Paul Sutcliffe

University of Kent

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.

The Skyrme model.

Skyrme parameters from spinning Skyrmions.

Multi-Skyrmions; shells & crystals.

New shapes for multi-Skyrmions.

Alpha particle model & cubes.

Conclusion.

.τπ iU Nonlinear pion theory:12 ππ

3 parameters, .,, meF

Topological solitons (Skyrmions); 33: SSU

Winding number, B, identified with Baryon number.

Use energy and length units of 2 & 4

eFe

F

Rescaled pion mass,

eF

mm 2

Two commonly used values; 526.0or ,0 mm

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

MeV138m

.526.0 giving MeV,108,84.4 mFe

MeV.186 valuealExperiment F

MeV276m MeV345m

.56.1 giving MeV,90 ,90.4 mFe

.0m

A problem with shells.

. like grows Size B . like grows size nucleiFor 31

B

0m

526.0m

shell

crystal

16.0for

winsCrystal

m

.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?

same orientation 900 twist lowers energy

Colour Skyrmions using pion field direction

no twist, face in 1200 twist, edge in

? ?

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.