Nucleon Polarizabilities: Theory and Experiments. Chung-Wen Kao Chung-Yuan Christian University. 2007.3 .30. NTU. Lattice QCD Journal Club. What is Polarizability?. Excited states. Electric Polarizability. Magnetic Polarizability.
Chung-Yuan Christian University
2007.3 .30. NTU. Lattice QCD Journal Club
Polarizability is a measures of rigidity of a system and deeply relates with the excited spectrum.
Forward spin polarizability
Backward spin polarizability
LO are determined by e, M κ
NLO are determined by
4 spin polarizabilities, first defined by Ragusa
Relate the real part amplitudes to the imaginary part
By Optical Theorem :
Therefore one gets following dispersion relations:
Expanded by incoming photon energy ν:
Comparing with the low energy expansion of forward amplitudes:
Forward virtual virtual Compton scattering (VVCS) amplitudes
h=±1/2 helicity of electron
The elastic contribution can be calculated from
the Born diagrams with Electromagnetic vertex
Expanded by incoming photon energy ν
Combine low energy expansion and dispersion relation one gets 4 sum rules
On spin-dependent vvcs amplitudes:
Generalized GDH sum rule
Generalized spin polarizability sum rule
measure the cross sections of Compton scattering to extract polarizabilities.
Left-hand and right-hand quark:
QCD Lagrangian is invariant if
Massless QCD Lagrangian has SU(2)LxSU(2)Rchiral symmetry.
QCD Lagrangian is invariant if θR=θL.
Therefore SU(2)LXSU(2)R →SU(2)V, ,if mu=md
SU(2)A is broken by the quark mass
Spontaneous symmetry breaking:
a system that is symmetric with respect to some symmetry group goes into a vacuum state that is not symmetric. The system no longer appears to behave in a symmetric manner.
V(φ)=aφ2+bφ4, a<0, b>0.
Mexican hat potential
U(1) symmetry is lost if one expands around the degenerated vacuum!
Furthermore it costs no energy to rum around the orbit →massless mode exists!! (Goldstone boson).
Start point of an EFT for pions.
an EFT for pions.
F=93 MeVisthe pion decay constant.
Lagrangian start fromL(2).
number of loop.
LO HBChPT (Bernard, Kaiser and Meissner , 1991)
LO HBChPT including Δ(1232)
Linearly polarized incoming photon+ unpolarized target:
Small energy, small cross section;
Large energy, large higher order terms contributes
LO+NLO HBChPT (Kao, Vanderhaeghen, 2002)
LO+NLO Manifest Lorentz invariant ChPT (Bernard, Hemmert Meissner
LO+NLO MLI ChPT
Kumar, Birse, McGovern (2000)
Plan experiments by HIGS, TUNL.
Detmold, Tiburzi, Walker-Loud, 2003
Background field method:
Two-point correlation function
Constant electric field at X1 direction
Polarizabilities, both theory and experiment.