Revisiting the top quark chromomagnetic dipole moment in the SM

TL;DR

This paper reevaluates the top quark's chromomagnetic dipole moment in the Standard Model, emphasizing the importance of off-shell gluon contributions and providing numerical estimates that align with experimental data.

Contribution

It demonstrates that the chromomagnetic dipole moment should be computed at off-shell gluon momenta, avoiding infrared divergences, and provides specific calculations at $q^2 = egative m_Z^2$ and $q^2 = m_Z^2$.

Findings

Re $ hinspace ext{μ}_t(-m_Z^2)$ matches experimental value.

Imaginary part of $ hinspace ext{μ}_t$ arises from flavor-changing currents.

Infrared divergence occurs at on-shell gluon ($q^2=0$), requiring off-shell evaluation.

Abstract

We revisit the anomalous chromomagnetic dipole moment in the Standard Model and show that its triple gluon vertex contribution, with the on-shell gluon ($q^2=0$), generates an infrared divergent pole. Consequently, the chromomagnetic dipole should not be perturbatively evaluated at $q^2=0$. Focusing on this top quark anomaly, denoted as $\hat{\mu}_t(q^2)$, we compute it with the off-shell gluon with a large momentum transfer, just as the $\alpha_s(m_Z^2)$ convention scale, for both spacelike $q^2=-m_Z^2$ and timelike $q^2=m_Z^2$ cases. We found that $\hat{\mu}_t(-m_Z^2)$ $=$ $-0.0224$ $-0.000925i$ and $\hat{\mu}_t(m_Z^2)$ $=$ $-0.0133$ $-0.0267i$. Our $\mathrm{Re}\thinspace\hat{\mu}_t(-m_Z^2)$ matches well with the current experimental value $\hat{\mu}_t^\mathrm{Exp}=-0.024_{-0.009}^{+0.013}(\mathrm{stat})_{-0.011}^{+0.016}(\mathrm{syst})$, and the $\mathrm{Im}\thinspace\hat{\mu}_t(-m_Z^2)$ part is induced by flavour changing charged currents.