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.

$\gamma $

INSPIRE   PDGID:
S041GGM
For angle $\gamma (\phi _{3}$) of the CKM unitarity triangle, see the review on “$\mathit CP$ Violation” in the Reviews section.
VALUE ($^\circ{}$) CL% DOCUMENT ID TECN  COMMENT
$\bf{ 65.9 {}^{+2.9}_{-3.1}}$ OUR EVALUATION  $~~$(Produced by HFLAV)
• • We do not use the following data for averages, fits, limits, etc. • •
$69$ ${}^{+13}_{-14}$ 1
AAIJ
2023BA
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$54.8$ ${}^{+6.0}_{-5.8}$ ${}^{+6.7}_{-4.3}$ 2
AAIJ
2023I
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$116$ ${}^{+12}_{-14}$ 3
AAIJ
2023N
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$78.4$ $\pm11.4$ $\pm1.1$ 4, 5
ABUDINEN
2022
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$65.4$ ${}^{+3.8}_{-4.2}$ 6
AAIJ
2021AM
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$68.7$ ${}^{+5.2}_{-5.1}$ 4
AAIJ
2021L
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$44$ $\pm12$ 7, 8
AAIJ
2021M
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8, 13 TeV
$5.7$ ${}^{+10.2}_{-8.8}$ $\pm6.7$ 9
RESMI
2019
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$87$ ${}^{+11}_{-12}$ 10
AAIJ
2018AD
 LHCB Repl. by AAIJ 2021L
$128$ ${}^{+17}_{-22}$ 11
AAIJ
2018U
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
$\text{ 5 - 86 or 185 - 266}$ 12
AAIJ
2018Z
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
$80$ ${}^{+21}_{-22}$ 13
AAIJ
2016AA
 LHCB Repl. by AAIJ 2016Z
$72.2$ ${}^{+6.8}_{-7.3}$ 14
AAIJ
2016AQ
 LHCB Repl. by AAIJ 2021AM
$71$ $\pm20$ 15, 16
AAIJ
2016Z
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
$74$ ${}^{+20}_{-19}$
AAIJ
2015BC
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
$63.5$ ${}^{+7.2}_{-6.7}$ 17, 18
AAIJ
2015K
 LHCB ${{\mathit p}}{{\mathit p}}$ at 7, 8 TeV
$62$ ${}^{+15}_{-14}$ 19
AAIJ
2014BA
 LHCB Repl. by AAIJ 2021L
$84$ ${}^{+49}_{-42}$ 20
AAIJ
2014BE
 LHCB Repl. by AAIJ 2014BA
$115$ ${}^{+28}_{-43}$ 21
AAIJ
2014BF
 LHCB Repl. by AAIJ 2018U
$72.6$ ${}^{+9.7}_{-17.2}$ 22
AAIJ
2013AK
 LHCB Repl. by AAIJ 2021AM
$69$ ${}^{+17}_{-16}$ 23
LEES
2013B
 BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$44$ ${}^{+43}_{-38}$ 24, 25
AAIJ
2012AQ
 LHCB Repl. by AAIJ 2013AK
$77.3$ ${}^{+15.1}_{-14.9}$ $\pm5.9$ 25, 26
AIHARA
2012
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$.
$68$ $\pm14$ $\pm5$ 27
DEL-AMO-SANCH..
2010F
 BABR Repl. by LEES 2013B
$7\text{ to }173 $ 95 28
DEL-AMO-SANCH..
2010G
 BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$78.4$ ${}^{+10.8}_{-11.6}$ $\pm9.6$ 29
POLUEKTOV
2010
BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$162$ $\pm56$ 30
AUBERT
2009R
 BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$
$76$ ${}^{+22}_{-23}$ $\pm7.1$ 31
AUBERT
2008AL
 BABR Repl. by DEL-AMO-SANCHEZ 2010F
$53$ ${}^{+15}_{-18}$ $\pm10$ 32
POLUEKTOV
2006
BELL Repl. by POLUEKTOV 2010
$70$ $\pm31$ ${}^{+18}_{-15}$ 33
AUBERT,B
2005Y
 BABR Repl. by AUBERT 2008AL
$77$ ${}^{+17}_{-19}$ $\pm17$ 34
POLUEKTOV
2004
BELL Repl. by POLUEKTOV 2006
1  Measured using ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}^{*}}{{\mathit K}^{\pm}}$ and ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}^{*}}{{\mathit \pi}^{\pm}}$ 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.
