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.

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

INSPIRE   JSON  (beta) PDGID:
S041A33
VALUE ($^\circ{}$) DOCUMENT ID TECN  COMMENT
$347.0$ ${}^{+8.7}_{-9.6}$ 1
ADACHI
2024T
 BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$)
• • We do not use the following data for averages, fits, limits, etc. • •
$311.8$ ${}^{+14.7}_{-15.0}$ ${}^{+15.0}_{-15.2}$ 2
AAIJ
2023I
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$298$ ${}^{+62}_{-118}$ 3
AAIJ
2023N
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$341.0$ $\pm17.0$ $\pm2.9$ 4
ABUDINEN
2022
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$291$ ${}^{+24}_{-26}$ 4
AAIJ
2021L
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
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  Measured using ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}}$ [ ${{\mathit K}^{\mp}}{{\mathit \pi}^{\pm}}{{\mathit \pi}^{\pm}}{{\mathit \pi}^{\mp}}$ ] ${{\mathit h}^{\pm}}$ decays in bins of the phase space of the ${{\mathit D}}$ decay. The third uncertainty includes systematic and finite knowledge of the ${{\mathit D}}$-meson decay parameters.
3  A model-dependent binned analysis of the decays ${{\mathit B}^{\pm}}$ $\rightarrow$ [ ${{\mathit K}^{+}}{{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ]$_{D}$ ${{\mathit h}^{\pm}}$is used.
4  Uses binned Dalitz plot analysis of ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit K}_S^0}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ from ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}}{{\mathit \pi}^{\pm}}$ modes. Strong phase measurements from CLEO-c and BES-III of the ${{\mathit D}}$ decay over the Dalitz plot are used as input. Value is modulo 180$^\circ{}$.
References