Determining the Determining the ++ quantum numbers quantum numbers through the Kthrough the Kp -> p ->
KK++n reaction n reaction
Determining the Determining the ++ quantum numbers quantum numbers through the Kthrough the Kp -> p ->
KK++n reaction n reaction
Tetsuo Hyodoa
a RCNP, Osaka b IFIC, Valencia
2003, August 8th
A. Hosakaa and E. Osetb
IntroductionIntroduction
+ : 5-quark (4 quark + 1 anti-quark)LEPS, T. Nakano et al., Phys. Rev. Lett. 91 (2003) 012002
Quantum numbers are not yet determined
We study K+p -> +K+n reaction todetermine the quantum numbers of +
Theory prediction Diakonov et al. (chiral quark soliton) Carlson et al. (quark model[QM]) Stancu et al. (QM + flavor-spin int.) Zhu (QCD sum rule) Capstick et al. (decay width analysis)
: 1/2+, I=0: 1/2, I=0: 1/2+, I=0: 1/2, I=0, 1, 2: 1/2, 3/2, 5/2, I=2
A model for p -> K0 A model for p -> K0
E. Oset and M.J. Vicente Vacas, PLB386, 39(1996)
Vertices are derived from the chiral Lagrangian
Proportional to vanishes
Assume final + is almost at rest
Dominant
DiagramsDiagrams
Tree level(background)
One loop
Possibilities of spin & parityPossibilities of spin & parity
1/2(KN s-wave resonance)1/2,3/2(KN p-wave resonance)
MR = 1540 MeV = 20 MeV
Resonance termResonance term
Amplitude of resonance term for K+p -> +K+n :
Angular dependenceAngular dependence
total resonance background
10
8
6
4
2
01.00.50.0-0.5-1.0
cosθ
10
8
6
4
2
01.00.50.0-0.5-1.0
cosθ5
4
3
2
1
01.00.50.0-0.5-1.0
cosθ
,I JP=0,1/2- ,I JP=0,1/2+
,I JP=0,3/2+
Mass distributionsMass distributions
10
8
6
4
2
015801560154015201500
MI
,I JP=0,1/2-
,I JP=0,1/2+
,I JP=0,3/2+kin( )=850 /Lab MeV cθ=0deg
3.5
3.0
2.5
2.0
1.5
1.0
0.5
0.015801560154015201500
MI
Polarization testPolarization test
Angular dependence : polarization testAngular dependence : polarization test
total resonance background
5
4
3
2
1
01.00.50.0-0.5-1.0
cosθ
20
15
10
5
01.00.50.0-0.5-1.0
cosθ5
4
3
2
1
01.00.50.0-0.5-1.0
cosθ
,I JP=0,1/2- ,I JP=0,1/2+
,I JP=0,3/2+
Polarization test
Mass distributions : polarization testMass distributions : polarization test
14
12
10
8
6
4
2
015801560154015201500
MI
,I JP=0,1/2-
,I JP=0,1/2+
,I JP=0,3/2+kin( )=850 /Lab MeV cθ=90deg
1.4
1.2
1.0
0.8
0.6
0.4
0.2
0.015801560154015201500
MI
Polarization test
ConclusionsConclusions
We calculate the p -> K0 reaction usinga chiral model, assuming the possible quantum numbers of + baryon.
� Resonance signal of the mass distribution is always seen in the forward direction. � If we find the resonance with polarization test, the quantum number of + can be determined as I=0, JP=1/2+
T. Hyodo, A. Hosaka, and E. Oset, nucl-th/0307105