High Energy Nuclear Physics

1
High Energy Nuclear Physics

• Fan Wang
• Dept. of Phys. Nanjing Univ.
• fgwang_at_chenwang.nju.edu.cn

2
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

3
Introduction

• Subjects of High Energy Nuclear Physics
• Hadron structure.
• Hadron interaction.
• Exotics.
• 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.

4
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.

5
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.

6
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.

7

• 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?

8
History of Nucleon Internal Structure

• 1. Nucleon anomalous magnetic moment
• Sterns measurement in 1933
• first indication of nucleon internal
  structure.
• 2. Nucleon rms radius
• Hofstaders measurement of the charge
• and magnetic rms radius of p and n in
  1956
• Yukawas meson cloud picture of nucleon,
• p-gtp n
• n-gtn p .

9

• 3. Gell-mann and Zweigs 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.

10

• 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.

11
There is no proton spin crisis but quark spin
confusion

• The DIS measured quark spin contributions are

While the pure valence q3 S-wave quark model
calculated ones are
.
12

• 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.

13

• 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 a0 ?u?d?s which is not the quark spin
contributions calculated in CQM. The CQM
calculated one is the matrix element of the Pauli
spin part only.
14
The axial vector current operator can be expanded
as
15

• 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.

16
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,

17
(No Transcript)
18
(No Transcript)
19
(No Transcript)
20
(No Transcript)
21
(No Transcript)
22
Where does the nucleon get its Spin

• As a QCD system the nucleon spin consists of the
  following four terms,

23

• 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?

24

• The quark orbital angular momentum operator can
  be expanded as,

25

• 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.

26

• 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.

27

• 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.

28
I.3 Gauge Invariance and canonical Commutation
relation of nucleon spin operator

• Up to now we use the following decomposition,

29

• 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.

30

• We can have the gauge invariant decomposition,

31

• 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.

32

• 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?

33
Gauge invariance and angular momentum algebra
both satisfied decomposition

• QED arXiv0709.3649hep-ph

34
(No Transcript)
35

• QCD arXiv0709.1284hep-ph

36
(No Transcript)
37

• 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.

38
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.

39
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.

40
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 (lt300 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.

41
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.

42
II.2 Lattice QCD

• Lattice QCD has started the calculation of
• NN interaction

43
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).

44

• 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

45
Dibaryon resonance signals
46
(No Transcript)
47
(No Transcript)
48
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.

49
(No Transcript)
50
(No Transcript)
51
(No Transcript)
52
(No Transcript)
53
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.

54
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,

55

• 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!

56

• 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.

57
Thanks