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 ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{\pm}}$ 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$^\circ{}$.
5  Supersedes AIHARA 2012.
6  AAIJ 2021AM presents a combination of existing measurements from LHCb collaboration. It includes also charm mixing parameters.
7  Measured in ${{\mathit B}_{{{s}}}^{0}}$ $\rightarrow$ ${{\mathit D}_{{{s}}}^{\pm}}{{\mathit K}^{\mp}}{{\mathit \pi}^{\pm}}{{\mathit \pi}^{\mp}}$ decays in restricted phase space with m(${{\mathit K}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$) $<$ $1950$ MeV, m(${{\mathit K}^{+}}{{\mathit \pi}^{-}}$) $<$ $1200$ MeV and m(${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$) $<$ $1200$ MeV. The value is modulo 180$^\circ{}$.
8  A model-independent coherence factor for the decay ${{\mathit B}_{{{s}}}}$ $\rightarrow$ ${{\mathit D}_{{{s}}}}{{\mathit K}}{{\mathit \pi}}{{\mathit \pi}}$ (in the restricted phase space region) is also reported.
9  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.
10  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.
11  Measured in ${{\mathit B}_{{{s}}}^{0}}$ $\rightarrow$ ${{\mathit D}_{{{s}}}^{\mp}}{{\mathit K}^{\pm}}$ decays, constraining $-2{{\mathit \beta}_{{{s}}}}$ by the measurement of ${{\mathit \phi}_{{{s}}}}$ = $0.030$ $\pm0.033$ from HFLAV. The value is modulo 180$^\circ{}$.
12  AAIJ 2018Z reports the intervals ($5 - 86)^\circ{}$ or ($185 - 266)^\circ{}$ at 68$\%$ C.L. The extraction uses the time dependent CP violation measurement in ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{\mp}}{{\mathit \pi}^{\pm}}$ decays with external input and some theoretical assumptions.
13  Uses Dalitz plot analysis of ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ decays coming from ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{*}{(892)}^{0}}$ modes. Measures $\mathit r_{{{\mathit B}^{0}}}$ = $0.39$ $\pm0.13$, and $\delta _{{{\mathit B}^{0}}}$ = $197$ ${}^{+24}_{-20}$ degrees.
14  A combination of measurements from analyses of time-integrated ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{+}}$, ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{(*)0}}$, ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{+}}{{\mathit \pi}^{-}}$, and ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{+}}{{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ tree-level decays. In addition, results from a time-dependent analysis of ${{\mathit B}_{{{s}}}^{0}}$ $\rightarrow$ ${{\mathit D}_{{{s}}}}{{\mathit K}}$ decays are included.
15  A model-independent binned Dalitz plot analysis of the decays ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{*0}}$, with ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ and ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$. The results cannot be combined with the model-dependent analysis of the same dataset reported in AAIJ 2016AA.
16  Angle $\gamma $ required to satisfy 0 $<$ $\gamma $ $<$ 180 degrees.
17  Obtained by measuring time-dependent $\mathit CP$ asymmetry in ${{\mathit B}_{{{s}}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ and using a U-spin relation between ${{\mathit B}_{{{s}}}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ and ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$.
18  Results are also presented using additional inputs on ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{0}}{{\mathit \pi}^{0}}$ and ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{0}}$ decays from other experiments and isospin symmetry assumptions. The dependence of the results on the maximum allowed amount of U-spin breaking up to 50$\%$ is also included.
19  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. Solution that satisfies 0 $<{{\mathit \gamma}}<$ 180 is chosen.
20  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.
21  Measured in ${{\mathit B}_{{{s}}}^{0}}$ $\rightarrow$ ${{\mathit D}_{{{s}}}^{\mp}}{{\mathit K}^{\pm}}$ decays, constraining $-2{{\mathit \beta}_{{{s}}}}$ by the measurement of ${{\mathit \phi}_{{{s}}}}$ = $0.01$ $\pm0.07$ $\pm0.0$ from AAIJ 2013AR. The value is modulo 180$^\circ{}$ at 68$\%$ CL.
