# $\boldsymbol Q$ MASS RATIO INSPIRE search

$\mathit Q{}\equiv\sqrt {({{\mathit m}^{2}}_{{{\mathit s}}}−{{\overline{\mathit m}}}{}^{2})/({{\mathit m}^{2}}_{{{\mathit d}}}−{{\mathit m}^{2}}_{{{\mathit u}}}) }$; ${{\overline{\mathit m}}}{}\equiv$ (${\mathit m}_{{{\mathit u}}}$ $+$ ${\mathit m}_{{{\mathit d}}})/$2
VALUE DOCUMENT ID TECN
• • • We do not use the following data for averages, fits, limits, etc. • • •
$22.1$ $\pm0.7$ 1
 2018
THEO
$22.0$ $\pm0.7$ 2
 2017
THEO
$21.6$ $\pm1.1$ 3
 2017
THEO
$23.4$ $\pm0.4$ $\pm0.5$ 4
 2016
LATT
$21.4$ $\pm0.4$ 5
 2015 F
THEO
$22.8$ $\pm0.4$ 6
 2005
THEO
$22.7$ $\pm0.8$ 7
 1996
THEO
1  COLANGELO 2018 obtain ${{\mathit Q}}$ from a dispersive analysis of ${{\mathit \eta}}$ $\rightarrow$ 3 ${{\mathit \pi}}$ decay.
2  COLANGELO 2017 obtain ${{\mathit Q}}$ from a dispersive analysis of KLOE collaboration data on ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ decays and chiral perturbation theory input.
3  GUO 2017 determine ${{\mathit Q}}$ from a dispersive model fit to KLOE and WASA-at-COSY data on ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ decay and matching to chiral perturbation theory .
4  FODOR 2016 is a lattice simulation with ${{\mathit N}_{{f}}}$ = 2 + 1 dynamical flavors and includes partially quenched QED effects.
5  GUO 2015F determine ${{\mathit Q}}$ from a Khuri-Treiman analysis of ${{\mathit \eta}}$ $\rightarrow$ 3 ${{\mathit \pi}}$ decays.
6  MARTEMYANOV 2005 determine $\mathit Q$ from ${{\mathit \eta}}$ $\rightarrow$ 3 ${{\mathit \pi}}$ decay.
7  ANISOVICH 1996 find $\mathit Q$ from ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ decay using dispersion relations and chiral perturbation theory.
References:
 COLANGELO 2018
EPJ C78 947 Dispersive analysis of $\eta \rightarrow 3 \pi$
 COLANGELO 2017
PRL 118 022001 The Decay ${{\mathit \eta}}$ $\rightarrow$ 3 ${{\mathit \pi}}$ : Study of the Dalitz Plot and Extraction of the Quark Mass Ratio
 GUO 2017
PL B771 497 Three-Body Final State Interaction in ${{\mathit \eta}}$ $\rightarrow$ 3 ${{\mathit \pi}}$ Updated
 FODOR 2016
PRL 117 082001 Up and Down Quark Masses and Corrections to Dashen's Theorem from Lattice QCD and Quenched QED
 GUO 2015F
PR D92 054016 Three-Body Final State Interaction in ${{\mathit \eta}}$ $\rightarrow$ 3 ${{\mathit \pi}}$
 MARTEMYANOV 2005
PR D71 017501 Light Quark Mass Ratio from the Dalitz Plot of ${{\mathit \eta}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ Decay
 ANISOVICH 1996
PL B375 335 Dispersive Analysis of the Decay ${{\mathit \eta}}$ $\rightarrow$ 3 ${{\mathit \pi}}$