Many-body study of the $g$ factor in boronlike argon

Highly accurate measurements of the $g$ factor of boronlike Ar are currently implemented within the ARTEMIS experiment at GSI (Darmstadt, Germany) and within the ALPHATRAP experiment at the MPIK (Heidelberg, Germany). A comparison with the corresponding theoretical predictions will allow one to test the modern methods of bound-state QED. However, at least three different theoretical values of the $g$ factor have been published up to date. The systematic study of the $g$-factor value of ${}^{40}\mathrm{Ar}^{13+}$ in the ground $\left[{\left(1s\right)}^2{\left(2s\right)}^{2}2p^1\right]{}^{2}P_{1/2}$ and the first excited $\left[{\left(1s\right)}^2{\left(2s\right)}^{2}2p^1\right]{}^{2}P_{3/2}$ states is performed within the high-order coupled cluster and configuration interaction theories up to the full configuration interaction treatment. Correlation contributions are discussed and results are compared with previous studies.