${\mathit {\mathit b}}$-quark mass corresponds to the “running mass” ${{\overline{\mathit m}}_{{b}}}({{\mathit \mu}}$ = ${{\overline{\mathit m}}_{{b}}}$) in the $\overline{\rm{}MS}$ scheme. We have converted masses in other schemes to the $\overline{\rm{}MS}$ mass using two-loop QCD perturbation theory with ${{\mathit \alpha}_{{s}}}({{\mathit \mu}}$ = ${{\overline{\mathit m}}_{{b}}}$) = $0.223$ $\pm0.008$. The value $4.18$ ${}^{+0.04}_{-0.03}$ (GeV) for the $\overline{\rm{}MS}$ mass corresponds to $4.78$ $\pm0.06$ 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.''

VALUE (GeV) DOCUMENT ID TECN $\bf{ 4.18 {}^{+0.03}_{-0.02}}$ OUR EVALUATION  of $\overline{\rm{}MS}$ Mass.  See the ideogram below. $4.202$ $\pm0.021$ 1 HATTON 2021 LATT $4.197$ $\pm0.008$ 2 NARISON 2020 THEO $4.049$ ${}^{+0.138}_{-0.118}$ 3 ABRAMOWICZ 2018 HERA $4.195$ $\pm0.014$ 4 BAZAVOV 2018 LATT $4.186$ $\pm0.037$ 5 PESET 2018 THEO $4.197$ $\pm0.022$ 6 KIYO 2016 THEO $4.183$ $\pm0.037$ 7 ALBERTI 2015 THEO $4.203$ ${}^{+0.016}_{-0.034}$ 8 BENEKE 2015 THEO $4.196$ $\pm0.023$ 9 COLQUHOUN 2015 LATT $4.176$ $\pm0.023$ 10 DEHNADI 2015 THEO $4.21$ $\pm0.11$ 11 BERNARDONI 2014 LATT $4.169$ $\pm0.002$ $\pm0.008$ 12 PENIN 2014 THEO $4.166$ $\pm0.043$ 13 LEE 2013 O LATT $4.247$ $\pm0.034$ 14 LUCHA 2013 THEO $4.171$ $\pm0.009$ 15 BODENSTEIN 2012 THEO $4.29$ $\pm0.14$ 16 DIMOPOULOS 2012 LATT $4.18$ ${}^{+0.05}_{-0.04}$ 17 LASCHKA 2011 THEO $4.186$ $\pm0.044$ $\pm0.015$ 18 AUBERT 2010 A BABR $4.163$ $\pm0.016$ 19 CHETYRKIN 2009 THEO $4.243$ $\pm0.049$ 20 SCHWANDA 2008 BELL • • We do not use the following data for averages, fits, limits, etc. • • $4.184$ $\pm0.011$ 21 NARISON 2018 A THEO $4.188$ $\pm0.008$ 22 NARISON 2018 B THEO $4.07$ $\pm0.17$ 23 ABRAMOWICZ 2014 A ZEUS $4.201$ $\pm0.043$ 24 AYALA 2014 A THEO $4.236$ $\pm0.069$ 25 NARISON 2013 THEO $4.213$ $\pm0.059$ 26 NARISON 2013 A THEO $4.235$ $\pm0.003$ $\pm0.055$ 27 HOANG 2012 THEO $4.212$ $\pm0.032$ 28 NARISON 2012 THEO $4.177$ $\pm0.011$ 29 NARISON 2012 THEO $4.171$ $\pm0.014$ 30 NARISON 2012 A THEO $4.164$ $\pm0.023$ 31 MCNEILE 2010 LATT $4.173$ $\pm0.010$ 32 NARISON 2010 THEO $5.26$ $\pm1.2$ 33 ABDALLAH 2008 D DLPH $4.42$ $\pm0.06$ $\pm0.08$ 34 GUAZZINI 2008 LATT $4.347$ $\pm0.048$ $\pm0.08$ 35 DELLA-MORTE 2007 LATT $4.164$ $\pm0.025$ 36 KUHN 2007 THEO $4.19$ $\pm0.40$ 37 ABDALLAH 2006 D DLPH $4.205$ $\pm0.058$ 38 BOUGHEZAL 2006 THEO $4.20$ $\pm0.04$ 39 BUCHMUELLER 2006 THEO $4.19$ $\pm0.06$ 40 PINEDA 2006 THEO $4.4$ $\pm0.3$ 41 GRAY 2005 LATT $4.22$ $\pm0.06$ 42 AUBERT 2004 X THEO $4.17$ $\pm0.03$ 43 BAUER 2004 THEO $4.22$ $\pm0.11$ 44 HOANG 2004 THEO $4.25$ $\pm0.11$ 45 MCNEILE 2004 LATT $4.22$ $\pm0.09$ 46 BAUER 2003 THEO $4.19$ $\pm0.05$ 47 BORDES 2003 THEO $4.20$ $\pm0.09$ 48 CORCELLA 2003 THEO $4.33$ $\pm0.10$ 49 DEDIVITIIS 2003 LATT $4.24$ $\pm0.10$ 50 EIDEMULLER 2003 THEO $4.207$ $\pm0.03$ 51 ERLER 2003 THEO $4.33$ $\pm0.06$ $\pm0.10$ 52 MAHMOOD 2003 CLEO $4.190$ $\pm0.032$ 53 BRAMBILLA 2002 THEO $4.346$ $\pm0.070$ 54 PENIN 2002 THEO 1  HATTON 2021 determine ${{\overline{\mathit m}}_{{b}}}$(3 GeV) = $4.513$ $\pm0.026$ 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 ${{\overline{\mathit m}}_{{b}}}/{{\overline{\mathit m}}_{{c}}}$ and ${{\overline{\mathit m}}_{{c}}}$ determinations. 2  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 ${\mathit {\mathit c}}$ and ${\mathit {\mathit b}}$ masses. 3  ABRAMOWICZ 2018 determine ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) = $4.049$ ${}^{+0.104}_{-0.109}{}^{+0.090}_{-0.032}{}^{+0.001}_{-0.031}$ from the production of ${\mathit {\mathit b}}$ 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. 4  BAZAVOV 2018 determine the ${\mathit {\mathit b}}$ mass using a lattice computation with staggered fermions and five active quark flavors. 