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Λ(1405) in a hybrid quark model

Introduction Formulation Results Summary. C. Nakamoto (Suzuka College of Technology) H. Nemura (Advanced Meson Science Laboratory, DRI, RIKEN). Λ(1405) in a hybrid quark model. Introduction. Λ(1405) 　⇒　 q 3 ? K N ? or q 4 q ?. －. －.

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Λ(1405) in a hybrid quark model

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  1. Introduction Formulation Results Summary C. Nakamoto (Suzuka College of Technology) H. Nemura (Advanced Meson Science Laboratory, DRI, RIKEN) Λ(1405) in a hybrid quark model PANIC05 24OCT2005

  2. Introduction Λ(1405)　⇒　q3 ?KN ?or q4q ? － － If we introduce the minimum realisticq-q interaction in a quark model, how is Λ(1405) represented? PANIC05 24OCT2005

  3. What is ‘the minimum realistic’? • Confinement mechanism between quarks （２）　Gluon-exchange effect （３）　Meson-exchange effect to describe the nuclear force If the quark-Hamiltonian includes these effects and reproduces the baryon ground states, how is Λ(1405) represented? PANIC05 24OCT2005

  4. ２．Formulation (1) Confinement mechanism between quarks ⇒confinement potential : - (λ・λ) ar A free parameter a mainly determines the energy shift of the baryon ground states. It is determined to reproduce the overall baryon ground states. a= 43.5 MeV・fm-1 PANIC05 24OCT2005

  5. (2) Gluon-exchange effect ⇒ one-gluon exchange potential 1/4 (λ・λ) αS ×[1/r-π/2{1/mi2+1/mj2+4/(3mimj)(σ・σ)}δ(r)] ・ the finite spatial extent of the constituent quarks δ(r) ⇒ Λ3/(8π3/2)exp[-1/2(Λr)2] αS = 1.38 (free parameter) mud = 340 MeV, ms = 580 MeV (free parameter) Λ= 5 fm-1 PANIC05 24OCT2005

  6. (3) Meson-exchange effect ⇒ NG-boson exchange potential ・ πand K-exchange potential with each form factor g82/(4π)μ2/(12mimj) ×[ exp(-μr)/r – (Λ/μ)2 exp(-Λr)/r ] ×(τ・τ or 2PF)(σ・σ) g82/(4π) = (3/5)2gπNN/(4π)mq2/mN2= 0.67 Λπ= 1.8 fm-1 ( free parameter) ΛK = 2.3 fm-1 ( free parameter) PANIC05 24OCT2005

  7. ・ σ- exchange potential as the chiral partner of π - gσ2/(4π) [ exp(-μr)/r – exp(-Λr)/r ] gσ2/(4π) = g82/(4π) = 0.67 μσ= √{(2mq)2+mπ2} = 694 MeV Λσ= 5 fm-1 PANIC05 24OCT2005

  8. 6 i=1 ∑ ∑ 6 i<j H = (mi+pi2/2mi)－Kcm • Quark-Hamiltonian + (UijConf+UijOGEP+Uijπ+UijK +Uijσ) ・UijConf ： confinement potential ・UijOGEP : one-gluon exchange potential ・Uijπ : π exchange ・UijK: K-meson exchange ・Uijσ : σ-meson exchange PANIC05 24OCT2005

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  10. Many-body calculation ⇒Stochastic Variational Method ( K.Varga and Y. Suzuki,PRC52 (1995) 2885) － We solve the five-body problem dynamically. PANIC05 24OCT2005

  11. Baryon ground states Ｎ(939) : 949 MeV Δ(1232) : 1245 MeV Λ(1116) : 1116 MeV Σ(1193) : 1235 MeV Ξ(1318) : 1320 MeV Results PANIC05 24OCT2005

  12. Baryon ground states Ｎ(939) : 949 MeV Δ(1232) : 1245 MeV Λ(1116) : 1116 MeV Σ(1193) : 1235 MeV Ξ(1318) : 1320 MeV Results Meson spectrum π(140) : 250 MeV K(496) : 526 MeV K*(892) : 905 MeV PANIC05 24OCT2005

  13. Baryon ground states Ｎ(939) : 949 MeV Δ(1232) : 1245 MeV Λ(1116) : 1116 MeV Σ(1193) : 1235 MeV Ξ(1318) : 1320 MeV Results Baryon excited states N(1440) : 1399 MeV Δ(1600) : 1609 MeV Λ(1600) : 1568 MeV Σ(1660) : 1648 MeV Ξ(unknown) : 1750 MeV Meson spectrum π(140) : 250 MeV K(496) : 526 MeV K*(892) : 905 MeV PANIC05 24OCT2005

  14. Contribution from each term N(949)K:1745Vconf:291Vcc:-911Vcm:-13 Vπ:(36 –148) Vσ:(–148 +97) Ｎ(1398) K:1711Vconf:489Vcc:-659Vcm:-30 Vπ:(25 –105) Vσ:(–99 +67) g82/(4π)μ2/(12mimj) ×[ exp(-μr)/r – (Λ/μ)2 exp(-Λr)/r ](τ・τ)(σ・σ) - gσ2/(4π) [ exp(-μr)/r – exp(-Λr)/r ] PANIC05 24OCT2005

  15. Baryon ground states Ｎ(939) : 949 MeV Δ(1232) : 1245 MeV Λ(1116) : 1116 MeV Σ(1193) : 1235 MeV Ξ(1318) : 1320 MeV Results Baryon excited states N(1440) : 1399 MeV Δ(1600) : 1609 MeV Λ(1600) : 1568 MeV Σ(1660) : 1648 MeV Ξ(unknown) : 1750 MeV Meson spectrum π(140) : 250 MeV K(496) : 526 MeV K*(892) : 905 MeV Λ(1405) q3 : 1421 MeV q4q : 1388 MeV － PANIC05 24OCT2005

  16. Summary • We investigated the baryon spectrum and the Λ(1405) in the minimum realistic quark model, involving a confinement potential, a one-gluon exchange potential and π, K and σ-exchange potentials. • Free parameters were determined to reproduce the baryon ground states. • Light mesons and some positive parity excited baryons including Roper resonance were reproduced reasonably. • Reproduction of Roper resonance may be due to the large contribution from short-range π-exchange potential because owing to the small cut-off parameter, and the introduction of σ-exchange potential between quarks. • Theenergy of q4q – state as Λ(1405) become lower than that of q3-state in the present model. • We will investigate further ; other set of parameters, contribution from the non-central force, channel-coupling effect… － PANIC05 24OCT2005

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