Mainz 2004 – wissenschaftliches Programm

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T: Teilchenphysik

T 605: Vermischtes

T 605.2: Vortrag

Donnerstag, 1. April 2004, 10:45–11:00, HS VI

Platonic Sphalerons — •Kari Myklevoll, Burkhard Kleihaus, and Jutta Kunz — Institut für Physik, Universität Oldenburg, Postfach 2503, D-26111 Oldenburg

The standard model does not absolutely conserve baryon and lepton number. In the electroweak interactions fermion number violation is associated with static, unstable solutions of the field equations, sphalerons, representing the top of energy barriers between topologically distinct vacua.

We here consider sphaleron solutions in Weinberg-Salam theory, which possess only discrete symmetries. Related to rational maps of degree N, these sphalerons carry fermion number N/2. The energy density of these sphalerons reflects their discrete symmetries. We present an N=3 sphaleron with tetrahedral energy density, an N=4 sphaleron with cubic energy density, and an N=5 sphaleron with octahedral energy density.

The modulus of the Higgs field of the platonic sphalerons has an intriguing node structure. The tetrahedral sphaleron, for instance, has five nodes, four located on the diagonals close to the maxima of the energy density, and one located at the origin, suggesting its interpretation as a superposition of four sphalerons (N=1) located at the nodes along spatial diagonals and one antisphaleron (N=−1) located at the origin.