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

INSPIRE JSON (beta) PDGID:

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 $1.35$.

$\overline{\rm{}MS}$ MASS (MeV)

DOCUMENT ID

TECN

$\bf{ 93.5 \pm0.8}$

OUR EVALUATION

See the ideogram below.

$98.7$ $\pm2.4$ ${}^{+4.0}_{-3.2}$

LATT

$95.7$ $\pm2.5$ $\pm2.4$

LATT

$92.47$ $\pm0.69$

LATT

$93.85$ $\pm0.75$

LATT

$87.6$ $\pm6.0$

ANANTHANARAYA..

THEO

$99.6$ $\pm4.3$

LATT

$94.4$ $\pm2.3$

LATT

$94$ $\pm9$

THEO

$95.5$ $\pm1.1$ $\pm1.5$

LATT

• • We do not use the following data for averages, fits, limits, etc. • •

$93.6$ $\pm0.8$

LATT

$102$ $\pm3$ $\pm1$

LATT

$96.2$ $\pm2.7$

LATT

$95$ $\pm6$

LATT

$97.6$ $\pm2.9$ $\pm5.5$

LATT

$92.4$ $\pm1.5$

LATT

$92.2$ $\pm1.3$

LATT

$107.3$ $\pm11.7$

LATT

$105$ $\pm3$ $\pm9$

LATT

$102$ $\pm8$

THEO

$90.1$ ${}^{+17.2}_{-6.1}$

LATT

$105.6$ $\pm1.2$

LATT

$119.5$ $\pm9.3$

LATT

$105$ $\pm6$ $\pm7$

THEO

$111$ $\pm6$ $\pm10$

LATT

$119$ $\pm5$ $\pm8$

LATT

$92$ $\pm9$

THEO

$87$ $\pm6$

LATT

$104$ $\pm15$

THEO

${}\geq{}\text{ 71 }\pm4, {}\leq{}\text{ 151 }\pm14$

THEO

$96$ ${}^{+5}_{-3}$ ${}^{+16}_{-18}$

THEO

$81$ $\pm22$

THEO

$125$ $\pm28$

THEO

$93$ $\pm32$

THEO

$76$ $\pm8$

LATT

$116$ $\pm6$ $\pm0.65$

LATT

$84.5$ ${}^{+12}_{-1.7}$

LATT

$106$ $\pm2$ $\pm8$

LATT

$92$ $\pm9$ $\pm16$

LATT

$117$ $\pm17$

THEO

$103$ $\pm17$

THEO

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	BAZAVOV 2018 determine the quark masses using a lattice computation with staggered fermions and four active quark flavors.

⁴

LYTLE 2018 combined with CHAKRABORTY 2015 determine ${{\overline{\mathit m}}_{{{s}}}}$(3 GeV) = $84.78$ $\pm0.65$ MeV from a lattice simulation with ${{\mathit n}_{{{f}}}}$ = 2+1+1 flavors. They also determine the quoted value ${{\overline{\mathit m}}_{{{s}}}}$(2 GeV) for ${{\mathit n}_{{{f}}}}$ = 4 dynamical flavors.

⁵	ANANTHANARAYAN 2016 determine ${{\overline{\mathit m}}_{{{s}}}}$(2 GeV) = $106.70$ $\pm9.36$ MeV and $74.47$ $\pm7.77$ MeV from fits to ALEPH and OPAL ${{\mathit \tau}}$ decay data, respectively. We have used the weighted average of the two.

⁶

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.

⁷	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.

⁸	BODENSTEIN 2013 determines ${\mathit m}_{{{\mathit s}}}$ from QCD finite energy sum rules, and the perturbative computation of the pseudoscalar correlator to five-loop order.

⁹	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.

¹⁰

CHAKRABORTY 2015 is a lattice QCD computation that determines ${\mathit m}_{{{\mathit c}}}$ and ${\mathit m}_{{{\mathit c}}}/{\mathit m}_{{{\mathit s}}}$ using pseudoscalar mesons masses tuned on gluon field configurations with 2+1+1 dynamical flavors of HISQ quarks with ${{\mathit u}}/{{\mathit d}}$ masses down to the physical value.

¹¹	FRITZSCH 2012 determine ${\mathit m}_{{{\mathit s}}}$ using a lattice computation with ${{\mathit n}_{{{f}}}}$ = 2 dynamical flavors.

¹²	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.

¹³	BLOSSIER 2010 determines quark masses from a computation of the hadron spectrum using ${{\mathit n}_{{{f}}}}$=2 dynamical twisted-mass Wilson fermions.

