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:
S041ARX
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 ($ 10^{-2} $) CL% DOCUMENT ID TECN  COMMENT
$\bf{ 9.88 {}^{+0.22}_{-0.21}}$ OUR EVALUATION  $~~$(Produced by HFLAV)
$11.5$ ${}^{+1.2}_{-1.3}$ 1
ADACHI
2024T
 BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$)
• • We do not use the following data for averages, fits, limits, etc. • •
$9.46$ $\pm0.31$ ${}^{+0.30}_{-0.24}$ 2
AAIJ
2023I
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$11.0$ $\pm2.0$ 3
AAIJ
2023N
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$12.9$ $\pm2.4$ $\pm0.2$ 4
ABUDINEN
2022
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$9.04$ ${}^{+0.77}_{-0.75}$ 5
AAIJ
2021L
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$32.3$ $\pm14.7$ $\pm5.6$ 6
RESMI
2019
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$8.6$ ${}^{+1.3}_{-1.4}$ 7
AAIJ
2018AD
 LHCB Repl. by AAIJ 2021L
$8.0$ ${}^{+1.9}_{-2.1}$ 4
AAIJ
2014BA
 LHCB Repl. by AAIJ 2021L
$6$ $\pm4$ 8
AAIJ
2014BE
 LHCB Repl. by AAIJ 2014BA
$9.7$ $\pm1.1$ 9
AAIJ
2013AE
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV
$9.2$ ${}^{+1.3}_{-1.2}$ 10
LEES
2013B
 BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$7$ $\pm4$ 11, 12
AAIJ
2012AQ
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV
$14.5$ $\pm3.0$ $\pm1.5$ 12, 13
AIHARA
2012
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$.
$<13$ 90 14
LEES
2011D
 BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$9.6$ $\pm2.9$ $\pm0.6$ 15
DEL-AMO-SANCH..
2010F
 BABR Repl. by LEES 2013B
$9.5$ ${}^{+5.1}_{-4.1}$ 16
DEL-AMO-SANCH..
2010H
 BABR Repl. by LEES 2013B
$16.0$ ${}^{+4.0}_{-3.8}$ ${}^{+5.1}_{-1.5}$ 17
POLUEKTOV
2010
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$8.6$ $\pm3.2$ $\pm1.5$ 18
AUBERT
2008AL
 BABR Repl. by DEL-AMO-SANCHEZ 2010F
$<19$ 90
HORII
2008
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$15.9$ ${}^{+5.4}_{-5.0}$ $\pm5.0$ 19
POLUEKTOV
2006
BELL Repl. by POLUEKTOV 2010
$12$ $\pm8$ $\pm5$ 20
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  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 ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{+}}$ decays, with ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$. Strong phase measurements from CLEO-c (LIBBY 2010) of the ${{\mathit D}}$ decay over the Dalitz plot are used as input. Supersedes AIHARA 2012.
5  Uses binned analysis of ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ from ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{\pm}}$ modes over the phase space. Strong phase measurements from CLEO-c and BES-III data of the ${{\mathit D}}$ decay over the phase space binning are used as input.
6  Uses binned analysis of ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}{{\mathit \pi}^{0}}$ from ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{\pm}}$ modes over the phase space. Strong phase measurements from RESMI 2018 analysis of CLEO-c data of the ${{\mathit D}}$ decay over the phase space binning are used as input.
7  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 ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{\pm}}$ modes. Strong phase measurements from CLEO-c of the ${{\mathit D}}$ decay over the Dalitz plot are used as input.
8  AAIJ 14BE uses model-dependent analysis of ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ amplitudes. The model is the same as in DEL-AMO-SANCHEZ 2010F.
9  Uses ${{\mathit B}^{\pm}}$ $\rightarrow$ [ ${{\mathit K}^{\pm}}{{\mathit \pi}^{\mp}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ ]$_{D}$ ${{\mathit h}^{\pm}}$ mode.
10  Reports combination of published measurements using GGSZ, GLW, and ADS methods.
11  Reports combined statistical and systematic uncertainties.
12  Uses binned Dalitz plot of ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ decays from ${{\mathit B}^{+}}$ $\rightarrow$ ${{\overline{\mathit D}}^{0}}{{\mathit K}^{+}}$. Measurement of strong phases in ${{\overline{\mathit D}}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Dalitz plot from LIBBY 2010 is used as input.
13  We combined the systematics in quadrature. The authors report separately the contribution to the systematic uncertainty due to the uncertainty on the bin-averaged strong phase difference between ${{\mathit D}^{0}}$ and ${{\overline{\mathit D}}^{0}}$ amplitudes. Superseded by ABUDINEN 2022.
14  Uses decays of neutral ${{\mathit D}}$ to ${{\mathit K}^{-}}{{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$.
15  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 0.037 $<{{\mathit r}_{{{B}}}}<$0.155.
16  Uses the Cabibbo suppressed decay of ${{\mathit B}^{+}}$ $\rightarrow$ ${{\overline{\mathit D}}}{{\mathit K}^{+}}$ followed by ${{\overline{\mathit D}}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$.
17  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 0.084 $<{{\mathit r}_{{{B}}}}<$ 0.239.
18  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.
19  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.
20  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