# High Energy Nuclear Physics Fan Wang Dept. of Phys. Nanjing Univ.

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High Energy Nuclear Physics Fan Wang Dept. of Phys. Nanjing Univ. fgwang@chenwang.nju.edu.cn

Outline Introduction I. Hadron structure I.1 Nucleon internal structure I.2 Nucleon Spin Structure I.3 Gauge invariance and canonical commutation relation of nucleon spin operators II. Hadron interaction II.1 Chiral perturbation II.2 Lattice approach II.3 QCD model approach III. Summary

Introduction Subjects of High Energy Nuclear Physics: 1.Hadron structure. 2.Hadron interaction. 3.Exotics. 4.Hadron and Quark-gluon matter. S.Olson will talk about the new hadron states, Y.G. Ma will talk about the heavy ion physics, I suppose I can leave the 3 and 4 subjects to them.

I. Hadron structure The most studied hadron structure is the nucleon, because it is the only stable one and so can be used as target for exp. study. Not only the em form factors have been measured but also the structure functions are measured. Even the flavor contents are separated. Good summary existed, such as J.P.Chen at CCAST.

I.1 Nucleon Internal Structure There are large amount of experimental data of nucleon internal structure, but no theory. Lattice QCD can calculate part of the observables of nucleon internal structure but even the fundamental ones are not decisive. Such as nucleon spin, magnetic momentum,… QCD models play decisive role.

I.2 Nucleon Spin Structure There are various reviews on the nucleon spin structure, such as B.W. Filippone & X.D. Ji, Adv. Nucl. Phys. 26(2001)1. S.D. Bass, Rev. Mod. Phys. 77,1257(2005). We will not repeat those but discuss two problems related to nucleon spin which we believe where confusions remain. 1.It is still a quite popular idea that the polarized deep inelastic lepton-nucleon scattering (DIS) measured quark spin invalidates the constituent quark model (CQM). I will show that this is not true. After introducing minimum relativistic modification, as usual as in other cases where the relativistic effects are introduced to the non-relativistic models, the DIS measured quark spin can be accomodated in CQM. 2.One has either gauge invariant or non-invariant decomposition of the total angular momentum operator of nucleon, a quantum gauge field system, but one has no gauge invariant and canonical commutation relation of the angular momentum operator both satisfied decomposition.

The question is that do we have to give up the two fundamental requirements, gauge invariance and canonical commutation relation for the individual component of the nucleon spin, to be satisfied together and can only keep one, such as gauge invariance, but the other one, the canonical commutation relation is violated Or both requirements can be kept somehow?

History of Nucleon Internal Structure 1. Nucleon anomalous magnetic moment Stern’s measurement in 1933; first indication of nucleon internal structure. 2. Nucleon rms radius Hofstader’s measurement of the charge and magnetic rms radius of p and n in 1956; Yukawa’s meson cloud picture of nucleon, p->p+ ; n+ ; n->n+ ; p+.

3. Gell-mann and Zweig’s quark model SU(3) symmetry: baryon qqq; meson q. SU(6) symmetry: B(qqq)=. color degree of freedom. quark spin contribution to proton spin, nucleon magnetic moments.

SLAC-MIT e-p deep inelastic scattering Bjorken scaling. quark discovered. there are really spin one half, fractional charge, colorful quarks within nucleon. c,b,t quark discovered in 1974, 1977,1997 complete the history of quark discovery. there are only three quark generations.

There is no proton spin crisis but quark spin confusion The DIS measured quark spin contributions are: While the pure valence q 3 S-wave quark model calculated ones are:.

It seems there are two contradictions between these two results: 1.The DIS measured total quark spin contribution to nucleon spin is about one third while the quark model one is 1; 2.The DIS measured strange quark contribution is nonzero while the quark model one is zero.

To clarify the confusion, first let me emphasize that the DIS measured one is the matrix element of the quark axial vector current operator in a nucleon state, Here a 0 = Δu+Δd+Δs which is not the quark spin contributions calculated in CQM. The CQM calculated one is the matrix element of the Pauli spin part only.

The axial vector current operator can be expanded as

Only the first term of the axial vector current operator, which is the Pauli spin part, has been calculated in the non-relativistic quark models. The second term, the relativistic correction, has not been included in the non-relativistic quark model calculations. The relativistic quark model does include this correction and it reduces the quark spin contribution about 25%. The third term, creation and annihilation, will not contribute in a model with only valence quark configuration and so it has never been calculated in any quark model as we know.

An Extended CQM with Sea Quark Components To understand the nucleon spin structure quantitatively within CQM and to clarify the quark spin confusion further we developed a CQM with sea quark components,

Where does the nucleon get its Spin As a QCD system the nucleon spin consists of the following four terms,

In the CQM, the gluon field is assumed to be frozen in the ground state and will not contribute to the nucleon spin. The only other contribution is the quark orbital angular momentum. One would wonder how can quark orbital angular momentum contribute for a pure S-wave configuration?

The quark orbital angular momentum operator can be expanded as,

The first term is the nonrelativistic quark orbital angular momentum operator used in CQM, which does not contribute to nucleon spin in a pure valence S-wave configuration. The second term is again the relativistic correction, which takes back the relativistic spin reduction. The third term is again the creation and annihilation contribution, which also takes back the missing spin.

