pdgLive

$\mathit CP$ VIOLATION OBSERVED

Re($\epsilon $)

$0.001596$ $\pm0.000013$

charge asymmetry in ${{\mathit K}_{{{\ell3}}}^{0}}$ decays

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

$0.00332$ $\pm0.00006$

$\mathit A_{\mathit L}({{\mathit \mu}}$) = $\lbrack{}\Gamma\mathrm {({{\mathit \pi}^{-}} {{\mathit \mu}^{+}} {{\mathit \nu}_{{{\mu}}}})}$ $−$ $\Gamma\mathrm {({{\mathit \pi}^{+}} {{\mathit \mu}^{-}} {{\overline{\mathit \nu}}_{{{\mu}}}})}$]/sum

$0.00304$ $\pm0.00025$

$\mathit A_{\mathit L}({{\mathit e}}$) = $\lbrack{}\Gamma\mathrm {({{\mathit \pi}^{-}} {{\mathit e}^{+}} {{\mathit \nu}_{{{e}}}})}$ $−$ $\Gamma\mathrm {({{\mathit \pi}^{+}} {{\mathit e}^{-}} {{\overline{\mathit \nu}}_{{{e}}}})}$]/sum

$0.00334$ $\pm0.00007$

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 $

$0.002243$ $\pm0.000014$

$\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 $

$0.9930$ $\pm0.0020$

Re($\epsilon {{}^\prime}/\epsilon $) = (1$−\vert \eta _{00}/\eta _{+−}\vert $)/3

$0.00168$ $\pm0.00020$ (S = 1.4)

Assuming $\mathit CPT$

$\phi _{+−}$, phase of $\eta _{+−}$

$43.51$ $\pm0.05$ $^\circ{}$ (S = 1.2)

$\phi _{00}$, phase of $\eta _{00}$

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

$\phi _{\epsilon }$ = (2$\phi _{+−}+\phi _{00}$)/3

$43.52$ $\pm0.04$ $^\circ{}$ (S = 1.2)

Not assuming $\mathit CPT$

$\phi _{+−}$, phase of $\eta _{+−}$

$43.4$ $\pm0.5$ $^\circ{}$ (S = 1.2)

$\phi _{00}$, phase of $\eta _{00}$

$43.7$ $\pm0.6$ $^\circ{}$ (S = 1.2)

$\phi _{\epsilon }$ = (2$\phi _{+−}+\phi _{00}$)/3

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

$\mathit CP$ asymmetry $\mathit A$ in ${{\mathit K}_L^0}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit e}^{+}}{{\mathit e}^{-}}$

$0.137$ $\pm0.015$

$\beta _{\mathit CP}$ 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)

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 $\eta _{+−{{\mathit \gamma}}}$

$44$ $\pm4$ $^\circ{}$

$\Gamma\mathrm {( {{\mathit K}_L^0} \rightarrow {{\mathit \pi}^{0}} {{\mathit \pi}^{0}})}$ $/$ $\Gamma\mathrm {(total)}$

$(8.64\pm{0.06})\times 10^{-4}$ (S = 1.8)

$\Gamma\mathrm {( {{\mathit K}_L^0} \rightarrow {{\mathit \pi}^{+}} {{\mathit \pi}^{-}})}$ $/$ $\Gamma\mathrm {(total)}$

$(1.967\pm{0.010})\times 10^{-3}$ (S = 1.5)

$\Delta \mathit A{}^{{{\mathit D}^{0}}}_{CP}$ = $\mathit A_{CP}({{\mathit K}^{+}}{{\mathit K}^{-}}$) $−$ $\mathit A_{CP}({{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$)

$-0.00154$ $\pm0.00029$

$\mathit A_{CP}$( ${{\mathit B}^{+}}$ $\rightarrow$ [ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ ]$_{{{\overline{\mathit D}}}}$ ${{\mathit K}^{*}{(892)}^{+}}$)

$-0.75$ $\pm0.16$

$\mathit A_{CP}$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}}_{CP(+1)}$ ${{\mathit K}^{+}}$)

$0.132$ $\pm0.015$ (S = 1.8)

