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

IMAGINARY PART OF $\mathit x$

INSPIRE   PDGID:

S013IMX

Assumes ${\mathit m}_{{{\mathit K}_L^0} }–{\mathit m}_{{{\mathit K}_S^0} }$ positive. See Listings above.

VALUE EVTS DOCUMENT ID TECN  COMMENT $0.0012$ $\pm0.0019$ $\pm0.0009$ 640k ANGELOPOULOS 2001 B CPLR ${{\mathit K}_{{e3}}}$ from ${{\mathit K}^{0}}$ • • We do not use the following data for averages, fits, limits, etc. • • $0.0012$ $\pm0.0019$ 640k 1 ANGELOPOULOS 1998 E CPLR ${{\mathit K}_{{e3}}}$ from ${{\mathit K}^{0}}$ $-0.10$ ${}^{+0.16}_{-0.19}$ 79 SMITH 1975 B WIRE ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{0}}{{\mathit \Lambda}}$ $-0.06$ $\pm0.05$ 4724 NIEBERGALL 1974 ASPK ${{\mathit K}^{+}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{0}}{{\mathit p}}{{\mathit \pi}^{+}}$ $-0.017$ $\pm0.060$ 1757 FACKLER 1973 OSPK ${{\mathit K}_{{e3}}}$ from ${{\mathit K}^{0}}$ $0.09$ $\pm0.07$ 1367 HART 1973 OSPK ${{\mathit K}_{{e3}}}$ from ${{\mathit K}^{0}}{{\mathit \Lambda}}$ $0.107$ ${}^{+0.092}_{-0.074}$ 1079 MALLARY 1973 OSPK ${{\mathit K}_{{e3}}}$ from ${{\mathit K}^{0}}{{\mathit \Lambda}}$ X $0.07$ ${}^{+0.06}_{-0.07}$ 410 2 BURGUN 1972 HBC ${{\mathit K}^{+}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{0}}{{\mathit p}}{{\mathit \pi}^{+}}$ $0.12$ ${}^{+0.17}_{-0.16}$ 100 3 GRAHAM 1972 OSPK ${{\mathit K}_{{\mu3}}}$ from ${{\mathit K}^{0}}{{\mathit \Lambda}}$ $0.05$ $\pm0.13$ 442 3 GRAHAM 1972 OSPK ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{0}}{{\mathit \Lambda}}$ $0.21$ ${}^{+0.15}_{-0.12}$ 126 MANN 1972 HBC ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit n}}{{\overline{\mathit K}}^{0}}$ $-0.04$ $\pm0.16$ 342 3 MANTSCH 1972 OSPK ${{\mathit K}_{{e3}}}$ from ${{\mathit K}^{0}}{{\mathit \Lambda}}$ $0.12$ ${}^{+0.08}_{-0.09}$ 222 2 BURGUN 1971 HBC ${{\mathit K}^{+}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{0}}{{\mathit p}}{{\mathit \pi}^{+}}$ $0.0$ $\pm0.08$ 252 WEBBER 1971 HBC ${{\mathit K}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit n}}{{\overline{\mathit K}}^{0}}$ $-0.08$ $\pm0.07$ 215 4 CHO 1970 DBC ${{\mathit K}^{+}}$ ${{\mathit d}}$ $\rightarrow$ ${{\mathit K}^{0}}{{\mathit p}}{{\mathit p}}$ $-0.11$ ${}^{+0.10}_{-0.11}$ 686 LITTENBERG 1969 OSPK ${{\mathit K}^{+}}$ ${{\mathit n}}$ $\rightarrow$ ${{\mathit K}^{0}}{{\mathit p}}$ $+0.22$ ${}^{+0.37}_{-0.29}$ 121 JAMES 1968 HBC ${{\overline{\mathit p}}}{{\mathit p}}$ $0.0$ $\pm0.25$ 116 FELDMAN 1967 B OSPK ${{\mathit \pi}^{-}}$ ${{\mathit p}}$ $\rightarrow$ ${{\mathit K}^{0}}{{\mathit \Lambda}}$ $-0.20$ $\pm0.10$ 335 4 HILL 1967 DBC ${{\mathit K}^{+}}$ ${{\mathit d}}$ $\rightarrow$ ${{\mathit K}^{0}}{{\mathit p}}{{\mathit p}}$ $-0.21$ ${}^{+0.11}_{-0.15}$ 196 AUBERT 1965 HLBC ${{\mathit K}^{+}}$ charge exch. $-0.44$ ${}^{+0.32}_{-0.19}$ 152 5 BALDO-CEOLIN 1965 HLBC ${{\mathit K}^{+}}$ charge exch. $+0.24$ ${}^{+0.40}_{-0.30}$ 109 6 FRANZINI 1965 HBC ${{\overline{\mathit p}}}{{\mathit p}}$ 1  Superseded by ANGELOPOULOS 2001B. 2  BURGUN 1972 is a final result which includes BURGUN 1971 . 3  First GRAHAM 1972 value is second GRAHAM 1972 value combined with MANTSCH 1972 . 4  Footnote 10 of HILL 1967 should read $+0.58$, not $-0.58$ (private communication) CHO 1970 is analysis of unambiguous events in new data and HILL 1967 . 5  BALDO-CEOLIN 1965 gives $\mathit x$ and $\theta $ converted by us to Re($\mathit x$) and Im($\mathit x$). 6  FRANZINI 1965 gives $\mathit x$ and $\theta $ for Re($\mathit x$) and Im($\mathit x$). See SCHMIDT 1967 .

