Aspects of Skyrmions
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Paul Sutcliffe
University of Kent
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Work with Richard Battye, Michael Atiyah, Steffen Krusch, Nick Manton.
Skyrmions and the pion mass,Battye & Sutcliffe, Nucl. Phys. B705, 384 (2004).
Skyrmions, instantons, mass and curvature,Atiyah & Sutcliffe, Phys. Lett. B605, 106 (2005).
Spinning Skyrmions and the Skyrme parameters,Battye, Krusch & Sutcliffe, hep-th/0507279.
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The Skyrme model.
Skyrme parameters from spinning Skyrmions.
Multi-Skyrmions; shells & crystals.
New shapes for multi-Skyrmions.
Alpha particle model & cubes.
Conclusion.
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.τπ iU Nonlinear pion theory:12 ππ
3 parameters, .,, meF
Topological solitons (Skyrmions); 33: SSU
Winding number, B, identified with Baryon number.
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Use energy and length units of 2 & 4
eFe
F
Rescaled pion mass,
eF
mm 2
Two commonly used values; 526.0or ,0 mm
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B=1. )ˆ)(exp( τx rifU
.0)( and ,)0( with,)( ffrf
Conserved quantities; spin J, and isospin I.
Isospin rotation
For B=1 Skyrmion, J=I.
Adkins, Nappi & Witten (1983); rigid body approximation.
MeV1232 massdelta spin withSkyrmion
MeV939 mass nucleon spin withSkyrmion
:energies matchingby and Fix
23
21
eF MeV.138or ,0 mm
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MeV138m
.526.0 giving MeV,108,84.4 mFe
MeV.186 valuealExperiment F
MeV276m MeV345m
.56.1 giving MeV,90 ,90.4 mFe
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.0m
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A problem with shells.
. like grows Size B . like grows size nucleiFor 31
B
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0m
526.0m
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shell
crystal
16.0for
winsCrystal
m
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.a triangle on particles- 3 is of model good A 12 Cron.a tetrahed on particles- 4 is O of model good A 16
The Skyrmion version of this is configurations formedfrom B=4 cubes.
B=12 Triangular symmetry.Are there 3 cubes here?
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same orientation 900 twist lowers energy
Colour Skyrmions using pion field direction
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no twist, face in 1200 twist, edge in
? ?
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Skyrme parameters should be changed from the values commonly used.
A large pion mass changes the shapes of multi-Skyrmions.
Symmetric shells are replaced by less symmetric non-spherical structures.
Crystal chunks and cubes may play an important role.
More field simulations currently in progress.
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