vertices and propagators :
kd 4 Regularization with form factors
22
222 )(
M
MM
k
mkF
from Bonn-Jülich or Nijmegen potential
)( 2kF
MBL MLBL
BKiBgL psBBK 5
]*2
*[*
KBBm
BKiBgLN
gvBBK
Dynamics
BBgL sBB
)( **** KKKKAgL KKKK
)()( ****
KKAAgL KK transition
meson baryon
meson
])()([ *********
KKKKKKAiQLKKK
photon meson
Y. Oh, H. Kim, PRC (2006)
Couplings
0.44
PSg 45.1
4
Vg 43.2
V
Tg g
g
Nijmegen: Rijken, Stoks, Yamamoto (1999)
0.10Ng (Nijmegen NSC97f)
12.10.1*
GeVgg NK Y. Oh, H. Kim, PRC (2006)
NKNKgggg *00* 2
)()(2
)(´)()(||´)( 22
21 puQF
m
qiQFpupNsspN s
N
s
)(4
)()( 22
22
12 QF
m
QQFQG s
N
ssE
)()()( 22
21
2 QFQFQG sssM
)()()()( 2222 QGQQGQFF sM
sE
s
)(
)()(
2
22
QG
QGQ
sE
pM
)
2(tan)1(21
1
2
2
2
4 Nm
Q
Strange form factors
0
212
22
)(6
q
s qFqd
dr )0()0( 2
ssMs FG
SAMPLE
Strange magnetic form factor GM
GeVKK 9.0*
GeVKK 1.1*
Forkel, Navarra, Nielsen, PRC (2000)
PRL, 78, 3824 (1997)
PRL, 84, 1106 (2000)
Carvalho, Navarra, Nielsen, (2006)
Strange magnetic form factor GM
GM
Q2 ( GeV2 )
GeVK 9.0GeV
K9.0* GeV1.1
No
GeVK 1.1GeV
K1.1*
GeV9.0
)(39.0)()( 222 QGQGQG sM
sE
sHAPPEX
GeVKK 9.0*
GeVKK 1.1*
Forkel, Navarra, Nielsen, PRC (2000)
HAPPEXPRL, 82, 1096 (1999)
Strange electric form factor GE
84.1)0(* s
KKF
0.8)0(* s
KKF
GeVKK 9.0*
GeVK 9.0GeV
K1.1*
Carvalho, Navarra, Nielsen, PRC (2005)
)()()()( 2222 QGQQGQFF sM
sE
s (2005)
GeVK 9.0GeV
K9.0*
GeVK 9.0GeV
K1.1*
Carvalho, Navarra, Nielsen, PRC (2005)
nucl-ex/0506021
PRL, 93, 022002 (2004)PRL, 94, 152001 (2005)
nucl-ex/0506011
)()()()( 2222 QGQQGQFF sM
sE
s Carvalho, Navarra, Nielsen, PRC (2005)
GeVK 9.0GeV
K9.0*
GeVK 9.0GeV
K1.1*
2Q2Q“best” case
“worst”caseGeV9.0
GeVKK 1.1*
GeV1.1
GeVKK 9.0*
Including Carvalho, Navarra, Nielsen, (2006)
Q2 ( GeV2 )
)()()()( 2222 QGQQGQFF sM
sE
s
“best” case
“worst”case
Carvalho, Navarra, Nielsen, (2006)
Summary and conclusion
Meson cloud model with:
Parameters: coupling constants and cut-offs: *KK
*Decuplet states with were not considered
Calculation of the nucleon strange form factors
2000: marginal description of GM and GE
only with suppression: *KNijmegen
2005: no description of GM , marginal description of GE
for larger Q2 and FFs : no agreement !
including marginal agreement!
Appendix
84.1)0(* s
KKFGoity, Musolf (1996)
ab
K
s
KKba kk
m
QFkKsskK
*
21
2
21*
*
* )()(||),(
K* - K transition
mK = 495 MeV mK* = 895 MeV m = 800 MeV
Masses
Some references:
W. Köpf, E. Henley (1994)
W. Köpf, S.J. Pollock, E. Henley (1992)
T. Cohen, H. Forkel, M. Nielsen (1993)
M. Musolf, M. Burkardt (1993)
H. Forkel, M. Nielsen, X. Jin, T. Cohen (1994)
Barz, Forkel, Hammer, Navarra, Nielsen, Ramsey-Musolf (1998)
H. Forkel, F. Navarra, M. Nielsen (2000)
F. Carvalho, F. Navarra, M. Nielsen (2005)
Data: A4 (2004); SAMPLE (2004); HAPPEX (2005); G0 (2005)
Data: SAMPLE (1997); HAPPEX (1999)
W. Melnitchouk, M. Malheiro (1997) ; (1999)
...
K K B
K* K* B
K K* B
Strange Dirac form factor F1
K = K* = 1.2 GeV
K = K* = 1.2 GeV
Strange Pauli form factor F2
K K B
K* K* B
K K* B
Strangeness radius Dsr 2
K K B
K* K* B
K K* B
total
Strangeness magnetic moment s
total
K K* B
K* K* B
K K B
,4Vg
Strangeness radius Dsr 2
-1.59, 3.26
-2.0, 4.0
-0.8, 4.0
-2.0, 2.0
-0.8, 2.0
-1.59, 3.26
-2.0, 4.0
-2.0, 2.0
-0.8, 2.0
-0.8, 4.0
Strangeness magnetic moment s
Strange magnetic form factor GM
84.1)0(* s
KKF0.8)0(* s
KKF
GeVK 1.1GeV
K1.1*
GeVK 9.0GeV
K9.0*
Carvalho, Navarra, Nielsen, PRC (2005)