Evidence for an anomalous like-sign dimuon charge asymmetry

We measure the charge asymmetry $A$ of like-sign dimuon events in $6.1{\mathrm{fb}}^{-1}$ of $p\overline{p}$ collisions recorded with the D0 detector at a center-of-mass energy $\sqrt{s}=1.96\mathrm{TeV}$ at the Fermilab Tevatron collider. From $A$, we extract the like-sign dimuon charge asymmetry in semileptonic $b$-hadron decays: $A_{\mathrm{sl}}^b=-0.00957\pm 0.00251(\mathrm{stat})\pm 0.00146(\mathrm{syst})$. This result differs by 3.2 standard deviations from the standard model prediction $A_{\mathrm{sl}}^b(\mathrm{SM})=(-{2.3}_{-0.6}^{+0.5})\times {10}^{-4}$ and provides first evidence of anomalous $CP$ violation in the mixing of neutral $B$ mesons.

Figure 1

The normalized muon $p_T$ distribution. The points correspond to the like-sign dimuon sample and the histogram corresponds to the inclusive muon sample. The distribution for the like-sign dimuon sample contains two entries per event.

Figure 2

The fraction of $K\to \mu$ tracks in the inclusive muon sample (a) and the like-sign dimuon sample (b), both as a function of the $p_T$ of the kaon.

Figure 3

The ratio $P(\pi \to \mu )/P(K\to \mu )$ as a function of the hadron transverse momentum. The horizontal dashed line shows the mean value of this ratio.

Figure 4

The ratio $P(p\to \mu )/P(K\to \mu )$ as a function of the particle transverse momentum. The horizontal dashed line shows the mean value of this ratio.

Figure 5

The ratio of multiplicities $n_{\pi }/n_K$, $n_p/n_K$, and $n_f/n_K$ as a function of the transverse momentum obtained from pythia.

Figure 6

The fraction of (a) $\pi \to \mu$ tracks and (b) $p\to \mu$ tracks in the inclusive muon sample as a function of the track transverse momentum. The horizontal dashed lines show the mean values of these fractions.

Figure 7

The fraction of (a) $\pi \to \mu$ tracks and (b) $p\to \mu$ tracks in the like-sign dimuon sample as a function of the track transverse momentum. The horizontal dashed lines show the mean values of these fractions.

Figure 8

The ${\mu }^{+}{\mu }^{-}$ invariant mass distributions used to obtain (a) ${\Sigma }_{23}=N_{23}+N_{32}$ and (b) ${\Delta }_{23}=N_{23}-N_{32}$. The solid lines present the result of the fit; the dashed lines show the nonresonant background contribution.

Figure 9

The ${\mu }^{+}{\mu }^{-}$ invariant mass distributions used to obtain (a) ${\Sigma }_2=N_{2+}+N_{2-}$ and (b) ${\Delta }_2=N_{2+}-N_{2-}$. The solid lines present the result of the fit; the dashed lines show the nonresonant background contribution.

Figure 10

Muon reconstruction asymmetry as a function of the muon $p_T$.

Figure 11

The asymmetry $a_K$ measured with (a) $K^{*0}\to K^{+}{\pi }^{-}$ and (b) $\varphi \to K^{+}{K}^{-}$ decays as a function of the $K\to \mu$ $p_T$.

Figure 12

The combined asymmetry $a_K$ as a function of $p_T$.

Figure 13

The asymmetry (a) $a_{\pi }$ and (b) $a_p$ as a function of the $p_T$ of the pion and proton, respectively.

Figure 14

(a) The asymmetry $a_{\mathrm{bkg}}$ (points with error bars) as expected from our measurements of the fractions and asymmetries of the background processes is compared to the measured asymmetry $a$ of the inclusive muon sample (shown as histogram, since the statistical uncertainties are negligible). The asymmetry from $CP$ violation is negligible compared to the background in the inclusive muon sample; (b) the difference $a-a_{\mathrm{bkg}}$. The horizontal dashed line shows the mean value of this difference.

Figure 15

Statistical (dashed line), systematic (dotted line), and total (full line) uncertainties on $A_{\mathrm{sl}}^b$ as a function of the parameter $\alpha$ of Eq. (66).

Figure 16

The observed and expected like-sign dimuon charge asymmetries in bins of dimuon invariant mass. The expected asymmetry is shown for (a) $A_{\mathrm{sl}}^b=0.0$ and (b) $A_{\mathrm{sl}}^b=-0.00957$.

