#### ${{\overline{\mathit m}}}$ = (${\mathit m}_{{{\mathit u}}}+{\mathit m}_{{{\mathit d}}})/$2

See the comments for the ${{\mathit u}}$ quark above.

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
 $\bf{ 3.45 {}^{+0.35}_{-0.15}}$ OUR EVALUATION See the ideogram below.
$3.636$ $\pm0.066$ ${}^{+0.060}_{-0.057}$ 1
 2021
LATT
$3.54$ $\pm0.12$ $\pm0.09$ 2
 2020
LATT
$3.9$ $\pm0.3$ 3
 2019
THEO
$4.7$ ${}^{+0.8}_{-0.7}$ 4
 2017
THEO
$3.70$ $\pm0.17$ 5
 2014
LATT
$3.45$ $\pm0.12$ 6
 2013
LATT
$3.469$ $\pm0.047$ $\pm0.048$ 7
 2011
LATT
$3.6$ $\pm0.2$ 8
 2010
LATT
$3.39$ $\pm0.06$ 9
 2010
LATT
• • We do not use the following data for averages, fits, limits, etc. • •
$3.59$ $\pm0.21$ 10
 2011 A
LATT
$3.40$ $\pm0.07$ 9
 2010
LATT
$4.1$ $\pm0.2$ 11
 2009
THEO
$3.72$ $\pm0.41$ 12
 2008
LATT
$3.85$ $\pm0.12$ $\pm0.4$ 13
 2008
LATT
$>=4.85 \pm0.20$ 14
 2008 B
THEO
$3.55$ ${}^{+0.65}_{-0.28}$ 15
 2008
LATT
$4.026$ $\pm0.048$ 16
 2008
LATT
$4.25$ $\pm0.35$ 17
 2007
LATT
$4.08$ $\pm0.25$ $\pm0.42$ 18
 2006
LATT
$4.7$ $\pm0.2$ $\pm0.3$ 19
 2006 A
LATT
$3.2$ $\pm0.3$ 20
 2006
LATT
$3.95$ $\pm0.3$ 21
 2006
THEO
$2.8$ $\pm0.3$ 22
 2004
LATT
$4.29$ $\pm0.14$ $\pm0.65$ 23
 2003
LATT
$3.223$ $\pm0.3$ 24
 2003 B
LATT
$4.4$ $\pm0.1$ $\pm0.4$ 25
 2003
LATT
$4.1$ $\pm0.3$ $\pm1.0$ 26
 2003
LATT
 1 ALEXANDROU 2021 determines the quark mass using a lattice calculation of the meson and baryon masses with a twisted mass fermion action. The simulations are carried out using 2+1+1 dynamical quarks with ${\mathit m}_{{{\mathit u}}}$ = ${\mathit m}_{{{\mathit d}}}{}\not={\mathit m}_{{{\mathit s}}}{}\not={\mathit m}_{{{\mathit c}}}$, including gauge ensembles close to the physical pion point.
 2 BRUNO 2020 determines the light quark mass using a lattice calculation with ${{\mathit n}_{{f}}}$ = 2+1 flavors of Wilson fermions. The scale has been set from ${{\mathit f}_{{\pi}}}$ and ${{\mathit f}_{{K}}}$ . The tuning was done using the masses of the lightest (${{\mathit \pi}}$ ) and strange (${{\mathit K}}$ ) pseudoscalar mesons.
 3 DOMINGUEZ 2019 determine the quark mass from a QCD finite energy sum rule for the divergence of the axial current.
 4 YUAN 2017 determine ${{\overline{\mathit m}}}$ using QCD sum rules in the isospin ${{\mathit I}}$ =0 scalar channel. At the end of the "Numerical Results" section of YUAN 2017 the authors discuss the significance of their larger value of the light quark mass compared to previous determinations.
 5 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.
 6 ARTHUR 2013 is a lattice computation using 2+1 dynamical domain wall fermions. Masses at ${{\mathit \mu}}$ = 3 GeV have been converted to ${{\mathit \mu}}$ = 2 GeV using conversion factors given in their paper.
 7 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.
 8 BLOSSIER 2010 determines quark masses from a computation of the hadron spectrum using ${{\mathit n}_{{f}}}$ =2 dynamical twisted-mass Wilson fermions.
 9 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 ${{\overline{\mathit m}}}$ 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 ratio, ${\mathit m}_{{{\mathit s}}}/{{\overline{\mathit m}}}$ .
 10 AOKI 2011A determine quark masses from a lattice computation of the hadron spectrum using ${{\mathit n}_{{f}}}$ = 2 + 1 dynamical flavors of domain wall fermions.
 11 DOMINGUEZ 2009 use QCD finite energy sum rules for the two-point function of the divergence of the axial vector current computed to order $\alpha {}^{4}_{s}$.
 12 ALLTON 2008 use a lattice computation of the ${{\mathit \pi}}$ , ${{\mathit K}}$ , and ${{\mathit \Omega}}$ masses with 2+1 dynamical flavors of domain wall quarks, and non-perturbative renormalization.
 13 BLOSSIER 2008 use a lattice computation of pseudoscalar meson masses and decay constants with 2 dynamical flavors and non-perturbative renormalization.
 14 DOMINGUEZ-CLARIMON 2008B obtain an inequality from sum rules for the scalar two-point correlator.
 15 ISHIKAWA 2008 use a lattice computation of the light meson spectrum with 2+1 dynamical flavors of $\cal O(\mathit a$) improved Wilson quarks, and one-loop perturbative renormalization.
 16 NAKAMURA 2008 do a lattice computation using quenched domain wall fermions and non-perturbative renormalization.
 17 BLUM 2007 determine quark masses from the pseudoscalar meson masses using a QED plus QCD lattice computation with two dynamical quark flavors.
 18 GOCKELER 2006 use an unquenched lattice computation of the axial Ward Identity with ${{\mathit n}_{{f}}}$ = 2 dynamical light quark flavors, and non-perturbative renormalization, to obtain ${{\overline{\mathit m}}}$ (2 GeV) = $4.08$ $\pm0.25$ $\pm0.19$ $\pm0.23$ MeV, where the first error is statistical, the second and third are systematic due to the fit range and force scale uncertainties, respectively. We have combined the systematic errors linearly.
 19 GOCKELER 2006A use an unquenched lattice computation of the pseudoscalar meson masses with ${{\mathit n}_{{f}}}$ = 2 dynamical light quark flavors, and non-perturbative renormalization.
 20 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.
 21 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.
 22 AUBIN 2004 perform three flavor dynamical lattice calculation of pseudoscalar meson masses, with one-loop perturbative renormalization constant.
 23 AOKI 2003 uses quenched lattice simulation of the meson and baryon masses with degenerate light quarks. The extrapolations are done using quenched chiral perturbation theory.
 24 The errors given in AOKI 2003B were ${}^{+0.046}_{-0.069}$. We changed them to $\pm0.3$ for calculating the overall best values. AOKI 2003B uses lattice simulation of the meson and baryon masses with two dynamical light quarks. Simulations are performed using the $\cal O(\mathit a$) improved Wilson action.
 25 BECIREVIC 2003 perform quenched lattice computation using the vector and axial Ward identities. Uses $\cal O(\mathit a$) improved Wilson action and nonperturbative renormalization.
 26 CHIU 2003 determines quark masses from the pion and kaon masses using a lattice simulation with a chiral fermion action in quenched approximation.

