Multi-Strangeness Dibaryon

T.Goldman, TD, LANLY.X.Liu, Peking Univ.X.F.Lu, Sichuan Univ.

J.L.Ping, Nanjing Normal Univ.Fan Wang, Nanjing Univ.

Contents

• “Discovery” of multi-quark states.• Candidates of multi-strangeness dibaryons.• RHIC is a factory of multi-quark.• Nonperturbative QCD basis of quark mode

ls.• Proposal

“Discovery” of Multiquark The “discovery” of multiquark states sets challenges as well asopportunities to quark models. Eleven groups claimed that they observed a penta quark state, called Θ+: Θ+: I=0, J=1/2, Parity=?, M=1540MeV, Γ≤25MeV, NA49 Ξ--: I=3/2, M=1862MeV, Γ≤ 18MeV, H1 Θc : I=0, M=3099 MeV, Four groups clamed that they observed tetra quark states . Up to now no dibaryon or hexa quark state has been observed . • If the Pendora box of multi quark really has been opened, all of these multiquark states should appear sooner or later. The discovery of multi-quark states sets challenges as well asopportunities to quark models, even lattice QCD and others. Four lattice QCD calculations gave totally different results. There have been more than 200 papers about pentaquark but noconsensus yet.

Candidates of Dibaryons Candidates of Multi-Strangeness Dibaryons. • Chiral soliton quark model prediction of theΘ+

played a vital role in the “discovery” of Θ+.

Quark model predictions of dibaryon:

1. H(uuddss) I=0,Jp=0+,S=-2 Wang Zhang others Threshold M(MeV) 2228 2223 deeply bound 2231 2230 2233 to unbound (2230-32) Quite impossible to be deeply bound. More than 25 years search with null result.

2. I=0,Jp=0+,S=-6 Wang Zhang Others Threshold M(MeV) 3298 3229 deeply bound 3345 3300 3292 to unbound (3300-

4) Similar to H particle, weakly bound orunbound.

3.N I=1/2,Jp=2+,S=-2 Wang Zhang Others ThresholdM(MeV) 2549 2561 deeply bound 2611 2557 2607 to unbound (2590)(keV) 12-22Decay mode N--> 1D2,3D2.

Quite possible a narrow resonance.

(Wang:PRL 59(87)627, 69(92)2901, PRC 51(95)3411, 62(00)054007, 65(02)044003, 69(04)065207;

Zhang:PRC 52(95)3393, 61(00)065204, NPA 683(01)487.)

RHIC, a multiquak factory RHIC is a factory of multiquark statesespecially multi strangeness dibaryons. High strangeness production. Hadronization and clustering at theboundary of fire ball. Shandong group estimation: no problem to produce N in one event, but hard to have in one event.

Nonperturbative QCD basis of quark models

Nonperturbative QCD basis of quark models. How reliable are these quark model predictions?

Wang(QDCSM or Nanjing-Los Alamos model) Zhang(chiral quark model or Tokyo-Tuebingen-Beijing -Salamanka model) both fit the existed NB scattering data(Zhang’s better)and deuteron properties(Wang’s better). The effective attraction developed in and N channels is quite model independent. There are many other quark models but I will not talkabout them here.

Quark-Goldstone boson coupling

From current-quark gluon QCD toconstituent quark Goldstone boson effective theory ‘t Hooft-Shuryak-Diakonov dilute instantonliquid vacuum(DILM). (NPB 203,245,461) Negele’s lattice QCD supports DILM(fig.1).(PRD49(94)6039) Our group reproduced part of Negele’s result. It has not been proved but might be a goodapproximation of QCD vacuum.

Current quark propagating within the DILM(fig.2) (NPB 272(86)457; hep-ph/0406043) Current quark m is dressed to be constituentquark M(q2) (fig.3)

The QCD Lagrangian is transformed to bethe effective Lagrangian c

aac FiqMi

/exp 52

Our group derive an effective Lagrangianbased on chiral symmetry spontaneouslybroken and its nonlinear realization,

The constituent quark field operator c is

related to the current quark operator by

c

c

f

ff

32

5

25

12/

4/2/

cdcbcdeabea

cbabcaaac

fff

fff

3

5

25

12/

4/2/

5i

c e

The form of dynamically derived effective Lagrangian, such as the former Diakonov’s Lagragian, is model dependent, but the nonlinear coupling is dictated by the chiral symmetryspontaneously broken as we did. The linear approximation of Zhang(NPA 683(01)487)and others, such as Glozman & Riska, Phys. Reports, 268(96)263,missed the higher order terms, which should be important for shortrange physics, such as multi quark study. The SU(3) extension of linear approximation is evenquestionable, the universal u,d,s-σquark meson couplingwill over estimate the σinduced attraction with strangenessparticles.

