Exotic baryon resonances in the chiral dynamics

Transcription

1 Exotic baryon resonances in the chiral dynamics Tetsuo Hyodo a A. Hosaka a, D. Jido b, S.I. Nam a, E. Oset c, A. Ramos d and M. J. Vicente Vacas c a RCNP, Osaka b ECT* c IFIC, Valencia d Barcelona Univ. 23, December 9th

2 Contents 1. Structure of Λ(145) 1. Motivation : Two poles?" 2. Chiral unitary model" 3. Pole structure of Λ(145)" 4. Photo-production of K*Λ(145) 2. Quantum numbers of Θ + 1. Present status of theoretical studies" 2. Chiral model for K + p -> π + KN 3. Results" 4. Polarization test

3 Motivations : Two poles? There are two poles of the scattering amplitude" around nominal Λ(145) energy region." Cloudy bag model" (199) J. Fink et al. PRC41, 272 Chiral unitary model" (21~) J. A. Oller et al. PLB5, 263 E. Oset et al. PLB527, 99 D. Jido et al. PRC66, 2523 T. Hyodo et al. PRC68, 1821 Λ(145) : J P =1/2 -, I=" ChU model, T. Hyodo

4 Chiral unitary model Flavor SU(3) meson-baryon scatterings (s-wave)" Chiral symmetry" Low energy " behavior" Unitarity of S-matrix" Non-perturbative" resummation" Dynamical" generation" Resonances" Λ(145), Λ(167), N(1535), Σ(162), Ξ(162)

5 Framework of the chiral unitary model Chiral perturbation theory" Unitarization Generated resonances are" expressed as poles of the " scattering amplitude." Resonances"

6 2 15 Total cross sections of K - p scatterings K - p π Λ 2 15 π + Σ σ T [mb] K n π Σ π Σ + 3 σ T [mb] Plab [MeV/c] Plab [MeV/c] Plab [MeV/c] 3 T. Hyodo, et al., Phys. Rev. C 68, 1821 (23)

7 Λ(145) in the chiral unitary model i (πσ) πσ mass distribution" i (KN) D. Jido, et al., Nucl. Phys. A 723, 25 (23)

8 Example : the π - p -> K πσ reaction Chiral unitary model" Chiral" term" N(171)"

9 Results for π - p -> K πσ Mass distribution Total cross sections [mb] Σ(1385) effect" Good agreement" apple There are two mechanisms in the initial" stage interaction, which filter each one" of the resonances." T. Hyodo, et al., nucl-th/375, Phys. Rev. C, in press

10 Photoproduction of K* Λ(145) Only K - p channel appears at the initial stage" Higher pole??"

11 1. γvp coupling" Effective interactions for meson part 2. VPP coupling"

12 Effective interaction for Σ(1385) 3. Σ(1385)MB coupling" SU(6) symmetry" 4. K - P -> Σ(1385) -> MB amplitude"

13 dσ/dm I [nb/mev] πσ invariant mass distribution P lab = 2.5 GeV/c sqrt s ~ 2.35 GeV Preliminary π Σ (~I=) average of charged πσ π Λ (I=1) M I [MeV]

14 Result : Total cross section π Σ (~I=) average of charged πσ π Λ (I=1) Preliminary.8 σ [µb].6.4 KππΣ K*Λ sqrt s

15 Summary and conclusions We study the structure of Λ(145) using " the chiral unitary model. apple There are two poles of the scattering " amplitude around nominal Λ(145)." Pole 1 ( i) : strongly couples to KN state" Pole 2 (139+66i) : strongly couples to πσ state" " apple By observing the πσ mass distribution in" the γp -> K*Λ(145) reaction, it could be " possible to isolate higher energy pole."

16 Appendix : other processes γp -> K - πσ J.C. Nacher, et al., PLB445, 55(1999) SPring-8" Κ - p -> γπσ J.C. Nacher, et al., PLB461, 299(1999) J-PARC?"

