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   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 $\mathit A$( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\overline{\mathit D}}^{*0}}{{\mathit K}^{+}}$ ),

"OUR EVALUATION" is provided by the Heavy Flavor Averaging Group (HFLAV).

VALUE DOCUMENT ID TECN  COMMENT
$\bf{ 0.104 {}^{+0.013}_{-0.014}}$ OUR EVALUATION
• • We do not use the following data for averages, fits, limits, etc. • •
$0.106$ ${}^{+0.019}_{-0.036}$ 1
LEES
2013B
 BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.133$ ${}^{+0.042}_{-0.039}$ $\pm0.013$ 2
DEL-AMO-SANCH..
2010F
 BABR Repl. by LEES 2013B
$0.096$ ${}^{+0.035}_{-0.051}$ 3
DEL-AMO-SANCH..
2010H
 BABR Repl. by LEES 2013B
$0.196$ ${}^{+0.072}_{-0.069}$ ${}^{+0.064}_{-0.017}$ 4
POLUEKTOV
2010
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$0.135$ $\pm0.050$ $\pm0.012$ 5
AUBERT
2008AL
 BABR Repl. by DEL-AMO-SANCHEZ 2010F
$0.175$ ${}^{+0.108}_{-0.099}$ $\pm0.050$ 6
POLUEKTOV
2006
BELL Repl. by POLUEKTOV 2010
$0.17$ $\pm0.10$ $\pm0.04$ 7
AUBERT,B
2005Y
 BABR Repl. by AUBERT 2008AL
1  Reports combination of published measurements using GGSZ, GLW, and ADS methods.
2  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.
3  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 ${{\overline{\mathit D}}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ .
4  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.
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.
7  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:
LEES 2013B
PR D87 052015 Observation of Direct $\mathit CP$ Violation in the Measurement of the Cabibbo-Kobayashi-Maskawa Angle $\gamma $ with ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}^{(*)}}{{\mathit K}^{(*)\pm}}$
DEL-AMO-SANCHEZ 2010F
PRL 105 121801 Evidence for Direct $\mathit CP$ Violation in the Measurement of the Cabbibo-Kobayashi-Maskawa Angle ${{\mathit \gamma}}$ with ${{\mathit B}^{\mp}}$ $\rightarrow$ ${{\mathit D}^{{(*)}}}{{\mathit K}^{{(*)}\mp}}$ Decays
DEL-AMO-SANCHEZ 2010H
PR D82 072006 Search for ${\mathit {\mathit b}}\rightarrow{\mathit {\mathit u}}$ Transitions in ${{\mathit B}^{-}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{-}}$ and ${{\mathit D}^{*}}{{\mathit K}^{-}}$ Decays
POLUEKTOV 2010
PR D81 112002 Evidence for Direct $\mathit CP$ Violation in the Decay ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}^{{(*)}}}{{\mathit K}^{\pm}}$ , ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}_{{s}}^{0}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and Measurement of the CKM Phase $\phi _{3}$
AUBERT 2008AL
PR D78 034023 Improved Measurement of the CKM Angle $\gamma $ in ${{\mathit B}^{\mp}}$ $\rightarrow$ ${{\mathit D}^{(*)}}{{\mathit K}^{(*)\mp}}$ Decays with a Dalitz Plot Analysis of ${{\mathit D}}$ Decays to ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit K}_S^0}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$
POLUEKTOV 2006
PR D73 112009 Measurement of ${{\mathit \phi}_{{3}}}$ with a Dalitz Plot Analysis of ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}^{{(*)}}}{{\mathit K}^{{(*)}+}}$ Decay
AUBERT,B 2005Y
PRL 95 121802 Measurement of the Cabibbo-Kobayashi-Maskawa Angle $\gamma $ in ${{\mathit B}^{\mp}}$ ${}^{(*)}$ ${{\mathit K}^{\mp}}$ Decays with a Dalitz Analysis of ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$