QDCSM Nanjing-Los Alamos model

• QCD basis of Nanjing-Los Alamos model

The constituent quark-Goldstone bosoncoupling effective Lagrangian is still anonperturbative strong interaction field theory.

We did a self consistent mean field approximationcalculation and found that the self-consistent meson mean field increases as the increasing of quarkexcitation, i.e., the mean field try to keep thequark confined, within a limited excitation.

-0.08

-0.07

-0.06

-0.05

-0.04

-0.03

-0.02

-0.01

0.00

20s13s

20s12s

20s11s

30s

GeV

fm420

Quenched lattice QCD calculation(hep-lat/0407001 andthe ref.’s there in)) shows that the ground state gluon fieldenergy for systems can all be expressedas

where the Lmin is the minimum length of the gluonflux tube or string.(fig.4)(hep-lat/0407 Unquench will modify the long range behavior bycolor screening(fig.5).

5,3,2,14 min

nCLkrr

AV nnji ji

jin

qqqqqqqqqq ,,

For individual color configuration, the quenched latticeQCD result can be approximately expressed by a twobody confinement potential,(Nuovo Cmento, 86A(85)283) Vij=-kλiλjrij

p p=1,2,

the unquenched one can be approximated as

Vij=-kλiλj rijp (1-exp(-μrij

p))/μ, p=1,2, μis color screening constant. These color configurations will be mixed due to gluon fluctuation and excitation.qq

• In the naïve quark model, meson and baryon have unique color structure: baryon meson

So De Rujula, Georgi, Glashow and Isgur can havesimple Hamiltonian for hadron spectroscopy.

• For pentaquark there are more color structures:

……

• In principle one should have a multi body interaction,multi channel coupling model. Numerically it is quiteInvolved.

We developed a quark delocalization, color screeningmodel (QDCSM), where the multi color couplings aremodeled by an extended effective matrix elementswithin a two cluster Hilbert space where the color screeningconstant μis left as a variational parameter; the multi quarkorbital configurations are modeled by means of delocalizedquark orbits within a two cluster space where thedelocalization parameterεis left as another variationalparameter.

•

The variational calculation will allow the multi quark system to adjust themselves to arrive at a

• self consistency.• We can not derive this model from QCD. The fitof hadron interaction data shows that this modelcomprises right physics at least partly.

Proposal

• H particle : At most weakly bound or unbound, keep it as acandidate at RHIC search , but not very promised.• Di- Possibly a weakly bound state, keep it as anothercandidate, but the production rate is very low.• N The most promised one, it is a very narrow resonancearound 2.55 GeV, even narrower than the Θ+.

Thanks 谢谢 (xie xie)

QDCSM

• Hamiltonian:

RGM

• Wavefunctions:

Model Parameters• M=313 MeV, b=0.602 fm, αs=1.555, a=25.03 MeV/fm2, Ms=63

4 MeV. r0=0.8 fm

are fixed by ground state masses of baryons

• μ=0.9 fm-2

Is fixed by deuteron properties, should be adjusted forevery multi quark system.

• Delocalization parameterεis determined for everyseparation and every channel by the dynamics of themulti quark system

Dibaryons• Deuteron(Strangeness=0,I=0,J=1) : Md=1875.8 MeV, =1.92 fm, PD=4.92%,

two-baryon state TheΔΔ components of deuteron is consistent with the Sa

lamanca result.

• H(Strangeness=-2,I=0,J=0): First predicted by Jaffe in 1977 with MIT bag model. MH=2228-2230 MeV.

A weakly bound or unbound one.

• d* (Strangeness=0,I=0,J=3): Md*=2165 MeV, =1.3 fm. (6-quark state) Γ(d*NN D-wave)=7 MeV. Quite different from Zhang’s ,because of the differentMechanisms of intermediate range attraction.

• di-Ω(Strangeness=-6,I=0,J=0): M Ω Ω=3300 MeV, =1.2 fm. (6-quark state) Quite different from Zhang’s, because of the differentmechanisms of intermediate range attraction.

• d’ (Strangeness=0,I=0,J=0,Parity=-): 2060 MeV Md’=2454 MeV. Original resonance signal disappeared later.

• ΔΔ(I=0,J=1):

MΔΔ=2078 MeV, Γ(ΔΔ NN S-wave)=147 MeV

• ΔΔ(I=1,J=0):

MΔΔ=2131 MeV, Γ(ΔΔ NN S-wave)=228 MeV

• ΔΔ(I=1,J=2):

MΔΔ=2205 MeV, Γ(ΔΔ NΔ S-wave)=10 MeV

• NΩ(I=1/2,J=2): MΔΔ=2549 MeV,

Γ (NΩΛΞ S=0, D-wave ) =0.012 MeV Γ (NΩΛΞ S=1, D-wave ) =0.022 MeVPysical reasons for narrow width:D-wave dicay, tensor interaction, no π in N channel,One quark must be exchanged between N and .

Quite possible a narrow resonance.