Color confinement Multi-quark Resonances

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Color confinement Multi-quark Resonances

• Fan Wang
• Dept. of Physics, Nanjing Univ.
• Joint Center for Particle-Nuclear Physics and
  Cosmology (CPNPC)
• of NJU and PMO
• J.L.Ping, H.R.Pang
• C.L.Chen

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Outline

• I. Introduction
• II. Color confinement resonance
• III. QCD models of multi-quark
• resonances
• IV. Final remarks

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I.Introduction

• S.Weinberg listed three kinds of microscopic
  resonances
• (The Quantum Theory of Fields, Cambridge Univ.
  Press, 1995, Vol. I, p.159.)
• (1) Strong interaction particles decay through
  electroweak interaction, neutron, hyperons, pion,
  kion, etc.
• (2) Potential barrier tunnel, alpha decay
• (3) Statistical fluctuation, compound nucleus.

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• Hadronic strong decay,
• S. Weinberg did not discuss these resonance,
• such as rho, omega, Delta, etc. in his book.
• I think the slow down of the decay of these
• resonances are due to creation in their
  decay
• process.
• There should be another kind resonance for
• multi-quark system due to color confinement ,
• which is different from all of those four known
• microscopic resonances.

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II.Color confinement resonance
Color structure of nucleon obtained from lattice
QCD
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Simplified version of the color structure, color
string

• nucleon meson

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Color structure of multi-quark systems
Five quark
Six quark
Hadron phase
Multi-quark phase
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QCD quark benzene

• QCD interaction should be able to form a quark
  benzene consisted of six quarks

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• Two hadrons collide each other, if they are close
• enough there should be a possibility that two
• hadrons rearrange there internal color structure
  to
• transform from hadron phase to multi-quark phase.
• Once the multi-quark is formed, it can not
• decay to hadrons directly due to color
  confinement.
• It must transform to color singlet substructure
• first then decay, so there must be resonance
• related to these genuine multi-quark system.

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• The product cross section and the decay
• width of multi-quark system are determined by
• the transition interaction between color singlet
• hadrons and genuine color multi-quark systems.
• Up to now we dont have any reliable
• information about this transition interaction.
• One possibility is that such a transition from
• color singlet hadrons to genuine color
  multi-quark
• system only takes place at short distances, i.e.
• through violent high energy processes only. The
• color singlet hadrons like the inertial elements.

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III.QCD models of multi-quark resonances

• Multi-quark study is an experimental issue
• because up to now no reliable theoretical method.
• QCD does not deny multi-quark state.
• There have been many claims about the signals
• of multi-quark state, but up to now no one is
  well
• established.
• d(m2.06 GeV,G0.5 MeV, I 0 ) had been
  a
• hot topic in 1990s.
• penta-quark had been listed as a four star
• resonance in PDG and regarded as a renaissance
• of hadron spectroscopy, but seems to disappear
• again.

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• Some real exotic meson states had been
• discussed in PDG, such as , but seem
• not robust against the new measurements.
• Recently there are discussions about the
• tetraquark Dso(2317), Ds1(2460), X(3872),
• X(3943), Y(3940) and Z(3930). We dont
• know their fate yet.
• BES continuously report signals of enhancement
  near the p threshold.

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• Experiments very need reliable theoretical
• predictions of multi-quark states.
• The most promising theoretical method for
• multi-quark calculation should be the lattice
• QCD. However the penta-quark study shows
• that the present version of lattice QCD is not
• sophisticated enough to predict the multi-
• quark state reliably.

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• Chiral perturbation is good for low energy hadron
  interactions. Is it good enough to predict the
  transition between color singlet hadrons and
  genuine color multi-quark state?
• Quite possible it is not, because there is only
  colorless hadron degree of freedom included, at
  least not economic.