5  PESET 2018 determine ${{\overline{\mathit m}}_{{c}}}({{\overline{\mathit m}}_{{c}}}$) and ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) using an N3LO calculation of the ${{\mathit \eta}_{{c}}}$, ${{\mathit \eta}_{{b}}}$ and ${{\mathit B}_{{c}}}$ masses. 6  KIYO 2016 determine ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) from the ${{\mathit \Upsilon}{(1S)}}$ mass at order ${{\mathit \alpha}_{{s}}^{3}}$ (N3LO). 7  ALBERTI 2015 determine ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) from fits to inclusive ${{\mathit B}}$ $\rightarrow$ ${{\mathit X}_{{c}}}{{\mathit e}}{{\overline{\mathit \nu}}}$ decay. They also find ${{\mathit m}}{}^{{\mathrm {kin}}}_{b}$(1 GeV) = $4.553$ $\pm0.020$ GeV. 8  BENEKE 2015 determine ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) using sum rules for ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ hadrons at order N3LO including finite ${\mathit m}_{{{\mathit c}}}$ effects. They find ${{\mathit m}}{}^{{\mathrm {PS}}}_{b}$(2 GeV) = $4.532$ ${}^{+0.013}_{-0.039}$ GeV, and ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) = $4.193$ ${}^{+0.022}_{-0.035}$ GeV. The value quoted is obtained using the four-loop conversion given in BENEKE 2016 . 9  COLQUHOUN 2015 determine ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) from moments of the vector current correlator computed with a lattice simulation using the NRQCD action. 10  DEHNADI 2015 determine ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) using sum rules for ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ hadrons at order ${{\mathit \alpha}_{{s}}^{3}}$ (N3LO), and fitting to both experimental data and lattice results. 11  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. 12  PENIN 2014 determine ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) = $4.169$ $\pm0.008$ $\pm0.002$ $\pm0.002$ using an estimate of the order ${{\mathit \alpha}_{{s}}^{3}}{\mathit {\mathit b}}$-quark vacuum polarization function in the threshold region, including finite ${\mathit m}_{{{\mathit c}}}$ effects. The errors of $\pm0.008$ from theoretical uncertainties, and $\pm0.002$ from ${{\mathit \alpha}_{{s}}}$ have been combined in quadrature. 13  LEE 2013O determines ${\mathit m}_{{{\mathit b}}}$ using lattice calculations of the ${{\mathit \Upsilon}}$ and ${{\mathit B}_{{s}}}$ binding energies in NRQCD, including three light dynamical quark flavors. The quark mass shift in NRQCD is determined to order ${{\mathit \alpha}_{{s}}^{2}}$, with partial ${{\mathit \alpha}_{{s}}^{3}}$ contributions. 14  LUCHA 2013 determines ${\mathit m}_{{{\mathit b}}}$ from QCD sum rules for heavy-light currents using the lattice value for ${{\mathit f}_{{B}}}$ of $191.5$ $\pm7.3$ GeV. 15  BODENSTEIN 2012 determine ${\mathit m}_{{{\mathit b}}}$ using sum rules for the vector current correlator and the ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Q}}{{\overline{\mathit Q}}}$ total cross-section. 16  DIMOPOULOS 2012 determine quark masses from a lattice computation using ${{\mathit n}_{{f}}}$ = 2 dynamical flavors of twisted mass fermions. 17  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. 18  AUBERT 2010A determine the ${\mathit {\mathit b}}$- and ${\mathit {\mathit c}}$-quark masses from a fit to the inclusive decay spectra in semileptonic ${{\mathit B}}$ decays in the kinetic scheme (and convert it to the $\overline{\rm{}MS}$ scheme). 19  CHETYRKIN 2009 determine ${\mathit m}_{{{\mathit c}}}$ and ${\mathit m}_{{{\mathit b}}}$ from the ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit Q}}{{\overline{\mathit Q}}}$ cross-section and sum rules, using an order ${{\mathit \alpha}_{{s}}^{3}}$ (N3LO) computation of the heavy quark vacuum polarization. 