Anisotropic Cross section QCD investigations of penta-quark baryons.

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(2) to give a further investigations of JP=1/2(- ) state utilizing another system ... (3) to give the anisotropic cross section QCD result on JP=3/2( ) channel ...
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Anisotropic Lattice QCD investigations of penta-quark baryons N. Ishii (TITECH, Japan) T. Doi (RIKEN BNL) H. Iida (TITECH, Japan) Y. Nemoto (Nagoya Univ.) M. Oka (TITECH, Japan) F. Okiharu (Nihon Univ., Japan) H. Suganuma (Kyoto Univ., Japan) Plan of the discussion: Introduction General Formalism Numerical Result on J P =1/2(±) A Further Investigation of the Negative equality state Hybrid Boundary Condition(HBC) strategy Numerical Result II Anisotropic Lattice QCD result on J P =3/2( ± ) Summary/Discussion START

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1. Presentation Since the principal disclosure of an obviously intriguing baryon by LEPS bunch at SPring-8, gigantic endeavors have been given to the investigations of penta quarks. ★ The equality of Θ + (1540) is a standout amongst the most essential themes. Test assurance of the equality of Θ + (1540) is troublesome. Hypothetical assessments are isolated into two pieces. Positive equality is upheld by Soliton models, Jaffe-Wilczek diquark model, ... Negative equality is bolstered by Naive quark models, QCD entirety principle, cross section QCD(?) …

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Lattice QCD investigations of the penta quarks ★ various grid QCD investigations of 5Q framework has been expanded as of late. Be that as it may, these outcomes are not achieved the accord yet. The point of this discussion is (1) to give a precise information utilizing anisotropic grid QCD . (2) to give a further investigations of J P =1/2( - ) state utilizing another technique with the Hybrid limit condition(HBC). (3) to give the anisotropic grid QCD result on J P =3/2( ± ) channel with countless setups as N conf =1000 .

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2.General Formalism ( Part I : J P =1/2(±)) Interpolating field for Θ + As embraced in (1) J.Sugiyama et al., PLB581,167(2004). (2) S.Sasaki, PRL93,152001 (2004). A non-NK sort administrator : (I=0, J=1/2 ) To diminish the cover with NK diffusing states Temporal correlator ("lower part ") ("upper segment ") Positive equality states overwhelm. Negative equality states command. Positive equality commitment can\'t get to be unimportant. Negative equality commitment can\'t get to be immaterial. T

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3. Numerical Result I time 2.2 fm Finer cross section dispersing along the worldly bearing Lattice Parameter Setup : Gage Config by standard Wilson gage activity : Lattice size : 12 3 ×96 [ (2.2fm) 3 ×4.4fm in physical unit] β = 5.75 Lattice dividing: from Sommer parameter r 0 . Anisotropic grid Renormalized anisotropy : a s/a t =4 for precise estimations of correlators and masses #(gauge config) = 504 The gage arrangements are isolated by 500 pseudo warmth shower clears, in the wake of skipping 10000 thermalization clears. O(a) enhanced Wilson quark (clover) activity . Spread source to diminish higher ghostly commitments These qualities covers

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Negative equality channel (J P =1/2( - )) Correlator Effective mass Single-state immersion is accomplished. Higher unearthly commitment is steadily diminished. best fit in the level Plateau Effective Mass: immaterial ! "normal" mass at time-cut t If then Existence of the level shows the single-state immersion of the correlator G(t). NK threshold(s-wave) By ignoring the collaboration amongst N and K:

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Positive equality channel J P =1/2(+) Correlator Effective mass Higher otherworldly commitment is continuously decreased. Level best fit in the level Single-state immersion is accomplished. L NK edge ( p-wave ) The quantized spatial momenta are because of the limit of the case .

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Chiral extrapolation NK limit (p-wave) At physical point (1) Positive equality: 2.25(11) GeV (2) Negative equality: 1.75(3) GeV NK edge (s-wave) Our information does not bolster the low-lying positive equality . To get a low-lying state, it ought to show up underneath the raised NK limit . For negative equality channel, m=1.75 GeV is somewhat near the observational quality 1.54 GeV. Be that as it may, it ought to be cleared up whether this state is a reduced 5Q reverberation or not . (We will play out a further study in this course from the following slide)

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4. Further investigation of the negative equality state. (a) NEW METHOD with Hybrid BC(HBC) Spatial force is quantized because of limited volume impact: 1. intermittent BC: 2. hostile to occasional BC : The spatial BOX L Hybrid Boundary Condition(HBC) Cosequence on hadrons

