cern.ch

Improved constraints on $\gamma$: CKM2014 update

[to restricted-access page]

Abstract

We report on an updated combination of all currently available tree-level measurements of the CKM angle $\gamma$ from LHCb . We use results obtained from time integrated analyses of $ B ^+ \rightarrow D h^+$ and $ B ^0 \!\rightarrow D K^{*0}$ decays, where $h^+$ corresponds to either $ K ^+$ or $\pi ^+$ and the $D$ meson decays into $ K ^+ K ^- $ , $\pi ^+ \pi ^- $ , $ K ^\pm \pi ^\mp $ , $ K ^0_{\rm\scriptscriptstyle S} K ^\pm \pi ^\mp $ , $ K ^0_{\rm\scriptscriptstyle S} \pi ^\pm \pi ^\mp $ , $ K ^0_{\rm\scriptscriptstyle S} K ^\pm K ^\mp $ , and $ K ^\pm \pi ^\mp \pi ^\pm \pi ^\mp $ . The effect of $ D ^0$ -- $\kern 0.2em\overline{\kern -0.2em D }{} ^0$ mixing is taken into account. In addition, we use results obtained from a time dependent analysis of $ B ^0_ s \rightarrow D_s^\mp K^\pm$ . We find a best fit value of $\gamma = 78.9 ^\circ$ and set confidence intervals on $\gamma$ using a frequentist procedure: $\gamma \in [71.5,84.7] ^\circ$ at $68\% $ confidence level (CL) and $\gamma \in [54.6,91.4] ^\circ$ at $95\% {\rm CL}$, where all values are modulo $180^\circ$. When combining results from $ B\rightarrow DK$ -like decays alone, i.e. excluding $ B\rightarrow D\pi$ decays, we find a best fit value of $\gamma = 72.9 ^\circ$ and set the confidence intervals: $\gamma \in [63.0,82.1] ^\circ$ at 68\% CL and $\gamma \in [52.0,90.5] ^\circ$ at 95\% CL. Using the best fit value and the 68\% CL interval, we find \begin{align*} \gamma = ( 73^{+9}_{-10} )^\circ\,. \end{align*}

Figures and captions

Left: Likelihood for $\delta_D^{K3\pi}$ and $\kappa_D^{K3\pi}$ obtained with CLEO-c data. Figure taken from Ref. [26]. Note that the axis labels uses the symbol $R_{K3\pi}$ to denote $\kappa_D^{K3\pi}$ . Right: Likelihood for $\delta_D^{K_SK\pi}$ and $\kappa_D^{K_SK\pi}$ . Figure taken from Ref. [27]. Note that the axis labels uses the symbol $R_{K^*K}$ to denote $\kappa_D^{K_SK\pi}$ , and $\delta_D^{K^*K}$ to denote $\delta_D^{K_SK\pi}$ .

CleoK3[..].pdf [601 KiB]
HiDef png [1 MiB]
Thumbnail [153 KiB]
CleoK3piNew.pdf
CleoKSKpi.pdf [374 KiB]
HiDef png [511 KiB]
Thumbnail [62 KiB]
CleoKSKpi.pdf

$ 1-{\rm CL}$ curves for the robust combination.

gammac[..].pdf [14 KiB]
HiDef png [193 KiB]
Thumbnail [57 KiB]
gammacombo_ckm2014robustNoDhpipi_g_pluginOnly_prelim.pdf
gammac[..].pdf [14 KiB]
HiDef png [187 KiB]
Thumbnail [59 KiB]
gammacombo_ckm2014robustNoDhpipi_d_dk_pluginOnly_prelim.pdf
gammac[..].pdf [14 KiB]
HiDef png [192 KiB]
Thumbnail [57 KiB]
gammacombo_ckm2014robustNoDhpipi_r_dk_pluginOnly_prelim.pdf

Profile likelihood contours, robust combination. The contours are the two-dimensional $1\sigma$ and $2\sigma$ contours.

gammac[..].pdf [14 KiB]
HiDef png [352 KiB]
Thumbnail [66 KiB]
gammacombo_ckm2014robustNoDhpipi_g_r_dk_prelim.pdf
gammac[..].pdf [14 KiB]
HiDef png [416 KiB]
Thumbnail [73 KiB]
gammacombo_ckm2014robustNoDhpipi_g_d_dk_prelim.pdf
gammac[..].pdf [14 KiB]
HiDef png [330 KiB]
Thumbnail [64 KiB]
gammacombo_ckm2014robustNoDhpipi_d_dk_r_dk_prelim.pdf

$ 1-{\rm CL}$ curves for the full combination.

