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

Re(x$_{+}$) INSPIRE search

A non-zero value would violate the $\Delta \mathit S$ = $\Delta \mathit Q$ rule in $\mathit CPT$ conserving transitions. x$_{+}$ is defined above in the Re(x$_{-}$) section.

S011XRP

VALUE ($ 10^{-3} $)

EVTS

DOCUMENT ID

TECN

$\bf{ -0.9 \pm3.0}$

OUR AVERAGE

$-2$ $\pm10$

BATLEY

2007

NA48

$-0.5$ $\pm3.6$

13k

AMBROSINO

2006

KLOE

$-1.8$ $\pm6.1$

ANGELOPOULOS

1998

CPLR

¹ Result obtained from the measurement $\Gamma $( ${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit e}}{{\mathit \nu}}$) $/$ $\Gamma $( ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit e}}{{\mathit \nu}}$) = $0.993$ $\pm0.34$, neglecting possible $\mathit CPT$ non-invariance and using PDG 2006 values of B( ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit e}}{{\mathit \nu}}$) = $0.4053$ $\pm0.0015$, ${\mathit \tau}_{{{\mathit L}}}$ = ($5.114$ $\pm0.021$) $ \times 10^{-8}$ s and ${\mathit \tau}_{{{\mathit S}}}$ = ($0.8958$ $\pm0.0005$) $ \times 10^{-10}~$s.

² Re(x$_{+}$) can be shown to be equal to the following combination of rates: Re(x$_{+}$) = ${1\over 2}{ \Gamma ( {{\mathit K}_S^0} \rightarrow {{\mathit \pi}} {{\mathit e}} {{\mathit \nu}}) − \Gamma ( {{\mathit K}_L^0} \rightarrow {{\mathit \pi}} {{\mathit e}} {{\mathit \nu}})\over \Gamma ( {{\mathit K}_S^0} \rightarrow {{\mathit \pi}} {{\mathit e}} {{\mathit \nu}}) + \Gamma ( {{\mathit K}_L^0} \rightarrow {{\mathit \pi}} {{\mathit e}} {{\mathit \nu}})}$ which is valid up to first order in terms violating $\mathit CPT$ and/or the $\Delta \mathit S$ = $\Delta \mathit Q$ rule.

³ Obtained neglecting $\mathit CPT$ violating amplitudes.

Conservation Laws:

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

References:

BATLEY

2007D

PL B653 145

Determination of the Relative Decay Rate ${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit e}}{{\mathit \nu}}$/ ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit e}}{{\mathit \nu}}$

AMBROSINO

2006E

PL B636 173

Study of the Branching Ratio and Charge Asymmetry for the Decay ${{\mathit K}_S^0}$ $\rightarrow$ ${{\mathit \pi}}{{\mathit e}}{{\mathit \nu}}$ with the KLOE Detector

ANGELOPOULOS

1998D

PL B444 38

Measurement of the ${{\mathit K}_L^0}$ $−$ ${{\mathit K}_S^0}$ Mass Difference using Semileptonic Decays of Tagged Neutral Kaons

Also

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 ${{\mathit e}}$ ${{\mathit \pi}}$ ${{\mathit \nu}}$