Study of $CP$-violating charge asymmetries of single muons and like-sign dimuons in $p\overline{p}$ collisions

We measure the inclusive single muon charge asymmetry and the like-sign dimuon charge asymmetry in $p\bar{p}$ collisions using the full data set of $10.4{\mathrm{fb}}^{-1}$ collected with the D0 detector at the Fermilab Tevatron. The standard model predictions of the charge asymmetries induced by $CP$ violation are small in magnitude compared to the current experimental precision, so nonzero measurements could indicate new sources of $CP$ violation. The measurements differ from the standard model predictions of $CP$ violation in these asymmetries with a significance of 3.6 standard deviations. These results are interpreted in a framework of $B$ meson mixing within the Cabibbo-Kobayashi-Maskawa formalism to measure the relative width difference $\mathrm{\Delta }{\mathrm{\Gamma }}_d/{\mathrm{\Gamma }}_d$ between the mass eigenstates of the $B^0$ meson system and the semileptonic charge asymmetries $a_{\mathrm{sl}}^d$ and $a_{\mathrm{sl}}^s$ of $B^0$ and $B_s^0$ mesons, respectively.

Figure 1

$IP$ distributions of one muon in the like-sign dimuon sample when the other muon has $IP$ in the $IP=1$ (full line), $IP=2$ (dashed line), and $IP=3$ (dotted line) ranges. The distributions are normalized to have the same number of entries in the first bin $[0,10]\mathrm{\mu m}$ (only a fraction of this bin is shown in the figure). The vertical dashed lines show the definition of boundaries of the $IP$ samples.

Figure 2

Definition of the nine $(p_T,|\eta |)$ bins. Global kinematic requirements are $1.5<p_T<25\mathrm{GeV}$, ($p_T>4.2\mathrm{GeV}$ or $|p_z|>5.4\mathrm{GeV}$), and $|\eta |<2.2$. See Sec. 3 for details.

Figure 3

Invariant mass $M(\mu \mu )$ of two muons in the (a) opposite-sign dimuon sample and (b) like-sign dimuon sample. The requirement $M({\mu }^{\pm }{\mu }^{\pm })>2.8\mathrm{GeV}$ is also shown.

Figure 4

Ratio of number of muon tracks with $\ge 2$ (upper curve) or $\ge 3$ (lower dashed curve) axial SMT hits to the number of muon tracks with $\ge 4$ axial SMT hits, as a function of $IP$, in the inclusive muon sample.

Figure 5

Ratio of the $K^{*0}\to K^{+}{\pi }^{-}$ reconstruction efficiencies ${ϵ}^i(K^{*0},IP)/{ϵ}^i(K^{*0})$ in a given $IP$ sample relative to that in the total inclusive muon sample. The vertical dashed lines separate the $(p_T,|\eta |)$ bins corresponding to the central, intermediate, and forward regions of the D0 detector, respectively.

Figure 6

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 $(p_T,|\eta |)$ bin $i$, respectively. Only statistical uncertainties are shown. The horizontal dashed lines show the mean values. The vertical dashed lines separate the $(p_T,|\eta |)$ bins corresponding to the central, intermediate, and forward regions of the detector, respectively.

Figure 7

Fraction of (a) $K\to \mu$ tracks, (b) $\pi \to \mu$ tracks, and (c) $p\to \mu$ tracks per event in the like-sign dimuon sample as a function of the kaon, pion, and proton $(p_T,|\eta |)$ bin $i$, respectively. Only statistical uncertainties are shown. The horizontal dashed lines show the mean values. The vertical dashed lines separate the $(p_T,|\eta |)$ bins corresponding to the central, intermediate, and forward regions of the D0 detector, respectively.

Figure 8

(a) Normalised distributions of $X$ variable defined in Eq. (46) for $S$ and $L$ muons in $(p_T,|\eta |)$ bin 2 of the inclusive muon sample. (b) Normalised distributions of $X$ for $K\to \mu$ and $\pi \to \mu$ muons.

Figure 9

(a) Normalised distributions of $Y$ variable defined in Eq. (47) for $S$ and $L$ muons in $(p_T,|\eta |)$ bin 2 of the inclusive muon sample. (b) Normalised distributions of $Y$ for $K\to \mu$ and $\pi \to \mu$ muons.

Figure 10

(a) Normalized distributions of the $X$ variable defined in Eq. (46) in $(p_T,|\eta |)$ bin 2 of the inclusive muon sample. Both the data and fitted distributions are shown. The filled histogram shows the contribution of $L$ muons. (b) Difference between data and fitted normalized distributions of $X$. The ${\chi }^2/\text{degrees}$ of freedom of the fit of these differences to their average is also shown.

Figure 11

(a) Normalized distributions of the $Y$ variable defined in Eq. (47) in $(p_T,|\eta |)$ bin 2 of the inclusive muon sample. Both the data and fitted distributions are shown. The filled histogram shows the contribution of $L$ muons. (b) Difference between data and fitted normalized distributions of $Y$. The ${\chi }^2/\text{degrees}$ of freedom of the fit of these differences to their average is also shown.

Figure 12

Asymmetries (a) $a_K$, (b) $a_{\pi }$, (c) $a_p$, and (d) $\delta$ as functions of the kaon, pion, proton, and muon $(p_T,|\eta |)$ bin $i$, respectively. Only statistical uncertainties are shown. The vertical dashed lines separate the $(p_T,|\eta |)$ bins corresponding to the central, intermediate, and forward regions of the D0 detector, respectively.

