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 PDGID:
S041ARZ
r$_{B}$ and $\delta _{B}$ are the amplitude ratio and relative strong phase between the amplitudes of $\mathit A_{CP}({{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit K}^{*+}}$) and $\mathit A_{CP}({{\mathit B}^{+}}$ $\rightarrow$ ${{\overline{\mathit D}}^{0}}{{\mathit K}^{*+}}$),
VALUE DOCUMENT ID TECN  COMMENT
$\bf{ 0.101 {}^{+0.016}_{-0.036}}$ OUR EVALUATION  $~~$(Produced by HFLAV)
$0.103$ $\pm0.010$ 1
AAIJ
2025R
 
LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
• • We do not use the following data for averages, fits, limits, etc. • •
$0.143$ ${}^{+0.048}_{-0.049}$ 2
LEES
2013B
 
BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.166$ ${}^{+0.073}_{-0.069}$ 3
DEL-AMO-SANCH..
2010F
 
BABR Repl. by LEES 2013B
$0.31$ $\pm0.07$ 4
AUBERT
2009AJ
 
BABR Repl. by LEES 2013B
$0.181$ ${}^{+0.088}_{-0.108}$ $\pm0.042$ 5
AUBERT
2008AL
 
BABR Repl. by AUBERT 2009AJ
$0.564$ ${}^{+0.216}_{-0.155}$ $\pm0.093$ 6
POLUEKTOV
2006
 
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
1  Extracted from ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{*\pm}}$ decays, using the ${{\mathit D}}$ decays: ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}^{\pm}}{{\mathit \pi}^{\mp}}$, ${{\mathit K}^{+}}{{\mathit K}^{-}}$, ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$, ${{\mathit K}^{\pm}}{{\mathit \pi}^{\mp}}{{\mathit \pi}^{\pm}}{{\mathit \pi}^{\mp}}$, ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$, ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$, and ${{\mathit K}_S^0}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$.
2  Reports combination of published measurements using GGSZ, GLW, and ADS methods.
3  DEL-AMO-SANCHEZ 2010F reports r$_{B}\cdot{}$k = $0.149$ ${}^{+0.066}_{-0.062}$ for k = 0.9.
4  Obtained by combining the GLW and ADS methods. The 2-sigma range corresponds to [0.17, 0.43].
5  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.
6  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.
Conservation Laws:
$\mathit CP$ INVARIANCE
References