Flavor violation in chromo- and electromagnetic dipole moments induced by $Z^{\prime }$ gauge bosons and a brief revisit of the Standard Model

The electromagnetic dipole moments of the tau lepton and the chromoelectromagnetic dipole moments of the top quark are estimated via flavor-changing neutral currents, mediated by a new neutral massive gauge boson. We predict them in the context of models beyond the Standard Model with extended current sectors, in which simple analytic expressions for the dipole moments are presented. For the different $Z^{\prime }$ gauge boson considered, the best prediction for the magnetic dipole moment of the tau lepton, $|a_{\tau }|$, is of the order of ${10}^{-8}$, while the highest value for the electric one, $|d_{\tau }|$, corresponds to ${10}^{-24}e\mathrm{cm}$; our main result for the chromomagnetic dipole moment of the top quark, $|{\widehat{\mu }}_t|$, is ${10}^{-6}$, and the value for the chromoelectric one, $|d_t|$, can be as high as ${10}^{-22}e\mathrm{cm}$. We compare our results, revisiting the corresponding Standard Model predictions, in which the chromomagnetic dipole moment of the top quark is carefully evaluated, finding explicit imaginary contributions.

Figure 1

Feynman diagrams corresponding to the $\tau \to \mu {\mu }^{+}{\mu }^{-}$ and $\tau \to e{e}^{+}{e}^{-}$ decays.

Figure 2

(a) Electromagnetic ($f=l$) and (b) chromoelectromagnetic ($f=q$) dipole moments at one-loop level mediated by a $Z^{\prime }$ gauge boson with FV.

Figure 3

$CP$ conservation: tau static anomalous magnetic dipole moment. (a) Contributions of the $Z^{\prime }$ gauge bosons. (b) Main contribution due to $Z_{\eta }^{\prime }$ and its subparts.

Figure 4

$CP$ violation: tau static electromagnetic dipole moments. (a) $a_{\tau }$, contributions of the $Z^{\prime }$ gauge bosons. (b) $a_{\tau }$, main contribution due to $Z_{\eta }^{\prime }$ and its subparts; (c) $d_{\tau }$, contributions of the $Z^{\prime }$ gauge bosons. (d) $d_{\tau }$, main contribution due to $Z_{\eta }^{\prime }$ and its subparts. (e) Phase between EDM and MDM.

Figure 5

$CP$ conservation: top magnetic dipole moment. (a) Contributions of the $Z^{\prime }$ gauge bosons from different models to the $\mathrm{Re}{\widehat{\mu }}_t$ generated by $q^2=0$, $\pm m_Z^2$ and (b) $\mathrm{Im}{\widehat{\mu }}_t$ generated by $q^2=m_Z^2$, where all the different $Z^{\prime }$ bosons share essentially the same imaginary value. (c) Main contribution due to $Z_S^{\prime }$ to $\mathrm{Re}{\widehat{\mu }}_t$ and (d) $\mathrm{Im}{\widehat{\mu }}_t$, which arise only from the nondiagonal subparts ${\widehat{\mu }}_{tu,tc}$.

Figure 6

$CP$ violation: top electromagnetic dipole moments. (a) Contributions of the $Z^{\prime }$ gauge bosons from different models to $\mathrm{Re}{\widehat{\mu }}_t$ and (b) the $\mathrm{Im}{\widehat{\mu }}_t$. (c) The $\mathrm{Re}{\widehat{d}}_t$ coming from the different $Z^{\prime }$ and (d) the $\mathrm{Im}{\widehat{d}}_t$. (e),(f) The respective real and imaginary parts generated by the subparts of the main contributor $Z_S^{\prime }$. (g) The phase.