$\mathit{b}$-quark mass corresponds to the “running mass” ${\bar{\mathit{m}}}_b(\mu$ = ${\bar{\mathit{m}}}_b$) in the $\overline{\mathrm{M}\mathrm{S}}$ scheme. We have converted masses in other schemes to the $\overline{\mathrm{M}\mathrm{S}}$ mass using two-loop QCD perturbation theory with ${\alpha }_s(\mu$ = ${\bar{\mathit{m}}}_b$) = $0.223$ $\pm 0.008$. The value $4.18$ ${}_{-0.03}^{+0.04}$ (GeV) for the $\overline{\mathrm{M}\mathrm{S}}$ mass corresponds to $4.78$ $\pm 0.06$ GeV for the pole mass, using the two-loop conversion formula. A discussion of masses in different schemes can be found in the “Note on Quark Masses.''

$\overline{\mathrm{M}\mathrm{S}}$ MASS (GeV) DOCUMENT ID TECN $\mathbf{4.183}\pm \mathbf{0.007}$ OUR EVALUATION  of $\overline{\mathrm{M}\mathrm{S}}$ Mass.  See the ideogram below. $3.94$ ${}_{-0.40}^{+0.46}$ 1 APARISI 2022 THEO $4.202$ $\pm 0.021$ 2 HATTON 2021 LATT $4.197$ $\pm 0.008$ 3 NARISON 2020 THEO $4.049$ ${}_{-0.118}^{+0.138}$ 4 ABRAMOWICZ 2018 HERA $4.195$ $\pm 0.014$ 5 BAZAVOV 2018 LATT $4.186$ $\pm 0.037$ 6 PESET 2018 THEO $4.197$ $\pm 0.022$ 7 KIYO 2016 THEO $4.183$ $\pm 0.037$ 8 ALBERTI 2015 THEO $4.203$ ${}_{-0.034}^{+0.016}$ 9 BENEKE 2015 THEO $4.196$ $\pm 0.023$ 10 COLQUHOUN 2015 LATT $4.176$ $\pm 0.023$ 11 DEHNADI 2015 THEO $4.21$ $\pm 0.11$ 12 BERNARDONI 2014 LATT $4.169$ $\pm 0.002$ $\pm 0.008$ 13 PENIN 2014 THEO $4.166$ $\pm 0.043$ 14 LEE 2013 O LATT $4.247$ $\pm 0.034$ 15 LUCHA 2013 THEO $4.171$ $\pm 0.009$ 16 BODENSTEIN 2012 THEO $4.29$ $\pm 0.14$ 17 DIMOPOULOS 2012 LATT $4.18$ ${}_{-0.04}^{+0.05}$ 18 LASCHKA 2011 THEO $4.186$ $\pm 0.044$ $\pm 0.015$ 19 AUBERT 2010 A BABR $4.163$ $\pm 0.016$ 20 CHETYRKIN 2009 THEO $4.243$ $\pm 0.049$ 21 SCHWANDA 2008 BELL • • We do not use the following data for averages, fits, limits, etc. • • $4.184$ $\pm 0.011$ 22 NARISON 2018 A THEO $4.188$ $\pm 0.008$ 23 NARISON 2018 B THEO $4.07$ $\pm 0.17$ 24 ABRAMOWICZ 2014 A ZEUS $4.201$ $\pm 0.043$ 25 AYALA 2014 A THEO $4.236$ $\pm 0.069$ 26 NARISON 2013 THEO $4.213$ $\pm 0.059$ 27 NARISON 2013 A THEO $4.235$ $\pm 0.003$ $\pm 0.055$ 28 HOANG 2012 THEO $4.212$ $\pm 0.032$ 29 NARISON 2012 THEO $4.177$ $\pm 0.011$ 30 NARISON 2012 THEO $4.171$ $\pm 0.014$ 31 NARISON 2012 A THEO $4.164$ $\pm 0.023$ 32 MCNEILE 2010 LATT $4.173$ $\pm 0.010$ 33 NARISON 2010 THEO $5.26$ $\pm 1.2$ 34 ABDALLAH 2008 D DLPH $4.42$ $\pm 0.06$ $\pm 0.08$ 35 GUAZZINI 2008 LATT $4.347$ $\pm 0.048$ $\pm 0.08$ 36 DELLA-MORTE 2007 LATT $4.164$ $\pm 0.025$ 37 KUHN 2007 THEO $4.19$ $\pm 0.40$ 38 ABDALLAH 2006 D DLPH $4.205$ $\pm 0.058$ 39 BOUGHEZAL 2006 THEO $4.20$ $\pm 0.04$ 40 BUCHMUELLER 2006 THEO $4.19$ $\pm 0.06$ 41 PINEDA 2006 THEO $4.4$ $\pm 0.3$ 42 GRAY 2005 LATT $4.22$ $\pm 0.06$ 43 AUBERT 2004 X THEO $4.17$ $\pm 0.03$ 44 BAUER 2004 THEO $4.22$ $\pm 0.11$ 45 HOANG 2004 THEO $4.25$ $\pm 0.11$ 46 MCNEILE 2004 LATT $4.22$ $\pm 0.09$ 47 BAUER 2003 THEO $4.19$ $\pm 0.05$ 48 BORDES 2003 THEO $4.20$ $\pm 0.09$ 49 CORCELLA 2003 THEO $4.33$ $\pm 0.10$ 50 DEDIVITIIS 2003 LATT $4.24$ $\pm 0.10$ 51 EIDEMULLER 2003 THEO $4.207$ $\pm 0.03$ 52 ERLER 2003 THEO $4.33$ $\pm 0.06$ $\pm 0.10$ 53 MAHMOOD 2003 CLEO $4.190$ $\pm 0.032$ 54 BRAMBILLA 2002 THEO $4.346$ $\pm 0.070$ 55 PENIN 2002 THEO 1  APARISI 2022 determine ${\mathit{m}}_b$ at the Higgs mass, ${\bar{\mathit{m}}}_b({\mathit{m}}_H$) = $2.60$ ${}_{-0.31}^{+0.36}$ GeV from Higgs boson decay rates at the LHC, which is used to obtain ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$). 