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$~$1 and 2.

VALUE (MeV) DOCUMENT ID TECN $\bf{ 2.16 {}^{+0.49}_{-0.26}}$ 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 $2.57$ $\pm0.26$ $\pm0.07$ 5 AOKI 2012 LATT $2.24$ $\pm0.10$ $\pm0.34$ 6 BLUM 2010 LATT $2.01$ $\pm0.14$ 7 MCNEILE 2010 LATT • • We do not use the following data for averages, fits, limits, etc. • • $2.15$ $\pm0.03$ $\pm0.10$ 8 DURR 2011 LATT $1.9$ $\pm0.2$ 9 BAZAVOV 2010 LATT $2.01$ $\pm0.14$ 7 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  AOKI 2012 is a lattice computation using 1 + 1 + 1 dynamical quark flavors. 6  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. 7  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 ${\mathit m}_{{{\mathit u}}}/{\mathit m}_{{{\mathit d}}}$. 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:

DOMINGUEZ 2019 JHEP 1902 057 Up- and down-quark masses from QCD sum rules BAZAVOV 2018 PR D98 054517 Up-, down-, strange-, charm-, and bottom-quark masses from four-flavor lattice QCD FODOR 2016 PRL 117 082001 Up and Down Quark Masses and Corrections to Dashen's Theorem from Lattice QCD and Quenched QED CARRASCO 2014 NP B887 19 Up, Down, Strange and Charm Quark Masses with $\mathit N_{f}$ = 2+1+1 Twisted Mass Lattice QCD AOKI 2012 PR D86 034507 1+1+1 Flavor QCD + QED Simulation at the Physical Point DURR 2011 PL B701 265 Lattice QCD at the Physical Point: Light Quark Masses BAZAVOV 2010 RMP 82 1349 Full Nonperturbative QCD Simulations with 2+1 Flavors of Improved Staggered Quarks BLUM 2010 PR D82 094508 Electromagnetic Mass Splittings of the Low Lying Hadrons and Quark Masses from 2+1 Flavor Lattice QCD+QED DAVIES 2010 PRL 104 132003 Precise Charm to Strange Mass Ratio and Light Quark Masses from Full Lattice QCD MCNEILE 2010 PR D82 034512 High-Precision ${\mathit {\mathit c}}$ and ${\mathit {\mathit b}}$ Masses, and QCD Coupling from Current-Current Correlators in Lattice and Continuum QCD DOMINGUEZ 2009 PR D79 014009 Up- and Down-Quark Masses from Finite-Energy QCD Sum Rules to Five Loops DEANDREA 2008 PR D78 034032 Determination of Light Quark Masses from ${{\mathit \eta}}$ $\rightarrow$ 3 ${{\mathit \pi}^{0}}$ BLUM 2007 PR D76 114508 Determination of Light Quark Masses from the Electromagnetic Splitting of Pseudoscalar Meson Masses Computed with Two Flavors of Domain Wall Fermions JAMIN 2006 PR D74 074009 Scalar ${{\mathit K}}{{\mathit \pi}}$ Form Factor and Light-Quark Masses MASON 2006 PR D73 114501 High-Precision Determination of the Light-Quark Masses from Realistic Lattice QCD NARISON 2006 PR D74 034013 Strange Quark Mass from ${{\mathit e}^{+}}{{\mathit e}^{-}}$ Revisited and Present Status of Light Quark Masses AUBIN 2004A PR D70 114501 Light Pseudoscalar Decay Constants, Quark Masses, and Low Energy Constants from three-flavor Lattice QCD