Evaluation of $\mathit{CP}$ violation in ${\mathrm{HfF}}^{+}$

CP violation effects produced by the nuclear magnetic quadrupole moment (MQM), electron electric dipole moment (EDM), and scalar-pseudoscalar nucleus-electron neutral current (SP) interaction in ${}^{177}\mathrm{Hf}{}^{19}\mathrm{F}^{+}$ and ${}^{179}\mathrm{Hf}{}^{19}\mathrm{F}^{+}$ are calculated. The role of the hyperfine interaction is investigated. It is shown that the MQM shift can be distinguished from the electron EDM and SP ones due to the implicit dependence of the MQM shift on the hyperfine sublevel. The MQM effect is expressed in terms of the proton (EDM), QCD vacuum angle $\theta$, and quark chromo-EDMs.

Figure 1

Calculated MQM energy shifts (in units of $M{W}_M$) for $J=1$, $H^3{\mathrm{\Delta }}_1{}^{177}\mathrm{Hf}{}^{19}\mathrm{F}^{+}$ as functions of $A_{\parallel }^{\mathrm{Hf}}$. Thick solid red, thick dashed green, and thick dotted blue lines correspond to $F_1=9/2$, $F_1=7/2$, and $F_1=5/2$, respectively. Horizontal thin solid red, thin dashed green, and thin dotted blue lines correspond to values obtained by Eq. (10). Vertical black lines correspond to the values $A_{\parallel }^{\mathrm{Hf}}=0$ and $A_{\parallel }^{\mathrm{Hf}}=-1429$ MHz obtained in calculations. $E=20$ V/cm, $eQ{q}_0=0$, and $eQ{q}_2=0$ in calculations.

Figure 2

Calculated MQM energy shifts (in units of $M{W}_M$) for $J=1$, $H^3{\mathrm{\Delta }}_1{}^{177}\mathrm{Hf}{}^{19}\mathrm{F}^{+}$ as functions of $eQ{q}_0$. Solid red, dashed green, and dotted blue lines correspond to $F_1=9/2$, $F_1=7/2$, and $F_1=5/2$, respectively. Vertical black lines correspond to the values $eQ{q}_0=0$ and $eQ{q}_0=-2100$ MHz obtained in calculations. $E=20$ V/cm, $A_{\parallel }^{\mathrm{Hf}}=-1429$ MHz, and $eQ{q}_2=0$ in calculations.

Figure 3

Calculated MQM energy shifts (in units of $M{W}_M$) for $J=1$, $H^3{\mathrm{\Delta }}_1{}^{177}\mathrm{Hf}{}^{19}\mathrm{F}^{+}$ as functions of $eQ{q}_2$. Solid red, dashed green, and dotted (blue) lines correspond to $F_1=9/2$, $F_1=7/2$, and $F_1=5/2$, respectively. $E=4$, 20, and 100 V/cm, $A_{\parallel }^{\mathrm{Hf}}=-1429$ MHz, and $eQ{q}_0=-2100$ MHz in calculations.