Conservation Laws:

$\Delta \mathit S$ = $\Delta \mathit Q$ RULE

References:

ANGELOPOULOS 2001B EPJ C22 55 $\mathit T$-Violation and $\mathit CPT$-Invariance Measurements in the CPLEAR Experiment: a Detailed Description of the Analysis of Neutral-Kaon Decays to ${{\mathit e}}{{\mathit \pi}}{{\mathit \nu}}$ ANGELOPOULOS 1998E PL B444 43 First Direct Observation of Time Reversal NonInvariance in the Neutral Kaon System SMITH 1975B Thesis UCSD unpub. Test of the $\Delta \mathit S$ = $\Delta \mathit Q$ Rule in ${{\mathit K}_{{e3}}}$ Decay NIEBERGALL 1974 PL 49B 103 Experimental Study of the $\Delta \mathit S/\Delta \mathit Q$ Rule in the Time Dependent Rate of ${{\mathit K}^{0}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit e}}{{\mathit \nu}}$ FACKLER 1973 PRL 31 847 Test of the $\Delta \mathit S$ = $\Delta \mathit Q$ Rule in ${{\mathit K}_{{e3}}}$ Decay HART 1973 NP B66 317 Test of the $\Delta \mathit S$ = $\Delta \mathit Q$ Rule in ${{\mathit K}_{{e3}}}$ Decay MALLARY 1973 PR D7 1953 Three Body Decays of ${{\mathit K}^{0}}$ Mesons Also PRL 25 1214 Measurement of the $\Delta \mathit S$ = $−\Delta \mathit Q$ Amplitude from ${{\mathit K}_{{e3}}^{0}}$ Decay BURGUN 1972 NP B50 194 Experimental Study of the Selection Rule $\Delta \mathit S$ = $−\Delta \mathit Q$ in ${{\mathit K}_{{e3}}^{0}}$ and ${{\mathit K}_{{\mu3}}^{0}}$ Decays GRAHAM 1972 NC 9A 166 Test of the $\Delta \mathit S$ = $\Delta \mathit Q$ Selection Rule in ${{\mathit K}_{{\mu3}}}$ Decay MANN 1972 PR D6 137 Test of $\Delta \mathit S$ = $\Delta \mathit Q$ in the Time Distribution of ${{\mathit K}}{}^{0}_{{{\mathit \ell}}3}$ Decays MANTSCH 1972 NC 9A 160 A Test of the $\Delta \mathit S$ = $\Delta \mathit Q$ Selection Rule in ${{\mathit K}_{{e3}}}$ Decay BURGUN 1971 LNC 2 1169 Results on the $\Delta \mathit S$ = $\Delta \mathit Q$ Rule from ${{\mathit K}_{{e3}}^{0}}$ and ${{\mathit K}_{{\mu3}}^{0}}$ Decays WEBBER 1971 PR D3 64 Experimental Test of the $\Delta \mathit S$ = $\Delta \mathit Q$ Rule in Leptonic Decays of ${{\mathit K}^{0}}$ Mesons Also PRL 21 498 Test of the $\Delta \mathit S$ = $\Delta \mathit Q$ Rule in Leptonic Decays of Neutral ${{\mathit K}}$ Mesons Also Thesis UCRL 19226 A test of the $\Delta \mathit S$ = $\Delta \mathit Q$ Rule in Leptonic Decays of Neutral ${{\mathit K}}$ Mesons CHO 1970 PR D1 3031 Study of the $\Delta \mathit S$ = $\Delta \mathit Q$ Rule in the Leptonic Decays of the Neutral ${{\mathit K}}$ Meson Also PRL 19 668 Test of the $\Delta \mathit S$ = $\Delta \mathit Q$ Rule in Leptonic Decay of Neutral ${{\mathit K}}$ Mesons LITTENBERG 1969 PRL 22 654 Test of the $\Delta \mathit S$ = $\Delta \mathit Q$ Rule in ${{\mathit K}^{0}}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit e}}{{\mathit \nu}}$ Decay JAMES 1968 NP B8 365 Experimental Investigation of $\Delta \mathit S/\Delta \mathit Q$ Rule in Leptonic ${{\mathit K}^{0}}$ Decays Also PRL 21 257 Experimental Determination of Re$\xi $ from ${{\mathit K}_{{\mu3}}^{0}}$ Decay FELDMAN 1967B PR 155 1611 Time Dependence of ${{\mathit K}_{{e3}}^{0}}$ Decays HILL 1967 PRL 19 668 Test of the $\Delta \mathit S$ = $\Delta \mathit Q$ Rule in Leptonic Decay of Neutral ${{\mathit K}}$ Mesons AUBERT 1965 PL 17 59 Leptonic Decays of ${{\mathit K}^{0}}$ Meson and $\mathit CP$ Violation Also PL 24B 75 Measurement of the ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \mu}^{-}}{{\overline{\mathit \nu}}_{{\mu}}}$ Decay Rate, Future Results on ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit e}^{-}}{{\overline{\mathit \nu}}_{{e}}}$ , and Measurement of the ${{\mathit K}_L^0}$ Mean Life BALDO-CEOLIN 1965 NC 38 684 Experimental Test of $\mathit CP$ Invariance and $\Delta \mathit S$ = $\Delta \mathit Q$ Selection Rule FRANZINI 1965 PR 140 B127 Some Features of ${{\mathit K}^{0}}$ Decay: The $\Delta \mathit S$ = $\Delta \mathit Q$ Rule, and $\Delta \mathit I={1\over 2}$ Rules for Leptonic and Three-Pion Decays

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