Current status of the standard model CKM fit and constraints on $\mathrm{\Delta }F=2$ new physics

This article summarizes the status of the global fit of the Cabibbo-Kobayashi-Maskawa (CKM) parameters within the Standard Model performed by the CKMfitter group. Special attention is paid to the inputs for the CKM angles $\alpha$ and $\gamma$ and the status of $B_s\to \mu \mu$ and $B_d\to \mu \mu$ decays. We illustrate the current situation for other unitarity triangles. We also discuss the constraints on generic $\mathrm{\Delta }F=2$ new physics. All results have been obtained with the CKMfitter analysis package, featuring the frequentist statistical approach and using Rfit to handle theoretical uncertainties.

Figure 1

Inputs for $\alpha$ used in the SM global fit. We show the world averages for $\pi \pi$, $\rho \pi$ and $\rho \rho$ separately.

Figure 2

Inputs for $\gamma$ used in the SM global fit (top). We show the world averages for the different methods, in the $(\gamma ,{\delta }_B)$ (middle) and $(\gamma ,r_B)$ (bottom) planes. Shaded areas (dashed lines) enclose points with $1-p<68.3\%$ (95.45%).

Figure 3

Constraint obtained for the $r_B$ parameter of the $B\to D{K}^{*0}$ mode. “LHCb $(D{K}^{*0})$” (dot-dashed line) includes only data from $D{K}^{*0}$, whereas “LHCb” (dashed line) involves all channels (including $D{K}^{*0}$).

Figure 4

Constraints on the CKM $({\overline{\rho }}_M,{\overline{\eta }}_M)$ coordinates with $M=db,sb,ds,ct,ut,uc$, from the global SM CKM fit. Regions outside the colored areas have $1-p>95.45\%$. For the combined fit the yellow area inscribed by the contour line represents points with $1-p<95.45\%$. The shaded area inside this region represents points with $1-p<68.3\%$.

Figure 5

Pulls for the SM global fit obtained by comparing the value of ${\chi }_{\text{min}}^2$ with and without including the measurement of the quantity. Notice that the different pulls are not necessarily independent.

Figure 6

Constraints on the CKM $(\overline{\rho },\overline{\eta })$ coordinates from the global SM CKM fit using only exclusive (top) and inclusive (bottom) determinations of $|V_{ub}|$ and $|V_{cb}|$ from semileptonic decays as inputs.

Figure 7

Prediction on $\mathcal{B}(B\to \tau \nu )$ and $\sin 2\beta$ coming from the global fit (without the corresponding inputs) compared to current experimental information (cross). Regions outside the colored areas are excluded at $1-p>95.45\%$.

Figure 8

Prediction of the two dileptonic branching ratios $\mathcal{B}(B_s\to \mu \mu )$ and $\mathcal{B}(B_d\to \mu \mu )$ coming from the global fit (without input on dileptonic branching ratios) compared to current experimental information [18]. $\mathcal{B}(B_s\to \mu \mu )$ is shown removing the $(1+y_s)=1.07$ increase due to time integration. The NNLO computation in Ref. [28] is indicated in colors, whereas the NLO computation used in Ref. [38] is the region delimited by the dashed line. Regions outside the colored areas are excluded at $1-p>95.45\%$. The oval contours are the experimental $1,2,3,\dots ,\sigma$ confidence regions [18].

Figure 9

Combined constraint on $2\beta +\gamma$ using relevant observables measured in the $B\to D\pi ,D^{*}\pi$ (top) and $D\rho$ (bottom) decays.

Figure 10

Complex parameters ${\mathrm{\Delta }}_d$ (up) and ${\mathrm{\Delta }}_s$ (down) in Scenario I, not including $A_{\text{SL}}$. The colored areas represent regions with $1-p<68.3\%$ for the individual constraints (${\alpha }_{\text{exp}}\equiv \alpha -{\varphi }_d^{\mathrm{\Delta }}/2$). The red area shows the region with $1-p<68.3\%$ for the combined fit, with the two additional contours delimiting the regions with $1-p<95.45\%$ and $1-p<99.73\%$.

Figure 11

Complex parameters ${\mathrm{\Delta }}_d$ (up) and ${\mathrm{\Delta }}_s$ (down) in Scenario I, including $A_{\text{SL}}$. The conventions are the same as in Fig. 10.