Compton Scattering Sum Rules for Massive Vector Bosons

Lagrangian in the limit of natural values. At tree level, the GDH can be confirmed.
However, at one-loop we find that the effective Lagrangian is not complete. An
additional self-interaction tadpole is needed to derive the anomalous magnetic moment.
Additionally, for the quadrupole sum rule, it is found that even at tree level polarization
effects might give a contribution, since the QSR yields a finite, non-zero result.
The SU(2) Yang-Mills ansatz and the resulting tadpole contribution is given in chapter 5,
where the complete Yang-Mills result at one-loop is discussed. As a concluding remark,
the anomalous magnetic moment for j = 1 is compared qualitatively to the value
for spin 1 /2. The relation to the experimental results for deuteron and W bosons is
commented upon.
The conclusion is followed by an appendix containing Feynman rules for both theories,
the vertex diagrams, and some helpful references on the handling of loop integrals.
Tools
In the course of this work, two major tools have been used in the calculation process.
Besides manual calculations, we used Nikhef’s FORM algebra manipulation program
[Ver00] and Wolfram’s Mathematica 6 suite. FORM has primarily been used to
derive the structures used in this work, i.e. the diagrams and the LETs, as well as
to confirm the Ward-Takahashi-identities. In Mathematica we derived the amplitude
decompositions and identified the LETs with the appropriate dispersion relations. The
sum rule tree-level integrations were done in Mathematica, which we also used to plot
the integrands.
For the creation of this work free software was used where possible. The thesis was
written in L A TEX using Kile and Aquamacs Emacs. The document is based on a
template by T. Beranek. It uses the KOMA-Script scrbook class. Also, the physicsrelated
TEX package PhysTEX by F. Jung [Jun02] was used, with some personal
extensions. All Feynman diagrams and other illustrations were either created in
JaxoDraw [BT04, BCKT08] or done using PGF and TikZ [Tan06].
Notation and Conventions
Throughout this thesis, the Einstein summation convention is used, i.e. summation is
implied over indices which appear twice. If not mentioned otherwise, latin letters imply
ix