Pentaquark in Anisotropic Grid QCD - A plausibility of another 5Q reverberation around 2.1 GeV.


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Pentaquark in Anisotropic Grid QCD - A probability of another 5Q reverberation around 2.1 GeV N. Ishii (TITECH, Japan) T. Doi (RIKEN BNL) H. Iida (TITECH, Japan) Y. Nemoto (Nagoya Univ.) M. Oka (TITECH, Japan)
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Slide 1

Pentaquark in Anisotropic Lattice QCD - A plausibility of another 5Q reverberation around 2.1 GeV 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 (TITECH, Japan) Plan of the discussion: Introduction General Formalism Numerical Result on J P =1/2(â±) A Further Investigation of the Negative equality state New system with Hybrid Boundary Condition(HBC) Numerical Result II First Lattice QCD result on J P =3/2( - ) - A plausibility of another 5Q reverberation around m=2.1 GeV . Outline/Discussion preparatory

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1. Presentation Since the first revelation of a plainly colorful baryon by LEPS bunch at SPring-8, colossal endeavors have been dedicated to the investigations of penta quarks. ★ The equality of Θ + (1540) is a standout amongst the most imperative subjects. Test determination of the equality of Θ + (1540) is troublesome. Hypothetical assessments are partitioned into two pieces. Positive equality is upheld by Soliton models, Jaffe-Wilczek diquark model, ... Negative equality is upheld by Naive quark models, QCD entirety guideline, …

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Lattice QCD investigations of the penta quarks There are various cross section QCD investigations of penta quarks. (1) F.Scikor et al., JHEP 11 (2003)070. (2) S.Sasaki, PRL 93 (2004) 152001. (3) T.- W.Chiu et al., hep-ph/0403020. (4) N.Mathur et al., PRD 70 (2004)0745008. (5) N.Ishii et al., PRD 71 (2005) 034001. (6) C.Alexandrou et al., hep-lat/0409065; hep-lat/0503013. (7) T.T.Takahashi et al., hep-lat/0410025; hep-lat/0503019. (8) D.Sigaev et al., MIT bunch. (9) B.G.Lasscock et al., hep-lat/0503008. (10) F.Scikor et al., hep-lat/0503012 . Then again, these studies have not came to the accord yet. The point of this discussion is (1) to give an exact information utilizing anisotropic cross section QCD . (2) to give a further investigations of negative equality state utilizing another system with the Hybrid limit condition(HBC). (3) to give the first cross section QCD result on J P =3/2( - ) channel . preparatory

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2.General Formalism ( Part I : J P =1/2(â±)) 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 lessen the cover with NK disseminating states Temporal correlator (“lower part ”) (“upper segment ”) Positive equality states command. Negative equality states command. Positive equality commitment can\'t get to be insignificant. Negative equality commitment can\'t get to be unimportant. T

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3. Numerical Result I time 2.2 fm Finer cross section dividing along the fleeting 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 dispersing: from Sommer parameter r 0 . Anisotropic cross section Renormalized anisotropy : a s/a t =4 for exact estimations of correlators and masses #(gauge config) = 504 The gage setups are isolated by 500 pseudo warmth shower clears, subsequent to skipping 10000 thermalization clears. O(a) enhanced Wilson quark (clover) activity . Spread source to diminish higher ghastly commitments These qualities covers

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Negative equality channel (J P =1/2( - )) Correlator Effective mass Single-state immersion is accomplished. Higher ghostly commitment is continuously decreased. best fit in the level Plateau Effective Mass: immaterial ! On the off chance that then Existence of the level demonstrates the single-state immersion of the correlator G(t). NK threshold(s-wave) By dismissing the connection in the middle of N and K:

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

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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 . For negative equality channel, m=1.75 GeV is fairly near the exact quality 1.54 GeV. Be that as it may, it ought to be cleared up whether this state is a smaller 5Q reverberation or not . (We will perform a further study in this bearing from the following slide)

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4. Further investigation of the negative equality state. (a) NEW METHOD with Hybrid BC(HBC) Spatial energy is quantized because of limited volume impact: 1. occasional BC: 2. hostile to intermittent BC : The spatial BOX L Hybrid Boundary Condition(HBC) L Cosequence on hadrons Expected results on the spectra Standar BC: Hybrid BC: NK limit is raised because of limited volume impact. Conservative 5Q reverberation states are relied upon to be less delicate to the change of limit condition. NK disseminating states HBC assists us with detectinging presence of minimal 5Q reverberation in the area as:

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A sample Response of a smaller reverberation state to the change of limit condition. For this reason, nucleon is not proper, in light of the fact that nucleon is sujbect to the counter intermittent BC . A limited reverberation is less delicate to the change of limit condition !

