ResultsSummer2022SM < UTfit

Standard Model Fit results: Summer 2022

CKM matrix looks like:

$V_{CKM}=\left(\begin{array}{ccc} (0.97431 \pm 0.00018) & (0.22517 \pm 0.00080) & (0.003721 \pm 0.000098)e^{i(-64.7 \pm 1.2)^\circ}\\ ( -0.22502 \pm 0.00078)e^{i(-179.03600 \pm 0.00085)^\circ} & (0.97344 \pm 0.00018)e^{i(-0.001862 \pm 0.000046)^\circ} & (0.04222 \pm 0.00051) \\ (0.00858 \pm 0.00010)e^{i(-22.33 \pm 0.62)^\circ} & ( -0.04127 \pm 0.00043)e^{i(-178.025 \pm 0.028)^\circ} & (0.999110 \pm 0.000018)\end{array}\right)$

Table of inputs, posterior values and predictions from the global fit.

Predictions are obtained by removing the given constraint from the global fit.

Parameter	Input value	Full fit	SM Prediction
$\bar{\rho}$		$0.1609 \pm 0.0095$
$\bar{\eta}$		$0.347 \pm 0.010$
$\rho$		$0.1653 \pm 0.0095$
$\eta$		$0.3559 \pm 0.0099$
		$0.828 \pm 0.011$
$\lambda$		$0.22519 \pm 0.00083$
$J_{cp}\cdot10^{5}$		$3.102 \pm 0.080$
$\sin\theta_{12}$		$0.22519 \pm 0.00083$
$\sin\theta_{23}$		$0.04200 \pm 0.00047$
$\sin\theta_{13}$		$0.003715 \pm 0.000093$
$\delta [^{\circ}]$		$1.137 \pm 0.022$
$\|V_{ud}\|$	$0.97433 \pm 0.00019$	$0.97431 \pm 0.00019$	$0.9738 \pm 0.0011$
$\|V_{ub}\|$	$0.00377 \pm 0.00024$	$0.003715 \pm 0.000093$	$0.00370 \pm 0.00011$
$\|V_{cb}\|$	$0.04125 \pm 0.00095$	$0.04200 \pm 0.00044$	$0.04222 \pm 0.00051$
$\alpha [^{\circ}]$	$94.9 \pm 4.7$	$92.4 \pm 1.3$	$92.2 \pm 1.6$
$\beta [^{\circ}]$		$22.47 \pm 0.65$	$22.46 \pm 0.68$
$\sin(2\beta)$	$0.688 \pm 0.020$	$0.706 \pm 0.015$	$0.736 \pm 0.028$
$\cos(2\beta)$			$0.707 \pm 0.016$
$\gamma [^{\circ}]$	$66.1 \pm 3.5$	$65.0 \pm 1.2$	$64.9 \pm 1.4$
$2\beta+\gamma [^{\circ}]$			$110.0 \pm 1.7$
$\beta_s$			$-0.0364 \pm 0.0011$
$m_{c}\mathrm{ [GeV/c^{2}]}$	$1.2900 \pm 0.0070$
$m_{b}\mathrm{ [GeV/c^{2}]}$	$4.196 \pm 0.014$
$m_{t}\mathrm{ [GeV/c^{2}]}$	$171.79 \pm 0.38$
$\|\epsilon_{k}\|$	$0.002228 \pm 0.000011$	$0.002226 \pm 0.000010$	$0.00200 \pm 0.00015$
$\epsilon^{\prime}/\epsilon$	$0.00166 \pm 0.00033$	$0.00161 \pm 0.00027$	$0.00158 \pm 0 .00045$
$\Delta m_{s} \mathrm{[ps^{-1}]}$	$17.741 \pm 0.020$	$17.739 \pm 0.020$	$17.94 \pm 0.69$
$\Delta m_{d} \mathrm{[ps^{-1}]}$	$0.5065 \pm 0.0019$	$0.5065 \pm 0.0018$	$0.519 \pm 0.023$
$B(B\rightarrow\tau\nu)$	$1.06 \pm 0.19$	$0.881 \pm 0.044$	$0.869 \pm 0.047$
$\bar {B}(B_{s}\rightarrow ll)\cdot10^{9}$	$3.41 \pm 0.29$	$3.25 \pm 0.12$	$3.47 \pm 0.14$

Global fit configurations to extract Lattice QCD parameter predictions:

Parameter	Input value $\hspace{2.0cm}$	Prediction
	Removing $\hat{B}_{k}$ from inputs
$\xi$	$1.230 \pm 0.023$	$1.217 \pm 0.014$
$\hat{B}_{k}$	$0.756 \pm 0.016$	$0.840 \pm 0.059$
	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 $\hat{B}_{K}$
$f_{B_{d}}\hat{B}_{d}^{1/2}$	$210.5 \pm 3.6$	$214.2 \pm 5.6$
$f_{B_{s}}\hat{B}_{s}^{1/2}$	$259.0 \pm 3.4$	$260.7 \pm 6.1$

