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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