2  HATTON 2021 determine ${\bar{\mathit{m}}}_b$(3 GeV) = $4.513$ $\pm 0.026$ GeV using a lattice QCD + quenched QED simulation using the HISQ action and including ${\mathit{n}}_f$ = 2+1+1 flavors of sea quarks, by combining their ${\bar{\mathit{m}}}_b/{\bar{\mathit{m}}}_c$ and ${\bar{\mathit{m}}}_c$ determinations. 3  NARISON 2020 determines the quark mass using QCD Laplace sum rules from the ${\mathit{B}}_c$ mass, combined with previous determinations of the QCD condensates and $\mathit{c}$ and $\mathit{b}$ masses. 4  ABRAMOWICZ 2018 determine ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) = $4.049$ ${}_{-0.109}^{+0.104}{}_{-0.032}^{+0.090}{}_{-0.031}^{+0.001}$ from the production of $\mathit{b}$ quarks in $\mathit{e}\mathit{p}$ collisions at HERA using combined H1 and ZEUS data. The experimental/fitting errors, and those from modeling and parameterization have been combined in quadrature. 5  BAZAVOV 2018 determine the $\mathit{b}$ mass using a lattice computation with staggered fermions and five active quark flavors. 6  PESET 2018 determine ${\bar{\mathit{m}}}_c({\bar{\mathit{m}}}_c$) and ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) using an N3LO calculation of the ${\eta }_c$, ${\eta }_b$ and ${\mathit{B}}_c$ masses. 7  KIYO 2016 determine ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) from the $\mathit{{\rm Y}}(1S)$ mass at order ${\alpha }_s^3$ (N3LO). 8  ALBERTI 2015 determine ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) from fits to inclusive $\mathit{B}$ $\to$ ${\mathit{X}}_c\mathit{e}\bar{\nu }$ decay. They also find $\mathit{m}{}_b^{\mathrm{kin}}$(1 GeV) = $4.553$ $\pm 0.020$ GeV. 9  BENEKE 2015 determine ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) using sum rules for ${\mathit{e}}^{+}$ ${\mathit{e}}^{-}$ $\to$ hadrons at order N3LO including finite ${\mathit{m}}_{\mathit{c}}$ effects. They find $\mathit{m}{}_b^{\mathrm{PS}}$(2 GeV) = $4.532$ ${}_{-0.039}^{+0.013}$ GeV, and ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) = $4.193$ ${}_{-0.035}^{+0.022}$ GeV. The value quoted is obtained using the four-loop conversion given in BENEKE 2016. 10  COLQUHOUN 2015 determine ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) from moments of the vector current correlator computed with a lattice simulation using the NRQCD action. 11  DEHNADI 2015 determine ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) using sum rules for ${\mathit{e}}^{+}$ ${\mathit{e}}^{-}$ $\to$ hadrons at order ${\alpha }_s^3$ (N3LO), and fitting to both experimental data and lattice results. 12  BERNARDONI 2014 determine ${\mathit{m}}_b$ from ${\mathit{n}}_f$ = 2 lattice calculations using heavy quark effective theory non-perturbatively renormalized and matched to QCD at 1/$\mathit{m}$ order. 