gammac[..].pdf [14 KiB]
HiDef png [191 KiB]
Thumbnail [57 KiB]
gammacombo_ckm2014fullNoDhpipi_r_dk_pluginOnly_prelim.pdf
gammac[..].pdf [14 KiB]
HiDef png [187 KiB]
Thumbnail [60 KiB]
gammacombo_ckm2014fullNoDhpipi_d_dk_pluginOnly_prelim.pdf
gammac[..].pdf [14 KiB]
HiDef png [180 KiB]
Thumbnail [52 KiB]
gammacombo_ckm2014fullNoDhpipi_r_dpi_pluginOnly_prelim.pdf
gammac[..].pdf [14 KiB]
HiDef png [208 KiB]
Thumbnail [60 KiB]
gammacombo_ckm2014fullNoDhpipi_d_dpi_pluginOnly_prelim.pdf
gammac[..].pdf [14 KiB]
HiDef png [159 KiB]
Thumbnail [48 KiB]
gammacombo_ckm2014fullNoDhpipi_g_pluginOnly_prelim.pdf

Profile likelihood contours, full combination. The contours are the two-dimensional $1\sigma$ and $2\sigma$ contours.

gammac[..].pdf [14 KiB]
HiDef png [348 KiB]
Thumbnail [65 KiB]
gammacombo_ckm2014fullNoDhpipi_g_r_dk_prelim.pdf
gammac[..].pdf [14 KiB]
HiDef png [381 KiB]
Thumbnail [68 KiB]
gammacombo_ckm2014fullNoDhpipi_g_d_dk_prelim.pdf
gammac[..].pdf [15 KiB]
HiDef png [549 KiB]
Thumbnail [84 KiB]
gammacombo_ckm2014fullNoDhpipi_g_r_dpi_prelim.pdf
gammac[..].pdf [16 KiB]
HiDef png [250 KiB]
Thumbnail [47 KiB]
gammacombo_ckm2014fullNoDhpipi_g_d_dpi_prelim.pdf
gammac[..].pdf [14 KiB]
HiDef png [295 KiB]
Thumbnail [60 KiB]
gammacombo_ckm2014fullNoDhpipi_d_dk_r_dk_prelim.pdf
gammac[..].pdf [20 KiB]
HiDef png [560 KiB]
Thumbnail [85 KiB]
gammacombo_ckm2014fullNoDhpipi_d_dpi_r_dpi_prelim.pdf

Comparing the robust and full combinations.

gammac[..].pdf [15 KiB]
HiDef png [204 KiB]
Thumbnail [58 KiB]
gammacombo_ckm2014robustNoDhpipi_ckm2014fullNoDhpipi_g_pluginOnly_prelim.pdf

Observed $p$-values of the coverage test. Left: robust combination, performed at the best fit point. Middle: full combination, performed at the $ r_B^{D\pi} = 0.027 $ best fit point. Right: full combination, performed at the $ r_B^{D\pi} = 0.006 $ local minimum. Filled blue corresponds to the {\sc Plugin} method, dashed red to the profile likelihood method.

gammac[..].pdf [14 KiB]
HiDef png [151 KiB]
Thumbnail [55 KiB]
gammacombo_ckm2014robustNoDhpipi_g_coverage_id0_pvalue.pdf
gammac[..].pdf [14 KiB]
HiDef png [148 KiB]
Thumbnail [54 KiB]
gammacombo_ckm2014fullNoDhpipi_g_coverage_id0_pvalue.pdf
gammac[..].pdf [14 KiB]
HiDef png [145 KiB]
Thumbnail [54 KiB]
gammacombo_ckm2014fullNoDhpipi_g_coverage_id1_pvalue.pdf

The 1D posterior PDFs for $\gamma$ (top left), $ r_B^{DK} $ (top right), and $\delta_B^{DK} $ (bottom), in the robust combination. Dark and light regions show the 68% and 95% probability intervals, respectively. These intervals are shown in Table 8.

LHCB_r[..].pdf [24 KiB]
HiDef png [252 KiB]
Thumbnail [49 KiB]
LHCB_robust_none_gamma.pdf
LHCB_r[..].pdf [23 KiB]
HiDef png [244 KiB]
Thumbnail [46 KiB]
LHCB_robust_none_rB.pdf
LHCB_r[..].pdf [24 KiB]
HiDef png [256 KiB]
Thumbnail [51 KiB]
LHCB_robust_none_deltaB.pdf

Tables and captions

Parameters used in the combined fits. The parameters listed below the horizontal line are constrained in the fit using external inputs. The phase differences $\delta_D^{K\pi}$ , $\delta_D^{K_SK\pi}$ , and $\delta_D^{K3\pi}$ are defined in accordance with Ref. [1]. They are shifted by $180^{\circ}$ with respect to the convention used by the HFAG. The parameters $q$ and $p$ of the $ B ^0_ s $ system are defined in Sec. 2.6.

Table_1.pdf [84 KiB]
HiDef png [92 KiB]
thumbnail [12 KiB]
tex code
Table_1.pdf

Observables used in the robust combination.

Table_2.pdf [95 KiB]
HiDef png [142 KiB]
thumbnail [22 KiB]
tex code
Table_2.pdf

Confidence intervals and central values for the robust combination.

