Using the latest LHCb measurements of timedependent CP violation in the B^0_s > K^+K^ decay, a Uspin relation between the decay amplitudes of B^0_s > K^+K^ and B^0 > \pi^+\pi^ decay processes allows constraints to be placed on the angle gamma of the unitarity triangle and on the B^0_s mixing phase 2\beta_s. Results from an extended approach, which uses additional inputs on B^0 > \pi^0\pi^0 and B^+ > \pi^+\pi^0 decays from other experiments and exploits isospin symmetry, are also presented. The dependence of the results on the maximum allowed amount of Uspin breaking is studied. At 68 probability, the value \gamma = ( 63.5 +7.2 6.7 ) degrees modulo 180 degrees is determined. In an alternative analysis, the value 2\beta_s = 0.12 +0.14 0.16 rad is found. In both measurements, the uncertainties due to Uspin breaking effects up to 50 are included.
Dependences of the $68\%$ (hatched areas) and $95\%$ (filled areas) probability intervals on the allowed amount of nonfactorizable Uspin breaking, for (a) $\gamma$ from analysis A and (b) $2\beta_s$ from analysis B. 
gammaFLtot.pdf [131 KiB] HiDef png [393 KiB] Thumbnail [231 KiB] *.C file 

phisFLtot.pdf [126 KiB] HiDef png [290 KiB] Thumbnail [165 KiB] *.C file 

Distributions of (a) $\gamma$ from analysis A and (b) $2\beta_s$ from analysis B, corresponding to $\kappa=0.5$. The hatched areas correspond to 68% probability intervals, whereas the filled areas correspond to 95% probability intervals. 
gammaF[..].pdf [148 KiB] HiDef png [193 KiB] Thumbnail [126 KiB] *.C file 

phisFL[..].pdf [146 KiB] HiDef png [161 KiB] Thumbnail [96 KiB] *.C file 

Dependences of the $68\%$ (hatched areas) and $95\%$ (filled areas) probability intervals on the allowed amount of nonfactorizable Uspin breaking, for (a) $\gamma$ from analysis C and (b) $2\beta_s$ from analysis D. 
gammaPlot.pdf [119 KiB] HiDef png [318 KiB] Thumbnail [193 KiB] *.C file 

phiSUspin.pdf [124 KiB] HiDef png [288 KiB] Thumbnail [164 KiB] *.C file 

Distributions of (a) $\gamma$ from analysis C and (b) $2\beta_s$ from analysis D, corresponding to $\kappa=0.5$. The hatched areas correspond to 68% probability intervals, whereas the filled areas correspond to 95% probability intervals. 
gammaC[..].pdf [145 KiB] HiDef png [199 KiB] Thumbnail [123 KiB] *.C file 

phisCn[..].pdf [144 KiB] HiDef png [155 KiB] Thumbnail [94 KiB] *.C file 

Results for (top) $\gamma$ and (bottom) $2\beta_s$ with 50% ($\kappa=0.5$) nonfactorizable Uspin breaking. As a comparison, other reference values are also reported. The most likely values are indicated by the vertical lines insides the boxes. The boxes and the error bars delimit the 68% and 95% probability intervals, respectively. 
gammaC[..].pdf [123 KiB] HiDef png [159 KiB] Thumbnail [86 KiB] *.C file 

phisCo[..].pdf [148 KiB] HiDef png [124 KiB] Thumbnail [71 KiB] *.C file 

Animated gif made out of all figures. 
PAPER2014045.gif Thumbnail 
Current knowledge of $ C P$ violation parameters and $ C P$ averaged branching fractions of $B^0\rightarrow \pi^+\pi^$, $B^0\rightarrow \pi^0\pi^0$, $B^+\rightarrow \pi^+\pi^0$ and $B^0_s \rightarrow K^+K^$ decays from BaBar, Belle, CDF and LHCb. The parameter $\rho(X, Y)$ is the statistical correlation between $X$ and $Y$. The first uncertainties are statistical and the second systematic. 
Table_1.pdf [69 KiB] HiDef png [72 KiB] Thumbnail [35 KiB] tex code 

Experimental inputs used for the determination of $\gamma$ and $2\beta_s$ from $B^0 \rightarrow \pi^+\pi^$ and $B^0_s \rightarrow K^+K^$ decays using Uspin symmetry. The parameter $\rho(X, Y)$ is the statistical correlation between $X$ and $Y$. For $C_{\pi^+\pi^}$ and $S_{\pi^+\pi^}$ we perform our own weighted average of BaBar, Belle and LHCb results, accounting for correlations. 
[Error creating the table]  
Ranges of flat priors used for the determination of $\gamma$ and $2\beta_s$ from $B^0 \rightarrow \pi^+\pi^$ and $B^0_s \rightarrow K^+K^$ decays using Uspin symmetry. 
Table_3.pdf [52 KiB] HiDef png [70 KiB] Thumbnail [34 KiB] tex code 

Results obtained from analyses A and B with $\kappa=0.5$. The results are given modulo $180^\circ$ for $\vartheta$, $\vartheta^\prime$ and $\gamma$. 
Table_4.pdf [54 KiB] HiDef png [77 KiB] Thumbnail [38 KiB] tex code 

Experimental inputs used for the determination of $\gamma$ and $2\beta_s$ from $B^0 \rightarrow \pi^+\pi^$, $B^0 \rightarrow \pi^0\pi^0$, $B^+ \rightarrow \pi^+\pi^0$ and $B^0_s \rightarrow K^+K^$ decays, using isospin and Uspin symmetries. The parameter $\rho(X, Y)$ is the statistical correlation between $X$ and $Y$. For $C_{\pi^+\pi^}$ and $S_{\pi^+\pi^}$ we perform our own weighted average of BaBar, Belle and LHCb results, accounting for correlations. 
[Error creating the table]  
Ranges of flat priors used for the determination of $\gamma$ and $2\beta_s$ from $B^0 \rightarrow \pi^+\pi^$, $B^0 \rightarrow \pi^0\pi^0$, $B^+ \rightarrow \pi^+\pi^0$ and $B^0_s \rightarrow K^+K^$ decays, using isospin and Uspin symmetries. 
Table_6.pdf [53 KiB] HiDef png [86 KiB] Thumbnail [39 KiB] tex code 

Results obtained from analyses C and D with $\kappa=0.5$. The results are given modulo $180^\circ$ for $\vartheta$, $\vartheta^\prime$ and $\gamma$. 
Table_7.pdf [55 KiB] HiDef png [91 KiB] Thumbnail [45 KiB] tex code 
Created on 11 July 2020.