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• Chiral quark model, here I mean quark
• models including Goldstone boson exchange,
• describes existed NN and N-hyperon
• interaction data well. Is it good enough for
• the transition between color singlet hadrons
• and genuine color multi-quark state is also
• questionable.
• Here one has to worry about that if
• Goldstone boson is a good effective
• degree of freedom for short range interaction.
• (N.Isgur)

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Lattice QCD results of the quark interaction PRL
86(2001)18,90(2003)182001,hep-lat/0407001
Suppose these lattice QCD results are
qualitatively correct, then multi-quark system is
a many body interaction multi-channel coupling
problem.
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• QCD models usually use the two body interaction,
  is the two body interaction a good approximation
  of the many body interaction obtained from
  lattice QCD calculation?

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A comparative calculation of the ground state
energy of 2,4,6,9,12 quark systems by two body
confinement and color string are shown
below.(n3 baryon masses of N and ? has been
used to fix model parameters, Nuovo Cimento,
86A(1985) 283.)

• Model n2 4
  6 9 12
• 1. m0
• Bag 0.65 1.47
  2.16 3.07 3.90
• NR p2 0.63 1.54
  2.43 3.76 5.09
• p1 0.66 1.51
  2.34 3.59 4.83
• String 1 0.54 1.47
  2.26 3.42 4.97
• 
  2.25
• 1.5
  1.51
• 
  
• 2. m0.19 GeV
• NR p2 0.68 1.49
  2.29 3.49 4.69
• p1 0.69 1.48
  2.25 3.41 4.57
• String 1 0.64 1.46
  2.22 3.34 4.63
• 
  2.21
• 1.5
  1.48

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Ground state energy estimate of quark benzene by
string model
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• The above results seem to show that diagonal
  matrix
• elements of the two body confinement interaction
  are not too far
• from the string ones. So the two body confinement
  interaction
• might be a good approximation to be used to
  calculate the
• diagonal matrix elements of multi quark systems.
• However such a two body confinement interaction
  used
• to study the NN interaction can not get even a
  qualitatively
• correct ones, i.e., the important intermediate
  range
• attraction is missing even after taking into
  account many
• channel coupling.
• We suspect that the failure of the multi channel
  coupling
• calculation to obtain enough intermediate range
  NN attraction is
• due to the two body confinement interaction is
  not a good
• approximation of the transition interaction
  between different
• color structures.

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Quark delocalization, color screening model
(QDCSM)

• Based on the above understanding, we take
  Isgur model as our starting point, but modify it
  for multi quark systems by two new ingredients
• 1. The confinement interaction is
  re-parameterized aimed to take into account the
  effect of multi channel coupling,
• especially the genuine color channels
  coupling
• 2. The quark delocalization, similar to the
  electron delocalization in molecule, is
  introduced to describe the effect of mutual
  distortion.

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• Color screening
• qq interaction intra baryon
• inter baryon
  different
• the color configuration mixing and channel
  coupling have been taken into account to some
  extent.
• three gluons exchange 0 (intra baryon)
  
• 0
  (inter baryons), etc.

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Quark delocalization the parameter eis
determined variationally by the dynamics of the
quark systems. of quark distribution and
gluon distribution has been taken into account to
some extent.

• the self-consistency

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Parameters of QDCSM

• mumd313 MeV
• ms560 MeV
• a1.54
• b0.603 fm
• a25.13 MeV/fm2
• µ1.0 fm-2
• Almost the same as Isgur model except
• the color screening

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• This model, without invoking meson exchange
• except pion, with only one additional adjustable
• parameter-the color screening constant µ
• reproduce the deuteron properties, the NN, N?,
• NS scattering data.
• Moreover it explains the long standing facts
• 1. The molecular force is similar to nuclear
  force
• except the energy and length scale
• 2. The nucleus can be approximated as a nucleon
  system.

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• Deuteron
• Mass 1876 MeV
• Radius 1.9 fm
• PD 4.5

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Comparison between QDCSM and Salamanca chiral
quark model

• To study which effect has been included in QDCSM,
  we make the following comparative study
• Take the Salamanca model as a typical example
  of chiral quark model, where the NN short range
  interaction is attributed to quark structure of
  nucleon and gluon exchange interaction, while the
  long and intermediate range parts are attributed
  to
• exchange.

