Transcript Review on Nucleon Spin Structure

High Energy Nuclear Physics
Fan Wang
Dept. of Phys. Nanjing Univ.
[email protected]
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+  0 ; n+   ;
n->n+  0 ; p+   .
• 3. Gell-mann and Zweig’s quark model
SU(3) symmetry:
baryon qqq; meson q q .
SU(6) symmetry:
1
B(qqq)=
[ ms (q3 )ms (q3 )  ma (q3 )ma (q3 )] .
2
color degree of freedom.
quark spin contribution to proton spin,
u 
4
1
; d   ; s  0.
3
3
nucleon magnetic moments.
p
3

n
2
• 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 q3 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 a0= 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, qq 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 Lq .
• 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 qq creation and
annihilation contribution, which also takes back
the missing spin.
• It is most interesting to note that the relativistic
correction and the qq 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 Lq and J g 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
3
q qq q, q q q, q
6
Dibaryon resonance signals
QCD model “prediction”
• Recently we did a coupled channel
calculations and found the N 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