SLIDE 1
Scale Dependence of Transversity Distributions and Tensor Charges of the Nucleon
Hanxin He China Institute of Atomic Energy
SLIDE 2 Contents
- 1. Quark distribution functions at leading twist and
their first moments--- nucleon’s charges *Helicity distributions and axial charges *Transversity distributions and tensor charges
- 2. Helicity distributions, axial charges and quark spin
comtribution to nucleon’s spin
- 3. Transversity distributions and tensor charges
* Theory estimates of tensor charges * Scale dependence: Perturbative evolutions * Scale dependence: Non-perturbative calculations
SLIDE 3 1.Quark distribution functions and their first moments
Longitudinally polarized Transversely polarized
SLIDE 4 Quark distribution functions at leading twist
Where q_f(x) ---find a quark parton probability in a nucleon
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Quark distribution functions at leading twist
The transversity distributions measure the difference of number of quarks(antiquarks) with transverse polarization parallel and antiparallel to the nucleon likewise polarized
SLIDE 6
SLIDE 7 Helicity distributions and axial charges
Where flavour singlet axial charge gives the quark spin contribution to nucleon’s spin =1.2601 =0.588 ( Flavor singlet )
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Transversity distributions and tensor charges
The flavor singlet tensor charge and isovector tensor charge can be defined
SLIDE 9 2.Axial Charges and Quark Spin Contribution to Nucleon Spin
All components are scale-dependent
SLIDE 10 * Nucleon spin sum rules
- -satisfying angular momentum
commutation relation
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Perturbative Evolutions of QCD angular momentum operators
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Quark spin contribution to nucleon spin
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Quark spin contribution to nucleon spin
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Quark spin contribution to nucleon spin
The measurement results are given at Q^2 =5 Gev^2
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- 3. Transversity Distributions and
Tensor Charges The first moment of
transversity distribution gives the tensor charge
SLIDE 17
Theory estimates of tensor charges —model calculation results
SLIDE 18 Theoretical Estimates of Tensor Charges
- QCD sun rules
- Lattice QCD
SLIDE 19
Tensor Charges in Effective Theory
SLIDE 20 Scale dependence of tensor Charge:
- QCD perturbative evolutions
Note that gluons do not enter the evolution equation for transversity distributions due to the chiral-odd property. The evolution equation of tensor charge at leading order
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* Perturbutive evolutions of tensor charges to next leading order(NLO)
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Perturbative evolution (to NLO)of flavor singlet tensor charge
SLIDE 23 * Effective theory analyses
QCD at low-energy is equivalent to an effective quark theory
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Axial charges and tensor charges in the effective theory
where
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Axial charges and tensor charges in the effective theory
Where m is dynamical mass
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Dynamically generated quark mass
QCD at low-energy scale is spontaneously chiral symmetry breaking, where quarks get dynamical mass
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Dynamically generated quark mass
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Axial charges of the proton and current quark spin contribution to proton spin
Which is exactly agreement with HERMES’s result.
The current quark spin contribution is
SLIDE 29 Quark spin contribution to nucleon spin
SLIDE 30 *Nonperturbative calculations:
Effective theory analyses of tensor charges
- Flavor singlet tensor charge of current quark
contributions (in the asymptotic limit)
SLIDE 31 Flavor singlet axial charge Flavor singlet tensor charge Isovector tensor charge
Where m is dynamic mass of quark in the chiral limit
SLIDE 32 Scale evolutions of tensor charge
Green line is given by effective theory, red line is given by AP equation of perturbative QCD.
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Flavor singlet tensor charge(green line) and axial charge(red line) with scale change
SLIDE 34 Conclusion(1)
- Tensor charges are strongly scale
dependent quantities.
- In the asymptotic limit, tensor charges are
For proton For neutron
SLIDE 35 Conclusion(2)
- Quark spin contribution to the nucleon spin is strongly
scale dependent
- Difference between tensor charge and axial charge
shows relativistic effects of quark motion in a nucleon
In asymptotic limit Non-relativistic limit
SLIDE 36
Scale dependence of flavor singlet tensor charge(green line) and axial charge(red line)
SLIDE 37 Measurements of transversity distributions and tensor charges
- HERMES, COMPASS and BELLE Collaborations
based on the combined global analysis of measured azimuthal asymmetries insemi-inclusive DIS(SIDIS) and those in processes
The results are(central values)
( From Phys.Rev.D75,054032(2007; arXiv:0809.3743 )
SLIDE 38 Measurements of transversity distributions and tensor charges
- Jlab measured the single target spin
asymmetry(SSA) in SIDIS
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