Chapter 2.6 - Constraining the CKM Matrix

The complete Chapter 2.6 document is available here.

Figures

• Figure 2.56 - The unitarity triangle indicating the relationship between the CKM elements.

• Figure 2.57 - The invariant mass distributions for charged and neutral $B$ mesons reconstructed via the decay modes $B^+ \to J/\psi K^+$ and $B^0 \to J/\psi K^{\ast 0}$ as observed by CDF.

• Figure 2.58 - The proper lifetime distributions for charged and neutral $B$ mesons reconstructed via the exclusive $B\to \psi K$ decay modes are shown in the upper plots. The lower plots display the background distributions for the $B$ sidebands.
  Plots for $B_u$
  Plots for $B_d$

• Figure 2.59 - Charm signals reconstructed in association with a high-$p_T$ lepton.
  (a): Signal for $\bar{B} \to D^0 \ell^- \bar\nu X; D^0 \to K^-\pi^+$ (+ c.c.)
  (b): Signal for $\bar{B} \to D^{*+} \ell^- \bar\nu X; D^{*+} \to D^0\pi^+; D^0 \to K^-\pi^+$ (+ c.c.)
  (c): Signal for $\bar{B} \to D^{*+} \ell^- \bar\nu X; D^{*+} \to D^0\pi^+; D^0 \to K^-\pi^+\pi^-\pi^+$ (+ c.c.)
  (d): Signal for $\bar{B} \to D^{*+} \ell^- \bar\nu X; D^{*+} \to D^0\pi^+; D^0 \to K^-\pi^+ X$ (+ c.c.)
  Mode (a) is dominated by $B^-$ decays and modes (b) -- (d) by $\bar{B}^0$ decays ($\Delta M$ is the mass difference between the $D^0\pi^+$ and the $D^0$). Shaded histograms show wrong--charge combinations (e.g. $\ell^- K^+$); in (a) these are scaled by 0.5 for display purposes.

• Figure 2.60 - Distributions of pseudo-proper decay lengths for lepton + ``$D$'' signal samples (points). In all the plots the fits are shown for the signal (dashed line), background (dotted line) and sum (solid line). The four decay channels are represented in (a) -- (d) as in the previous figure.

• Figure 2.61 - CDF and combined LEP (1995) results for $b$ hadron lifetimes.

• Figure 2.62 - CDF's $B^0 \to J/\psi K_S$ signal from RunI. For the plot on the right, SVX track information has been required for muons from the $J/\psi$. It is noted that the $S/N$ improves to $2.3:1$ without additional loss of signal if the transverse decay length ($L_{xy}$) is required to be greater than zero.
  Left plot.
  Right plot.

• Figure 2.63 - $J/\psi \to e^+ e^-$ signal from a test trigger during Run I.

• Figure 2.64 - Mass distribution for the combination $B^0 \to \pi^+\pi^-$, $B^0 \to K\pi$, $B_s \to K\pi$ and $B_s \to K K$ assuming all charged kaons to be pions. The assumed mass resolution is $\sim$20~MeV/c$^2$. (Note that the vertical scale should be treated as arbitrary.)

• Figure 2.65 - Left: The reconstructed mass distribution for $B_s \to J/\psi \phi$ decays. SVX track information has been required for the muons from the $J/\psi$. Right: The uncertainty on the $C\!P$ asymmetry for $B_s \to J/\psi \phi$ as a function of the $B_s$ mixing parameter $x_s$.

• Figure 2.66 - Two studies of $B^0 - \bar{B}^0$ mixing performed by CDF using different dilepton triggers. Results of a fit to the like-sign fraction vs proper lifetime are shown on the left for a Run Ia sample (20 pb$^{-1}$) collected using a dimuon trigger and on the right for a combined Run Ia and Run Ib sample (110 pb$^{-1}$) collected with an electron-muon trigger. In both cases, one lepton was associated with a secondary vertex and the other lepton served as a flavor tag. For these fits, maximal $B_s$ mixing is assumed.

• Figure 2.67 - Two studies of $B^0 - \bar{B}^0$ mixing performed by CDF using lepton triggers and different tagging strategies. Left: The $b\bar{b}$ same sign fraction as a function of proper time for events from the Run~Ib inclusive electron and muon triggers. The trigger lepton is associated with a secondary vertex which gives the proper time. An additional soft lepton or the jet charge of an opposite side jet is used for a flavor tag. The dashed histogram represents the result of an unbinned likelihood fit for $\Delta m_d$. Right: Measurement of the asymmetry $(N_R-N_W)/(N_R+N_W)$ as a function of proper time for charged $B$ (upper plot) and neutral $B$ (lower plot) mesons reconstructed from a single lepton trigger sample and flavor tagged using a same-side pion tag. Here, the charge of the $B$ meson is determined by reconstructing the $D^0$ or $D^{*+}$ meson from the semileptonic decay. A clear mixing signal is present for the neutral $B$ while no mixing is observed for charged $B$ mesons.

• Figure 2.68 - Left: invariant mass distribution for $D_s$ mesons produced in right-sign ($D_s^+ \ell^-$) events with $D_s^+ \to \phi \pi^+$ and $\phi \to K^+ K^-$; the wrong-sign combinations are shown as a shaded histogram. There is also evidence of the Cabibbo suppressed decay $D^+ \to \phi \pi^+$. Right: pseudo--ctau distributions for the $B_s$ signal and background (shaded).

• Figure 2.69 - Left: A Monte Carlo simulation of the reconstructed $B_s$ mixing signal for a Run~II sample with the CDF~II detector. Right: Relative uncertainty on $x_s$ for fully reconstructed $B_s$ decays.

• Figure 2.70 - On the left: Limit from Run I on the ratio of production and decay of $B_c \to J/\psi \pi$ vs. $B^+ \to J/\psi \pi^+$ as a function of lifetime. On the right: the signal for $B^+ \to J/\psi \pi^+$ is seen as an enhancement in the $J/\psi \pi$ distribution at the upper edge of the $J/\psi K$ contribution which dominates the lower edge of the plot.