13  PENIN 2014 determine ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) = $4.169$ $\pm 0.008$ $\pm 0.002$ $\pm 0.002$ using an estimate of the order ${\alpha }_s^3\mathit{b}$-quark vacuum polarization function in the threshold region, including finite ${\mathit{m}}_{\mathit{c}}$ effects. The errors of $\pm 0.008$ from theoretical uncertainties, and $\pm 0.002$ from ${\alpha }_s$ have been combined in quadrature. 14  LEE 2013O determines ${\mathit{m}}_{\mathit{b}}$ using lattice calculations of the $\mathit{{\rm Y}}$ and ${\mathit{B}}_s$ binding energies in NRQCD, including three light dynamical quark flavors. The quark mass shift in NRQCD is determined to order ${\alpha }_s^2$, with partial ${\alpha }_s^3$ contributions. 15  LUCHA 2013 determines ${\mathit{m}}_{\mathit{b}}$ from QCD sum rules for heavy-light currents using the lattice value for ${\mathit{f}}_B$ of $191.5$ $\pm 7.3$ GeV. 16  BODENSTEIN 2012 determine ${\mathit{m}}_{\mathit{b}}$ using sum rules for the vector current correlator and the ${\mathit{e}}^{+}$ ${\mathit{e}}^{-}$ $\to$ $\mathit{Q}\bar{\mathit{Q}}$ total cross-section. 17  DIMOPOULOS 2012 determine quark masses from a lattice computation using ${\mathit{n}}_f$ = 2 dynamical flavors of twisted mass fermions. 18  LASCHKA 2011 determine the $\mathit{b}$ mass from the charmonium spectrum. The theoretical computation uses the heavy potential to order 1/${\mathit{m}}_{\mathit{Q}}$ obtained by matching the short-distance perturbative result onto lattice QCD result at larger scales. 19  AUBERT 2010A determine the $\mathit{b}$- and $\mathit{c}$-quark masses from a fit to the inclusive decay spectra in semileptonic $\mathit{B}$ decays in the kinetic scheme (and convert it to the $\overline{\mathrm{M}\mathrm{S}}$ scheme). 20  CHETYRKIN 2009 determine ${\mathit{m}}_{\mathit{c}}$ and ${\mathit{m}}_{\mathit{b}}$ from the ${\mathit{e}}^{+}$ ${\mathit{e}}^{-}$ $\to$ $\mathit{Q}\bar{\mathit{Q}}$ cross-section and sum rules, using an order ${\alpha }_s^3$ (N3LO) computation of the heavy quark vacuum polarization. 21  SCHWANDA 2008 measure moments of the inclusive photon spectrum in $\mathit{B}$ $\to$ ${\mathit{X}}_s\gamma$ decay to determine ${\mathit{m}}_b^{1S}$. We have converted this to $\overline{\mathrm{M}\mathrm{S}}$ scheme. 22  NARISON 2018A determines ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) as a function of ${\alpha }_s$ using QCD exponential sum rules and their ratios evaluated at the optimal scale $\mu$ = 9.5 GeV at N2LO-N3LO of perturbative QCD and including condensates up to dimension $6-8$ in the (axial-)vector and (pseudo-)scalar bottomonium channels. 23  NARISON 2018B determines ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) using QCD vector moment sum rules and their ratios at N2LO-N3LO of perturbative QCD and including condensates up to dimension 8. 24  ABRAMOWICZ 2014A determine ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) = $4.07$ $\pm 0.14$ ${}_{-0.07}^{+0.01}{}_{-0.00}^{+0.05}{}_{-0.05}^{+0.08}$ from the production of $\mathit{b}$ quarks in $\mathit{e}\mathit{p}$ collisions at HERA. The errors due to fitting, modeling, PDF parameterization, and theoretical QCD uncertainties due to the values of ${\alpha }_s$, ${\mathit{m}}_c$, and the renormalization scale $\mu$ have been combined in quadrature. 