${\mathit {\mathit d}}$-QUARK MASS

INSPIRE   PDGID:
Q123DM
See the comment 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$~$2 and 3 in the “Quark masses” review.
VALUE (MeV) DOCUMENT ID TECN
$\bf{ 4.70 \pm0.07}$ OUR EVALUATION  See the ideogram below.
$5.3$ $\pm0.4$ 1
DOMINGUEZ
2019
THEO
$4.675$ $\pm0.056$ 2
BAZAVOV
2018
LATT
$4.67$ $\pm0.06$ $\pm0.06$ 3
FODOR
2016
LATT
$5.03$ $\pm0.26$ 4
CARRASCO
2014
LATT
$4.65$ $\pm0.15$ $\pm0.32$ 5
BLUM
2010
LATT
$4.77$ $\pm0.15$ 6
MCNEILE
2010
LATT
• • We do not use the following data for averages, fits, limits, etc. • •
$3.68$ $\pm0.29$ $\pm0.10$ 7
AOKI
2012
LATT
$4.79$ $\pm0.07$ $\pm0.12$ 8
DURR
2011
LATT
$4.6$ $\pm0.3$ 9
BAZAVOV
2010
LATT
$4.79$ $\pm0.16$ 6
DAVIES
2010
LATT
$5.3$ $\pm0.4$ 10
DOMINGUEZ
2009
THEO
$4.7$ $\pm0.8$ 11
DEANDREA
2008
THEO
$5.49$ $\pm0.39$ 12
BLUM
2007
LATT
$4.8$ $\pm0.5$ 13
JAMIN
2006
THEO
$4.4$ $\pm0.3$ 14
MASON
2006
LATT
$5.1$ $\pm0.4$ 15
NARISON
2006
THEO
$3.9$ $\pm0.5$ 16
AUBIN
2004A
 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 ${\mathit m}_{{{\mathit d}}}$ 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 ${\mathit m}_{{{\mathit d}}}$(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 perform three flavor dynamical lattice calculation of pseudoscalar meson masses, with continuum estimate of electromagnetic effects in the kaon masses, and one-loop perturbative renormalization constant.

           ${\mathit {\mathit d}}$-QUARK MASS (MeV)
References