17 Θ + baryon : Introduction Θ + : 5-quark (4 quark + 1 anti-quark)" LEPS, T. Nakano et al., Phys. Rev. Lett. 91 (23) 122 S = +1, M Θ ~ 154 MeV, Γ Θ < 25 MeV 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 : 1 + 8) J. Sugiyama et al. (QCD sum rule) F. Csikor et al. (Lattice QCD) S. Sasaki (Lattice QCD) : 1/2 +, I= : 1/2 - : 1/2 -, 3/2 -, 5/2 -, I=2 : 1/2 + (strong π) : 1/2 +, I= : 1/2 -, I= : 1/2 + -> 1/2 - : 1/2 -

18 Photo-production process Assuming the quantum numbers (spin, parity), " we can calculate a reaction" γp -> K Θ +, γn -> K - Θ + W. Liu et al. nucl-th/3834 S. I. Nam et al. hep-ph/38313 W. Liu et al. nucl-th/3923 Y. Oh et al. hep-ph/31117 l Model (mechanism) dependence" Initial cm energy ~ 2 GeV (p cm ~ 75 MeV) " not low energy -> linear or nonlinear?" N* resonances, K* exchange, Κ 1 exchange, " l Form factor dependence" Monopole, dipole, value of Λ, " l Unknown parameters" γθθ coupling, K*pΘ coupling, "

19 We propose" Motivation and advantage K + p -> π + Θ + -> π + K + n(k p)" l Low energy model is sufficient (p cm ~ 35 MeV)" l take decay into account -> background estimation" -> Width independent" l Hadronic process : clear mechanism" to extract a qualitative behavior which depends" on the quantum numbers of Θ +." Determination of quantum numbers" New : pp -> Σ + Θ +, A. W. Thomas, K. Hicks, and A. Hosaka, hep-ph/31283

20 A model for Κ + p -> π + K + n E. Oset and M. J. Vicente Vacas, PLB386, 39(1996) Vertices are derived from the chiral Lagrangian" Dominant" Proportional to" vanishes " Assume final π + is almost at rest"

21 Diagrams Tree level" (background)" One loop"

22 Possibilities of spin & parity 1/2 - (KN s-wave resonance)" 1/2 +, 3/2 + (KN p-wave resonance)" M R = 154 MeV Γ = 2 MeV

23 Resonance term Amplitude of resonance term for K + p -> π + K + n :"

24 Angular dependence d 2 σ/dm I dcosθ [µb/mev] d 2 σ/dm I dcosθ [µb/mev] cos θ.5 1. d 2 σ/dm I dcosθ [µb/mev] I,J P =,1/2 - I,J P =,1/2 + I,J P =,3/ cos θ cos θ total resonance background.5 1.

25 Mass distributions I,J P =,1/2 - I,J P =,1/2 + I,J P =,3/2 + k in (Lab) = 85 MeV/c θ = 9 deg d 2 σ/dm I dcosθ [µb/mev] d 2 σ/dm I dcosθ [µb/mev] M I M I

26 Polarization test # Same result is obtained for final pk "

27 Angular dependence : polarization test d 2 σ/dm I dcosθ [µb/mev] cos θ.5 1. d 2 σ/dm I dcosθ [µb/mev] I,J P =,1/2 - I,J P =,1/ cos θ.5 1. d 2 σ/dm I dcosθ [µb/mev] I,J P =,3/ cos θ.5 1. total resonance background Polarization test

28 Mass distributions : polarization test I,J P =,1/2 - I,J P =,1/2 + I,J P =,3/2 + k in (Lab) = 85 MeV/c θ = 9 deg Polarization test d 2 σ/dm I dcosθ [µb/mev] d 2 σ/dm I dcosθ [µb/mev] M I M I

29 Incomplete polarization d 2 σ/dm I dcosθ [µb/mev] I,J P =,1/2 - I,J P =,1/2 + 8 %" %" Polarization k in (Lab) = 85 MeV/c θ = 9 deg 1 %" M I

30 Conclusion We calculate the K + p -> π KN reaction using" a chiral model, assuming the possible " quantum numbers of Θ + baryon. " apple If we find the resonance with polarization " test, the quantum number of Θ + can be" determined as I=, J P =1/2 + " T. Hyodo, et al, nucl-th/3715, Phys. Lett. B, in press E. Oset, et al, nucl-th/31214, Hyp3 proceedings

31 Future work apple Full calculation of the present reaction" without approximation of kinematics" -> information from π + angular dependence" apple photo-production of K* and Θ V. Kubarovsky et al., hep-ex/3788"