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Expected outcome on the range Periodic BC(PBC): Hybrid BC(HBC): NK scrambling states r = p 3/L min ★ A comparable circumstance as the p-wave case can be presented in the s-wave case by utilizing HBC. ★ HBC helps us to elucidate whether there exists a smaller 5Q reverberation state in the district as NK-limit is raised up because of limited voluem impact ( ~ 200 MeV if L ~ 2fm. ) Compact 5Q reverberation state is relied upon to be less delicate to the change of the limit condition. ~ 200 MeV S-wave

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Numerical result II Periodic BC(PBC) Hybrid BC(HBC) NK threshold(s-wave) NK threshold(s-wave) The level is moved above by the normal sum. (1) No minimized 5Q reverberation exists in the locale as (2) The state saw in the negative equality channel ends up being a NK dissipating state . The jumping parameter prompts m N =1.74 GeV, m K =0.79 GeV Expected movement of the NK edge for L=2.15 fm is

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Combining the outcomes from the other quark masses information focuses The best fit quality on the level. strong lines NK(s-wave) limit We have not found a minimized 5Q reverberation in J P =1/2( - ) in our estimation.

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Part II Numerical result on J P =3/2(±) channel Spin of Θ + is likewise not yet decided tentatively . J P =3/2( - ) plausibility can settle the riddle of the slender rot width. (proposed by A.Hosaka et al., PRD71,074021(2005).) Advantage: (an) It permits the setup of (0s) 5 . (b) It rots into a d-wave KN state. Smothered cover to d-wave KN state The rot width is relied upon to be fundamentally slender . Burden: (a) The shading attractive association makes it monstrous. In the event that some commitment can scratch off the shading attractive cooperation to make its mass around 1540, we will get a penta-quark with a fundamentally limit width.

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Rarita-Schwinger introducing fields NK * - sort shading intertwined NK * - sort diquark-sort turn 3/2 projection framework: turn 1/2 commitments + higher otherworldly commitments Temporal correlator ("lower segment ") ("upper segment ") Negative equality states rule. Positive equality states overwhelm. Negative equality commitment can\'t get to be unimportant. Positive equality commitment can\'t get to be unimportant. T

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J P =3/2( - )state (powerful mass plot) This correlator is excessively boisterous !

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Chiral extrapolation (J P =3/2( - )) Physical quark mass area ○ (circle) from NK*-sort correlator □ (box) from shading intertwined NK*-sort correlator ★ Results from diquark-sort correlator are not appeared because of immense factual mistake. NK* scrambling states In the physical quark mass area NK*-sort: m 5Q = 2.17(4) GeV Color-melded NK*-sort: m 5Q = 2.11(4) GeV No confirmation for a low-lying 5Q state To acquire a low-lying 5Q state , it ought to show up beneath the raised NK threshold(d-wave) in any event in the light quark mass locale.

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J P =3/2(+) state (powerful mass plot)

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Chiral extrapolation (J P =3/2(+)) Physical quark mass district ○ (circle) from NK*-sort correlator □ (box) from shading melded NK*-typecorrelator △ (triangle) from diquark-sort correlator ? In the physical quark mass area, NK*-sort: m 5Q = 2.64(7) GeV Color-combined NK*-sort: m 5Q = 2.48(10) GeV Diquark-sort: m 5Q =2.42(6) GeV No proof for a low-lying 5Q states. NK* diffusing states

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6. Outline/talk We have contemplated Θ + (1540) by utilizing the anisotropic cross section QCD . For acuracy, (a) renormalized anisotropy a s/a t = 4 (b) O(a) enhanced Wilson (clover) activity for quarks (c) spread source (d) substantial number of gage arrangements : Ncf=1000 (for J P =3/2(±) states) J P =1/2(±) Non-NK sort inserting field: J P =1/2(+): m 5Q = 2.25(11) GeV - too gigantic to be in any way distinguished as Θ + (1540) J P =1/2( - ): m 5Q = 1.75(4) GeV - fairly near the watched esteem. We have proposed another strategy (Hybrid BC [HBC]). HBC investigation demonstrates the state(1.75 GeV) is not a minimized 5Q state but rather a NK scrambling state . J P =3/2( ± ) [A huge insights as Ncf=1000 has played a vital role.] Three-sorts of adding field(NK*-sort, shading intertwined NK*-sort, diquark - sort) Only gigantic states after the chiral extrapolation: J P =3/2( - ): J P =3/2(+): HBC investigation is performed. Minimal 5Q resonances are not found in our figuring. Taking after possibilies would enthusiasm for Θ + (1540): (a) little quark mass impacts (and/or more detailed chiral extrapolation), (b) extensive spatial volume, (c) dynamical quark(including πKN hepta-quark picture), (d) elaborate interjecting fields to fit the diquark picture.

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