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Anisotropic lattice QCD studies of penta-quarks and tetra-quarks

Anisotropic lattice QCD studies of penta-quarks and tetra-quarks. N. Ishii (Univ. of Tokyo) in collaboration with

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Anisotropic lattice QCD studies of penta-quarks and tetra-quarks

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  1. Anisotropic lattice QCD studies of penta-quarks and tetra-quarks N. Ishii (Univ. of Tokyo) in collaboration with T. Doi (Riken BNL)H. Iida (TITECH)Y. Nemoto (Nagoya Univ.)M. Oka (TITECH)F. Okiharu (Nihon Univ.)H. Suganuma (Kyoto Univ.)K. Tsumura (Kyoto Univ.) Plan of the talk:1 Introduction2 General Formalisms3 Numerical Results4 Summary/Discussion(5 Tetra-quarks(4Q)) See Phys.Rev.D71,034001(2005); D72,074503(2005) for detail. START

  2. 1.Introduction • One of the most important issues for Θ+(1540) is to understand • its extremely narrow decay width Γ<1 MeV. • Several ideas have been proposed as • I=2 assignment • Jaffe-Wilczek’s diquark picture ⇒ JP=1/2(+) and 3/2(+) • πKN hepta-quark picture ⇒ JP=1/2(+) • The string picture • JP=3/2(-) assignment ⇒ JP=3/2(-) • In this talk, we are mainly interested in JP=3/2(±) possibilities: • We first present our numerical results on JP=1/2(±) penta-quarks brieflyemplyoing a diquak-type interpolating fieldusing a flavor dependent boundary condition(HBC) • We then present our numerical results on JP=3/2(±) penta-quarksemploying three Rarita-Schwinger interpolating fieldsusing 1000 gauge field configurations for high statistics

  3. 2.General Formalism time 2.2 fm Finer lattice spacing along the temporal direction • Lattice QCD Setup: • Gauge Config by standard Wilson gaugeaction: • Lattice size : 123×96[(2.2fm)3×4.4fm in physical unit] • β= 5.75 • Lattice spacing: from Sommer parameter r0. • Anisotropic latticeRenormalized anisotropy: as/at=4for accurate measurements of correlators and masses • #(gauge config) = 504 for JP=1/2(±)= 1000 for JP=3/2(±) • O(a) improved Wilson quark (clover) action.The quark mass covers the region ms < mq < 2 m s • Smeared source to reduce higher spectral contributions

  4. The interpolating fields We consider the following iso-scalar interpolating fields: ★ A diquark-type interplating fields for JP=1/2(±) states: (scalar) (pseudo scalar) ★ Three Rarita-Schwinger interplating fields for JP=3/2(±) states: NK*-type color-twisted NK*-type diquark-type (scalar) (vector)

  5. Hybrid Boundary Condition(HBC) Spatial momentum is quantized due to finite volume effect: 1. periodic BC: 2. anti-periodic BC: The spatial BOX L L L We utilize a flavor dependent spatial BC (Hybrid BC (HBC)).(We use HBCin addition to the standard periodic BC(PBC)) Hybrid Boundary Condition(HBC) Cosequence on hadrons With HBC ◎ NK and NK* threshold energies(s-wave) are raised due to , ◎Θ+,if it is a compact resonance, will not be affected so much. HBC can be used to determine whether a state is a compact resonance or not. ※In the case of p/d wave, HBC serves as another boundary condition(other than PBC).

  6. 3.Numerical Results: JP=1/2(±) states (effective mass plots) JP=1/2(-) plateau NK-threshold (s-wave) JP=1/2(+) plateau NK-threshold (p-wave) “Effective mass” is defined as which can be considered as an “weighted average” of massesat each time-slice t. Excited state contributions are reducing A single state dominate the correlator G(t) in this region. • JP=1/2(-) state:A state appears slightly above the NK threshold (mN+mK). • JP=1/2(+) state:A state appears above the raised NK threshold(due to the finite box).⇒ rather massive !

  7. Chiral extrapolation (JP=1/2(±)) NK threshold (p-wave) At physical point (1) JP=1/2(+):2.24(11) GeV(2) JP=1/2(-):1.75(3) GeV NK threshold (s-wave) • Our data does not support a low-lying JP=1/2(+) penta-quark. • For JP=1/2(-) state, the mass(1.75 GeV) is OK !Still, it is necessary to check whether it is not an NK scattering state but a compact resonance.⇒ HBC analysis

  8. HBC analysis (JP=1/2(-) state) NK-threshold (PBC) NK-threshold (HBC) PBC HBC • NK(s-wave) threshold is raised up by 210 MeV. • The best fit mass m5Q is raised up by a similar amount. • ★ No compact 5Q resonance exists in the region: • ★The state observed in JP=1/2(-) is an NK scattering state.

  9. Numerical Results: JP=3/2(-) state (effective mass plot) “Effective mass” is defined as which can be considered as an “weighted average” of massesat each time-slice t. plateau twisted plateau × The plateaus appearabove the NK*-threshold andabove the raised NK threshold. This correlator is too noisy !Fit is not performed.

  10. Chiral extrapolation (JP=3/2(-)) Physical quark mass region ○(circle)from NK*-type correlator □(box)from color-twisted NK*-type correlator Due to the limited time, we cannot show HBC analysis. HBC analysis suggeststhese states areNK*(s-wave) scattering states • In the physical quark mass region • NK*-type:m5Q= 2.17(4) GeV • Color-twisted NK*-type: m5Q= 2.11(4) GeV • No evidence for a low-lying 5Q state

  11. JP=3/2(+) state (effective mass plot) twisted plateau plateau The plateaus appearabove the raised NK*-threshold andabove the raised NK threshold. plateau

  12. Chiral extrapolation (JP=3/2(+)) Physical quark mass region ○(circle)from NK*-type correlator □(box)from color-twisted NK*-type correlator △(triangle) from diquark-type correlator Due to the limited time, we cannot show HBC analysis. HBC analysis suggests: N*K*(s-wave) scattering state • In the physical quark mass region, • NK*-type:m5Q= 2.64(7) GeV • Color-twisted NK*-type: m5Q= 2.48(10) GeV • Diquark-type:m5Q=2.42(6) GeV • No evidence for a low-lying 5Q states. NK*(p-wave) scattering states

  13. 4. Summary/discussion • We have studied spin=1/2 and 3/2 penta-quarks by using the anisotropic lattice QCD. For acuracy,(a) renormalized anisotropy as /at = 4(b) O(a) improved Wilson (clover) action for quarks(c) smeared source(d) large number of gauge configurations: Ncf=1000 for JP=3/2(±) • JP=1/2(±) [with a diquark-type interpolating field] • JP=1/2(-) state: JP=1/2(+) state: • HBC analysis shows thatthe state at 1.75 GeV is an NK scattering state. • JP=3/2(±) [A large statistics as Ncf=1000 has played an important role.] • Three interpolating fields (NK*-type, color-twisted NK*-type, diquark-type) • Only massive states after the chiral extrapolation:JP=3/2(-) state: JP=3/2(+) state: • HBC analysis suggests that these 5Q states are NK* and N*K* scattering states. • Following possibilies would be interesting for Θ+(1540): • Small quark mass effect(and/or elaborate chiral extrapolation) • Large spatial volume • Dynamical quarks • Elaborate interpolating fields to fit the diquark picture • πKN hepta-quark picture Too heavy to be identified as Θ+(1540) See for detail:Phys. Rev. D71,034001 (2005)Phys. Rev. D72,074503 (2005)

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