Renormalization group running effects in $p$ $p$ $\rightarrow t \bar th$ in the SMEFT

We analyze the effects of renormalization group running of the Wilson coefficients in the SMEFT in the context of single Higgs production in association with a top-antitop pair, following the work presented in [Di Noi, Gröber, '23]. In particular, we analyze the differential cross section with respect to the Higgs trasnverse momentum. We extend the usual ${O}({\alpha_s})$ analysis including also the top Yukawa running effects, whose impact can be significant when large Wilson coefficients are considered. We employ a dynamical and a fixed renormalization scale with different set-ups for the Wilson coefficients, defined at the TeV scale. Additionally, we comment on the accuracy of the widely-used first leading-logarithm approximation.