$m_b$ at $m_H$: the running bottom quark mass and the Higgs boson

We present a new measurement of the bottom quark mass in the $\bar{MS}$ scheme at the renormalization scale of the Higgs boson mass from measurements of Higgs boson decay rates at the LHC: $m_b(m_H)= 2.60^{+0.36}_{-0.31}$ GeV. The measurement has a negligible theory uncertainty and excellent prospects to improve at the HL-LHC and a future Higgs factory. Confronting this result, and $m_b(m_b)$ from low-energy measurements and $m_b(m_Z)$ from $Z-$pole data, with the prediction of the scale evolution of the renormalization group equations, we find strong evidence for the "running" of the bottom quark mass.

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