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.

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

INSPIRE   JSON  (beta) PDGID:
S041DRY
VALUE ($^\circ{}$) DOCUMENT ID TECN  COMMENT
$\bf{ 312.2 {}^{+6.3}_{-7.1}}$ OUR EVALUATION  $~~$(Produced by HFLAV)
$342$ ${}^{+14}_{-16}$ 1
ADACHI
2024T
 BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$)
• • We do not use the following data for averages, fits, limits, etc. • •
$310$ ${}^{+15}_{-20}$ 2
AAIJ
2024H
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$311$ $\pm14$ 3
AAIJ
2023BA
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$294$ ${}^{+21}_{-31}$ 4
LEES
2013B
 BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$278$ $\pm21$ $\pm6$ 5
DEL-AMO-SANCH..
2010F
 BABR Repl. by LEES 2013B
$341.9$ ${}^{+18.0}_{-19.6}$ $\pm23.1$ 6
POLUEKTOV
2010
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$297$ ${}^{+27}_{-29}$ $\pm6.4$ 7
AUBERT
2008AL
 BABR Repl. by DEL-AMO-SANCHEZ 2010F
$302.0$ ${}^{+33.8}_{-35.1}$ $\pm23.7$ 8
POLUEKTOV
2006
BELL Repl. by POLUEKTOV 2010
$296$ $\pm41$ ${}^{+20}_{-19}$ 9
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. We added 360$^\circ{}$ to the value of ($-66$ ${}^{+21}_{-31})^\circ{}$ quoted by LEES 2013B.
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 236$^\circ{}<{{\mathit \delta}_{{{B}}}^{*}}<322^\circ{}$.
6  Uses Dalitz plot analysis of ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ decays from ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}^{*}}{{\mathit K}^{+}}$ modes. The corresponding two standard deviation interval is 296.5$^\circ{}<{{\mathit \delta}_{{{B}}}^{*}}<$ 382.7$^\circ{}$.
7  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.
8  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.
9  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