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 resonances IV. Final remarks

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.

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.

II.Color confinement resonance Color structure of nucleon obtained from lattice QCD

Simplified version of the color structure, color string nucleon meson

Color structure of multi-quark systems Hadron phase Multi- quark phase Five quarkSix quark

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

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.

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 don’t 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.

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’(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 again.

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 don’t know their fate yet. BES continuously report signals of enhancement near the p threshold.

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.

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.

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)

Lattice QCD results of the quark interaction PRL 86(2001)18,90(2003)182001,hep-lat/ Suppose these lattice QCD results are qualitatively correct, then multi-quark system is a many body interaction multi-channel coupling problem.

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?

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. (n=3 baryon masses of N and ∆ has been used to fix model parameters, Nuovo Cimento, 86A(1985) 283.) Model n= m=0 Bag NR p= p= String = = m=0.19 GeV NR p= p= String = =

Ground state energy estimate of quark benzene by string model

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.

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.

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.

Quark delocalization: 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. the self-consistency

Parameters of QDCSM m u =m d =313 MeV m s =560 MeV α=1.54 b=0.603 fm a=25.13 MeV/fm 2 μ=1.0 fm -2 Almost the same as Isgur model except the color screening

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, NΛ, NΣ 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.

Deuteron Mass: 1876 MeV Radius: 1.9 fm P D : 4.5%

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.

Hamiltonian of Salamanca model

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.

Salamanca and extended QDCSM model parameters

Deuteron properties Salamanca model extended QDCSM

NN scattering phase shifts

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.

The match of QDCSM to chiral quark model is not unique, but also limited.

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.)

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.

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

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: M~ MeV, Γ~6-8 MeV, the production cross sections are ~ nb/sr at 3 in ed scattering (PRC 61(2000) ; 62(2000) ) ~100 nb in πd scattering (PRC 39(1989)1889.) ~100 nb/sr at 7 in pd scattering (PRC 57 (1998) 1962; 65(2002) )

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/ ), SATURNE (PRC 60(1999) , ) measurement.

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.

QDCSM predicted another six quark state M(MeV) threshold 2611  (keV) Decay mode N  -->  1 D 2, 3 D 2. 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.) N  I=1/2,J p =2 +,S=-3

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.

Thanks