Standard Model fit
The CKM matrix
\[V_{CKM}= \begin{pmatrix}
(0.97431 \pm 0.00018) & (0.22517 \pm 0.00080) & (0.003721 \pm 0.000098)e^{i(-64.7 \pm 1.2)^\circ}\\
( -0.22502 \pm 0.00078)e^{i(-179.03600 \pm 0.00085)^\circ} & (0.97344 \pm 0.00018)e^{i(-0.001862 \pm 0.000046)^\circ} & (0.04222 \pm 0.00051) \\
(0.00858 \pm 0.00010)e^{i(-22.33 \pm 0.62)^\circ} & ( -0.04127 \pm 0.00043)e^{i(-178.025 \pm 0.028)^\circ} & (0.999110 \pm 0.000018)
\end{pmatrix} \]
Fit results
Predictions are obtained by removing the given constraint from the global fit.
| Parameter | Input value | Full fit | SM Prediction | Pull |
|---|---|---|---|---|
| \(\bar{\rho}\) | \(-\) | \(0.1609 \pm 0.0095\) | \(-\) | \(-\) |
| \(\bar{\eta}\) | \(-\) | \(0.347 \pm 0.010\) | \(-\) | \(-\) |
| \(\rho\) | \(-\) | \(0.1653 \pm 0.0095\) | \(-\) | \(-\) |
| \(\eta\) | \(-\) | \(0.3559 \pm 0.0099\) | \(-\) | \(-\) |
| \(A\) | \(-\) | \(0.828 \pm 0.011\) | \(-\) | \(-\) |
| \(\lambda\) | \(-\) | \(0.22519 \pm 0.00083\) | \(-\) | \(-\) |
| \(J_{cp}\cdot10^{5}\) | \(-\) | \(3.102 \pm 0.080\) | \(-\) | \(-\) |
| \(\sin\theta_{12}\) | \(-\) | \(0.22519 \pm 0.00083\) | \(-\) | \(-\) |
| \(\sin\theta_{23}\) | \(-\) | \(0.04200 \pm 0.00047\) | \(-\) | \(-\) |
| \(\sin\theta_{13}\) | \(-\) | \(0.003715 \pm 0.000093\) | \(-\) | \(-\) |
| \(\delta [^{\circ}]\) | \(-\) | \(1.137 \pm 0.022\) | \(-\) | \(-\) |
| \(\|V_{ud}\|\) | \(0.97433 \pm 0.00019\) | \(0.97431 \pm 0.00019\) | \(0.9738 \pm 0.0011\) | \(0.0\) |
| \(\|V_{ub}\|\) | \(0.00377 \pm 0.00024\) | \(0.003715 \pm 0.000093\) | \(0.00370 \pm 0.00011\) | \(0.2\) |
| \(\|V_{cb}\|\) | \(0.04125 \pm 0.00095\) | \(0.04200 \pm 0.00044\) | \(0.04222 \pm 0.00051\) | \(0.6\) |
| \(\alpha [^{\circ}]\) | \(94.9 \pm 4.7\) | \(92.4 \pm 1.3\) | \(92.2 \pm 1.6\) | \(0.6\) |
| \(\beta [^{\circ}]\) | \(-\) | \(22.47 \pm 0.65\) | \(22.46 \pm 0.68\) | \(-\) |
| \(\sin(2\beta)\) | \(0.688 \pm 0.020\) | \(0.706 \pm 0.015\) | \(0.736 \pm 0.028\) | \(1.4\) |
| \(\cos(2\beta)\) | \(-\) | \(-\) | \(0.707 \pm 0.016\) | \(-\) |
| \(\gamma [^{\circ}]\) | \(66.1 \pm 3.5\) | \(65.0 \pm 1.2\) | \(64.9 \pm 1.4\) | \(0.3\) |