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Numerical result II Standard BC Hybrid BC The level is moved above by the normal sum. (1) No minimized 5Q reverberation exists in the area as (2) The state saw in the negative equality channel ends up being a NK dissipating state . The bouncing parameter prompts m N =1.74 GeV, m K =0.79 GeV Expected movement of the NK limit for L=2.15 fm is

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

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Part II First cross section QCD result on J P =3/2(- ) channel Spin of Θ + is likewise not yet decided tentatively . J P =3/2( - ) plausibility can comprehend the slender\'s riddle rot width. (proposed by A.Hosaka et al., hep-ph/0409102.) Advantage: (an) It permits the setup of (0s) 5 . (b) It rots into a d-wave KN state. Stifled cover to d-wave KN state The rot width is relied upon to be essentially limited . Impediment: (a) The shading attractive collaboration makes it gigantic. In the event that some commitment can wipe out the shading attractive cooperation to make its mass around 1540, we will acquire a penta-quark with an essentially limit width. There have been no grid QCD counts for J P =3/2 penta-quark yet.

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Interpolating field (J P =3/2(- )) turn 1/2 commitments + higher phantom commitments turn 3/2 projection framework: Temporal correlator (“lower part ”) (“upper segment ”) Negative equality states command. Positive equality states command. Negative equality commitment can\'t get to be immaterial. Positive equality commitment can\'t get to be immaterial. T NK * - sort introducing field (I=0, Rarita-Schwinger formalism)

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viable mass plot (J P =3/2(- )) NK* edge (s-wave): NK limit (d-wave): Excited state’s commitment is continuously decreased. Single-state immersion is required to be accomplished. level best-fit Best-fit mass in the level: NK*(s-wave) NK(d-wave) The best-fit mass is situated over the NK* limit and NK edge !

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Standard BC v.s. Cross breed BC (J P =3/2(- )) turn This state may be a smaller reverberation state . Half and half BC 70 MeV StandardBC level NK * (s-wave) 200MeV up best-fit best-fit 40MeV up NK * (s-wave) NK(d-wave) 70MeV down NK(d-wave) preparatory After turning the limit condition to HBC: The best\'s area fit mass is verging on unaltered . It shows up underneath NK* limit by 70 MeV .

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Chiral extrapolation (J P =3/2( - )) Physical area: m 5Q = 2.14(5) GeV preparatory NK* edge (s-wave) J P =3/2( - ) m 5Q = 2.14(5) GeV would be too enormous to possibly be recognized as Θ + (1540). This may be another minimized 5Q reverberation around 2.1 GeV. (J P =3/2( - ), I=0, S=+1) Several remarks on this state : (1) Quenched QCD results ought to be comprehended to contain about ±10% slip. (The mass is better comprehended to be situated in the area 1.9 GeV – 2.3 GeV.) (2) The rot width could be less slender. - The state shows up above NK* edge. - Quenched QCD tends to disparage the rot width. (K* does not rot) (3) Still, it is fascinating to research this state into point of interest.

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6. Outline/exchange We have concentrated on Θ + (1540) by utilizing the anisotropic grid QCD . For acuracy, (a) renormalized anisotropy a s/a t = 4 (b) O(a) enhanced Wilson (clover) activity for quarks (c) spread source J P =1/2(â±) Non-NK sort inserting field: Positive equality: m 5Q = 2.25(11) GeV - too huge to be in any way recognized as Θ + (1540) Negative equality: m 5Q = 1.75(4) GeV - fairly near the watched worth. We have proposed another technique (Hybrid BC [HBC]). HBC examination demonstrates the state(1.75 GeV) is not a conservative 5Q state but rather a NK scrambling state . J P =3/2( - ) [1 st cross section QCD result] NK*-sort introducing field : HBC examination demonstrates there is a state, which may be a minimized 5Q reverberation . Chiral extrapolation prompts m 5Q = 2.14(5) GeV - too enormous to possibly be distinguished as Θ + (1540). A probability of another 5Q reverberation . (J P =3/2( - ), I=0, S=+1) Following possibilies would be fascinating for Θ + (1540): (a) little quark mass impacts (and/or more expound chiral extrapolation), (b) huge spatial volume, (c) dynamical quark(including πKN hepta-quark pictur

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