CP VIOLATION PARAMETERS IN ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{+}}$ AND SIMILAR DECAYS

The parameters ${{\mathit r}}_{{{\mathit B}^{+}}}$ and $\delta _{{{\mathit B}^{+}}}$ are the magnitude ratio and strong phase difference between the amplitudes of A(${{\mathit B}^{+}}$ $\rightarrow$ ${{\overline{\mathit D}}^{(*)0}}{{\mathit K}^{(*)+}}$) and A(${{\mathit B}^{-}}$ $\rightarrow$ ${{\mathit D}^{(*)0}}{{\mathit K}^{(*)-}}$). The measured observables are defined as ${{\mathit x}}_{\pm{}}$ = ${{\mathit r}}_{{{\mathit B}^{+}}}$ cos($\delta _{{{\mathit B}^{+}}}$ $\pm{}{{\mathit \gamma}}$) and ${{\mathit y}}_{\pm{}}$ = ${{\mathit r}}_{{{\mathit B}^{+}}}$ sin($\delta _{{{\mathit B}^{+}}}$ $\pm{}$ $\gamma $), and can be used to measure the CKM angle $\gamma $.
"OUR EVALUATION" is provided by the Heavy Flavor Averaging Group (HFLAV). It is derived from combinations of their results on ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{+}}$ and related processes.

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

INSPIRE   JSON  (beta) PDGID:
S041ARY
r$_{B}$ and $\delta _{B}$ are the amplitude ratio and relative strong phase between the amplitudes of $\mathit A({{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}^{*0}}{{\mathit K}^{+}}$) and $\mathit A({{\mathit B}^{+}}$ $\rightarrow$ ${{\overline{\mathit D}}^{*0}}{{\mathit K}^{+}}$),
VALUE DOCUMENT ID TECN  COMMENT
$\bf{ 0.103 {}^{+0.010}_{-0.011}}$ OUR EVALUATION  $~~$(Produced by HFLAV)
$0.229$ ${}^{+0.068}_{-0.067}$ 1
ADACHI
2024T
 BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$)
• • We do not use the following data for averages, fits, limits, etc. • •
$0.080$ ${}^{+0.022}_{-0.023}$ 2
AAIJ
2024H
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$0.15$ $\pm0.03$ 3
AAIJ
2023BA
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$0.106$ ${}^{+0.019}_{-0.036}$ 4
LEES
2013B
 BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.133$ ${}^{+0.042}_{-0.039}$ $\pm0.013$ 5
DEL-AMO-SANCH..
2010F
 BABR Repl. by LEES 2013B
$0.096$ ${}^{+0.035}_{-0.051}$ 6
DEL-AMO-SANCH..
2010H
 BABR Repl. by LEES 2013B
$0.196$ ${}^{+0.072}_{-0.069}$ ${}^{+0.064}_{-0.017}$ 7
POLUEKTOV
2010
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.135$ $\pm0.050$ $\pm0.012$ 8
AUBERT
2008AL
 BABR Repl. by DEL-AMO-SANCHEZ 2010F
$0.175$ ${}^{+0.108}_{-0.099}$ $\pm0.050$ 9
POLUEKTOV
2006
BELL Repl. by POLUEKTOV 2010
$0.17$ $\pm0.10$ $\pm0.04$ 10
AUBERT,B
2005Y
 BABR Repl. by AUBERT 2008AL
1  Uses combined sample of Belle and Belle II experiments in ${{\mathit B}^{+}}$ decays to ${{\mathit D}}{{\mathit K}^{+}}$, ${{\mathit D}^{*}}{{\mathit K}^{+}}$, and ${{\mathit D}}{{\mathit \pi}^{+}}$ final states.
2  Extracted from yields of partially reconstructed ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}^{*}}{{\mathit K}^{\pm}}$, ${{\mathit D}^{*}}$ $\rightarrow$ ${{\mathit D}}{{\mathit \pi}^{0}}$ $/$ ${{\mathit \gamma}}$ , ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $/$ ${{\mathit K}_S^0}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ decays. The uncertainty is predominantly statistical. Its correlation with the AAIJ 2023BA result is found to be less than 3$\%$.
3  Measured using ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}^{*}}{{\mathit K}^{\pm}}$ decays analysing the signal yield variation with the fully reconstructed ${{\mathit D}^{*}}$ $\rightarrow$ ${{\mathit D}}{{\mathit \pi}^{0}}$ $/$ ${{\mathit \gamma}}$ , ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $/$ ${{\mathit K}_S^0}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ decays. The model-independent approach uses external strong phase input from BESIII and CLEO collaborations.
4  Reports combination of published measurements using GGSZ, GLW, and ADS methods.
5  Uses Dalitz plot analysis of ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$, ${{\mathit K}_S^0}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ decays from ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}^{(*)}}{{\mathit K}^{(*)+}}$ modes. The corresponding two standard deviation interval is 0.049 $<{{\mathit r}^{*}_{B}}<$0.215.
6  Uses the Cabibbo suppressed decay of ${{\mathit B}^{+}}$ $\rightarrow$ ${{\overline{\mathit D}}^{*}}{{\mathit K}^{+}}$ followed by ${{\overline{\mathit D}}^{*}}$ $\rightarrow$ ${{\overline{\mathit D}}}{{\mathit \pi}^{0}}$ or ${{\overline{\mathit D}}}{{\mathit \gamma}}$, and ${{\overline{\mathit D}}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$.
7  Uses Dalitz plot analysis of ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ decays from ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}^{*0}}{{\mathit K}^{+}}$ modes. The corresponding two standard deviation interval is 0.061 $<{{\mathit r}^{*}_{B}}<$ 0.271.
8  Uses Dalitz plot analysis of ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ decays coming from ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}^{(*)}}{{\mathit K}^{(*)\pm}}$ modes.
9  Uses a Dalitz plot analysis of the ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ decays; Combines the ${{\mathit D}}{{\mathit K}^{+}}$, ${{\mathit D}^{*}}{{\mathit K}^{+}}$ and ${{\mathit D}}{{\mathit K}^{*+}}$ modes.
10  Uses a Dalitz analysis of neutral ${{\mathit D}}$ decays to ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ in the processes ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}^{{(*)}}}{{\mathit K}^{\pm}}$, ${{\mathit D}^{*}}$ $\rightarrow$ ${{\mathit D}}{{\mathit \pi}^{0}}$, ${{\mathit D}}{{\mathit \gamma}}$.
Conservation Laws:
$\mathit CP$ VIOLATION OBSERVED
References