20  SCHWANDA 2008 measure moments of the inclusive photon spectrum in ${{\mathit B}}$ $\rightarrow$ ${{\mathit X}_{{s}}}{{\mathit \gamma}}$ decay to determine ${{\mathit m}_{{b}}^{1S}}$. We have converted this to $\overline{\rm{}MS}$ scheme. 21  NARISON 2018A determines ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) as a function of ${{\mathit \alpha}_{{s}}}$ 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. 22  NARISON 2018B determines ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) using QCD vector moment sum rules and their ratios at N2LO-N3LO of perturbative QCD and including condensates up to dimension 8. 23  ABRAMOWICZ 2014A determine ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) = $4.07$ $\pm0.14$ ${}^{+0.01}_{-0.07}{}^{+0.05}_{-0.00}{}^{+0.08}_{-0.05}$ from the production of ${\mathit {\mathit b}}$ 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 ${{\mathit \alpha}_{{s}}}$, ${{\mathit m}_{{c}}}$, and the renormalization scale $\mu $ have been combined in quadrature. 24  AYALA 2014A determine ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) from the ${{\mathit \Upsilon}{(1S)}}$ mass computed to N3LO order in perturbation theory using a renormalon subtracted scheme. 25  NARISON 2013 determines ${\mathit m}_{{{\mathit b}}}$ using QCD spectral sum rules to order ${{\mathit \alpha}_{{s}}^{2}}$ (NNLO) and including condensates up to dimension 6. 26  NARISON 2013A determines ${\mathit m}_{{{\mathit b}}}$ using HQET sum rules to order ${{\mathit \alpha}_{{s}}^{2}}$ (NNLO) and the ${{\mathit B}}$ meson mass and decay constant. 27  HOANG 2012 determine ${\mathit m}_{{{\mathit b}}}$ using non-relativistic sum rules for the ${{\mathit \Upsilon}}$ system at order ${{\mathit \alpha}_{{s}}^{2}}$ (NNLO) with renormalization group improvement. 28  NARISON 2012 determines ${\mathit m}_{{{\mathit b}}}$ using exponential sum rules for the vector current correlator to order ${{\mathit \alpha}_{{s}}^{3}}$, including the effect of gluon condensates up to dimension eight. 29  Determines ${\mathit m}_{{{\mathit b}}}$ to order ${{\mathit \alpha}_{{s}}^{3}}$ (N3LO), including the effect of gluon condensates up to dimension eight combining the methods of NARISON 2012 and NARISON 2012A. 30  NARISON 2012A determines ${\mathit m}_{{{\mathit b}}}$ using sum rules for the vector current correlator to order ${{\mathit \alpha}_{{s}}^{3}}$, including the effect of gluon condensates up to dimension eight. 31  MCNEILE 2010 determines ${\mathit m}_{{{\mathit b}}}$ by comparing order ${{\mathit \alpha}_{{s}}^{3}}$ (N3LO) perturbative results for the pseudo-scalar current to lattice simulations with ${{\mathit n}_{{f}}}$ = 2+1 sea-quarks by the HPQCD collaboration. 32  NARISON 2010 determines ${\mathit m}_{{{\mathit b}}}$ from ratios of moments of vector current correlators computed to order ${{\mathit \alpha}_{{s}}^{3}}$ and including the dimension-six gluon condensate. These values are taken from the erratum to that reference. 33  ABDALLAH 2008D determine ${{\overline{\mathit m}}_{{b}}}({{\mathit M}_{{Z}}}$) = $3.76$ $\pm1.0$ GeV from a leading order study of four-jet rates at LEP. 34  GUAZZINI 2008 determine ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) from a quenched lattice simulation of heavy meson masses. The $\pm0.08$ is an estimate of the quenching error. 35  DELLA-MORTE 2007 determine ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) from a computation of the spin-averaged ${{\mathit B}}$ meson mass using quenched lattice HQET at order 1/${{\mathit m}}$. The $\pm0.08$ is an estimate of the quenching error. 