¹⁴	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.

¹⁵

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 ${\mathit m}_{{{\mathit s}}}$ is obtained from this using the value of ${\mathit m}_{{{\mathit c}}}$ from ALLISON 2008 or MCNEILE 2010.

¹⁶	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.

¹⁷	BLOSSIER 2008 use a lattice computation of pseudoscalar meson masses and decay constants with 2 dynamical flavors and non-perturbative renormalization.

¹⁸	DOMINGUEZ 2008A make determination from QCD finite energy sum rules for the pseudoscalar two-point function computed to order $\alpha {}^{4}_{s}$.

¹⁹	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.

²⁰	NAKAMURA 2008 do a lattice computation using quenched domain wall fermions and non-perturbative renormalization.

²¹	BLUM 2007 determine quark masses from the pseudoscalar meson masses using a QED plus QCD lattice computation with two dynamical quark flavors.

²²	CHETYRKIN 2006 use QCD sum rules in the pseudoscalar channel to order ${{\mathit \alpha}_{{{s}}}^{4}}$.

²³

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 ${{\overline{\mathit m}}_{{{s}}}}$(2 GeV) = $111$ $\pm6$ $\pm4$ $\pm6$ 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.

²⁴	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.

²⁵	JAMIN 2006 determine ${{\overline{\mathit m}}_{{{s}}}}$(2 GeV) from the spectral function for the scalar ${{\mathit K}}{{\mathit \pi}}$ form factor.

²⁶	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.

²⁷	NARISON 2006 uses sum rules for ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ hadrons to order ${{\mathit \alpha}_{{{s}}}^{3}}$.

²⁸	NARISON 2006 obtains the quoted range from positivity of the spectral functions.

²⁹

BAIKOV 2005 determines ${{\overline{\mathit m}}_{{{s}}}}({{\mathit M}_{{{\tau}}}}$) = $100$ ${}^{+5}_{-3}{}^{+17}_{-19}$ from sum rules using the strange spectral function in ${{\mathit \tau}}$ decay. The computations were done to order ${{\mathit \alpha}_{{{s}}}^{3}}$, with an estimate of the ${{\mathit \alpha}_{{{s}}}^{4}}$ terms. We have converted the result to ${{\mathit \mu}}$ = 2 GeV.

³⁰	GAMIZ 2005 determines ${{\overline{\mathit m}}_{{{s}}}}$(2 GeV) from sum rules using the strange spectral function in ${{\mathit \tau}}$ decay. The computations were done to order ${{\mathit \alpha}_{{{s}}}^{2}}$, with an estimate of the ${{\mathit \alpha}_{{{s}}}^{3}}$ terms.

³¹	GORBUNOV 2005 use hadronic tau decays to N3LO, including power corrections.

³²	NARISON 2005 determines ${{\overline{\mathit m}}_{{{s}}}}$(2 GeV) from sum rules using the strange spectral function in ${{\mathit \tau}}$ decay. The computations were done to order ${{\mathit \alpha}_{{{s}}}^{3}}$.

³³	AUBIN 2004 perform three flavor dynamical lattice calculation of pseudoscalar meson masses, with one-loop perturbative renormalization constant.

³⁴

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. Determines m$_{s}=113.8$ $\pm2.3$ ${}^{+5.8}_{-2.9}$ using ${{\mathit K}}$ mass as input and m$_{s}=142.3$ $\pm5.8$ ${}^{+22}_{-0}$ using ${{\mathit \phi}}$ mass as input. We have performed a weighted average of these values.

³⁵	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.

³⁶	BECIREVIC 2003 perform quenched lattice computation using the vector and axial Ward identities. Uses $\cal O(\mathit a$) improved Wilson action and nonperturbative renormalization. They also quote ${{\overline{\mathit m}}}$/m$_{s}=24.3$ $\pm0.2$ $\pm0.6$.

³⁷	CHIU 2003 determines quark masses from the pion and kaon masses using a lattice simulation with a chiral fermion action in quenched approximation.

³⁸	GAMIZ 2003 determines ${\mathit m}_{{{\mathit s}}}$ from SU(3) breaking in the ${{\mathit \tau}}~$hadronic width. The value of $\mathit V_{{{\mathit u}} {{\mathit s}}}$ is chosen to satisfy CKM unitarity.

³⁹	GAMIZ 2003 determines ${\mathit m}_{{{\mathit s}}}$ from SU(3) breaking in the ${{\mathit \tau}}~$hadronic width. The value of $\mathit V_{{{\mathit u}} {{\mathit s}}}$ is taken from the PDG.

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

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