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 $\mathit A_{\mathit L}({{\mathit e}}$)

$0.00332$ $\pm0.00006$

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

$0.00334$ $\pm0.00007$

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 = 1.3)

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

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

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

$-0.451$ $\pm0.026$

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

$-0.37$ $\pm0.08$

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

$0.027$ $\pm0.008$

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

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

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

$0.37$ $\pm0.10$

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

$-0.122$ $\pm0.021$

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

$-0.66$ $\pm0.04$

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

$-0.033$ $\pm0.008$

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

$0.057$ $\pm0.013$

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

$0.40$ $\pm0.06$

$\mathit A_{CP}$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit f}_{{0}}{(1370)}}{{\mathit \pi}^{+}}$ )

$0.72$ $\pm0.22$

$65.9$ ${}^{+3.3}_{-3.5}$ $^\circ{}$

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

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

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

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

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

$-0.0834$ $\pm0.0032$

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

$0.19$ $\pm0.05$

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

$-0.27$ $\pm0.04$

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

$-0.83$ $\pm0.09$

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

$-0.80$ $\pm0.09$

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

$-0.59$ $\pm0.14$ (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)

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

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

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

$0.58$ $\pm0.17$

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

$0.63$ $\pm0.06$

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

$0.698$ $\pm0.027$ (S = 1.6)

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

$0.698$ $\pm0.024$ (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$(2\beta _{{\mathrm {eff}}})$( ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit K}_S^0}$ )

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

$85.2$ ${}^{+4.8}_{-4.3}$ $^\circ{}$

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

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

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

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

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

$0.162$ $\pm0.035$

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).

Except where otherwise noted, content of the 2023 Review of Particle Physics is licensed under a Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) license. The publication of the Review of Particle Physics is supported by US DOE, MEXT (Japan), INFN (Italy), JPS and CERN. Individual collaborators receive support for their PDG activities from their respective institutes or funding agencies. © 2023. See LBNL disclaimers.