Bottom quark electroweak dipole moments at a high-energy $\mu -$collider

We study the sensitivity of a high-energy $\mu -$collider with center of mass energy in the multi–TeV range in testing electroweak dipole interactions of the $b-$quark. We parametrize the relevant deformations in the language of the Standard Model effective field theory, where the dominant modifications arise at the $d=6$ level. We analyse ${\mu }^{+}{\mu }^{-}\to b\bar{b}$ and ${\mu }^{+}{\mu }^{-}\to b\bar{b}h$ scatterings, performing a study at the level of a fast detector simulation. Owing the chiral structure of the dipole interaction, the study of the ${\mu }^{+}{\mu }^{-}\to b\bar{b}h$ process allows to enforce the stronger bounds on the Wilson coefficients of the $d=6$ operators. The limits that can be obtained surpass present and future bounds from EW precision measurements also improving upon the ones arising from the measurement of the $\mathrm{\Delta }F=1$ transitions $B\to X_s\gamma$.