The ${{\mathit u}}$-, ${{\mathit d}}$-, and ${{\mathit s}}$-quark masses are estimates of so-called “current-quark masses,” in a mass- independent subtraction scheme such as $\overline{\rm{}MS}$. The ratios ${\mathit m}_{{{\mathit u}}}/{\mathit m}_{{{\mathit d}}}$ and ${\mathit m}_{{{\mathit s}}}/{\mathit m}_{{{\mathit d}}}$ are extracted from pion and kaon masses using chiral symmetry. The estimates of ${{\mathit d}}$ and ${{\mathit u}}$ masses are not without controversy and remain under active investigation. Within the literature there are even suggestions that the ${{\mathit u}}~$quark could be essentially massless. The ${{\mathit s}}$-quark mass is estimated from SU(3) splittings in hadron masses.

We have normalized the $\overline{\rm{}MS}$ masses at a renormalization scale of $\mu $ = 2 GeV. Results quoted in the literature at $\mu $ = 1 GeV have been rescaled by dividing by $1.35$. The values of “Our Evaluation” were determined in part via Figures$~$2 and 3 in the “Quark masses” review.

VALUE (MeV) DOCUMENT ID TECN $\bf{ 2.16 \pm0.07}$ OUR EVALUATION  See the ideogram below. $2.6$ $\pm0.4$ 1 DOMINGUEZ 2019 THEO $2.130$ $\pm0.041$ 2 BAZAVOV 2018 LATT $2.27$ $\pm0.06$ $\pm0.06$ 3 FODOR 2016 LATT $2.36$ $\pm0.24$ 4 CARRASCO 2014 LATT $2.24$ $\pm0.10$ $\pm0.34$ 5 BLUM 2010 LATT $2.01$ $\pm0.14$ 6 MCNEILE 2010 LATT • • We do not use the following data for averages, fits, limits, etc. • • $2.57$ $\pm0.26$ $\pm0.07$ 7 AOKI 2012 LATT $2.15$ $\pm0.03$ $\pm0.10$ 8 DURR 2011 LATT $1.9$ $\pm0.2$ 9 BAZAVOV 2010 LATT $2.01$ $\pm0.14$ 6 DAVIES 2010 LATT $2.9$ $\pm0.2$ 10 DOMINGUEZ 2009 THEO $2.9$ $\pm0.8$ 11 DEANDREA 2008 THEO $3.02$ $\pm0.33$ 12 BLUM 2007 LATT $2.7$ $\pm0.4$ 13 JAMIN 2006 THEO $1.9$ $\pm0.2$ 14 MASON 2006 LATT $2.8$ $\pm0.2$ 15 NARISON 2006 THEO $1.7$ $\pm0.3$ 16 AUBIN 2004 A LATT 1  DOMINGUEZ 2019 determine the quark mass from a QCD finite energy sum rule for the divergence of the axial current. 2  BAZAVOV 2018 determine the quark masses using a lattice computation with staggered fermions and four active quark flavors. 3  FODOR 2016 is a lattice simulation with ${{\mathit n}_{{{f}}}}$ = 2 + 1 dynamical flavors and includes partially quenched QED effects. 4  CARRASCO 2014 is a lattice QCD computation of light quark masses using 2 + 1 + 1 dynamical quarks, with ${{\mathit m}_{{{u}}}}$ = ${{\mathit m}_{{{d}}}}{}\not=$ ${{\mathit m}_{{{s}}}}{}\not=$ ${{\mathit m}_{{{c}}}}$. The ${\mathit {\mathit u}}$ and ${\mathit {\mathit d}}$ quark masses are obtained separately by using the ${{\mathit K}}$ meson mass splittings and lattice results for the electromagnetic contributions. 5  BLUM 2010 determines light quark masses using a QCD plus QED lattice computation of the electromagnetic mass splittings of the low-lying hadrons. The lattice simulations use 2+1 dynamical quark flavors. 