It is most interesting to note that the relativistic correction and the creation and annihilation terms of the quark spin and the orbital angular momentum operator are exact the same but with opposite sign. Therefore if we add them together we will have where the, are the non-relativistic part of the quark spin and angular momentum operator.

The above relation tell us that the nucleon spin can be either solely attributed to the quark Pauli spin, as did in the last thirty years in CQM, and the nonrelativistic quark orbital angular momentum does not contribute to the nucleon spin; or part of the nucleon spin is attributed to the relativistic quark spin, it is measured in DIS and better to call it axial charge to distinguish it from the Pauli spin which has been used in quantum mechanics over seventy years, part of the nucleon spin is attributed to the relativistic quark orbital angular momentum, it will provide the exact compensation missing in the relativistic “quark spin” no matter what quark model is used. one must use the right combination otherwise will misunderstand the nucleon spin structure.

I.3 Gauge Invariance and canonical Commutation relation of nucleon spin operator Up to now we use the following decomposition,

Each term in this decompositon satisfies the canonical commutation relation of angular momentum operator, so they are qualified to be called quark spin, orbital angular momentum, gluon spin and orbital angular momentum operators. However they are not gauge invariant except the quark spin.

We can have the gauge invariant decomposition,

However and no longer satisfy the canonical commutation relation of angular momentum operator and so they are not the quark orbital angular momentum and gluon total angular momentum. One can not have gauge invariant gluon spin and orbital angular momentum operator separately.

How to reconcile these two fundamental requirements, the gauge invariance and canonical commutation relation? One choice is to keep gauge invariance and give up canonical commutation relation. This choice has misleading the high energy spin physics study about 10 years. Is this the unavoidable choice?

Gauge invariance and angular momentum algebra both satisfied decomposition QED arXiv:0709.3649[hep-ph]

QCD arXiv:0709.1284[hep-ph]

The present parton distribution is based on wrong quark and gluon momentum operators, the quark /gluon share the nucleon momentum half/half need to be studied further. The present measurement of gluon spin has no theoretical sound basis. Preliminary results show that gluon contribution to nucleon spin is not large. The nucleon spin is mainly carried by quark spin and orbital angular momentum. The quark orbital angular momentum measurement is very expected.

I.4 Hydrogen atom has the same problem Hydrogen atom is a U(1) gauge field system, where we always use the canonical momentum, orbital angular momentum, they are not the gauge invariant ones. Even the Hamiltonian of the hydrogen atom used in Schroedinger equation is not a gauge invariant one. One has to understand their physical meaning in the same manner as we suggested above. Coulomb gauge results are physical and gauge invariant. The multipole radiation analysis is physical and gauge invariant.

II.Hadron Interaction Hadron interaction includes baryon-baryon, baryon-meson, meson-meson interactions. We will mainly talk about baryon-baryon interactions, because NN interaction has the most abundant experimental data.

II.1 Chiral perturbation One of the important feature of low energy QCD is the chiral symmetry spontaneous breaking, pion, even the whole pseudo-scalar mesons, is Goldstone boson. The low energy (<300 MeV) hadron interactions can be described by ChPT. The NNNL order ChPT describes the NN interaction well. However it is almost impossible to extend ChPT to the resonance energy region.

II.2 Lattice QCD approach Lattice QCD calculations for B-B meson and NN interactions have been done by different groups. One can hope finally we will be able to obtain the hadron interaction from QCD. The present lattice QCD can not calculate the broad resonance because it is not a single eigen state but a collective state.

II.2 Lattice QCD Lattice QCD has started the calculation of NN interaction

II.3 QCD model approach There are different QCD model approaches *R-matrix approach with bag model core; Skyrmion soliton model; Goldstone boson exchange model; *chiral quark model (ChQM); *Quark delocalization color screening model (QDCSM).

These QCD models, especially the last two, ChQM and QDCSM describe the NN interaction qualitatively well, quantitatively not as well as one boson meson exchange model and chiral perturbation. More interesting is if these QCD models can study something new? For example, the exotics

Dibaryon resonance signals

QCD model “prediction” Recently we did a coupled channel calculations and found the and the channel coupling will introduce the resonances in NN scattering, a typical Feshbach resonance or the so called CDD resonances.

A few lessons 1.The channel coupling effects are very large (few hundred MeV) in cases. 2. The bare quark model calculations might be misleading not only for exotics but also for hadron resonances. 3. The missing hadrons might be not missing but not exist due to the coupling to open channels.

VI. Summary 1.The DIS measured quark spin is better to be called quark axial charge, it is not the quark spin calculated in CQM. 2.One can either attribute the nucleon spin solely to the quark Pauli spin, or partly attribute to the quark axial charge partly to the relativistic quark orbital angular momentum. The following relation should be kept in mind,

3. The nucleon internal structure, especially the nucleon spin structure study is misleading by the wrong quark orbital angular momentum, gluon spin, gluon orbital angular momentum operators. 4. The chiral perturbation is almost impossible to extend to the resonance energy region. The present Lattice QCD is impossible to calculate the broad resonance. Quark model is easy to extend to the resonance energy region and almost the unique one for the study of broad resonances temporary. However it is a model!

5. The bare quark model calculated hadron spectroscopy should be upgraded to include the open channel coupling, especially for the exotic calculations. The missing resonance and the rarity of exotics might be due to the coupling to the scattering hadron channels.

Thanks

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