Review on Nucleon Spin Structure. X.S.Chen, Dept. of Phys., Sichuan Univ. T.Goldman, TD, LANL X.F.Lu, Dept. of Phys., Sichuan Univ. D.Qing, CERN Fan Wang, Dept. of Phys. Nanjing Univ. Outline. Introduction There is no proton spin crisis but quark spin confusion
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Review on Nucleon Spin Structure
X.S.Chen, Dept. of Phys., Sichuan Univ.
T.Goldman, TD, LANL
X.F.Lu, Dept. of Phys., Sichuan Univ.
D.Qing, CERN
Fan Wang, Dept. of Phys. Nanjing Univ.
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.
One can keep both requirements,
The DIS measured quark spin contributions are:
While the pure valence q3 S-wave quark model calculated ones are:
.
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.
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
where the , are the non-relativistic part of
the quark spin and angular momentum operator.
exact compensation missing in the relativistic “quark spin” no matter what quark model is used.
however its matrix element in a J=0 state,
is SO(3) rotational invariant.
Where
and
have been used in the derivation. Taking into account that the nucleon ground state has fixed J, we have
This confirms our qualitative argument that the matrix element for a color singlet nucleon ground state of the gauge variant part is identically zero and therefore the matrix element of the gauge non-invariant quark orbital angular momentum operator for a nucleon ground state is gauge invariant.
equation is not a gauge invariant one.
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.We suggest to use the canonical momentum, angular momentum, etc.
in hadron physics as have been used
in atomic, nuclear physics so long a time, but should be noted that only their matrix elements for selected states of these operators are gauge invariant and measurable ones.