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STRANGE MESONS ($\mathit S$ = $\pm1$, $\mathit C$ = $\mathit B$ = 0) ${{\mathit K}^{+}}$ = ${\mathit {\mathit u}}$ ${\mathit {\overline{\mathit s}}}$, ${{\mathit K}^{0}}$ = ${\mathit {\mathit d}}$ ${\mathit {\overline{\mathit s}}}$, ${{\overline{\mathit K}}^{0}}$ = ${\mathit {\overline{\mathit d}}}$ ${\mathit {\mathit s}}$, ${{\mathit K}^{-}}$ = ${\mathit {\overline{\mathit u}}}$ ${\mathit {\mathit s}}$, similarly for ${{\mathit K}^{*}}$'s

INSPIRE   JSON PDGID: S013

${{\mathit K}_L^0}$ $I(J^P)$ = $1/2(0^{-})$

See related reviews:
$\mathit V_{{\mathit {\mathit u}}{\mathit {\mathit d}}}$, $\mathit V_{{\mathit {\mathit u}}{\mathit {\mathit s}}}$ the Cabibbo Angle, and CKM Unitarity
$\mathit CP$ Violation in ${{\mathit K}_L^0}$ Decays
$\Delta \mathit S$ = $\Delta \mathit Q$ in ${{\mathit K}^{0}}$ Decays

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$\Delta \mathit m$ ($52.81$ $\pm0.09$) $ \times 10^{8}$ $\hbar{}$ s${}^{-1}$

${{\mathit K}_L^0}$ MEAN LIFE ($5.099$ $\pm0.021$) $ \times 10^{-8}$ s

▸  exp ENERGY DEPENDENCE OF ${{\mathit K}_L^0}$ DALITZ PLOT

LINEAR COEFFICIENT $\mathit g$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $0.678$ $\pm0.008$  (S = 1.5)

QUADRATIC COEFFICIENT $\mathit h$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $0.076$ $\pm0.006$

QUADRATIC COEFFICIENT $\mathit k$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $0.0099$ $\pm0.0015$

LINEAR COEFFICIENT $\mathit j$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ ($\mathit CP$-VIOLATING TERM)

QUADRATIC COEFFICIENT $\mathit f$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ ($\mathit CP$-VIOLATING TERM)

QUADRATIC COEFFICIENT $\mathit h$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ $0.0006$ $\pm0.0012$

▸  exp ${{\mathit K}_L^0}$ FORM FACTORS

$\lambda _{+}$ (LINEAR ENERGY DEPENDENCE OF $\mathit f_{+}$ IN ${{\mathit K}_{{{e3}}}^{0}}$ DECAY) $0.0282$ $\pm0.0004$  (S = 1.1)

$\lambda _{+}$ (LINEAR ENERGY DEPENDENCE OF $\mathit f_{+}$ IN ${{\mathit K}_{{{\mu3}}}^{0}}$ DECAY) $0.0271$ $\pm0.0010$  (S = 1.4)

$\lambda _{0}$ (LINEAR ENERGY DEPENDENCE OF $\mathit f_{0}$ IN ${{\mathit K}_{{{\mu3}}}^{0}}$ DECAY) $0.0138$ $\pm0.0018$  (S = 2.2)

$\lambda $'$_{+}$(LINEAR ${{\mathit K}_{{{e3}}}^{0}}$ FORM FACTOR FROM QUADRATIC FIT) $0.0240$ $\pm0.0012$  (S = 1.2)

$\lambda $''$_{+}$(QUADRATIC ${{\mathit K}_{{{e3}}}^{0}}$ FORM FACTOR) $0.0016$ $\pm0.0005$  (S = 1.1)

$\lambda $'$_{+}$(LINEAR ${{\mathit K}_{{{\mu3}}}^{0}}$ FORM FACTOR FROM QUADRATIC FIT) $0.0189$ $\pm0.0024$

$\lambda $''$_{+}$(QUADRATIC ${{\mathit K}_{{{\mu3}}}^{0}}$ FORM FACTOR) $0.0020$ $\pm0.0005$  (S = 1.2)