25  AYALA 2014A determine ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) from the $\mathit{{\rm Y}}(1S)$ mass computed to N3LO order in perturbation theory using a renormalon subtracted scheme. 26  NARISON 2013 determines ${\mathit{m}}_{\mathit{b}}$ using QCD spectral sum rules to order ${\alpha }_s^2$ (NNLO) and including condensates up to dimension 6. 27  NARISON 2013A determines ${\mathit{m}}_{\mathit{b}}$ using HQET sum rules to order ${\alpha }_s^2$ (NNLO) and the $\mathit{B}$ meson mass and decay constant. 28  HOANG 2012 determine ${\mathit{m}}_{\mathit{b}}$ using non-relativistic sum rules for the $\mathit{{\rm Y}}$ system at order ${\alpha }_s^2$ (NNLO) with renormalization group improvement. 29  NARISON 2012 determines ${\mathit{m}}_{\mathit{b}}$ using exponential sum rules for the vector current correlator to order ${\alpha }_s^3$, including the effect of gluon condensates up to dimension eight. 30  Determines ${\mathit{m}}_{\mathit{b}}$ to order ${\alpha }_s^3$ (N3LO), including the effect of gluon condensates up to dimension eight combining the methods of NARISON 2012 and NARISON 2012A. 31  NARISON 2012A determines ${\mathit{m}}_{\mathit{b}}$ using sum rules for the vector current correlator to order ${\alpha }_s^3$, including the effect of gluon condensates up to dimension eight. 32  MCNEILE 2010 determines ${\mathit{m}}_{\mathit{b}}$ by comparing order ${\alpha }_s^3$ (N3LO) perturbative results for the pseudo-scalar current to lattice simulations with ${\mathit{n}}_f$ = 2+1 sea-quarks by the HPQCD collaboration. 33  NARISON 2010 determines ${\mathit{m}}_{\mathit{b}}$ from ratios of moments of vector current correlators computed to order ${\alpha }_s^3$ and including the dimension-six gluon condensate. These values are taken from the erratum to that reference. 34  ABDALLAH 2008D determine ${\bar{\mathit{m}}}_b({\mathit{M}}_Z$) = $3.76$ $\pm 1.0$ GeV from a leading order study of four-jet rates at LEP. 35  GUAZZINI 2008 determine ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) from a quenched lattice simulation of heavy meson masses. The $\pm 0.08$ is an estimate of the quenching error. 36  DELLA-MORTE 2007 determine ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) from a computation of the spin-averaged $\mathit{B}$ meson mass using quenched lattice HQET at order 1/$\mathit{m}$. The $\pm 0.08$ is an estimate of the quenching error. 37  KUHN 2007 determine ${\bar{\mathit{m}}}_b(\mu$ = 10 GeV) = $3.609$ $\pm 0.025$ GeV and ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) from a four-loop sum-rule computation of the cross-section for ${\mathit{e}}^{+}$ ${\mathit{e}}^{-}$ $\to$ hadrons in the bottom threshold region. 38  ABDALLAH 2006D determine ${\mathit{m}}_{\mathit{b}}({\mathit{M}}_Z$) = $2.85$ $\pm 0.32$ GeV from $\mathit{Z}$-decay three-jet events containing a $\mathit{b}$-quark. 39  BOUGHEZAL 2006 $\overline{\mathrm{M}\mathrm{S}}$ scheme result comes from the first moment of the hadronic production cross-section to order ${\alpha }_s^3$. 