The top quark chromomagnetic dipole moment in the SM from the 4-body vertex function

A new proposal to compute the anomalous chromomagnetic dipole moment of the top quark, $\hat{\mu}_t$, in the Standard Model is presented. On the basis of the 5-dimensional effective Lagrangian operator that characterizes the quantum-loop induced chromodipolar vertices $gt\bar{t}$ and $ggt\bar{t}$, the $\hat{\mu}_t$ anomaly is derived via radiative correction at the 1-loop level from the non-Abelian 4-body vertex function $ggt\bar{t}$. We evaluate $\hat{\mu}_t(s)$ as a function of the energy scale $s=\pm E^2$, for $E=[10,1000]$ GeV, taking into account the running of the quark masses and alpha strong through the $\overline{\mathrm{MS}}$ scheme. In particular, we find that at the typical energy scale $E=m_Z$ for high-energy physics, similarly to $\alpha_s(m_Z^2)$, $\alpha(m_Z^2)$ and $s_W(m_Z^2)$, the spacelike evaluation yields $\hat{\mu}_t(-m_Z^2)$ $=$ $-0.025$$+$$0.00384i$ and the timelike $\hat{\mu}_t(m_Z^2)$ $=$ $-0.0318$$-$$0.0106i$. This Re$\thinspace\hat{\mu}_t(-m_Z^2)$ $=$ $-0.025$ from $ggt\bar{t}$ is even closer to the experimental central value $\hat{\mu}_t^\mathrm{Exp}=$ $-0.024$, than that coming from the known 3-body vertex function $gt\bar{t}$, $-0.0224$. Once again, the Im$\thinspace\hat{\mu}_t(-m_Z^2)$ part is due to the contribution of virtual charged currents, just like in the $gt\bar{t}$ case. We can infer that the spacelike prediction is the favored one.