$\lambda _{0}$(LINEAR $\mathit f_{0}{{\mathit K}_{{{\mu3}}}^{0}}$ FORM FACTOR FROM QUADRATIC FIT) $0.0107$ $\pm0.0014$  (S = 1.3)

$M{}^{{{\mathit e}}}_{V}$ (POLE MASS FOR ${{\mathit K}_{{{e3}}}^{0}}$ DECAY) $875$ $\pm5$ MeV

$M{}^{{{\mathit \mu}}}_{V}$ (POLE MASS FOR ${{\mathit K}_{{{\mu3}}}^{0}}$ DECAY) $878$ $\pm6$ MeV (S = 1.1)

$M{}^{{{\mathit \mu}}}_{S}$ (POLE MASS FOR ${{\mathit K}_{{{\mu3}}}^{0}}$ DECAY) $1220$ $\pm80$ MeV (S = 2.3)

${{\mathit \Lambda}_{{{+}}}}$ (DISPERSIVE VECTOR FORM FACTOR FOR ${{\mathit K}_{{{\mu3}}}^{0}}$ DECAY) $0.0251$ $\pm0.0006$  (S = 1.5)

ln$\mathit (C)$ (DISPERSIVE SCALAR FORM FACTOR FOR ${{\mathit K}_{{{\mu3}}}^{0}}$ DECAY) $0.175$ $\pm0.018$  (S = 2.0)

$\mathit a_{1}(\mathit t_{0}$, $\mathit Q{}^{2}$) FORM FACTOR PARAMETER $1.02$ $\pm0.04$

$\mathit a_{2}(\mathit t_{0}$, $\mathit Q{}^{2}$) FORM FACTOR PARAMETER $0.8$ $\pm2.2$

$\vert \mathit f_{\mathit S}/\mathit f_{+}\vert $ FOR ${{\mathit K}_{{{e3}}}^{0}}$ DECAY $0.015^{+0.014}_{-0.016}$

$\vert \mathit f_{\mathit T}/\mathit f_{+}\vert $ FOR ${{\mathit K}_{{{e3}}}^{0}}$ DECAY $0.05^{+0.04}_{-0.05}$

$\vert \mathit f_{\mathit T}/\mathit f_{+}\vert $ FOR ${{\mathit K}_{{{\mu3}}}^{0}}$ DECAY $0.12$ $\pm0.12$

$\alpha _{{{\mathit K}^{*}}}$ DECAY FORM FACTOR FOR ${{\mathit K}_{{{L}}}}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}{{\mathit \gamma}}$, ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}{{\mathit \ell}^{'+}}{{\mathit \ell}^{'-}}$ $-0.205$ $\pm0.022$  (S = 1.8)

$\alpha _{{{\mathit K}^{*}}}$ DECAY FORM FACTOR FOR ${{\mathit K}_{{{L}}}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \gamma}}$ $-0.217$ $\pm0.034$  (S = 2.4)

$\alpha _{{{\mathit K}^{*}}}$ DECAY FORM FACTOR FOR ${{\mathit K}_{{{L}}}}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{{\mathit \gamma}}$ $-0.158$ $\pm0.027$

$\alpha {}^{{\mathrm {eff}}}_{{{\mathit K}^{*}}}$ DECAY FORM FACTOR FOR ${{\mathit K}_{{{L}}}}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ $-0.14$ $\pm0.22$

$\alpha _{DIP}$ DECAY FORM FACTOR FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}{{\mathit \gamma}}$, ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \ell}^{+}}{{\mathit \ell}^{-}}{{\mathit \ell}^{'+}}{{\mathit \ell}^{'-}}$ $-1.69$ $\pm0.08$  (S = 1.7)

$\alpha _{DIP}$ DECAY FORM FACTOR FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \gamma}}$ $-1.73$ $\pm0.05$

$\alpha _{DIP}$ DECAY FORM FACTOR FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{{\mathit \gamma}}$ $-1.54$ $\pm0.10$

