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. Outline. I. Introduction II. Color confinement resonance III. QCD models of multi-quark
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Dept. of Physics, Nanjing Univ.
Joint Center for Particle-Nuclear Physics and Cosmology (CPNPC)
of NJU and PMO
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.
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
multi-quark system due to color confinement ,
which is different from all of those four known
Color structure of nucleon obtained from lattice QCD
enough there should be a possibility that two
hadrons rearrange there internal color structure to
transform from hadron phase to multi-quark phase.
decay to hadrons directly due to color confinement.
first then decay, so there must be resonance
related to these genuine multi-quark system.
width of multi-quark system are determined by
the transition interaction between color singlet
hadrons and genuine color multi-quark systems.
information about this transition interaction.
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.
because up to now no reliable theoretical method.
QCD does not deny multi-quark state.
of multi-quark state, but up to now no one is well
d’(m=2.06 GeV,Γ=0.5 MeV, I =0 ) had been a
hot topic in 1990’s.
penta-quark had been listed as a four star
resonance in PDG and regarded as a renaissance
of hadron spectroscopy, but seems to disappear
discussed in PDG, such as , but seem
not robust against the new measurements.
tetraquark Dso(2317), Ds1(2460), X(3872),
X(3943), Y(3940) and Z(3930). We don’t
know their fate yet.
predictions of multi-quark states.
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.
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
Goldstone boson is a good effective
degree of freedom for short range interaction.
Suppose these lattice QCD results are qualitatively correct, then multi-quark system is a many body interaction multi-channel coupling problem.
A comparative calculation of the ground state energy of 2, body interaction a good approximation of the many body interaction obtained from lattice QCD calculation?4,6,9,12 quark systems by two body confinement and color string are shown below.(n=3 baryon masses of N and ∆ has been used to fix model parameters, Nuovo Cimento, 86A(1985) 283.)
Model n=2 4 6 9 12
Bag 0.65 1.47 2.16 3.07 3.90
NR p=2 0.63 1.54 2.43 3.76 5.09
p=1 0.66 1.51 2.34 3.59 4.83
String =1 0.54 1.47 2.26 3.42 4.97
2. m=0.19 GeV
NR p=2 0.68 1.49 2.29 3.49 4.69
p=1 0.69 1.48 2.25 3.41 4.57
String =1 0.64 1.46 2.22 3.34 4.63
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.
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
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
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.
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.
Quark delocalization: model
the parameter εis determined variationally by the dynamics of the quark systems.
of quark distribution and gluon distribution has been taken into account to some extent.
Almost the same as Isgur model except
the color screening
except pion, with only one additional adjustable
parameter-the color screening constant μ
reproduce the deuteron properties, the NN, NΛ,
NΣ scattering data.
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.
Mass: 1876 MeV
Radius: 1.9 fm
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
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.
Yukawa meson exchange model
chiral perturbation theory;
(bag R-matrix, chiral quark model, QDCSM, etc.)
It is good that multi quark state, if established, will be very helpful in discriminating various quark models and understanding the low energy QCD.
there should be strong attraction in the
M~2170-2190 MeV, Γ~6-8 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 πd scattering (PRC 39(1989)1889.)
~100 nb/sr at 7 in pd scattering (PRC 57
(1998) 1962; 65(2002) 034012.)
These estimates seem to be ruled out by merged into one genuine six-quark one and we called it d*. The estimated mass and width are:
LAMPF (PRL 49(1982) 255),
COSY (PRL 78 (1997)1652, 85(2000)1819, nucl-ex/
SATURNE (PRC 60(1999) 054001, 054002) measurement.
may need a resonance to explain the low mass
a new hidden color channel coupling to the usual color singlet channel.
QDCSM predicted another six quark state
M(MeV) 2549-2557 threshold 2611
Decay mode N--> 1D2,3D2. D-wave decay, no strong
πtensor 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.
(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.)