Measurement of the $\mathrm{t\overline{t}H}$ and $\mathrm{tH}$ production rates in the $\mathrm{H}\to\mathrm{b\overline{b}}$ decay channel with $138\,\mathrm{fb}^{-1}$ of proton-proton collision data at $\sqrt{s}=13\,\mathrm{TeV}$

An analysis of the production of a Higgs boson (H) in association with a top quark-antiquark pair ($\mathrm{t\overline{t}H}$) or a single top quark ($\mathrm{tH}$) in the channel where the Higgs boson decays into a bottom quark-antiquark pair ($\mathrm{H}\to\mathrm{b\overline{b}}$) is presented. The analysis utilises proton-proton collision data collected at the CERN LHC with the CMS experiment at $\sqrt{s}=13\,\mathrm{TeV}$ between 2016 and 2018, which correspond to an integrated luminosity of $138\,\mathrm{fb}^{-1}$. All three decay channels of the $\mathrm{t\overline{t}}$ system are considered. Various signal interpretations are performed. The observed $\mathrm{t\overline{t}H}$ production rate relative to the standard model (SM) expectation is $0.33\pm0.26 = 0.33\pm0.17\,(\text{stat})\pm0.21\,(\text{syst})$. Additionally, the $\mathrm{t\overline{t}H}$ production rate is determined in intervals of Higgs boson $p_{\mathrm{T}}$. An upper limit at $95\%$ confidence level on the $\mathrm{tH}$ production rate of 14.6 times the SM expectation is observed, with an expectation of $19.3^{+9.2}_{-6.0}$. Finally, constraints are derived on the strength and structure of the coupling between the Higgs boson and the top quark from simultaneous extraction of the $\mathrm{t\overline{t}H}$ and $\mathrm{tH}$ production rates. $$\textit{This document has been revised with respect to the version dated August 22nd, 2023.}$$