Compton Scattering Sum Rules for Massive Vector Bosons

Introduction
Historical Background
In the mid-1960s, S.D. Drell and A.C. Hearn, and, independently, S.B. Gerasimov,
developed a relation to determine the anomalous magnetic moment from polarized
Compton scattering (CS) on nuclei in the framework of dispersion theory, the GDH
sum rule (in short, GDH) [Ger66, DH66]. Sum rules are a special kind of dispersion
relations. Dispersion relations are useful as it is possible e.g. to calculate 2-loop
contributions from pure one-loop cross sections (c.f. [Kni96]). In case of the GDH, the
sum rule allows the exact calculation of the anomalous magnetic moment from the
measured cross section, i.e. connect a low-energy constant to a dynamical spectral
integral.
The GDH sum rule has later been extended to particles of arbitrary spin [Lin71].
With the advent of quantum chromodynamics (QCD) as a complete theory of strong
interactions, however, interest in the dispersion theoretic approach has languished. In
recent years, the GDH has come to new fame. New experiments, e.g. at the Mainz
Mikrotron facility (MAMI) [Tho06], and theoretical predictions, e.g. by L. Tiator
[Tia00, Tia02] and D. Drechsel et al. [DKT01], further solidified the validity of the
sum rule.
In 1966, Hosoda and Yamamoto showed [HY66] that the sum rule can also be
gained from equal-times current algebra theory. The dispersion theoretic approach
however is stronger as the current algebra approach relies on some assumptions which
cannot be proven generally [ibid., footnote 2]. For this reason, we will focus solely on
the dispersion theory approach in this work.
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