A search for time-dependent violation of the charge-parity symmetry in <math><msup><mi>D</mi><mn>0</mn></msup><mo>→</mo><mrow><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></mrow></math> and <math><msup><mi>D</mi><mn>0</mn></msup><mo>→</mo><mrow><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></mrow></math> decays is performed at the LHCb experiment using proton-proton collision data recorded from 2015 to 2018 at a center-of-mass energy of 13 TeV, corresponding to an integrated luminosity of <math><mn>6</mn><mtext> </mtext><mtext> </mtext><msup><mi>fb</mi><mrow><mo>−</mo><mn>1</mn></mrow></msup></math>. The <math><msup><mi>D</mi><mn>0</mn></msup></math> meson is required to originate from a <math><mrow><msup><mi>D</mi><mo>*</mo></msup><mo>(</mo><mn>2010</mn><msup><mo>)</mo><mo>+</mo></msup></mrow><mo>→</mo><mrow><msup><mi>D</mi><mn>0</mn></msup><msup><mi>π</mi><mo>+</mo></msup></mrow></math> decay, such that its flavor at production is identified by the charge of the accompanying pion. The slope of the time-dependent asymmetry of the decay rates of <math><msup><mi>D</mi><mn>0</mn></msup></math> and <math><mrow><msup><mrow><mover><mrow><mi>D</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mn>0</mn></mrow></msup></mrow></math> mesons into the final states under consideration is measured to be <math><mrow><mi>Δ</mi><msub><mi>Y</mi><mrow><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></mrow></msub></mrow><mo>=</mo><mo>(</mo><mo>−</mo><mn>2.3</mn><mo>±</mo><mn>1.5</mn><mo>±</mo><mn>0.3</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, <math><mrow><mi>Δ</mi><msub><mi>Y</mi><mrow><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></mrow></msub></mrow><mo>=</mo><mo>(</mo><mo>−</mo><mn>4.0</mn><mo>±</mo><mn>2.8</mn><mo>±</mo><mn>0.4</mn><mo>)</mo><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>4</mn></mrow></msup></math>, where the first uncertainties are statistical and the second are systematic. These results are compatible with the conservation of the charge-parity symmetry at the level of 2 standard deviations and improve the precision by nearly a factor of 2.

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Search for time-dependent <math><mi>C</mi><mi>P</mi></math> violation in <math><msup><mi>D</mi><mn>0</mn></msup><mo>→</mo><msup><mi>K</mi><mo>+</mo></msup><msup><mi>K</mi><mo>−</mo></msup></math> and <math><msup><mi>D</mi><mn>0</mn></msup><mo>→</mo><msup><mi>π</mi><mo>+</mo></msup><msup><mi>π</mi><mo>−</mo></msup></math> decays