Simultaneous determination of CKM angle $\gamma$ and charm mixing parameters

Information

LHCb-PAPER-2021-033
CERN-EP-2021-183
arXiv:2110.02350 [PDF]

(Submitted on 05 Oct 2021)
JHEP 12 (2021) 141
Inspire 1939295

Tools

Abstract

A combination of measurements sensitive to the $CP$ violation angle $\gamma$ of the Cabibbo-Kobayashi-Maskawa unitarity triangle and to the charm mixing parameters that describe oscillations between $D^0$ and $\bar{D}^0$ mesons is performed. Results from the charm and beauty sectors, based on data collected with the LHCb detector at CERN's Large Hadron Collider, are combined for the first time. This method provides an improvement on the precision of the charm mixing parameter $y$ by a factor of two with respect to the current world average. The charm mixing parameters are determined to be $x = (0.400^{ +0.052}_{ -0.053})\%$ and $y = (0.630^{ +0.033}_{ -0.030})\%$. The angle $\gamma$ is found to be $\gamma = (65.4^{ +3.8}_{ -4.2})^\circ$ and is the most precise determination from a single experiment.

Figures and captions

Leading-order Feynman diagrams for $ B ^- \rightarrow Dh^-$ decays with a (left) favoured $ b \rightarrow c $ and (right) suppressed $ b \rightarrow u $ quark transition.	feynma[..].pdf [10 KiB] HiDef png [123 KiB] Thumbnail [72 KiB] *.C file
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One dimensional $ 1-{\rm CL}$ profiles for $\gamma $ from the combination using inputs from $ B ^0_ s $ (light blue), $ B ^0$ (orange), $ B ^+ $ mesons (red) and all species together (dark blue).	gammac[..].pdf [16 KiB] HiDef png [431 KiB] Thumbnail [237 KiB] *.C file
Two-dimensional profile likelihood contours for (left) the charm mixing parameters $ x$ and $ y$ , and (right) the $\phi$ and $ \|q/p\|$ parameters. The blue contours show the current charm world average from Ref. [11]; the brown contours show the result of this combination. Contours are drawn out from 1 ($68.3\%$) to 5 standard deviations.	gammac[..].pdf [97 KiB] HiDef png [505 KiB] Thumbnail [300 KiB] *.C file
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Profile likelihood contours for the beauty decay parameters versus $\gamma $ , showing the breakdown of sensitivity amongst different sub-combinations of modes. The contours indicate the 68.3% and 95.4% confidence region.	gammac[..].pdf [26 KiB] HiDef png [427 KiB] Thumbnail [258 KiB] *.C file
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Profile likelihood contours for the charm decay parameters, showing the breakdown of sensitivity amongst different sub-combinations of modes. The contours indicate the 68.3% and 95.4% confidence region.	gammac[..].pdf [19 KiB] HiDef png [497 KiB] Thumbnail [315 KiB] *.C file
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Pulls of the input observables, part 1 of 3.	pulls_[..].pdf [17 KiB] HiDef png [133 KiB] Thumbnail [150 KiB] *.C file
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Pulls of the input observables, part 2 of 3.	pulls_[..].pdf [19 KiB] HiDef png [263 KiB] Thumbnail [283 KiB] *.C file
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Pulls of the input observables, part 3 of 3.	pulls_[..].pdf [13 KiB] HiDef png [62 KiB] Thumbnail [75 KiB] *.C file
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One dimensional $ 1-{\rm CL}$ profile for $\gamma $ from all inputs used in the combination.	gammac[..].pdf [14 KiB] HiDef png [169 KiB] Thumbnail [134 KiB] *.C file
Evolution of the LHCb combination result for $\gamma $ , with the central values and $1\sigma$ uncertainties in black. This result is the 2021 data point, the value and uncertainty are highlighted by the dashed blue line and band, respectively.	gamma_[..].pdf [14 KiB] HiDef png [148 KiB] Thumbnail [113 KiB] *.C file
Animated gif made out of all figures.	PAPER-2021-033.gif Thumbnail

Tables and captions

Measurements used in the combination. Inputs from the charm system appear in the lower part of the table. Those that are new, or that have changed, since the previous combination [17] are highlighted in bold. Measurements denoted by (*) include only a fraction of the Run 2 sample, corresponding to data taken in 2015 and 2016. Where multiple references are cited, measured values are taken from the most recent results, which include information from the others.	Table_1.pdf [84 KiB] HiDef png [182 KiB] Thumbnail [84 KiB] tex code
Auxiliary inputs used in the combination. Those highlighted in bold have changed since the previous combination [17].	Table_2.pdf [99 KiB] HiDef png [78 KiB] Thumbnail [34 KiB] tex code
Confidence intervals and central values for each of the parameters of interest. Entries marked with an asterisk show where the scan has hit a physical boundary at the lower limit.	Table_3.pdf [99 KiB] HiDef png [270 KiB] Thumbnail [123 KiB] tex code
Confidence intervals and best-fit values for $\gamma $ when splitting the combination inputs by initial $B$ meson species.	Table_4.pdf [63 KiB] HiDef png [42 KiB] Thumbnail [20 KiB] tex code
Confidence intervals and best-fit values for $\gamma $ when splitting the combination inputs by time-dependent and time-integrated methods.	Table_5.pdf [63 KiB] HiDef png [31 KiB] Thumbnail [15 KiB] tex code
Reduced correlation matrix for the parameters of greater interest. Values smaller than $0.001$ are replaced with a - symbol.	Table_6.pdf [52 KiB] HiDef png [54 KiB] Thumbnail [24 KiB] tex code
Correlation matrix of the fit result, part 1 of 3. Values smaller than $0.001$ are replaced with a - symbol.	Table_7.pdf [73 KiB] HiDef png [73 KiB] Thumbnail [29 KiB] tex code
Correlation matrix of the fit result, part 2 of 3. Values smaller than $0.001$ are replaced with a - symbol.	Table_8.pdf [75 KiB] HiDef png [91 KiB] Thumbnail [37 KiB] tex code
Correlation matrix of the fit result, part 3 of 3. Values smaller than $0.001$ are replaced with a - symbol.	Table_9.pdf [74 KiB] HiDef png [50 KiB] Thumbnail [21 KiB] tex code
Contributions to the total $\chi^2$ and the number of observables of each input measurement.	Table_10.pdf [84 KiB] HiDef png [222 KiB] Thumbnail [116 KiB] tex code