Fit Results on the $\bar{\rho}$ - $\bar{\eta}$ complex plane:

Full fit result for $\,\bar{\rho} - \bar{\eta}$


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Angles-only result for $\,\bar{\rho} - \bar{\eta}$


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Sides-only result for $\,\bar{\rho} - \bar{\eta}$


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Tree-only result for $\,\bar{\rho} - \bar{\eta}$


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1D Probability Density plots for input values, posterior values, predictions and pulls:

Full fit result for $\,\bar{\rho}$

$0.1609 \pm 0.0095$ 95% prob:[0.1429, 0.1797] 99% prob:[0.1343, 0.1885]
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Full fit result for $\,\bar{\eta}$

$0.347 \pm 0.010$ 95% prob:[0.3279, 0.3664] 99% prob:[0.3184, 0.3772]
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Full fit result for $\,\rho$

$0.1653 \pm 0.0095$ 95% prob:[0.1464, 0.1842] 99% prob:[0.1376, 0.1933]
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Full fit result for $\,\eta$

$0.3559 \pm 0.0099$ 95% prob:[0.3364, 0.3759] 99% prob:[0.3269, 0.3871]
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Full fit result for $\,A$

$0.828 \pm 0.011$ 95% prob:[0.807, 0.850] 99% prob:[0.795, 0.795] U [0.795, 0.861]
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Full fit result for $\,\lambda$

$0.22519 \pm 0.00083$ 95% prob:[0.22354, 0.22674] 99% prob:[0.22277, 0.22764]
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Full fit result for $\,J_{cp}\cdot10^{5}$

$3.102 \pm 0.080$ 95% prob:[2.949, 3.259] 99% prob:[2.879, 3.335]
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Prediction for $\,\|V_{ud}\|$

$0.9738 \pm 0.0011$ 95% prob:[0.97393, 0.97467] 99% prob:[0.97374, 0.97485]
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Full fit result for $\,\sin\theta_{12}$

$0.22519 \pm 0.00083$ 95% prob:[0.22354, 0.22674] 99% prob:[0.22277, 0.22764]
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Full fit result for $\,\sin\theta_{23}$

$0.04200 \pm 0.00047$ 95% prob:[0.04111, 0.04290] 99% prob:[0.04067, 0.04333]
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Full fit result for $\,\sin\theta_{13}$

$0.003715 \pm 0.000093$ 95% prob:[0.003534, 0.003895] 99% prob:[0.003450, 0.003984]
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Full fit result for $\,\delta [^{\circ}]$

$1.137 \pm 0.022$ 95% prob:[1.092, 1.181] 99% prob:[1.070, 1.201]
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Fit Input for $\,\|V_{ub}\|$

Gaussian likelihood used $0.00377 \pm 0.00024$
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Full Fit result for $\,\|V_{ub}\|$

$0.003715 \pm 0.000093$ 95% prob:[0.003534, 0.003894] 99% prob:[0.003453, 0.003977]
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SM Fit prediction for $\,\|V_{ub}\|$

$0.00370 \pm 0.00011$ 95% prob:[0.003532, 0.003922] 99% prob:[0.003437, 0.004024]
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Compatibility Plot for $\,\|V_{ub}\|$

${\rm pull}(\|V_{ub}\|) = -0.2$
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Fit Input for $\,\|V_{cb}\|$

Gaussian likelihood used $0.04125 \pm 0.00095$
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Full Fit result for $\,\|V_{cb}\|$

$0.04200 \pm 0.00044$ 95% prob:[0.04112, 0.04290] 99% prob:[0.04069, 0.04332]
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SM Fit prediction for $\,\|V_{cb}\|$

$0.04222 \pm 0.00051$ 95% prob:[0.04106, 0.04311] 99% prob:[0.04059, 0.04360]
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Compatibility Plot for $\,\|V_{cb}\|$

${\rm pull}(\|V_{cb}\|) = +0.7$
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Fit Input for $\,\alpha [^{\circ}]$

Gaussian likelihood used $94.9 \pm 4.7$
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Full Fit result for $\,\alpha [^{\circ}]$

$92.4 \pm 1.3$ 95% prob:[89.7, 95.3] 99% prob:[88.3, 96.7]
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SM Fit prediction for $\,\alpha [^{\circ}]$

$92.2 \pm 1.6$ 95% prob:[89.1, 95.2] 99% prob:[87.7, 96.7]
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Compatibility Plot for $\,\alpha [^{\circ}]$

${\rm pull}(\alpha ) = -0.6$
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Full Fit result for $\,\beta [^{\circ}]$

$22.47 \pm 0.65$ 95% prob:[21.21, 23.79] 99% prob:[20.59, 24.43]
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SM Fit prediction for $\,\beta [^{\circ}]$

$22.46 \pm 0.68$ 95% prob:[21.23, 23.90] 99% prob:[20.60, 24.58]
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Fit Input for $\,\sin(2\beta)$

