Abstract
The magnetic moment of the ρ-meson is calculated in the framework of a low-energy effective field theory of the strong interactions. We find that the complex-valued strong interaction corrections to the gyromagnetic ratio are small leading to a value close to the real tree level result, gρ=2. This is in a reasonably good agreement with the available lattice QCD calculations for this quantity.
Highlights
Phenomenological low-energy chiral Lagrangians with vector mesons were considered already in the 1960s, see e.g. Refs. [1,2,3]
The chiral symmetry of QCD has been taken into account in the framework of effective field theories describing the interaction of vector mesons with pseudoscalars and baryons, see, e.g., Refs. [4,5,6,7,8,9,10,11,12,13,14]
We specify only those terms of the Lagrangian which are relevant for the calculation of the magnetic moment of the ρ-meson presented in this work: F2 Lπ = 4 Tr
Summary
Phenomenological low-energy chiral Lagrangians with vector mesons were considered already in the 1960s, see e.g. Refs. [1,2,3]. We start with the most general chirally invariant effective Lagrangian of vector mesons interacting with pions in the presence of external fields. It contains an infinite number of terms which respect the underlying symmetries of QCD. Based on renormalization-group arguments, this large scale can be expected to be given by masses of heavy hadrons multiplied with some numerical factors such as e.g. 4π Mρ Due to this assumption, only a finite number of terms of the effective Lagrangian has to be considered in our calculation. We further emphasize that while the considered EFT is self-consistent and leads to systematic perturbative results for physical quantities, we can only assume that the obtained results can be matched to the corresponding QCD observables. We apply the complex mass renormalization scheme [19,20] and calculate the magnetic moment of the vector meson and its pion mass dependence at one-loop order
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