40  BUCHMUELLER 2006 determine ${\mathit{m}}_b$ and ${\mathit{m}}_c$ by a global fit to inclusive $\mathit{B}$ decay spectra. 41  PINEDA 2006 $\overline{\mathrm{M}\mathrm{S}}$ scheme result comes from a partial NNLL evaluation (complete at order ${\alpha }_s^2$ (NNLO)) of sum rules of the bottom production cross-section in ${\mathit{e}}^{+}{\mathit{e}}^{-}$ annihilation. 42  GRAY 2005 determines ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) from a lattice computation of the $\mathit{{\rm Y}}$ spectrum. The simulations have 2+1 dynamical light flavors. The $\mathit{b}$ quark is implemented using NRQCD. 43  AUBERT 2004X obtain ${\mathit{m}}_{\mathit{b}}$ from a fit to the hadron mass and lepton energy distributions in semileptonic $\mathit{B}$ decay. The paper quotes values in the kinetic scheme. The $\overline{\mathrm{M}\mathrm{S}}$ value has been provided by the BABAR collaboration. 44  BAUER 2004 determine ${\mathit{m}}_{\mathit{b}}$, ${\mathit{m}}_{\mathit{c}}$ and ${\mathit{m}}_{\mathit{b}}-{\mathit{m}}_{\mathit{c}}$ by a global fit to inclusive $\mathit{B}$ decay spectra. 45  HOANG 2004 determines ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) from moments at order ${\alpha }_s^2$ of the bottom production cross-section in ${\mathit{e}}^{+}{\mathit{e}}^{-}$ annihilation. 46  MCNEILE 2004 use lattice QCD with dynamical light quarks and a static heavy quark to compute the masses of heavy-light mesons. 47  BAUER 2003 determine the b quark mass by a global fit to $\mathit{B}$ decay observables. The experimental data includes lepton energy and hadron invariant mass moments in semileptonic $\mathit{B}$ $\to$ ${\mathit{X}}_c\ell {\nu }_{\ell }$ decay, and the inclusive photon spectrum in $\mathit{B}$ $\to$ ${\mathit{X}}_s\gamma$ decay. The theoretical expressions used are of order 1/m${}^3$, and $\alpha {}_s^2{\beta }_0$. 48  BORDES 2003 determines m${}_b$ using QCD finite energy sum rules to order $\alpha {}_s^2$. 49  CORCELLA 2003 determines ${\bar{\mathit{m}}}_b$ using sum rules computed to order $\alpha {}_s^2$. Includes charm quark mass effects. 50  DEDIVITIIS 2003 use a quenched lattice computation of heavy-heavy and heavy-light meson masses. 51  EIDEMULLER 2003 determines ${\bar{\mathit{m}}}_b$ and ${\bar{\mathit{m}}}_c$ using QCD sum rules. 52  ERLER 2003 determines ${\bar{\mathit{m}}}_b$ and ${\bar{\mathit{m}}}_c$ using QCD sum rules. Includes recent BES data. 53  MAHMOOD 2003 determines $\mathit{m}{}_b^{1S}$ by a fit to the lepton energy moments in $\mathit{B}$ $\to$ ${\mathit{X}}_c\ell {\nu }_{\ell }$ decay. The theoretical expressions used are of order 1/m${}^3$ and $\alpha {}_s^2{\beta }_0$. We have converted their result to the $\overline{\mathrm{M}\mathrm{S}}$ scheme. 54  BRAMBILLA 2002 determine ${\bar{\mathit{m}}}_b({\bar{\mathit{m}}}_b$) from a computation of the $\mathit{{\rm Y}}(1S)$ mass to order ${\alpha }_s^4$, including finite ${\mathit{m}}_c$ corrections. 55  PENIN 2002 determines ${\bar{\mathit{m}}}_b$ from the spectrum of the $\mathit{{\rm Y}}$ system.

$\mathit{b}$-QUARK $\overline{\mathrm{M}\mathrm{S}}$ MASS (GeV)

References