Download Multi-Strangeness Di

Multi-Strangeness Dibaryon
T.Goldman, TD, LANL
Y.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
models.
• Proposal
“Discovery” of Multiquark
The “discovery” of multiquark states sets challenges as well as
opportunities 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 as
opportunities 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 no
consensus 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 or
unbound.
3.N I=1/2,Jp=2+,S=-2
Wang Zhang Others
Threshold
M(MeV) 2549 2561 deeply bound 2611
2557 2607 to unbound
(2590)
(keV) 12-22
Decay 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 states
especially multi strangeness dibaryons.
High strangeness production.
Hadronization and clustering at the
boundary 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 talk
about them here.
Quark-Goldstone boson coupling
From current-quark gluon QCD to
constituent quark Goldstone boson effective theory
‘t Hooft-Shuryak-Diakonov dilute instanton
liquid vacuum(DILM). (NPB 203,245,461)
Negele’s lattice QCD supports DILM(fig.1).(PRD
49(94)6039)
Our group reproduced part of Negele’s result.
It has not been proved but might be a good
approximation 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 constituent
quark M(q2) (fig.3)
The QCD Lagrangian is transformed to be
the effective Lagrangian



  c i     M q2 exp i 5 aa / F  c
Our group derive an effective Lagrangian
based on chiral symmetry spontaneously
broken and its nonlinear realization,
 

   c  5    / 2 f        / 4 f2
 
 
 2
  5             / 12 f3   c



  c   5a  a / 2 f  a f abcb c / 4 f2
  5a f abe f cdebc d / 12 f3   c
The constituent quark field operator c is
related to the current quark operator  by
c  e
 i 5 

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 symmetry
spontaneously 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 short
range physics, such as multi quark study.
The SU(3) extension of linear approximation is even
questionable, the universal u,d,s-σquark meson coupling
will over estimate the σinduced attraction with strangeness
particles.
QDCSM
Nanjing-Los Alamos model
• QCD basis of Nanjing-Los Alamos model
The constituent quark-Goldstone boson
coupling effective Lagrangian is still a
nonperturbative strong interaction field theory.
We did a self consistent mean field approximation
calculation and found that the self-consistent meson
mean field increases as the increasing of quark
excitation, i.e., the mean field try to keep the
quark confined, within a limited excitation.
0
0.00
2
4
-0.01
-0.02
-0.03
30s
-0.04
20s11s
-0.05
20s12s
-0.06
20s13s
-0.07
-0.08
GeV
fm
Quenched lattice QCD calculation(hep-lat/0407001 and
the ref.’s there in)) shows that the ground state gluon field
energy for qq , qqq, qqqqq systems can all be expressed
as
V   An 
i j
i   j
4
1
   kn Lmin  Cn , n  2,3,5
ri  rj
where the Lmin is the minimum length of the gluon
flux tube or string.(fig.4)(hep-lat/0407
Unquench will modify the long range behavior by
color screening(fig.5).
For individual color configuration, the quenched lattice
QCD result can be approximately expressed by a two
body confinement potential,(Nuovo Cmento, 86A(85)283)
Vij=-kλiλjrijp p=1,2,
the unquenched one can be approximated as
Vij=-kλiλj rijp (1-exp(-μrijp))/μ, p=1,2,
μis color screening constant.
These color configurations will be mixed due to gluon
fluctuation and q q excitation.
• In the naïve quark model, meson and baryon have
unique color structure:
baryon
meson
So De Rujula, Georgi, Glashow and Isgur can have
simple 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 quite
Involved.
We developed a quark delocalization, color screening
model (QDCSM), where the multi color couplings are
modeled by an extended effective matrix elements
within a two cluster Hilbert space where the color screening
constant μis left as a variational parameter; the multi quark
orbital configurations are modeled by means of delocalized
quark orbits within a two cluster space where the
delocalization parameterεis left as another variational
parameter.
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 fit
of hadron interaction data shows that this model
comprises right physics at least partly.
•
Proposal
• H particle :
At most weakly bound or unbound, keep it as a
candidate at RHIC search , but not very promised.
• Di-
Possibly a weakly bound state, keep it as another
candidate, but the production rate is very low.
• N
The most promised one, it is a very narrow resonance
around 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=634 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 for
every multi quark system.
• Delocalization parameterεis determined for every
separation and every channel by the dynamics of the
multi 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
Salamanca 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 different
Mechanisms 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 different
mechanisms 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 (NΩΛΞ S=0, D-wave ) =0.012 MeV
Γ (NΩΛΞ S=1, D-wave ) =0.022 MeV
Pysical 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.