$\mathit A_{ADS}$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{+}}$)

$-0.451$ $\pm0.026$

$\mathit A_{CP}$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit K}^{+}}$)

$-0.37$ $\pm0.08$

$\mathit A_{CP}$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$)

$0.015$ $\pm0.006$ (S = 1.4)

$\mathit A_{CP}$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit f}_{{{2}}}{(1270)}}{{\mathit K}^{+}}$)

$-0.68$ ${}^{+0.19}_{-0.17}$

$\mathit A_{CP}$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit \rho}^{0}}{{\mathit K}^{+}}$)

$0.160$ $\pm0.021$

$\mathit A_{CP}$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}$)

$-0.115$ $\pm0.008$

$\mathit A_{CP}$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}$( ${{\mathit K}^{+}}{{\mathit K}^{-}})_{{\mathit S}{\mathrm -wave}}$)

$-0.66$ $\pm0.04$

$\mathit A_{CP}$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit K}^{+}}$)

$-0.036$ $\pm0.004$

$\mathit A_{CP}$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$)

$0.076$ $\pm0.008$ (S = 1.5)

$\mathit A_{CP}$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit f}_{{{2}}}{(1270)}}{{\mathit \pi}^{+}}$)

$0.40$ $\pm0.06$

$65.9$ ${}^{+2.9}_{-3.1}$ $^\circ{}$

r$_{B}$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit K}^{+}}$)

$0.0994$ $\pm0.0026$

$\delta _{B}$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit K}^{+}}$)

$127.7$ ${}^{+3.6}_{-3.9}$ $^\circ{}$

r$_{B}$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit K}^{*+}}$)

$0.101$ ${}^{+0.016}_{-0.034}$

$\delta _{B}$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit K}^{*+}}$)

$48$ ${}^{+59}_{-16}$ $^\circ{}$

r$_{B}$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}^{*0}}{{\mathit K}^{+}}$)

$0.104$ ${}^{+0.013}_{-0.014}$

$\delta _{B}$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}^{*0}}{{\mathit K}^{+}}$)

$314.8$ ${}^{+7.9}_{-9.9}$ $^\circ{}$

$\mathit A_{CP}$ ( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit \pi}^{-}}$)

$-0.0831$ $\pm0.0031$

$\mathit A_{CP}$( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit \eta}}{{\mathit K}^{*}{(892)}^{0}}$)

$0.19$ $\pm0.05$

$\mathit A_{CP}$( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}^{*}{(892)}^{+}}{{\mathit \pi}^{-}}$)

$-0.27$ $\pm0.04$

$\mathit S_{{{\mathit D}^{*}{(2010)}^{-}} {{\mathit D}^{+}}}$ ( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{*}{(2010)}^{-}}{{\mathit D}^{+}}$)

$-0.83$ $\pm0.09$

$\mathit S_{{{\mathit D}^{*}{(2010)}^{+}} {{\mathit D}^{-}}}$ ( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{*}{(2010)}^{+}}{{\mathit D}^{-}}$)

$-0.80$ $\pm0.09$

$\mathit S_{{{\mathit D}^{*+}} {{\mathit D}^{*-}}}$ ( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{*+}}{{\mathit D}^{*-}}$)

$-0.59$ $\pm0.14$ (S = 1.8)

$\mathit S_{+}$ ( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{*+}}{{\mathit D}^{*-}}$)

$-0.73$ $\pm0.09$

$\mathit S_{{{\mathit D}^{+}} {{\mathit D}^{-}}}$ ( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{+}}{{\mathit D}^{-}}$)

$-0.76$ ${}^{+0.15}_{-0.13}$ (S = 1.2)

$\mathit S_{{{\mathit J / \psi}{(1S)}} {{\mathit \pi}^{0}}}$ ( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}{(1S)}}{{\mathit \pi}^{0}}$)

$-0.88$ $\pm0.32$ (S = 2.2)

$\mathit S$( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}{(1S)}}{{\mathit \rho}^{0}}$)