$\alpha _{DIP}$ DECAY FORM FACTOR FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $-1.6$ $\pm0.4$

a$_{1}$/a$_{2}$ FORM FACTOR FOR M1 DIRECT EMISSION AMPLITUDE $-0.737$ $\pm0.014$ GeV${}^{2}$

$\bar f_{S}$ DECAY FORM FACTOR FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}{{\mathit e}^{\mp}}{{\mathit \nu}_{{{e}}}}$ $0.049$ $\pm0.011$  (S = 1.7)

$\bar f_{P}$ DECAY FORM FACTOR FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}{{\mathit e}^{\mp}}{{\mathit \nu}_{{{e}}}}$ $-0.052$ $\pm0.012$

$\lambda _{g}$ DECAY FORM FACTOR FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}{{\mathit e}^{\mp}}{{\mathit \nu}_{{{e}}}}$ $0.085$ $\pm0.020$

$\bar h$ DECAY FORM FACTOR FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}{{\mathit e}^{\mp}}{{\mathit \nu}_{{{e}}}}$ $-0.30$ $\pm0.13$

$\mathit L_{3}$ CHIRAL PERT. THEO. PARAM. FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{\pm}}{{\mathit \pi}^{0}}{{\mathit e}^{\mp}}{{\mathit \nu}_{{{e}}}}$ $-0.00396$ $\pm0.00028$  (S = 1.6)

$\mathit a_{\mathit V}$, VECTOR MESON EXCHANGE CONTRIBUTION $-0.43$ $\pm0.06$  (S = 1.5)

▸  exp CHARGE ASYMMETRY IN ${{\mathit K}_{{{\ell3}}}^{0}}$ DECAYS

$\mathit A_{\mathit L}$ = weighted average of $\mathit A_{\mathit L}({{\mathit \mu}}$) and $\mathit A_{\mathit L}({{\mathit e}}$) $0.00332$ $\pm0.00006$

$\mathit A_{\mathit L}({{\mathit \mu}}$) = [$\Gamma\mathrm {({{\mathit \pi}^{-}} {{\mathit \mu}^{+}} {{\mathit \nu}_{{{\mu}}}})}$ $−$ $\Gamma\mathrm {({{\mathit \pi}^{+}} {{\mathit \mu}^{-}} {{\overline{\mathit \nu}}_{{{\mu}}}})}$]/SUM $0.00304$ $\pm0.00025$

$\mathit A_{\mathit L}({{\mathit e}}$) = [$\Gamma\mathrm {({{\mathit \pi}^{-}} {{\mathit e}^{+}} {{\mathit \nu}_{{{e}}}})}$ $−$ $\Gamma\mathrm {({{\mathit \pi}^{+}} {{\mathit e}^{-}} {{\overline{\mathit \nu}}_{{{e}}}})}$]/SUM $0.00334$ $\pm0.00007$

▸  exp PARAMETERS FOR ${{\mathit K}_L^0}$ $\rightarrow$ 2 ${{\mathit \pi}}$ DECAY

$\vert \eta _{00}\vert $ = $\vert A({{\mathit K}_L^0}$ $\rightarrow$ 2 ${{\mathit \pi}^{0}}$) / A(${{\mathit K}_S^0}$ $\rightarrow$ 2 ${{\mathit \pi}^{0}})\vert $ $0.002220$ $\pm0.000011$  (S = 1.8)

$\vert \eta _{+−}\vert $ = $\vert A({{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$) / A(${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}})\vert $ $0.002226$ $\pm0.000007$

$\vert \epsilon \vert $ = (2$\vert \eta _{+−}\vert $ + $\vert \eta _{00}\vert $)/3 $0.002228$ $\pm0.000011$  (S = 1.8)

$\vert \eta _{00}/\eta _{+−}\vert $ [1] $0.9930$ $\pm0.0020$

Re($\epsilon {{}^\prime}/\epsilon $) = (1$−\vert \eta _{00}/\eta _{+−}\vert $)/3 [1] $0.00166$ $\pm0.00023$  (S = 1.6)

$\phi _{+−}$ $43.4$ $\pm0.5$ $^\circ{}$ (S = 1.2)