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Hamiltonian of Salamanca model
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Extended QDCSM

• Replace the OGE part of QDCSM by the OGE and OPE
  part of Salamanca model one get the
• Hamiltonian of the extended QDCSM.
• or alternatively, start from Salamanca model,
• drop their meson exchange term,
  
• replace their confinement term by the
• color screening one, one also get the
• Hamiltonian of the extended QDCSM.

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Salamanca and extended QDCSMmodel parameters
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Deuteron properties

• Salamanca model extended
  QDCSM

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NN scattering phase shifts
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• These comparisons show that the meson
  exchange of the Salamanca chiral quark model can
  be replaced by quark delocalization, i.e., the
  mutual distortion of interacting nucleons, and
  color screening.
• The meson exchange is known can be
  replaced by the quark gluon exchange.
• It is possible to describe the short and
  intermediate range NN interaction by quark gluon
  exchange instead of the meson.

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The match of QDCSM to chiral quark model is not
unique, but also limited.
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Different models fit the existed baryon
interaction data qualitatively,quantitatively
different.

• Yukawa meson exchange model
• (Bonn,Nijmegen,Paris)
• chiral perturbation theory
• quark model
• (bag R-matrix, chiral quark model, QDCSM, etc.)

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Different models give qualitatively different
predictions on multi-quark states

• Even limiting to quark models, which fit the
  existing NN, NY interaction data, these models
  still predict the multi-quark resonances quite
  different.
• It is bad for multi-quark state search,
• It is good that multi quark state, if
  established, will be very helpful in
  discriminating various quark models and
  understanding the low energy QCD.

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• Almost all quark models predict
• there should be strong attraction in the
• channel.

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• QDCSM predict in this case the six quarks are
  completely merged into one genuine six-quark one
  and we called it d. The estimated mass and
  width are
• M2170-2190 MeV, G6-8 MeV,
• the production cross sections are
• 0.2-10 nb/sr at 3 in ed scattering (PRC
  61(2000) 064001 62(2000) 018201.)
• 100 nb in pd scattering (PRC 39(1989)1889.)
• 100 nb/sr at 7 in pd scattering (PRC 57
• (1998) 1962 65(2002) 034012.)

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• However the new measurement of
• may need a resonance to explain the low
  mass
• enhancement.

These estimates seem to be ruled out by LAMPF
(PRL 49(1982) 255), COSY (PRL 78 (1997)1652,
85(2000)1819, nucl-ex/ 0407015), SATURNE (PRC
60(1999) 054001, 054002) measurement.
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• The ground state energy of quark benzene is close
  to that of d, so six quark benzene component
  should mix in the d with other components as
  shown before.
• Quark benzene should also effect the NN
  scattering,
• a new hidden color channel coupling to the
  usual color singlet channel.

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N? I1/2,Jp2,S-3

• QDCSM predicted another six quark state
• M(MeV) 2549-2557 threshold 2611
• ?(keV) 12-22
• Decay mode N?--gt ?? 1D2,3D2. D-wave decay, no
  strong
• ptensor interaction in N? channel, one quark must
  be
• exchanged to form ?? from N?. These factors all
  suppress
• the decay rate and make N? quite a narrow
  resonance.
• This state might be created in RHIC and detected
  by STAR through the reconstruction of ?? decay
  product.
• (WangPRL 59(87)627, 69(92)2901, PRC 51(95)3411,
  62(00)054007, 65(02)044003, 69(04)065207
• ZhangPRC 52(95)3393, 61(00)065204, NPA
  683(01)487.)

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Final remark

• QED interaction is simple, but the QED matter is
  almost countless QCD interaction is rich and
  varied, however the QCD matter is very limited.
• If the low energy QCD confinement interaction is
  color screened so perfect such that the residual
  interaction is so weak and leaves only one
  deuteron in the universe and no any other multi
  quark state, it is certainly interesting.
• it seems not the time to stop our search for
  multi quark state yet! Only if our understanding
  of quark confinement is qualitatively incorrect,
  otherwise color confinement multiquark resonance
  is unavoidable.

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Thanks