Table_3.pdf [38 KiB]
HiDef png [154 KiB]
thumbnail [22 KiB]
tex code
Table_3.pdf

Observables used in the full combination in addition to those of the robust combination given in Table 2.

Table_4.pdf [57 KiB]
HiDef png [30 KiB]
thumbnail [5 KiB]
tex code
Table_4.pdf

Confidence intervals and central values for the full combination. The two columns correspond to the two minima found by the fit. The most probable value is given in the left column, corresponding to a large value of $ r_B^{D\pi}$ .

Table_5.pdf [38 KiB]
HiDef png [172 KiB]
thumbnail [26 KiB]
tex code
Table_5.pdf

Fit probabilities of the best fit values of the two combinations.

Table_6.pdf [37 KiB]
HiDef png [45 KiB]
thumbnail [7 KiB]
tex code
Table_6.pdf

Measured coverage $\alpha$ of the confidence intervals for $\gamma$ , measured at the best fit points, for both the {\sc Plugin} and profile likelihood methods. The expected coverage is denoted as $\eta$. In case of the full combination, the local maxima are labeled with $ r_B^{D\pi}$ , as this parameter is expected to affect the coverage.

Table_7.pdf [46 KiB]
HiDef png [130 KiB]
thumbnail [19 KiB]
tex code
Table_7.pdf

Credibility regions and most probable values for the hadronic parameters extracted from the robust combination. The second part of the table repeats the frequentist results for comparison.

Table_8.pdf [38 KiB]
HiDef png [75 KiB]
thumbnail [11 KiB]
tex code
Table_8.pdf

Statistical $ D ^0 \rightarrow K^\pm\pi^\mp\pi^+\pi^-$ ADS correlations.

Table_9.pdf [48 KiB]
HiDef png [42 KiB]
thumbnail [6 KiB]
tex code
Table_9.pdf

Systematic $ D ^0 \rightarrow K^\pm\pi^\mp\pi^+\pi^-$ ADS correlations.

Table_10.pdf [48 KiB]
HiDef png [35 KiB]
thumbnail [5 KiB]
tex code
Table_10.pdf

Statistical $ D ^0 \rightarrow K ^0_{\rm\scriptscriptstyle S} h^+h^-$ GGSZ correlations.

Table_11.pdf [38 KiB]
HiDef png [32 KiB]
thumbnail [4 KiB]
tex code
Table_11.pdf

Systematic $ D ^0 \rightarrow K ^0_{\rm\scriptscriptstyle S} h^+h^-$ GGSZ correlations.

Table_12.pdf [38 KiB]
HiDef png [34 KiB]
thumbnail [5 KiB]
tex code
Table_12.pdf

Statistical $ D\rightarrow K ^0_{\rm\scriptscriptstyle S} K\pi$ GLS correlations. Only the ratio observables were found to have non$-$zero correlations.

Table_13.pdf [47 KiB]
HiDef png [36 KiB]
thumbnail [5 KiB]
tex code
Table_13.pdf

Statistical $ B ^0 \rightarrow D K^{*0}$ GLW/ADS correlations.

Table_14.pdf [69 KiB]
HiDef png [34 KiB]
thumbnail [5 KiB]
tex code
Table_14.pdf

Systematic $ B ^0 \rightarrow D K^{*0}$ GLW/ADS correlations.

Table_15.pdf [62 KiB]
HiDef png [37 KiB]
thumbnail [5 KiB]
tex code
Table_15.pdf

Statistical $ D ^0 \rightarrow h^+h^-$ GLW/ADS correlations. Note that the order differs from Eqns. ???ff.

Table_16.pdf [56 KiB]
HiDef png [46 KiB]
thumbnail [6 KiB]
tex code
Table_16.pdf

Systematic $ D ^0 \rightarrow h^+h^-$ GLW/ADS correlations. Note that the order differs from Eqns. ???ff.

Table_17.pdf [56 KiB]
HiDef png [39 KiB]
thumbnail [6 KiB]
tex code
Table_17.pdf

Statistical $ B ^0_ s \rightarrow D_s^\mp K^\pm$ correlations.

Table_18.pdf [39 KiB]
HiDef png [44 KiB]
thumbnail [7 KiB]
tex code
Table_18.pdf

Systematic $ B ^0_ s \rightarrow D_s^\mp K^\pm$ correlations.

Table_19.pdf [39 KiB]
HiDef png [40 KiB]
thumbnail [6 KiB]
tex code
Table_19.pdf

Correlations of the HFAG charm parameters (FPCP 2014, "Fit 3", $ C\!P$ violation allowed).

Table_20.pdf [56 KiB]
HiDef png [39 KiB]
thumbnail [6 KiB]
tex code
Table_20.pdf

Created on 12 May 2018.Citation count from INSPIRE on 12 May 2018.