| \(2\beta+\gamma [^{\circ}]\) | \(-\) | \(-\) | \(110.0 \pm 1.7\) | \(-\) |
| \(\beta_s\) | \(-\) | \(-\) | \(-0.0364 \pm 0.0011\) | \(-\) |
| \(m_{c}\mathrm{ [GeV/c^{2}]}\) | \(1.2900 \pm 0.0070\) | \(-\) | \(-\) | \(-\) |
| \(m_{b}\mathrm{ [GeV/c^{2}]}\) | \(4.196 \pm 0.014\) | \(-\) | \(-\) | \(-\) |
| \(m_{t}\mathrm{ [GeV/c^{2}]}\) | \(171.79 \pm 0.38\) | \(-\) | \(-\) | \(-\) |
| \(\|\epsilon_{k}\|\) | \(0.002228 \pm 0.000011\) | \(0.002226 \pm 0.000010\) | \(0.00200 \pm 0.00015\) | \(0.1\) |
| \(\epsilon^{\prime}/\epsilon\) | \(0.00166 \pm 0.00033\) | \(0.00161 \pm 0.00027\) | \(0.00158 \pm 0 .00045\) | \(0.3\) |
| \(\Delta m_{s} \mathrm{[ps^{-1}]}\) | \(17.741 \pm 0.020\) | \(17.739 \pm 0.020\) | \(17.94 \pm 0.69\) | \(0.3\) |
| \(\Delta m_{d} \mathrm{[ps^{-1}]}\) | \(0.5065 \pm 0.0019\) | \(0.5065 \pm 0.0018\) | \(0.519 \pm 0.023\) | \(0.5\) |
| \(B(B\rightarrow\tau\nu)\) | \(1.06 \pm 0.19\) | \(0.881 \pm 0.044\) | \(0.869 \pm 0.047\) | \(1.0\) |
| \(\bar {B}(B_{s}\rightarrow ll)\cdot10^{9}\) | \(3.41 \pm 0.29\) | \(3.25 \pm 0.12\) | \(3.47 \pm 0.14\) | \(0.0\) |
Global fit configurations to extract Lattice QCD parameter predictions
| Parameter | Input value | Prediction |
|---|---|---|
| Removing \(\hat{B}_{k}\) from inputs | ||
| \(\hat{B}_{k}\) | \(0.756 \pm 0.016\) | \(0.840 \pm 0.059\) |
| Use only \(\hat{B}_{B_{s}}\) and \(\hat{B}_{B_{s}}/\hat{B}_{B_{d}}\) | ||
| \(f_{B_{d}}\) | \(190.5 \pm 1.3\) | \(190.2 \pm 7.2\) |
| \(f_{B_{s}}\) | \(230.1 \pm 1.2\) | \(229.4 \pm 7.2\) |
| \(\xi\) | \(1.208 \pm 0.059\) | \(1.204 \pm 0.027\) |
| Use only the ratios \(f_{B_{s}}/f_{B_{d}}\) and \(\hat{B}_{B_{s}}/\hat{B}_{B_{d}}\) | ||
| \(f_{B_{d}}\hat{B}_{d}^{1/2}\) | \(214.2 \pm 5.6\) | \(216.9 \pm 5.3\) |
| \(f_{B_{s}}\hat{B}_{s}^{1/2}\) | \(260.7 \pm 6.1\) | \(264.4 \pm 6.0\) |
| \(\xi\) | \(1.208 \pm 0.051\) | \(1.219 \pm 0.021\) |
| Use only \(\hat{B}_{K}\) | ||
| \(f_{B_{d}}\hat{B}_{d}^{1/2}\) | \(210.5 \pm 3.6\) | \(214.2 \pm 5.6\) |
| \(f_{B_{s}}\hat{B}_{s}^{1/2}\) | \(259.0 \pm 3.4\) | \(260.7 \pm 6.1\) |
| \(\xi\) | \(1.230 \pm 0.023\) | \(1.217 \pm 0.014\) |