determining the q + quantum numbers through the k + p -> p + kn reaction

Determining the Determining the ++ quantum numbers quantum numbers through the Kthrough the Kp -> p ->

KN reaction KN reaction

Determining the Determining the ++ quantum numbers quantum numbers through the Kthrough the Kp -> p ->

KN reaction KN reaction

Tetsuo Hyodoa,

a RCNP, Osaka b IFIC, Valencia

2003, October 23rd

A. Hosakaa, M. J. Vicente Vacasb and E. Osetb

ContentsContents

1. Introduction1. Status of theoretical studies2. Photo-production process

2.The K+p -> +K+n(K0p) reaction1. Motivation & advantage2. Model for the reaction3. Numerical results4. Conclusions

3.Future (current) works1. Full calculation2. K* production

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

Theory prediction D. Diakonov et al. (chiral quark soliton) Naive quark model S. Capstick et al. (isotensor formulation) A. Hosaka (chiral potential) R. L. Jaffe et al. (qq-qq-q : 10 + 8) J. Sugiyama et al. (QCD sum rule) F. Csikor et al. (Lattice QCD) S. Sasaki (Lattice QCD)

: 1/2+, I=0: 1/2

: 1/2, 3/2, 5/2, I=2: 1/2+ (strong ): 1/2+, I=0: 1/2, I=0: 1/2+ -> 1/2

: 1/2

Photo-production processPhoto-production process

W. Liu et al. nucl-th/0308034S. I. Nam et al. hep-ph/0308313W. Liu et al. nucl-th/0309023Y. Oh et al. hep-ph/0310117

p -> K0, n -> K

Model (mechanism) dependence

Form factor dependence

Unknown parameters

Initial cm energy ~ 2 GeV (pcm ~ 750 MeV) not low energy -> linear or nonlinear?N* resonances, K* exchange, exchange,…

Monopole, dipole… , value of , …

coupling, K*p coupling, …

Assuming the quantum numbers (spin, parity), we can calculate a reaction

Motivation and advantageMotivation and advantage

K+p -> ++ -> +K+n(K0p) Low energy model is sufficient (pcm ~ 350 MeV) take decay into account -> background estimation -> Width independent Hadronic process : clear mechanism

We propose

to extract a qualitative behavior which dependson the quantum numbers of .

Determination of quantum numbers

A model for p -> +K+n A model for p -> +K+n

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

0.00.50.0-0.5-.0

cosθ

0

8

6

4

2

0.00.50.0-0.5-.0

cosθ5

4

3

2

0.00.50.0-0.5-.0

cosθ

,I JP=0,/2- ,I JP=0,/2+

,I JP=0,3/2+

Mass distributionsMass distributions

8

6

4

2

0580560540520500

MI

,I JP=0,/2-

,I JP=0,/2+

,I JP=0,3/2+kin( )=850 /Lab MeV cθ=90deg

.4

.2

.0

0.8

0.6

0.4

0.2

0.0580560540520500

MI

Polarization testPolarization test

# Same result is obtained for final pK0

Angular dependence : polarization testAngular dependence : polarization test

total resonance background

5

4

3

2

1

0.00.50.0-0.5-.0

cosθ

20

5

0

5

0.00.50.0-0.5-.0

cosθ5

4

3

2

0.00.50.0-0.5-.0

cosθ

,I JP=0,/2- ,I JP=0,/2+

,I JP=0,3/2+

Polarization test

Mass distributions : polarization testMass distributions : polarization test

14

12

10

8

6

4

2

0580560540520500

MI

,I JP=0,/2-

,I JP=0,/2+

,I JP=0,3/2+kin( )=850 /Lab MeV cθ=90deg

.4

.2

.0

0.8

0.6

0.4

0.2

0.0580560540520500

MI

Polarization test

Incomplete polarizationIncomplete polarization

14

12

10

8

6

4

2

0580560540520500

MI

,I JP=0,/2-

,I JP=0,/2+ kin( )=850 /Lab MeV cθ=90deg

Polarization

100 %80 % 0 %

ConclusionConclusion

We calculate the Kp -> 0KN reaction usinga chiral model, assuming the possible quantum numbers of + baryon. � 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

Future workFuture work

� Full calculation of the present reaction without approximation of kinematics -> information from + angular dependence� photo-production of K* and V. Kubarovsky et al., hep-ex/0307088

Photo-production of K* and Photo-production of K* and

Preliminary

60

50

40

30

20

10

03.02.52.01.51.00.50.0

θ[ ]rad

0

8

6

4

2

3.02.52.0.5.00.50.0

θ[ ]rad

0.3

0.2

0.

0.03.02.52.0.5.00.50.0

θ[ ]rad

30

25

20

5

0

5

03.02.52.0.5.00.50.0

θ[ ]rad

( ) Angular dependence upper and( ) integrated lower cross sections

of -> *p K- ,K exchangeGeV

:[units μ ]bJP=/2+ JP=/2-