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Search for time-dependent $CP$ violation in $D^0 \to K^+ K^-$ and $D^0 \to \pi^+ \pi^-$ decays

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Abstract

A search for charge-parity ( $ C P$ ) violation in the time-dependent decay rates of $ D ^0 \rightarrow K ^+ K ^- $ and $ D ^0 \rightarrow \pi ^+ \pi ^- $ decays is reported. The data correspond to an integrated luminosity of $1.9\text{ fb} ^{-1} $ collected by the LHCb detector in 2015--2016 in $ p $ $ p $ collisions at a centre-of-mass energy of $13\text{ Te V} $. The flavour of the $ D ^0$ meson is inferred from the charge of the pion in $ D ^{*}(2010)^{+} \rightarrow D ^0 \pi ^+ $ decays. The asymmetries of the time-dependent decay rates of $ D ^0$ and $\overline{ D }{} {}^0$ decays, sensitive to $ C P$ violation in the mixing and in the interference between mixing and decay, are measured to be $ A_{\Gamma} ( K ^+ K ^- ) = (1.3 \pm 3.5 \pm 0.7)\times 10^{-4}$ and $ A_{\Gamma} (\pi ^+ \pi ^- ) = (11.3 \pm 6.9 \pm 0.8)\times 10^{-4}$, where the first uncertainties are statistical and the second are systematic.

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Distributions of $\Delta m$ for the (a) $ D ^0 \rightarrow K ^- \pi ^+ $ , (b) $ D ^0 \rightarrow K ^+ K ^- $ and (c) $ D ^0 \rightarrow \pi ^+ \pi ^- $ samples. The signal region and the region used for the sideband subtraction to remove the combinatorial background (red filled area) are delimited by the vertical dashed lines.

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(Left) sum and (right) asymmetry of the distributions of $ D ^0$ and $\overline{ D }{} {}^0$ candidates, in (top) $ q_\text{tag} \theta_x$ versus $k$ and (bottom) $ q_\text{tag} \theta_x$ versus $\theta_y$ planes, for the 2016 Mag Up $ D ^0 \rightarrow K ^- \pi ^+ $ subsample. The angle $\theta_{x(y)} \equiv \arctan(p_{x(y)} / p_z)$ is the emission angle of the $ D ^0$ in the bending (vertical) plane, $k \equiv 1/\sqrt{p_x^2 + p_z^2}$ and $ q_\text{tag}$ is the sign of the charge of the tagging pion.

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Fit to the time-dependent asymmetry of the $ D ^0 \rightarrow K ^- \pi ^+ $ sample (red) before the kinematic weighting of $ D ^0$ and $\overline{ D }{} {}^0$ candidates and the subtraction of secondary decays, but with a cut $\lvert\text{TIP}\rvert < 40 \upmu\text{m} $ to reduce their amount, and (black) after the kinematic weighting and the subtraction of secondary decays, for the (left) 2016 Mag Up and (right) 2016 MagDown subsamples.

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Transverse IP distributions of the $ D ^0 \rightarrow K ^+ K ^- $ 2016 Mag Up subsample for the $(a)$ first, $(b)$ middle and $(c)$ last time bin. The results of the fit are superimposed.

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Fraction of secondary decays fitted to the TIP distribution (within the $\lvert \text{TIP} \rvert < 200 \upmu\text{m} $ range) as a function of decay time, for the $ D ^0 \rightarrow K ^- \pi ^+ $ 2016 Mag Up subsample. Black dots are the fractions of secondary decays returned by the baseline fit model, whereas other points correspond to alternative models used to assess systematic uncertainties on the measurement of $ A_{\Gamma}$ . Splines are drawn through the points.

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Results of the fits to the time-dependent asymmetry for each subsample, including their weighted average, labelled "avg.". In the labels, 2015 (2016) is abbreviated as 15 (16) and Mag Up ( MagDown ) is abbreviated as Up (Dw). Numerical values and fit qualities ( $\chi^2/\mathrm{ndf}$ ) are reported on the right of each plot. Solid red squares correspond to asymmetries measured before the kinematic weighting of $ D ^0$ and $\overline{ D }{} {}^0$ candidates and without the subtraction of secondary decays, which are suppressed with a cut $\lvert \text{TIP} \rvert < 40 \upmu\text{m} $ instead. Empty black dots correspond to asymmetries measured after the kinematic weighting and disentangling the asymmetry of primary decays in the fit to the TIP distributions in the $\lvert \text{TIP} \rvert < 200 \upmu\text{m} $ range.

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Measured asymmetry of the primary decays in bins of $t/\tau_{ D ^0 } $, where $\tau_{ D ^0 } = 0.410\text{ ps} $ [33], for (top) the $ D ^0 \rightarrow K ^- \pi ^+ $ , (centre) $ D ^0 \rightarrow K ^+ K ^- $ and (bottom) $ D ^0 \rightarrow \pi ^+ \pi ^- $ decay channels, averaged over the full 2015--2016 data sample. The solid lines show the linear fit, whose slope is equal to $- A_{\Gamma} $.