22  Presents a confidence region 55.4$^\circ{}<\gamma <$ 82.3$^\circ{}$ at 68$\%$ CL with best fit value 72.6$^\circ{}$ and includes both statistical and systematic uncertainties. The corresponding 95$\%$ CL is 40.2 $^\circ{}<\gamma <$ 92.7$^\circ{}$. The value is determined from combination of measuremets using ${{\mathit D}}$ meson decaying to ${{\mathit K}^{+}}{{\mathit K}^{-}}$, ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$, ${{\mathit K}^{\pm}}{{\mathit \pi}^{\mp}}$, ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$, ${{\mathit K}_S^0}$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$, and ${{\mathit K}^{\pm}}{{\mathit \pi}^{\mp}}{{\mathit \pi}^{\pm}}{{\mathit \pi}^{\mp}}$. Combines ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{\pm}}$ and ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}}{{\mathit \pi}^{\pm}}$.
23  Reports combination of published measurements using GGSZ, GLW, and ADS methods. Reports also 2$\sigma $ range of $41 - 102^\circ{}$ and a 5.9$\sigma $ significance for $\gamma $( ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}^{(*)0}}{{\mathit K}^{(*)+}}$) ${}\not=$ 0 hypothesis.
24  Reports combined statistical and systematic uncertainties.
25  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.
26  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.
27  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 ${{\mathit B}^{+}}$ $\rightarrow$ ${{\mathit D}^{(*)}}{{\mathit K}^{+}}$, ${{\mathit D}}{{\mathit K}^{*+}}$ modes. The corresponding two standard deviation interval for $\gamma $ is 39$^\circ{}<\gamma <$ 98$^\circ{}$. CP conservation in the combined result is ruled out with a significance of 3.5 standard deviations.
28  Reports confidence intervals for the CKM angle $\gamma $ from the measured values of the GLW parameters using ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{\pm}}$ decays with ${{\mathit D}}$ mesons decaying to non-$\mathit CP({{\mathit K}}{{\mathit \pi}}$), $\mathit CP$-even (${{\mathit K}^{+}}{{\mathit K}^{-}}$, ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$), and $\mathit CP$-odd (${{\mathit K}_S^0}$ ${{\mathit \pi}^{0}}$, ${{\mathit K}_S^0}$ ${{\mathit \omega}}$) states.
29  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 for $\gamma $ is 54.2$^\circ{}<\gamma <$ 100.5$^\circ{}$. CP conservation in the combined result is ruled out with a significance of 3.5 standard deviations.
30  Uses Dalitz plot analysis of ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ decays coming from ${{\mathit B}^{0}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit K}^{*0}}$ modes. The corresponding 95$\%$ CL interval is 77$^\circ{}<\gamma <$ 247$^\circ{}$. A 180 degree ambiguity is implied.
31  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. The corresponding two standard deviation interval is 29$^\circ{}<\gamma <$ 122$^\circ{}$.
32  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. The corresponding two standard deviations interval for gamma is 8$^\circ{}<\gamma <$ 111$^\circ{}$.
33  Uses a Dalitz plot analysis of neutral ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ decays coming from ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{\pm}}$ and ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}^{{*0}}}{{\mathit K}^{\pm}}$ followed by ${{\mathit D}^{{*0}}}$ $\rightarrow$ ${{\mathit D}}{{\mathit \pi}^{0}}$, ${{\mathit D}}{{\mathit \gamma}}$. The corresponding two standard deviations interval for gamma is 12$^\circ{}$ $<$ $\gamma $ $<$ 137$^\circ{}$. AUBERT,B 2005Y also reports the amplitude ratios and the strong phases.
34  Uses a Dalitz plot analysis of the 3-body ${{\mathit D}}$ $\rightarrow$ ${{\mathit K}_S^0}$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ decays coming from ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}}{{\mathit K}^{\pm}}$ and ${{\mathit B}^{\pm}}$ $\rightarrow$ ${{\mathit D}^{{*}}}{{\mathit K}^{\pm}}$ followed by ${{\mathit D}^{*}}$ $\rightarrow$ ${{\mathit D}}{{\mathit \pi}^{0}}$; here we use ${{\mathit D}}$ to denote that the neutral ${{\mathit D}}$ meson produced in the decay is an admixture of ${{\mathit D}^{0}}$ and ${{\overline{\mathit D}}^{0}}$. The corresponding two standard deviations interval for $\gamma $ is 26${}^{^\circ{}}$ $<\gamma <$ 126${}^{^\circ{}}$. POLUEKTOV 2004 also reports the amplitude ratios and the strong phases.
Conservation Laws:
$\mathit CP$ VIOLATION OBSERVED
References