Figure 13

(a) The asymmetry $a_{\mathrm{bkg}}^i$ (points with error bars representing the statistical uncertainties), shown in each $(p_T,|\eta |)$ bin $i$, is compared to the measured asymmetry $a^i$ for the total inclusive muon sample (shown as a histogram, since the statistical uncertainties are negligible). The asymmetry from $CP$ violation is negligible compared to the background uncertainty in the inclusive muon sample. The vertical dashed lines separate the $(p_T,|\eta |)$ bins corresponding to the central, intermediate, and forward regions of the D0 detector, respectively. (b) The asymmetry $a_{CP}^i$. The horizontal dashed line shows the value of $a_{CP}$ defined as the weighted sum in Eq. (11).

Figure 14

Same as Fig. 13 for the $IP=1$ sample.

Figure 15

Same as Fig. 13 for the $IP=2$ sample.

Figure 16

Same as Fig. 13 for the $IP=3$ sample.

Figure 17

(a) The asymmetry $A_{\mathrm{bkg}}^i$ (points with error bars), shown in each $(p_T,|\eta |)$ bin $i$, is compared to the measured asymmetry $A^i$ for the like-sign dimuon sample (shown as a histogram). The error bars represent the statistical uncertainty of the difference $A^i-A_{\mathrm{bkg}}^i$. The vertical dashed lines separate the $(p_T,|\eta |)$ bins corresponding to the central, intermediate, and forward regions of the D0 detector, respectively. The last bin separated by the vertical line shows the values of $A_{\mathrm{bkg}}$ defined as the weighted sum in Eq. (25) and $A$ defined as the weighted sum in Eq. (19) and their statistical uncertainties. (b) The asymmetry $A_{CP}^i$. The last bin separated by the vertical line shows the value of $A_{CP}$ defined as the weighted sum in Eq. (26) and its statistical uncertainty. The horizontal dashed line corresponds to this value of $A_{CP}$.

Figure 18

The asymmetry $A_{CP}^i$ as a function of $(p_T,|\eta |)$ bin $i$ in different (${IP}_1$, ${IP}_2$) samples. The error bars represent its statistical uncertainty. The vertical dashed lines separate the $(p_T,|\eta |)$ bins corresponding to the central, intermediate, and forward regions of the D0 detector, respectively. The last bin separated by the vertical line shows the value of $A_{CP}$ defined as the weighted sum in Eq. (26) and its statistical uncertainty. The horizontal dashed line corresponds to this value of $A_{CP}$.

Figure 19

The asymmetry $A_{CP}^i$ as a function of $(p_T,|\eta |)$ bin $i$ in different (${IP}_1$, ${IP}_2$) samples. The error bars represent its statistical uncertainty. The vertical dashed lines separate the $(p_T,|\eta |)$ bins corresponding to the central, intermediate, and forward regions of the D0 detector, respectively. The last bin separated by the vertical line shows the value of $A_{CP}$ defined as the weighted sum in Eq. (26) and its statistical uncertainty. The horizontal dashed line corresponds to this value of $A_{CP}$.

Figure 20

(a) Asymmetry $a_{CP}$ measured in different $IP$ samples. (b) Asymmetry $A_{CP}$ measured in different ${IP}_1$, ${IP}_2$ samples. The thick error bar for each measurement presents the statistical uncertainty, while the thin error bar shows the total uncertainty. The filled boxes show the SM prediction. The half-width of each box corresponds to the theoretical uncertainty.

Figure 21

The 68% and 95% confidence level contours in the $a_{\mathrm{sl}}^d\text{−}{a}_{\mathrm{sl}}^s$ plane obtained from the fit of the inclusive single muon and like-sign dimuon asymmetries with fixed value of $\mathrm{\Delta }{\mathrm{\Gamma }}_d/{\mathrm{\Gamma }}_d=0.0042$ corresponding to the expected SM value (55), which has an uncertainty $\pm 0.0008$. The independent measurements of $a_{\mathrm{sl}}^d$ [29] and $a_{\mathrm{sl}}^s$ [30] by the D0 collaboration are also shown. The error bands represent $\pm 1$ standard deviation uncertainties of these measurements.

Figure 22

The 68% and 95% confidence level contours in the $a_{\mathrm{sl}}^d\text{−}{a}_{\mathrm{sl}}^s$ plane obtained from the fit of the inclusive single muon and like-sign dimuon asymmetries with fixed value of $\mathrm{\Delta }{\mathrm{\Gamma }}_d/{\mathrm{\Gamma }}_d=0.0150$ corresponding to the experimental world average value (56), which has an uncertainty $\pm 0.0180$. The independent measurements of $a_{\mathrm{sl}}^d$ [29] and $a_{\mathrm{sl}}^s$ [30] by the D0 collaboration are also shown. The error bands represent $\pm 1$ standard deviation uncertainties of these measurements.

Figure 23

The 68% (full line) and 95% (dashed line) confidence level contours in the $a_{\mathrm{sl}}^d\text{−}{a}_{\mathrm{sl}}^s$ plane representing the profile of the results given by Eqs. (96, 97, 98, 99, 100) at the best fit value of $\mathrm{\Delta }{\mathrm{\Gamma }}_d/{\mathrm{\Gamma }}_d=0.0050$ corresponding to Eq. (98). The contours with filled area show the 68% and 95% confidence level contours in the $a_{\mathrm{sl}}^d\text{−}{a}_{\mathrm{sl}}^s$ plane representing the profile of the results obtained by the combination of all D0 measurements and given by Eqs. (101, 102, 103, 104, 105) at the best fit value of $\mathrm{\Delta }{\mathrm{\Gamma }}_d/{\mathrm{\Gamma }}_d=0.0079$ corresponding to Eq. (103). The independent measurements of $a_{\mathrm{sl}}^d$ [29] and $a_{\mathrm{sl}}^s$ [30] by the D0 collaboration are also shown. The error bands represent $\pm 1$ standard deviation uncertainties of these measurements.