1 Erratum to: Eur. Phys. J. C https://doi.org/10.1140/epjc/s10052-019-7159-8

In the Introduction section of the original article [1], the parameter \(\lambda \) was defined erroneously. The correct definition is \(\lambda \equiv \left( {q}/{p}\right) \left( {\overline{A}}/{A}\right) \).

In Table 4, the systematic uncertainties due to the mass-width parametrisation, the mass dependence on the decay time and angles and the multiple candidates were erroneously documented. The corrected table is shown as Table 1.

As a result, the total systematic uncertainty on the parameter \(\delta _{\parallel }\) changes from \(0.037\text { rad}\) to \(0.036\text { rad}\), and on the parameter \(|A_{0}|^2\) from 0.0024 to 0.0023, both in Table 4 and in Eq. (15) of the original paper. The remaining systematic uncertainties are unchanged. The corrected Eq. (15) is

$$\begin{aligned} \phi _{s}&= -0.083\pm 0.041\pm 0.006\text { rad}\nonumber \\ |\lambda |&= 1.012\pm 0.016\pm 0.006 \nonumber \\ \Gamma _{s}-\Gamma _{d}&= -0.0041\pm 0.0024\pm 0.0015\text { ps} ^{-1} \nonumber \\ \Delta \Gamma _{s}&= 0.077\pm 0.008\pm 0.003\text { ps} ^{-1} \nonumber \\ \Delta m_{s}&= 17.703\pm 0.059\pm 0.018 \text { ps} ^{-1} \nonumber \\ |A_{\perp }|^2&= 0.2456\pm 0.0040\pm 0.0019\nonumber \\ |A_0|^2&= 0.5186\pm 0.0029\pm 0.0023 \nonumber \\ \delta _\perp -\delta _0&= 2.64\pm 0.13\pm 0.10 \text { rad}\nonumber \\ \delta _\parallel -\delta _0&= 3.06^{\,+\,0.08}_{\,-\,0.07}\pm 0.04 \text { rad}. \end{aligned}$$
(1)

These changes have a small impact on the average of Run 1 and Run 2 \({{B} ^0_{s}} \rightarrow J/\psi {{K} ^+} {{K} ^-} \) results presented in Eq. (16) in the original article, which changes to

$$\begin{aligned} \phi _{s}&= -0.081\pm 0.032\text { rad}\, \nonumber \\ |\lambda |&= 0.994\pm 0.013\, \nonumber \\ \Gamma _{s}&= 0.6572\pm 0.0023\text { ps} ^{-1} \,\nonumber \\ \Delta \Gamma _{s}&= 0.0777\pm 0.0062\text { ps} ^{-1} \,\nonumber \\ \Delta m_{s}&= 17.694 \pm 0.042\text { ps} ^{-1} \,\nonumber \\ |A_{\perp }|^2&= 0.2489 \pm 0.0035\, \nonumber \\ |A_0|^2&= 0.5195 \pm 0.0034\, \nonumber \\ \delta _\perp -\delta _{0}&= 2.87 \pm 0.11\text { rad}\,\nonumber \\ \delta _\parallel -\delta _{0}&= 3.153 \pm 0.079\text { rad}. \end{aligned}$$
(2)

The resulting correlation matrix is shown in Table 2, which replaces Table 6 of the original article.

The average of all LHCb measurements presented in Eq. (17) in the original article changes to

$$\begin{aligned} \phi _{s}&= -0.042 \pm 0.025\text { rad}\, \nonumber \\ |\lambda |&= 0.993 \pm 0.010\, \nonumber \\ \Gamma _{s}&= 0.6563 \pm 0.0021\text { ps} ^{-1} \,\nonumber \\ \Delta \Gamma _{s}&= 0.0813 \pm 0.0048\text { ps} ^{-1}. \end{aligned}$$
(3)

The resulting correlation matrix is shown in Table 3, which replaces Table 7 of the original article.

The changes in the combined results are small, the largest being \(\Delta \Gamma _{s}\) in the \(\text{ B }\) combination. It is at the level of 11% of the total uncertainty. These changes do not affect the conclusions of the paper.

Furthermore, Fig. 12 in the original article, presenting the combined LHCb results, is amended to reflect the changes and the correct version is shown in Fig. 1.

Table 1 Summary of the systematic uncertainties
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Table 2 Correlation matrix for the results in Eq. (2) taking into account correlated systematics between Run 1 and the 2015 and 2016 results
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Table 3 Correlation matrix for the results in Eq. (3) obtained taking into account correlated systematics between the considered analyses
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Fig. 1
figure 1

Regions of 68% confidence level in the \(\phi _s-\Delta \Gamma _s\) plane for the individual LHCb measurements and a combined contour (in blue). The \({{B} ^0_{s}} \rightarrow J/\psi {{K} ^+} {{K} ^-} \) (magenta) and \({{B} ^0_{s}} \rightarrow J/\psi {{\pi } ^+} {{\pi } ^-} \) [2] (red) contours show the Run 1 and Run 2 combined numbers. The \(\phi _s\) [3] and \(\Delta \Gamma _{s}\) [4] predictions are indicated by the thin black rectangle

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