Figure 17

Comparison of $A_{\mathrm{sl}}^b$ in data with the standard model prediction for $a_{\mathrm{sl}}^d$ and $a_{\mathrm{sl}}^s$. Also shown are the existing measurements of $a_{\mathrm{sl}}^d$ [24] and $a_{\mathrm{sl}}^s$ [25]. The error bands represent the $\pm 1$ standard deviation uncertainties on each individual measurement.

Figure 18

The 68% and 95% C.L. regions of probability for $\Delta {\Gamma }_s$ and ${\varphi }_s$ values obtained from this measurement, considering the experimental constraints on $a_{\mathrm{sl}}^d$ [24]. The solid and dashed curves show, respectively, the 68% and 95% C.L. contours from the $B_s^0\to J/\psi \varphi$ measurement [26]. Also shown is the standard model (SM) prediction for ${\varphi }_s$ and $\Delta {\Gamma }_s$.

Figure 19

Probability contours in the $({\varphi }_s,\Delta {\Gamma }_s)$ plane for the combination of this measurement with the result of Ref. [26], using the experimental constraints on $a_{\mathrm{sl}}^d$ [24].

Figure 20

The ${\pi }^{+}{\pi }^{-}$ invariant mass distribution of $K_S$ candidates in the inclusive muon sample for $\pi \to \mu$ with $7.0<p_T<10.0\mathrm{GeV}$. (a) The sum of the distributions for positive and negative $\pi \to \mu$ tracks and (b) their difference. The solid lines present the result of the fit; the dashed lines show the background contribution.

Figure 21

(a) The $K_S{\pi }^{+}$ invariant mass distribution of $K^{*+}$ candidates in the inclusive muon sample. The solid line presents the result of the fit; the dashed line shows the background contribution. (b) The difference between data and the fit result.

Figure 22

(a) The $K^{+}{\pi }^{-}$ invariant mass distribution of $K^{*0}$ candidates in the inclusive muon sample. The solid line corresponds to the result of the fit and the dashed line shows the contribution from the combinatorial background. The shaded histogram is the contribution of ${\rho }^0\to {\pi }^{+}{\pi }^{-}$ events. (b) The difference between data and the result of the fit.

Figure 23

(a) The $K^{+}{\pi }^{-}$ invariant mass distribution of $K^{*0}$ candidates in the like-sign dimuon sample. The solid line corresponds to the result of the fit and the dashed line shows the contribution from the combinatorial background. The shaded histogram is the contribution of ${\rho }^0\to {\pi }^{+}{\pi }^{-}$ events. (b) The difference between data and the result of the fit.

Figure 24

The $K^{+}{\pi }^{-}$ invariant mass distribution of simulated ${\rho }^0\to {\pi }^{+}{\pi }^{-}$ decays, where the mass of the charged kaon is assigned to one of the two reconstructed tracks.

Figure 25

(a) The difference of the $K^{+}{\pi }^{-}$ and $K^{-}{\pi }^{+}$ mass distributions of $K^{*0}$ candidates in the inclusive muon sample. The solid line represents the result of the fit, while the dashed line shows the background contribution. (b) The difference between data and the result of the fit.

Figure 26

The $K^{+}{K}^{-}$ invariant mass distribution of $\varphi (1020)$ candidates in the inclusive muon sample for $K\to \mu$ with $4.2<p_T<7.0\mathrm{GeV}$. (a) The sum of distributions of positive and negative $K\to \mu$ tracks and (b) their difference. The solid lines present the result of the fit and the dashed lines show the background contribution.

Figure 27

The $p{\pi }^{-}$ invariant mass distribution of $\Lambda$ candidates in the inclusive muon sample for $p\to \mu$ with $4.2<p_T<7.0\mathrm{GeV}$. (a) The sum of distributions of positive and negative $p\to \mu$ tracks and (b) their difference. The solid lines present the result of the fit and the dashed lines show the background contribution.

Figure 28

(a) The expected (points with errors) and measured (histogram with negligible uncertainties) track reconstruction asymmetry. (b) The quantity ${\delta }_{\mathrm{track}}=a_{\mathrm{track}}-a_K^{\mathrm{track}}{f}_K^{\mathrm{track}}$.