# ${\boldsymbol {\boldsymbol u}}$-QUARK MASS INSPIRE search

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
$\bf{ 2.2 {}^{+0.5}_{-0.4}}$ OUR EVALUATION
$2.27$ $\pm0.06$ $\pm0.06$ 1
 2016
LATT
$2.36$ $\pm0.24$ 2
 2014
LATT
$2.57$ $\pm0.26$ $\pm0.07$ 3
 2012
LATT
$2.15$ $\pm0.03$ $\pm0.10$ 4
 2011
LATT
$1.9$ $\pm0.2$ 5
 2010
LATT
$2.24$ $\pm0.10$ $\pm0.34$ 6
 2010
LATT
$2.01$ $\pm0.14$ 7
 2010
LATT
$2.9$ $\pm0.2$ 8
 2009
THEO
• • • We do not use the following data for averages, fits, limits, etc. • • •
$2.01$ $\pm0.14$ 7
 2010
LATT
$2.9$ $\pm0.8$ 9
 2008
THEO
$3.02$ $\pm0.33$ 10
 2007
LATT
$2.7$ $\pm0.4$ 11
 2006
THEO
$1.9$ $\pm0.2$ 12
 2006
LATT
$2.8$ $\pm0.2$ 13
 2006
THEO
$1.7$ $\pm0.3$ 14
 2004 A
LATT
1  FODOR 2016 is a lattice simulation with ${{\mathit N}_{{f}}}$ = 2 + 1 dynamical flavors and includes partially quenched QED effects.
2  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.
3  AOKI 2012 is a lattice computation using 1 + 1 + 1 dynamical quark flavors.
4  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.
5  BAZAVOV 2010 is a lattice computation using 2+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  DOMINGUEZ 2009 use QCD finite energy sum rules for the two-point function of the divergence of the axial vector current computed to order $\alpha {}^{4}_{s}$.
9  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 ${\mathit m}_{{{\mathit d}}}$.
10  BLUM 2007 determine quark masses from the pseudoscalar meson masses using a QED plus QCD lattice computation with two dynamical quark flavors.
11  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.
12  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.
13  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.
14  AUBIN 2004A employ a partially quenched lattice calculation of the pseudoscalar meson masses.

${\mathit {\mathit u}}$-QUARK MASS (MeV)
References:
 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
 PDG 2006
JP G33 1 Review of Particle Physics 2006