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Template fit to the $m( h ^+ h ^- )$ distribution for the (left) $ D ^0 \rightarrow K ^+ K ^- $ and (right) $ D ^0 \rightarrow \pi ^+ \pi ^- $ samples after the $\Delta m$ sideband subtraction. The vertical dashed lines delimit the signal region. The $m( h ^+ h ^- )$ template of the $ D ^+_ s \rightarrow K ^+ K ^- \pi ^+ $ decay has a negative contribution to the left of the known $ D ^0$ mass due to the sideband subtraction. For $ D ^+_ s \rightarrow K ^+ K ^- \pi ^+ $ decays, $m( h ^+ h ^- )$ is nearly linearly correlated with $\Delta m$ .

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(Left) sum and (right) asymmetry of the distributions of the tagging pion of $ D ^0$ and $\overline{ D }{} {}^0$ candidates, in (top) $ q_\text{tag} \theta_x$ versus $k$ and (bottom) $ q_\text{tag} \theta_x$ versus $\theta_y$ planes, for the 2016 Mag Up $ D ^0 \rightarrow K ^- \pi ^+ $ subsample. The angle $\theta_{x(y)} \equiv \arctan(p_{x(y)} / p_z)$ is the emission angle of the $\pi ^{+}_{\mathrm{ \scriptscriptstyle tag}}$ in the bending (vertical) plane, $k \equiv 1/\sqrt{p_x^2 + p_z^2}$ is proportional to the curvature of the $\pi ^{+}_{\mathrm{ \scriptscriptstyle tag}}$ , and $ q_\text{tag}$ is the sign of its charge.

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Normalised distribution and asymmetry of the $ D ^0$ transverse momentum for (left) the 2016 Mag Up and (right) 2016 MagDown sample, for the $ D ^0 \rightarrow K ^- \pi ^+ $ decay mode.

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Normalised distributions of the measured transverse momentum of the $ D ^0$ in all bins of decay time.

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Effect of the kinematic weighting on the measured value of $ A_{\Gamma}$ . The measured value corresponds to $(87.7 \pm 0.8)\%$ of the artificial value injected in the $ D ^0 \rightarrow K ^- \pi ^+ $ sample.

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Transverse IP distributions of the $ D ^0 \rightarrow K ^- \pi ^+ $ 2016 Mag Up subsample for the (left) first, (centre) middle and (right) last time bin. The results of the fit are superimposed.

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Transverse IP distributions of the $ D ^0 \rightarrow \pi ^+ \pi ^- $ 2016 Mag Up subsample for the (left) first, (centre) middle and (right) last time bin. The results of the fit are superimposed.

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Fit to the time-dependent asymmetry of the $ D ^0 \rightarrow K ^- \pi ^+ $ sample (red) before the kinematic weighting of $ D ^0$ and $\overline{ D }{} {}^0$ candidates and the subtraction of secondary decays, but with a cut $\lvert\text{TIP}\rvert < 40 \upmu\text{m} $ to reduce their amount, and (black) after the kinematic weighting and the subtraction of secondary decays. The figures correspond to the (top) 2015 and (bottom) 2016 subsamples, and to the (left) Mag Up and (right) 2016 MagDown subsamples.

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Fit to the time-dependent asymmetry of the $ D ^0 \rightarrow K ^+ K ^- $ sample (red) before the kinematic weighting of $ D ^0$ and $\overline{ D }{} {}^0$ candidates and the subtraction of secondary decays, but with a cut $\lvert\text{TIP}\rvert < 40 \upmu\text{m} $ to reduce their amount, and (black) after the kinematic weighting and the subtraction of secondary decays. The figures correspond to the (top) 2015 and (bottom) 2016 subsamples, and to the (left) Mag Up and (right) 2016 MagDown subsamples.

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Fit to the time-dependent asymmetry of the $ D ^0 \rightarrow \pi ^+ \pi ^- $ sample (red) before the kinematic weighting of $ D ^0$ and $\overline{ D }{} {}^0$ candidates and the subtraction of secondary decays, but with a cut $\lvert\text{TIP}\rvert < 40 \upmu\text{m} $ to reduce their amount, and (black) after the kinematic weighting and the subtraction of secondary decays. The figures correspond to the (top) 2015 and (bottom) 2016 subsamples, and to the (left) Mag Up and (right) 2016 MagDown subsamples.

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Template fit to the $m( h ^+ h ^- )$ distribution for the (top) $ D ^0 \rightarrow K ^+ K ^- $ and (bottom) $ D ^0 \rightarrow \pi ^+ \pi ^- $ samples. The vertical dashed lines delimit the signal region.

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Tables and captions

Systematic uncertainties on the measurement of $ A_{\Gamma}$ , in units of $10^{-4}$.

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Created on 11 July 2020.