36  KUHN 2007 determine ${{\overline{\mathit m}}_{{b}}}({{\mathit \mu}}$ = 10 GeV) = $3.609$ $\pm0.025$ GeV and ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) from a four-loop sum-rule computation of the cross-section for ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ hadrons in the bottom threshold region. 37  ABDALLAH 2006D determine ${\mathit m}_{{{\mathit b}}}({{\mathit M}_{{Z}}}$) = $2.85$ $\pm0.32$ GeV from ${{\mathit Z}}$-decay three-jet events containing a ${{\mathit b}}$-quark. 38  BOUGHEZAL 2006 $\overline{\rm{}MS}$ scheme result comes from the first moment of the hadronic production cross-section to order ${{\mathit \alpha}_{{s}}^{3}}$. 39  BUCHMUELLER 2006 determine ${{\mathit m}_{{b}}}$ and ${{\mathit m}_{{c}}}$ by a global fit to inclusive ${{\mathit B}}$ decay spectra. 40  PINEDA 2006 $\overline{\rm{}MS}$ scheme result comes from a partial NNLL evaluation (complete at order ${{\mathit \alpha}_{{s}}^{2}}$ (NNLO)) of sum rules of the bottom production cross-section in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ annihilation. 41  GRAY 2005 determines ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) from a lattice computation of the ${{\mathit \Upsilon}}$ spectrum. The simulations have 2+1 dynamical light flavors. The ${{\mathit b}}$ quark is implemented using NRQCD. 42  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 $\overline{\rm{}MS}$ value has been provided by the BABAR collaboration. 43  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. 44  HOANG 2004 determines ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) from moments at order ${{\mathit \alpha}_{{s}}^{2}}$ of the bottom production cross-section in ${{\mathit e}^{+}}{{\mathit e}^{-}}$ annihilation. 45  MCNEILE 2004 use lattice QCD with dynamical light quarks and a static heavy quark to compute the masses of heavy-light mesons. 46  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 ${{\mathit B}}$ $\rightarrow$ ${{\mathit X}_{{c}}}{{\mathit \ell}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ decay, and the inclusive photon spectrum in ${{\mathit B}}$ $\rightarrow$ ${{\mathit X}_{{s}}}{{\mathit \gamma}}$ decay. The theoretical expressions used are of order 1/m${}^{3}$, and $\alpha {}^{2}_{s}\beta _{0}$. 47  BORDES 2003 determines m$_{b}$ using QCD finite energy sum rules to order $\alpha {}^{2}_{s}$. 48  CORCELLA 2003 determines ${{\overline{\mathit m}}_{{b}}}$ using sum rules computed to order $\alpha {}^{2}_{s}$. Includes charm quark mass effects. 49  DEDIVITIIS 2003 use a quenched lattice computation of heavy-heavy and heavy-light meson masses. 50  EIDEMULLER 2003 determines ${{\overline{\mathit m}}_{{b}}}$ and ${{\overline{\mathit m}}_{{c}}}$ using QCD sum rules. 51  ERLER 2003 determines ${{\overline{\mathit m}}_{{b}}}$ and ${{\overline{\mathit m}}_{{c}}}$ using QCD sum rules. Includes recent BES data. 52  MAHMOOD 2003 determines ${{\mathit m}}{}^{1S}_{b}$ by a fit to the lepton energy moments in ${{\mathit B}}$ $\rightarrow$ ${{\mathit X}_{{c}}}{{\mathit \ell}}{{\mathit \nu}_{{{{\mathit \ell}}}}}$ decay. The theoretical expressions used are of order 1/m${}^{3}$ and $\alpha {}^{2}_{s}\beta _{0}$. We have converted their result to the $\overline{\rm{}MS}$ scheme. 53  BRAMBILLA 2002 determine ${{\overline{\mathit m}}_{{b}}}({{\overline{\mathit m}}_{{b}}}$) from a computation of the ${{\mathit \Upsilon}{(1S)}}$ mass to order ${{\mathit \alpha}_{{s}}^{4}}$, including finite ${{\mathit m}_{{c}}}$ corrections. 54  PENIN 2002 determines ${{\overline{\mathit m}}_{{b}}}$ from the spectrum of the ${{\mathit \Upsilon}}$ system.

${\mathit {\mathit b}}$-QUARK $\overline{\rm{}MS}$ MASS (GeV)

References:

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