  We consider a flux-threaded Aharonov-Bohm ring with an embedded quantum dot
coupled to two normal leads. The local Rashba spin-orbit interaction acting on
the dot electrons leads to a spin-dependent phase factor in addition to the
Aharonov-Bohm phase caused by the external flux. Using the numerical
renormalization group method, we find a splitting of the Kondo resonance at the
Fermi level which can be compensated by an external magnetic field. To fully
understand the nature of this compensation effect, we perform a scaling
analysis and derive an expression for the effective magnetic field. The
analysis is based on a tight-binding model which leads to an effective Anderson
model with a spin-dependent density of states for the transformed lead states.
We find that the effective field originates from the combined effect of Rashba
interaction and magnetic flux and that it contains important corrections due to
electron-electron interactions. We show that the compensating field is an
oscillatory function of both the spin-orbit and the Aharonov-Bohm phases.
Moreover, the effective field never vanishes due to the particle-hole symmetry
breaking independently of the gate voltage.
