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Universal Binding and Recoil Corrections to Bound State $g$-Factors

The leading relativistic and recoil corrections to bound state $g$-factors of particles with arbitrary spin are calculated. It is shown that these corrections are universal for any spin and depend only on the free particle gyromagnetic ratios. To prove this universality we develop NRQED for charged particles with an arbitrary spin. The coefficients in the NRQED Hamiltonian for higher spin particles are determined only by the requirements of Lorentz invariance and local charge conservation in the respective relativistic theory. For spin one charged particles the NRQED Hamiltonian follows from the renormalizable QED of the charged vector bosons. We show that universality of the leading relativistic and recoil corrections can be explained with the help of the Bargmann-Michael-Telegdi equation.