$\phi _{00}$ $43.52$ $\pm0.05$ $^\circ{}$ (S = 1.2)

$\phi _{\epsilon }$ $43.5$ $\pm0.5$ $^\circ{}$ (S = 1.3)

Im($\epsilon {{}^\prime}/\epsilon $) = $−(\phi _{00}$ $−$ $\phi _{+−}$)/3 $-0.002$ $\pm0.005$ $^\circ{}$ (S = 1.7)

▸  exp DECAY-PLANE ASYMMETRY IN ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ DECAYS

$\mathit CP$ ASYMMETRY $\mathit A$ in ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ $0.137$ $\pm0.015$

▸  exp PARAMETERS FOR ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ DECAYS

$\beta _{\mathit CP}$ from ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ $-0.19$ $\pm0.07$

$\gamma _{\mathit CP}$ from ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ $0.01$ $\pm0.11$  (S = 1.6)

▸  exp CHARGE ASYMMETRY IN ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ DECAYS

LINEAR COEFFICIENT $\mathit j$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $0.0012$ $\pm0.0008$

QUADRATIC COEFFICIENT $\mathit f$ FOR ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ $0.004$ $\pm0.006$

▸  exp PARAMETERS for ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ DECAY

$\vert \eta _{+−{{\mathit \gamma}}}\vert $ = $\vert A({{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ , $\mathit CP$ violating)/A(${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}})\vert $ $0.00235$ $\pm0.00007$

$\phi _{+−{{\mathit \gamma}}}$ = phase of $\eta _{+−{{\mathit \gamma}}}$ $44$ $\pm4$ $^\circ{}$

$\vert \epsilon {}^{'}_{+−{{\mathit \gamma}}}\vert /\epsilon $ for ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ <0.3   CL=90%

$\vert $g$_{E1}\vert $ for ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ < 0.21   CL=90%

▸  exp $\mathit T$ VIOLATION TESTS IN ${{\mathit K}_L^0}$ DECAYS

Im($\xi $) in ${{\mathit K}_{{{\mu3}}}^{0}}$ DECAY (from transverse ${{\mathit \mu}}$ pol.) $-0.007$ $\pm0.026$

▸  exp $\mathit CPT$-INVARIANCE TESTS IN ${{\mathit K}_L^0}$ DECAYS

$\Delta \phi $ $0.006$ $\pm0.014$ $^\circ{}$ (S = 1.7)

PHASE DIFFERENCE $\phi _{+−}$ $−$ $\phi _{{\mathrm {SW}}}$ $0.6$ $\pm1.2$ $^\circ{}$

Re(${2\over 3}\eta _{+−}$ $+$ ${1\over 3}\eta _{00})−{\mathit A_{L}\over 2}$ ($-0.3$ $\pm3.5$) $ \times 10^{-5}$

▸  exp $\mathit x$ = A(${{\overline{\mathit K}}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \ell}^{+}}{{\mathit \nu}})/A({{\mathit K}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \ell}^{+}}{{\mathit \nu}}$) = A($\Delta \mathit S=−\Delta \mathit Q)/A(\Delta \mathit S=\Delta \mathit Q$)