$-0.66$ ${}^{+0.16}_{-0.12}$

$\mathit S_{{{\mathit K}^{0}} {{\mathit \pi}^{0}}}$ ( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}^{0}}{{\mathit \pi}^{0}}$)

$0.64$ $\pm0.13$

$\mathit S_{{{\mathit \eta}^{\,'}} {{\mathit K}^{0}}}$ ( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit \eta}^{\,'}}{{\mathit K}^{0}}$)

$0.63$ $\pm0.06$

$\mathit S_{{{\mathit K}^{+}} {{\mathit K}^{-}} {{\mathit K}_S^0} }$ ( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit K}_S^0}$ nonresonant)

$-0.66$ $\pm0.11$

$\mathit S_{{{\mathit K}^{+}} {{\mathit K}^{-}} {{\mathit K}_S^0} }$ ( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit K}_S^0}$ inclusive)

$-0.65$ $\pm0.12$

$\mathit C_{{{\mathit \pi}} {{\mathit \pi}}}$ ( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$)

$-0.314$ $\pm0.030$

$\mathit S_{{{\mathit \pi}} {{\mathit \pi}}}$ ( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$)

$-0.670$ $\pm0.030$

$\Delta \mathit C_{{{\mathit \rho}} {{\mathit \pi}}}$ ( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit \rho}^{+}}{{\mathit \pi}^{-}}$)

$0.27$ $\pm0.06$

$\mathit S_{{{\mathit \eta}_{{{c}}}} {{\mathit K}_S^0} }$ ( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit \eta}_{{{c}}}}{{\mathit K}_S^0}$ )

$0.93$ $\pm0.17$

sin$(2\beta )$ ( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}}{{\mathit K}_S^0}$ )

$0.709$ $\pm0.011$

$\mathit S_{{{\mathit J / \psi}{(nS)}} {{\mathit K}^{0}}}$ ( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit J / \psi}{(nS)}}{{\mathit K}^{0}}$)

$0.708$ $\pm0.016$ (S = 1.4)

$\mathit S_{{{\mathit \chi}_{{{c1}}}} {{\mathit K}_S^0} }$ ( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit \chi}_{{{c1}}}}{{\mathit K}_S^0}$ )

$0.63$ $\pm0.10$

sin$(2\beta _{{\mathrm {eff}}})$( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit K}_S^0}$ )

$0.77$ ${}^{+0.13}_{-0.12}$

$84.1$ ${}^{+4.5}_{-3.8}$ $^\circ{}$

$\mathit r_{{{\mathit B}^{0}}}$( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{*0}}$)

$0.257$ ${}^{+0.021}_{-0.023}$

$\delta _{{{\mathit B}^{0}}}$( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{*0}}$)

$194.1$ ${}^{+9.6}_{-8.8}$ $^\circ{}$

$\mathit C_{{{\mathit K}} {{\mathit K}}}$( ${{\mathit B}_{{{s}}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$)

$0.162$ $\pm0.035$

r$_{B}$( ${{\mathit B}_{{{s}}}^{0}}$ $\rightarrow$ ${{\mathit D}_{{{s}}}^{\mp}}{{\mathit K}^{\pm}}$)

$0.37$ ${}^{+0.10}_{-0.09}$

r$_{B}$( ${{\mathit B}_{{{s}}}^{0}}$ $\rightarrow$ ${{\mathit D}_{{{s}}}^{\mp}}{{\mathit K}^{\pm}}{{\mathit \pi}^{\pm}}{{\mathit \pi}^{\mp}}$)

$0.47$ $\pm0.08$

$\delta _{B}$( ${{\mathit B}_{{{s}}}^{0}}$ $\rightarrow$ ${{\mathit D}_{{{s}}}^{\pm}}{{\mathit K}^{\mp}}$)

$358$ $\pm14$ $^\circ{}$

$\mathit A_{CP}$( ${{\mathit B}_{{{s}}}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit K}^{-}}$)

$0.224$ $\pm0.012$

[1]	Re($\epsilon {{}^\prime}/\epsilon $) = $\epsilon {{}^\prime}/\epsilon $ to a very good approximation provided the phases satisfy $\mathit CPT$ invariance.

[2]	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).

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