Relating bottom quark mass in $\overline{\mathrm{DR}}$ and $\overline{\mathrm{MS}}$ regularization schemes

The value of the bottom quark mass at ${Q=M}_Z$ in the $\overline{\mathrm{DR}}$ scheme is an important input for the analysis of supersymmetric models with a large value of $\tan \beta .$ Conventionally, however, the running bottom quark mass extracted from experimental data is quoted in the $\overline{\mathrm{MS}}$ scheme at the scale ${Q=m}_b.$ We describe a two loop procedure for the conversion of the bottom quark mass from the $\overline{\mathrm{MS}}$ to $\overline{\mathrm{DR}}$ scheme. The Particle Data Group value $m_b^{\overline{\mathrm{MS}}}{(m}_b^{\overline{\mathrm{MS}}})=4.2\mathrm{}\pm 0.2\mathrm{GeV}$ corresponds to a range of 2.65–3.03 GeV for $m_b^{\overline{\mathrm{DR}}}{(M}_Z).\mathrm{}$