REAL PART OF $\mathit x$ $-0.002$ $\pm0.006$

IMAGINARY PART OF $\mathit x$ $0.0012$ $\pm0.0021$

${{\mathit K}_L^0}$ DECAY MODES

Mode   Fraction ($\Gamma_i$ / $\Gamma$) Scale Factor/ Conf. Level P(MeV/c)   ▸  exp Semileptonic modes $\Gamma_{1}$ ${{\mathit \pi}^{\pm}}{{\mathit e}^{\mp}}{{\mathit \nu}_{{{e}}}}$ [2] ($40.55$ $\pm0.11$ ) $\%$ S=1.7  229   $\Gamma_{2}$ ${{\mathit \pi}^{\pm}}{{\mathit \mu}^{\mp}}{{\mathit \nu}_{{{\mu}}}}$ [2] ($27.04$ $\pm0.07$ ) $\%$ S=1.1  216   $\Gamma_{3}$ (${{\mathit \pi}}{{\mathit \mu}}$ atom) ${{\mathit \nu}}$ ($1.05$ $\pm0.11$) $ \times 10^{-7}$ 188   $\Gamma_{4}$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{\pm}}{{\mathit e}^{\mp}}{{\mathit \nu}}$ [2] ($5.20$ $\pm0.11$) $ \times 10^{-5}$ 207   $\Gamma_{5}$ ${{\mathit \pi}^{\pm}}{{\mathit e}^{\mp}}{{\mathit \nu}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ [2] ($1.26$ $\pm0.04$) $ \times 10^{-5}$ 229   ▸  exp Hadronic modes, including Charge conjugation${\times }$Parity Violating ($\mathit CPV$) modes $\Gamma_{6}$ 3 ${{\mathit \pi}^{0}}$ ($19.52$ $\pm0.12$ ) $\%$ S=1.6  139   $\Gamma_{7}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ ($12.54$ $\pm0.05$ ) $\%$ 133   $\Gamma_{8}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ CPV [3] ($1.967$ $\pm0.010$) $ \times 10^{-3}$ S=1.5  206   $\Gamma_{9}$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ CPV ($8.64$ $\pm0.06$) $ \times 10^{-4}$ S=1.8  209   ▸  exp Semileptonic modes with photons $\Gamma_{10}$ ${{\mathit \pi}^{\pm}}{{\mathit e}^{\mp}}{{\mathit \nu}_{{{e}}}}{{\mathit \gamma}}$ [4] [5] [2] ($3.79$ $\pm0.06$) $ \times 10^{-3}$ 229   $\Gamma_{11}$ ${{\mathit \pi}^{\pm}}{{\mathit \mu}^{\mp}}{{\mathit \nu}_{{{\mu}}}}{{\mathit \gamma}}$ ($5.65$ $\pm0.23$) $ \times 10^{-4}$ 216   ▸  exp Hadronic modes with photons or ${{\mathit \ell}}{{\overline{\mathit \ell}}}$ pairs $\Gamma_{12}$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \gamma}}$ $<2.43$ $\times 10^{-7}$ CL=90% 209   $\Gamma_{13}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ [4] [5] ($4.15$ $\pm0.15$) $ \times 10^{-5}$ S=2.8  206   $\Gamma_{14}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$ (DE) ($2.84$ $\pm0.11$) $ \times 10^{-5}$ S=2.0  206   $\Gamma_{15}$ ${{\mathit \pi}^{0}}$2 ${{\mathit \gamma}}$ [4] ($1.273$ $\pm0.033$) $ \times 10^{-6}$ 230   $\Gamma_{16}$ ${{\mathit \pi}^{0}}{{\mathit \gamma}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ ($1.62$ $\pm0.17$) $ \times 10^{-8}$ 230   ▸  exp Other modes with photons or ${{\mathit \ell}}{{\overline{\mathit \ell}}}$ pairs $\Gamma_{17}$ 2 ${{\mathit \gamma}}$ ($5.47$ $\pm0.04$) $ \times 10^{-4}$ S=1.1  249   $\Gamma_{18}$ 3 ${{\mathit \gamma}}$ $<7.4$ $\times 10^{-8}$ CL=90% 249   $\Gamma_{19}$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \gamma}}$ ($9.4$ $\pm0.4$) $ \times 10^{-6}$ S=2.0  249   $\Gamma_{20}$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{{\mathit \gamma}}$ ($3.59$ $\pm0.11$) $ \times 10^{-7}$ S=1.3  225   $\Gamma_{21}$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ $<2.3$ $\times 10^{-9}$ CL=90% 119   $\Gamma_{22}$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit \gamma}}{{\mathit \gamma}}$ [4] ($5.95$ $\pm0.33$) $ \times 10^{-7}$ 249   $\Gamma_{23}$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{{\mathit \gamma}}{{\mathit \gamma}}$ [4] ($1.0^{+0.8}_{-0.6}$) $ \times 10^{-8}$ 225   ▸  exp Charge conjugation ${\times }$ Parity ($\mathit CP$) or Lepton Family number ($\mathit LF$) violating modes, or $\Delta \mathit S$ = 1 weak neutral current ($\mathit S1$) modes $\Gamma_{24}$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ S1 ($6.84$ $\pm0.11$) $ \times 10^{-9}$ 225   $\Gamma_{25}$ ${{\mathit e}^{+}}{{\mathit e}^{-}}$ S1 ($9^{+6}_{-4}$) $ \times 10^{-12}$ 249   $\Gamma_{26}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ S1 [4] ($3.11$ $\pm0.19$) $ \times 10^{-7}$ 206   $\Gamma_{27}$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ S1 $<6.6$ $\times 10^{-9}$ CL=90% 209   $\Gamma_{28}$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ S1 $<9.2$ $\times 10^{-11}$ CL=90% 57   $\Gamma_{29}$ ${{\mathit \mu}^{+}}{{\mathit \mu}^{-}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ S1 ($2.69$ $\pm0.27$) $ \times 10^{-9}$ 225   $\Gamma_{30}$ ${{\mathit e}^{+}}{{\mathit e}^{-}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ S1 ($3.56$ $\pm0.21$) $ \times 10^{-8}$ 249   $\Gamma_{31}$ ${{\mathit \pi}^{0}}{{\mathit \mu}^{+}}{{\mathit \mu}^{-}}$ CP|S1 [6] $<3.8$ $\times 10^{-10}$ CL=90% 177   $\Gamma_{32}$ ${{\mathit \pi}^{0}}{{\mathit e}^{+}}{{\mathit e}^{-}}$ CP|S1 [6] $<2.8$ $\times 10^{-10}$ CL=90% 230   $\Gamma_{33}$ ${{\mathit \pi}^{0}}{{\mathit \nu}}{{\overline{\mathit \nu}}}$ CP|S1 [7] $<3.0$ $\times 10^{-9}$ CL=90% 230   $\Gamma_{34}$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \nu}}{{\overline{\mathit \nu}}}$ S1 $<8.1$ $\times 10^{-7}$ CL=90% 209   $\Gamma_{35}$ ${{\mathit e}^{\pm}}{{\mathit \mu}^{\mp}}$ LF [2] $<4.7$ $\times 10^{-12}$ CL=90% 238   $\Gamma_{36}$ ${{\mathit e}^{\pm}}{{\mathit e}^{\pm}}{{\mathit \mu}^{\mp}}{{\mathit \mu}^{\mp}}$ LF [2] $<4.12$ $\times 10^{-11}$ CL=90% 225   $\Gamma_{37}$ ${{\mathit \pi}^{0}}{{\mathit \mu}^{\pm}}{{\mathit e}^{\mp}}$ LF [2] $<7.6$ $\times 10^{-11}$ CL=90% 217   $\Gamma_{38}$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}{{\mathit \mu}^{\pm}}{{\mathit e}^{\mp}}$ LF $<1.7$ $\times 10^{-10}$ CL=90% 159   ▸  exp Lorentz invariance violating modes $\Gamma_{39}$ ${{\mathit \pi}^{0}}{{\mathit \gamma}}$ $<1.7$ $\times 10^{-7}$ CL=90% 230

[1] Re($\epsilon {{}^\prime}/\epsilon $) = $\epsilon {{}^\prime}/\epsilon $ to a very good approximation provided the phases satisfy $\mathit CPT$ invariance. [2] The value is for the sum of the charge states or particle/antiparticle states indicated. [3] This mode includes gammas from inner bremsstrahlung but not the direct emission mode ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \gamma}}$(DE). [4] See the Particle Listings below for the energy limits used in this measurement. [5] Most of this radiative mode, the low-momentum ${{\mathit \gamma}}$ part, is also included in the parent mode listed without ${{\mathit \gamma}}$'s. [6] Allowed by higher-order electroweak interactions. [7] Violates $\mathit CP$ in leading order. Test of direct $\mathit CP$ violation since the indirect $\mathit CP$-violating and $\mathit CP$-conserving contributions are expected to be suppressed.

Constrained Fit information