Measurement of the anomalous like-sign dimuon charge asymmetry with $9{\mathrm{fb}}^{-1}$ of $p\overline{p}$ collisions

We present an updated measurement of the anomalous like-sign dimuon charge asymmetry $A_{\mathrm{sl}}^b$ for semileptonic $b$-hadron decays in $9.0{\mathrm{fb}}^{-1}$ of $p\overline{p}$ collisions recorded with the D0 detector at a center-of-mass energy of $\sqrt{s}=1.96\mathrm{TeV}$ at the Fermilab Tevatron collider. We obtain $A_{\mathrm{sl}}^b=(-0.787\pm 0.172(\mathrm{stat})\pm 0.093(\mathrm{syst}))\%$. This result differs by 3.9 standard deviations from the prediction of the standard model and provides evidence for anomalously large $CP$ violation in semileptonic neutral $B$ decay. The dependence of the asymmetry on the muon impact parameter is consistent with the hypothesis that it originates from semileptonic $b$-hadron decays.

Figure 1

Smallest muon momentum required to penetrate the calorimeter and toroids at different pseudorapidities, $|\eta |$ (solid line), and the momentum selection used in this analysis (dashed line).

Figure 2

The ${\pi }^{+}{\pi }^{-}$ invariant mass distribution for $K_S^0$ candidates in the inclusive-muon sample with at least one pion identified as a muon with $4.2<p_T(K_S^0)<5.6\mathrm{GeV}$. The solid line represents the result of the fit to the $K_S^0$ content, and the dashed line represents the fitted background contribution.

Figure 3

(a) The $K_S^0{\pi }^{+}$ invariant mass distribution for $K^{*+}$ candidates in the inclusive-muon sample. The $K_S^0$ candidate is required to have $480<M({\pi }^{+}{\pi }^{-})<515\mathrm{MeV}$ and $4.2<p_T(K_S^0)<5.6\mathrm{GeV}$. The solid line represents the result of the fit to the $K^{*+}$ content, and the dashed line shows the background contribution. (b) Difference between data and the result of the fit.

Figure 4

(a) The $K^{+}{\pi }^{-}$ invariant mass distribution for $K^{*0}$ candidates in the inclusive-muon sample for all kaons with $4.2<p_T(K^{+})<5.6\mathrm{GeV}$. The solid line corresponds to the result of the fit to the $K^{*0}$ content, and the dashed line shows the contribution from combinatorial background. The shaded histogram is the contribution from ${\rho }^0\to {\pi }^{+}{\pi }^{-}$ events. (b) Difference between data and the result of the fit.

Figure 5

The fraction of (a) $K\to \mu$ tracks, (b) $\pi \to \mu$ tracks and (c) $p\to \mu$ tracks in the inclusive-muon sample as a function of the kaon, pion and proton $p_T$, respectively. The horizontal dashed lines show the mean values.

Figure 6

(a) The $K^{+}{\pi }^{-}$ invariant mass distribution of $K^{*0}$ candidates in the like-sign dimuon sample for all kaons with $4.2<p_T(K^{+})<5.6\mathrm{GeV}$. The solid line corresponds to the result of the fit to the $K^{*0}$ content, and the dashed line shows the contribution from combinatorial background. The shaded histogram is the contribution from ${\rho }^0\to {\pi }^{+}{\pi }^{-}$ events. (b) Difference between data and the result of the fit.

Figure 7

(a) The $K^{+}{\pi }^{-}$ invariant mass distribution $P_2(M_{K\pi };\xi )$ obtained using Eq. (20) for $\xi =0.88$ for all kaons with $4.2<p_T(K^{+})<5.6\mathrm{GeV}$. The dashed line shows the contribution from the combinatorial background. (b) Difference between data and the result of the fit.

Figure 8

The correction coefficient $\kappa$ as a function of the kaon transverse momentum. The horizontal dashed line shows the mean value.

Figure 9

The ratio of $\pi \to \mu$ detection efficiencies for the inclusive-muon and dimuon data as a function of the muon transverse momentum. The horizontal dashed line shows the mean value for $p_T(K)>4.2\mathrm{GeV}$.

Figure 10

The ratio $R_K$ obtained using (a) $K^{*0}$ production, (b) $K_S^0$ production, and (c) combination of these two channels as a function of the kaon transverse momentum. The horizontal dashed lines show the mean values.

Figure 11

The difference $R_K(K^{*0})-R_K(K_S^0)$ as a function of kaon transverse momentum. The horizontal dashed line shows the mean value.

Figure 12

The values of (a) $F_K$, (b) $F_{\pi }$ and (c) $F_p$ in the like-sign dimuon sample as a function of the kaon, pion and proton $p_T$, respectively. The horizontal dashed lines show the mean values.

Figure 13

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

Figure 14

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

Figure 15

(a) The asymmetry $a_{\mathrm{bkg}}$ (points with error bars representing the total uncertainties), expected from the measurements of the fractions and asymmetries for background processes, is compared to the measured asymmetry $a$ for the inclusive-muon sample (shown as a 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.

Figure 16

Comparison of $A_{\mathrm{sl}}^b$ in data with the SM prediction for $a_{\mathrm{sl}}^d$ and $a_{\mathrm{sl}}^s$. Also shown are the measurements of $a_{\mathrm{sl}}^d$ [3] and $a_{\mathrm{sl}}^s$ [19]. The error bands represent the $\pm 1$ standard deviation uncertainties on each individual measurement. The 95% CL band is also given for this $A_{\mathrm{sl}}^b$ measurement.

Figure 17

(a) The asymmetry $a_{\mathrm{bkg}}$ (points with error bars representing the total uncertainties), as expected from the measurements of the fractions and asymmetries of the background processes, is compared to the measured asymmetry $a$ of the inclusive-muon sample (shown as a histogram, since the statistical uncertainties are negligible) as a function of the absolute value of muon pseudorapidity $|\eta (\mu )|$. 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.

Figure 18

The observed and expected like-sign dimuon charge asymmetries in bins of dimuon invariant mass. The expected asymmetry is shown for (a) $A_{\mathrm{sl}}^b=A_{\mathrm{sl}}^b(\mathrm{SM})$ and (b) $A_{\mathrm{sl}}^b=-0.787\%$.

Figure 19

The muon IP distribution in the inclusive-muon sample (bullets). The solid line represents the muon IP distribution in simulation. The shaded histogram is the contribution from $L$ muons in simulation.

Figure 20

The normalized IP distribution for muons produced in oscillating decays of $B^0$ mesons (points with error bars) and $B_s^0$ mesons (solid histogram) in simulation.

Figure 21

Measurements of $A_{\mathrm{sl}}^b$ with different muon IP selections in the $(a_{\mathrm{sl}}^d,a_{\mathrm{sl}}^s)$ plane. The bands represent the $\pm 1$ standard deviation uncertainties on each individual measurement. The ellipses represent the 68% and 95% two-dimensional CL regions, respectively, of $a_{\mathrm{sl}}^s$ and $a_{\mathrm{sl}}^s$ values obtained from the measurements with IP selections.