${{\overline{\mathit m}}}$ = (${\mathit m}_{{{\mathit u}}}+{\mathit m}_{{{\mathit d}}})/$2 (MeV)
References:
 ALEXANDROU 2021
PR D104 074515 Quark masses using twisted mass fermion gauge ensembles
 BRUNO 2020
EPJ C80 169 Light quark masses in ${N_\mathrm{f}=2+1}$ lattice QCD with Wilson fermions
 DOMINGUEZ 2019
JHEP 1902 057 Up- and down-quark masses from QCD sum rules
 YUAN 2017
PR D96 014034 Constraint on the Light Quark Mass ${\mathit m}_{{{\mathit q}}}$ from QCD Sum Rules in the $\mathit I = 0$ Scalar Channel
 CARRASCO 2014
NP B887 19 Up, Down, Strange and Charm Quark Masses with $\mathit N_{f}$ = 2+1+1 Twisted Mass Lattice QCD
 ARTHUR 2013
PR D87 094514 Domain Wall QCD with Near-Physical Pions
 AOKI 2011A
PR D83 074508 Continuum Limit Physics from 2+1 Flavor Domain Wall QCD
 DURR 2011
PL B701 265 Lattice QCD at the Physical Point: Light Quark Masses
 BLOSSIER 2010
PR D82 114513 Average up/down, strange, and charm Quark Masses with $\mathit N_{f}$=2 Twisted-Mass Lattice QCD
 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
 ALLTON 2008
PR D78 114509 Physical Results from 2+1 Flavor Domain Wall QCD and SU(2) Chiral Perturbation Theory
 BLOSSIER 2008
JHEP 0804 020 Light Quark Masses and Pseudoscalar Decay Constants from $\mathit N_{f}$ = 2 Lattice QCD with Twisted Mass Fermions
 DOMINGUEZ-CLARIMON 2008B
PL B660 49 Bounds on the Light Quark Masses: The Scalar Channel Revisited
 ISHIKAWA 2008
PR D78 011502 Light Quark Masses from Unquenched Lattice QCD
 NAKAMURA 2008
PR D78 034502 Precise Determination of $\mathit B_{K}$ and Light Quark Masses in Quenched Domain-wall QCD
 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
 GOCKELER 2006
PR D73 054508 Estimating the Unquenched Strange Quark Mass from the Lattice Axial Ward Identity
 GOCKELER 2006A
PL B639 307 Determination of Light and Strange Quark Masses from Two-Flavour Dynamical Lattice QCD
 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 2004
PR D70 031504 First Determination of the Strange and Light Quark Masses from Full Lattice QCD
 AOKI 2003
PR D67 034503 Light Hadron Spectrum and Quark Masses from Quenched Lattice QCD
 AOKI 2003B
PR D68 054502 Light Hadron Spectroscopy with Two Flavors of $\mathit O(a)$-improved Dynamical Quarks
 BECIREVIC 2003
PL B558 69 Continuum Determination of Light Quark Masses from Quenched Lattice QCD
 CHIU 2003
NP B673 217 Light Quark Masses, Chiral Condensate and Quark Gluon Condensate in Quenched Lattice QCD with Exact Chiral Symmetry