Gaussian likelihood used $0.688 \pm 0.020$
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Full Fit result for $\,\sin(2\beta)$

$0.706 \pm 0.015$ 95% prob:[0.674, 0.738] 99% prob:[0.658, 0.753]
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SM Fit prediction for $\,\sin(2\beta)$

$0.706 \pm 0.015$ 95% prob:[0.674, 0.738] 99% prob:[0.658, 0.753]
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Compatibility Plot for $\,\sin(2\beta)$

${\rm pull}(sin(2\beta)) = +0.7$
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Full fit result for $\,\cos(2\beta)$

$0.707 \pm 0.016$ 95% prob:[0.675, 0.738] 99% prob:[0.658, 0.752]
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Fit Input for $\,\gamma [^{\circ}]$

Gaussian likelihood used $66.1 \pm 3.5$
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Full Fit result for $\,\gamma [^{\circ}]$

$65.0 \pm 1.2$ 95% prob:[62.5, 67.6] 99% prob:[61.2, 68.8]
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SM Fit prediction for $\,\gamma [^{\circ}]$

$64.4 \pm 2.1$ 95% prob:[60.0, 68.9] 99% prob:[57.6, 71.3]
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Compatibility Plot for $\,\gamma [^{\circ}]$

${\rm pull}(\gamma ) = -0.4$
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Full fit result for $\,2\beta+\gamma [^{\circ}]$

$110.0 \pm 1.7$ 95% prob:[106.5, 113.5] 99% prob:[104.7, 115.4]
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Fit Input for $\,\|\epsilon_{k}\|$

$0.002228 \pm 0.000011$ 95% prob:0 99% prob:0
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Full Fit result for $\,\|\epsilon_{k}\|$

$0.002226 \pm 0.000010$ 95% prob:[0.002205, 0.002248] 99% prob:[0.002194, 0.002259]
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SM Fit prediction for $\,\|\epsilon_{k}\|$

$0.00200 \pm 0.00015$ 95% prob:[0.002205, 0.002248] 99% prob:[0.002193, 0.002259]
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Compatibility Plot for $\,\|\epsilon_{k}\|$

${\rm pull}(\|\epsilon_{k}\|) = -0.1$
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Fit Input for $\,\epsilon^{\prime}/\epsilon$

Gaussian likelihood used $0.00166 \pm 0.00033$
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Full Fit result for $\,\epsilon^{\prime}/\epsilon$

$0.00161 \pm 0.00027$ 95% prob:[0.00108, 0.00215] 99% prob:[0.00085, 0.00243]
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SM Fit prediction for $\,\epsilon^{\prime}/\epsilon$

$0.00152 \pm 0.00047$ 95% prob:[0.00072, 0.00250] 99% prob:[0.00044, 0.00304]
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Compatibility Plot for $\,\epsilon^{\prime}/\epsilon$

${\rm pull}(\epsilon^{\prime}/\epsilon) = -0.3$
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Fit Input for $\,\Delta m_{s} \mathrm{[ps^{-1}]}$

Gaussian likelihood used $17.741 \pm 0.020$
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Full Fit result for $\,\Delta m_{s} \mathrm{[ps^{-1}]}$

$17.739 \pm 0.020$ 95% prob:[17.702, 17.781] 99% prob:[17.681, 17.801]
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SM Fit prediction for $\,\Delta m_{s} \mathrm{[ps^{-1}]}$

$17.94 \pm 0.69$ 95% prob:[16.64, 19.34] 99% prob:[15.98, 20.12]
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Fit Input for $\,\Delta m_{d} \mathrm{[ps^{-1}]}$

$0.5065 \pm 0.0019$ 95% prob:0 99% prob:0
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Full Fit result for $\,\Delta m_{d} \mathrm{[ps^{-1}]}$

$0.5065 \pm 0.0018$ 95% prob:[0.5027, 0.5103] 99% prob:[0.5008, 0.5122]
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SM Fit prediction for $\,\Delta m_{d} \mathrm{[ps^{-1}]}$

$0.519 \pm 0.023$ 95% prob:[0.476, 0.566] 99% prob:[0.455, 0.589]
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Compatibility Plot for $\,\Delta m_{d} \mathrm{[ps^{-1}]}$

${\rm pull}(\Delta m_{d} ) = +0.5$
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Fit Input for $\,B(B\rightarrow\tau\nu)$

Gaussian likelihood used $1.06 \pm 0.19$
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Full Fit result for $\,B(B\rightarrow\tau\nu)$

$0.881 \pm 0.044$ 95% prob:[0.793, 0.971] 99% prob:[0.755, 1.019]
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SM Fit prediction for $\,B(B\rightarrow\tau\nu)$

$0.869 \pm 0.047$ 95% prob:[0.780, 0.965] 99% prob:[0.740, 1.014]
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Compatibility Plot for $\,B(B\rightarrow\tau\nu)$

${\rm pull}( B(B\rightarrow\tau\nu) ) = 1.0$
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