Magnetic Polarizability of Hadrons from Dynamical Configurations
Scott Moerschbacher
The George Washington University
Lattice 2008, July 14
Outline of Talk
Magnetic Polarizability Physics Lattice Calculation Results of Simulations Future Possibilities
Classical Polarizability
The polarizability is the proportionality constant between the induced dipole moment and the field.
0Bm M
diaM
paraM
202
1BU M
Lattice Approach
CP-PACS Dynamical Configurations:
Simulation Parameters
Lattice Approach
Nucleon interpolating fields
Correlation Functions
Background Field Method
Introduce the magnetic field as a phase onto the lattice links
)(e)()( xiqaAxUxU
iqAigG
Covariant Derivative:
Linear vs. exponential
Do we linear-ize??
Extraction of Polarizability
Expand the mass shift as a polynomial in the field:
Lat 16—EMass Shifts—Linear
Lat 16—EMass Shifts—Linear
Lat 16—EMass Shifts—Exp
Lat 16—EMass Shifts—Exp
Lat 12—Polarizabilty—Exp
Lat 12—Polarizabilty—Linear
Lat 16—Polarizabilty—Linear
Lat 16—Polarizabilty—Exp
Conclusions…
What have we learned?? a=0.2 is too coarse Perhaps the field should be introduced as
an exponential phase…
What next??
Better statistics Introduce the field at the point of
configuration generation And of coarse.. Smaller spacings and
quark masses..
Extra Slides…
Extra Slides… Extra Slides… Extra Slides…
Lat 16—Polarizabilty—Exp
Proton Polarizability--Linear
Mass Shifts--Exponential
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