# Determination of $\gamma$ and $-2\beta_s$ from charmless two-body decays of beauty mesons

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## Abstract

Using the latest LHCb measurements of time-dependent CP violation in the B^0_s -> K^+K^- decay, a U-spin 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 U-spin 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 U-spin breaking effects up to 50% are included.

## Figures and captions

 Dependences of the $68\%$ (hatched areas) and $95\%$ (filled areas) probability intervals on the allowed amount of non-factorizable U-spin breaking, for (a) $\gamma$ from analysis A and (b) $-2\beta_s$ from analysis B. gammaFLtot.pdf [131 KiB] HiDef png [483 KiB] Thumbnail [83 KiB] *.C file phisFLtot.pdf [126 KiB] HiDef png [350 KiB] Thumbnail [65 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 [301 KiB] Thumbnail [48 KiB] *.C file phisFL[..].pdf [146 KiB] HiDef png [229 KiB] Thumbnail [39 KiB] *.C file Dependences of the $68\%$ (hatched areas) and $95\%$ (filled areas) probability intervals on the allowed amount of non-factorizable U-spin breaking, for (a) $\gamma$ from analysis C and (b) $-2\beta_s$ from analysis D. gammaPlot.pdf [119 KiB] HiDef png [403 KiB] Thumbnail [73 KiB] *.C file phiSUspin.pdf [124 KiB] HiDef png [335 KiB] Thumbnail [63 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 [310 KiB] Thumbnail [49 KiB] *.C file phisCn[..].pdf [144 KiB] HiDef png [225 KiB] Thumbnail [38 KiB] *.C file Results for (top) $\gamma$ and (bottom) $-2\beta_s$ with 50% ($\kappa=0.5$) non-factorizable U-spin 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 [202 KiB] Thumbnail [38 KiB] *.C file phisCo[..].pdf [148 KiB] HiDef png [169 KiB] Thumbnail [31 KiB] *.C file Animated gif made out of all figures. PAPER-2014-045.gif Thumbnail

## Tables and captions

 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 [13 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 U-spin 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 U-spin symmetry. Table_3.pdf [52 KiB] HiDef png [67 KiB] Thumbnail [13 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 [14 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 U-spin 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 U-spin symmetries. Table_6.pdf [53 KiB] HiDef png [80 KiB] Thumbnail [14 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 [92 KiB] Thumbnail [17 KiB] tex code

Created on 11 December 2018.Citation count from INSPIRE on 11 December 2018.