6  DAVIES 2010 and MCNEILE 2010 determine ${{\overline{\mathit m}}_{{{c}}}}({{\mathit \mu}})/{{\overline{\mathit m}}_{{{s}}}}({{\mathit \mu}}$) = $11.85$ $\pm0.16$ using a lattice computation with ${{\mathit n}_{{{f}}}}$ = 2 + 1 dynamical fermions of the pseudoscalar meson masses. Mass ${\mathit m}_{{{\mathit u}}}$ is obtained from this using the value of ${\mathit m}_{{{\mathit c}}}$ from ALLISON 2008 or MCNEILE 2010 and the BAZAVOV 2010 values for the light quark mass ratios, ${\mathit m}_{{{\mathit s}}}/{{\overline{\mathit m}}}$ and ${\mathit m}_{{{\mathit u}}}/{\mathit m}_{{{\mathit d}}}$. 7  AOKI 2012 is a lattice computation using 1 + 1 + 1 dynamical quark flavors. 8  DURR 2011 determine quark mass from a lattice computation of the meson spectrum using ${{\mathit n}_{{{f}}}}$ = 2 + 1 dynamical flavors. The lattice simulations were done at the physical quark mass, so that extrapolation in the quark mass was not needed. The individual ${\mathit m}_{{{\mathit u}}}$, ${\mathit m}_{{{\mathit d}}}$ values are obtained using the lattice determination of the average mass ${\mathit m}_{\mathrm {ud}}$ and of the ratio ${\mathit m}_{{{\mathit s}}}/{\mathit m}_{\mathrm {ud}}$ and the value of $\mathit Q$ = (${{\mathit m}^{2}}_{{{\mathit s}}}$ $−$ ${{\mathit m}^{2}}_{\mathrm {ud}}$) $/$ (${{\mathit m}^{2}}_{{{\mathit d}}}$ $−$ ${{\mathit m}^{2}}_{{{\mathit u}}}$) as determined from ${{\mathit \eta}}$ $\rightarrow$ 3 ${{\mathit \pi}}$ decays. 9  BAZAVOV 2010 is a lattice computation using 2+1 dynamical quark flavors. 10  DOMINGUEZ 2009 use QCD finite energy sum rules for the two-point function of the divergence of the axial vector current computed to order $\alpha {}^{4}_{s}$. 11  DEANDREA 2008 determine ${\mathit m}_{{{\mathit u}}}−{\mathit m}_{{{\mathit d}}}$ from ${{\mathit \eta}}$ $\rightarrow$ 3 ${{\mathit \pi}^{0}}$, and combine with the PDG 2006 lattice average value of ${\mathit m}_{{{\mathit u}}}+{\mathit m}_{{{\mathit d}}}$ = $7.6$ $\pm1.6$ to determine ${\mathit m}_{{{\mathit u}}}$ and ${\mathit m}_{{{\mathit d}}}$. 12  BLUM 2007 determine quark masses from the pseudoscalar meson masses using a QED plus QCD lattice computation with two dynamical quark flavors. 13  JAMIN 2006 determine ${\mathit m}_{{{\mathit u}}}$(2 GeV) by combining the value of ${\mathit m}_{{{\mathit s}}}$ obtained from the spectral function for the scalar ${{\mathit K}}{{\mathit \pi}}$ form factor with other determinations of the quark mass ratios. 14  MASON 2006 extract light quark masses from a lattice simulation using staggered fermions with an improved action, and three dynamical light quark flavors with degenerate ${\mathit {\mathit u}}$ and ${\mathit {\mathit d}}$ quarks. Perturbative corrections were included at NNLO order. The quark masses ${\mathit m}_{{{\mathit u}}}$ and ${\mathit m}_{{{\mathit d}}}$ were determined from their (${\mathit m}_{{{\mathit u}}}+{\mathit m}_{{{\mathit d}}})/$2 measurement and AUBIN 2004A ${\mathit m}_{{{\mathit u}}}/{\mathit m}_{{{\mathit d}}}$ value. 15  NARISON 2006 uses sum rules for ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ hadrons to order ${{\mathit \alpha}_{{{s}}}^{3}}$ to determine ${\mathit m}_{{{\mathit s}}}$ combined with other determinations of the quark mass ratios. 16  AUBIN 2004A employ a partially quenched lattice calculation of the pseudoscalar meson masses.

${\mathit {\mathit u}}$-QUARK MASS (MeV)

References