Mass distribution of (top) $ D ^0 \rightarrow \pi ^+ \pi ^- \mu^+\mu^-$ and (bottom) $ D ^0 \rightarrow K ^+ K ^- \mu^+\mu^-$ candidates with fit projections overlaid.

Measured observables for (left) $ D ^0 \rightarrow \pi ^+ \pi ^- \mu^+\mu^-$ and (right) $ D ^0 \rightarrow K ^+ K ^- \mu^+\mu^-$ decays in $ m(\mu ^+ \mu ^- )$ regions. No measurement is performed in the regions indicated by the vertical gray bands. The horizontal bands correspond to the measurements integrated in the dimuon mass, including candidates from all $ m(\mu ^+ \mu ^- )$ ranges. The high-mass region of $ D ^0 \rightarrow \pi ^+ \pi ^- \mu^+\mu^-$ extends to $1590.5\text{ Me V /}c^2 $ and has been truncated on the plots for a clearer visualization of the other regions.

Decay topology of $ D ^0 \rightarrow h^+h^-\mu^+\mu^-$ decays illustrating the definition of the decay angles $\theta_{\mu}$, $\theta_{h}$ and $\phi$.

Animated gif made out of all figures.

Observable $ A_{ C P }$ for (top) $ D ^0 \rightarrow \pi ^+ \pi ^- \mu^+\mu^-$ and (bottom) $ D ^0 \rightarrow K ^+ K ^- \mu^+\mu^-$ decays in the dimuon-mass regions. The first uncertainty is statistical, the second systematic.

Angular observables $\langle S_{\mathrm{i}} \rangle $ for (top) $ D ^0 \rightarrow \pi ^+ \pi ^- \mu^+\mu^-$ and (bottom) $ D ^0 \rightarrow K ^+ K ^- \mu^+\mu^-$ decays in the different dimuon-mass regions reported in the first column. The first uncertainty is statistical and the second systematic.

Angular observables $\langle A_{\mathrm{i}} \rangle $ for (top) $ D ^0 \rightarrow \pi ^+ \pi ^- \mu^+\mu^-$ and (bottom) $ D ^0 \rightarrow K ^+ K ^- \mu^+\mu^-$ decays in the different dimuon-mass regions reported in the first column. The first uncertainty is statistical and the second systematic.

Correlation matrix for the observables $ A_{ C P } $, $\langle S_i \rangle$ and $\langle A_i \rangle$ for $ D ^0 \rightarrow \pi ^+ \pi ^- \mu^+\mu^-$ decays measured in the dimuon-mass-integrated interval.

Correlation matrix for the observables $ A_{ C P } $, $\langle S_i \rangle$ and $\langle A_i \rangle$ for $ D ^0 \rightarrow \pi ^+ \pi ^- \mu^+\mu^-$ decays measured in the interval $m(\mu^+\mu^-) <525 \text{ Me V /}c^2 $.

Correlation matrix for the observables $ A_{ C P } $, $\langle S_i \rangle$ and $\langle A_i \rangle$ for $ D ^0 \rightarrow \pi ^+ \pi ^- \mu^+\mu^-$ decays measured in the interval $ 565 < m(\mu^+\mu^-) <780 \text{ Me V /}c^2 $.

Correlation matrix for the observables $ A_{ C P } $, $\langle S_i \rangle$ and $\langle A_i \rangle$ for $ D ^0 \rightarrow \pi ^+ \pi ^- \mu^+\mu^-$ decays measured in the interval $780 < m(\mu^+\mu^-) <950 \text{ Me V /}c^2 $.

Correlation matrix for the observables $ A_{ C P } $, $\langle S_i \rangle$ and $\langle A_i \rangle$ for $ D ^0 \rightarrow \pi ^+ \pi ^- \mu^+\mu^-$ decays measured in the interval $950 < m(\mu^+\mu^-) <1020 \text{ Me V /}c^2 $.

Correlation matrix for the observables $ A_{ C P } $, $\langle S_i \rangle$ and $\langle A_i \rangle$ for $ D ^0 \rightarrow \pi ^+ \pi ^- \mu^+\mu^-$ decays measured in the interval $1020 \text{ Me V /}c^2 < m(\mu^+\mu^-) <1100 \text{ Me V /}c^2 $.

Correlation matrix for the observables $ A_{ C P } $, $\langle S_i \rangle$ and $\langle A_i \rangle$ for $ D ^0 \rightarrow K ^+ K ^- \mu^+\mu^-$ decays measured in the dimuon-mass-integrated interval.

Correlation matrix for the observables $ A_{ C P } $, $\langle S_i \rangle$ and $\langle A_i \rangle$ for $ D ^0 \rightarrow K ^+ K ^- \mu^+\mu^-$ decays measured in the interval $m(\mu^+\mu^-) <525 \text{ Me V /}c^2 $.

Correlation matrix for the observables $ A_{ C P } $, $\langle S_i \rangle$ and $\langle A_i \rangle$ for $ D ^0 \rightarrow K ^+ K ^- \mu^+\mu^-$ decays measured in the interval $m(\mu^+\mu^-) >565 \text{ Me V /}c^2 $.

# This ZIP file contains supplemetary material for the publication # LHCb-PAPER-2021-035. The files are: # # Supplementary-LHCb-PAPER-2021-035.pdf : An overview of the extra figures *.pdf, *.png, *.eps, *.C : The figures in various formats