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A$_{\Gamma }$

INSPIRE   PDGID:

S032AG

A$_{\Gamma }$ is the decay-rate asymmetry for $\mathit CP$-even final states A$_{\Gamma }$ = (${{\overline{\mathit \tau}}_{{+}}}−$ ${{\mathit \tau}_{{+}}}$) $/$ (${{\overline{\mathit \tau}}_{{+}}}+$ ${{\mathit \tau}_{{+}}}$). See the note on “${{\mathit D}^{0}}--{{\overline{\mathit D}}^{0}}$ Mixing” above.

VALUE ($ 10^{-3} $) EVTS DOCUMENT ID TECN  COMMENT $\bf{ (89 \pm113) \times 10^{-3}}$ OUR EVALUATION  See the ideogram below. $\bf{ 0.09 \pm0.17}$ OUR AVERAGE  Error includes scale factor of 1.5.  See the ideogram below. $0.23$ $\pm0.15$ $\pm0.03$ 1 AAIJ 2021 AI LHCB ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ $0.40$ $\pm0.28$ $\pm0.04$ 1 AAIJ 2021 AI LHCB ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $-0.44$ $\pm0.23$ $\pm0.06$ 21M 2 AAIJ 2020 LHCB ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ $0.25$ $\pm0.43$ $\pm0.07$ 7M 3 AAIJ 2020 LHCB ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ $-0.3$ $\pm2.0$ $\pm0.7$ 4 STARIC 2016 BELL ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(nS)}}$ $-1.2$ $\pm1.2$ 1.8M 5 AALTONEN 2014 Q CDF ${{\mathit p}}{{\overline{\mathit p}}}$ , $\sqrt {s }$ = 1.96 TeV $0.9$ $\pm2.6$ $\pm0.6$ 0.7M LEES 2013 BABR ${{\mathit e}^{+}}$ ${{\mathit e}^{-}}$ $\rightarrow$ ${{\mathit \Upsilon}{(4S)}}$ $-5.9$ $\pm5.9$ $\pm2.1$ 6 AAIJ 2012 K LHCB ${{\mathit p}}{{\mathit p}}$ at 7 TeV, 2010 data. • • We do not use the following data for averages, fits, limits, etc. • • $-0.30$ $\pm0.32$ $\pm0.10$ 9.6M 6 AAIJ 2017 AK LHCB Repl. by AAIJ 2020 $0.46$ $\pm0.58$ $\pm0.12$ 3.0M 7 AAIJ 2017 AK LHCB Repl. by AAIJ 2020 $-1.34$ $\pm0.77$ ${}^{+0.26}_{-0.34}$ 2.3M 8 AAIJ 2015 AA LHCB Repl. by AAIJ 2020 $-0.92$ $\pm1.45$ ${}^{+0.25}_{-0.33}$ 0.8M 9 AAIJ 2015 AA LHCB Repl. by AAIJ 2020 $-0.35$ $\pm0.62$ $\pm0.12$ 6 AAIJ 2014 AL LHCB Repl. by AAIJ 2017AK $0.33$ $\pm1.06$ $\pm0.14$ 7 AAIJ 2014 AL LHCB Repl. by AAIJ 2017AK $2.6$ $\pm3.6$ $\pm0.8$ AUBERT 2008 U BABR See LEES 2013 $0.1$ $\pm3.0$ $\pm2.5$ STARIC 2007 BELL Repl. by STARIC 2016 $8$ $\pm6$ $\pm2$ AUBERT 2003 P BABR ${{\mathit e}^{+}}{{\mathit e}^{-}}$ $\approx{}{{\mathit \Upsilon}{(4S)}}$ 1  Requires ${{\mathit D}^{0}}$ to originate from ${{\mathit D}^{*}{(2010)}^{+}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit \pi}^{+}}$ . AAIJ 2021AI measures the parameter $\Delta {{\mathit Y}_{{f}}}$ $\simeq{}$ $−{{\mathit A}_{{\Gamma}}^{f}}$ up to 1$\%$ corrections from ${{\mathit y}_{{CP}}^{f}}$. 2  Measured using ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ decays, combines measurements with ${{\mathit D}^{0}}$ either from partially reconstructed semileptonic ${{\mathit B}}$ hadron decays or from ${{\mathit D}^{*+}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit \pi}^{+}}$ . 3  Measured using ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ decays, combines measurements with ${{\mathit D}^{0}}$ either from partially reconstructed semileptonic ${{\mathit B}}$ hadron decays or from ${{\mathit D}^{*+}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit \pi}^{+}}$ . 4  An improved measurement of ${{\overline{\mathit D}}^{0}}−{{\mathit D}^{0}}$ mixing and a search for $\mathit CP$ violation in ${{\mathit D}^{0}}$ decays to $\mathit CP$-even final states ${{\mathit K}^{+}}{{\mathit K}^{-}}$ and ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ using the final Belle data sample of 976 fb${}^{-1}$. 5  Combined result from ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ and ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ , with ${{\mathit D}^{0}}$ from ${{\mathit D}^{*+}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit \pi}^{+}}$ (and cc). 6  Measured using ${{\mathit D}^{*+}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ decays (and cc). 7  Measured using ${{\mathit D}^{*+}}$ $\rightarrow$ ${{\mathit D}^{0}}{{\mathit \pi}^{+}}$ , ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ decays (and cc). 8  Measured using ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ decays, with ${{\mathit D}^{0}}$ from partially reconstructed semileptonic ${{\mathit B}}$ hadron decays. 9  Measured using ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ decays, with ${{\mathit D}^{0}}$ from partially reconstructed semileptonic ${{\mathit B}}$ hadron decays.

A$_{\Gamma }$ ($ 10^{-3} $)

Conservation Laws:

$\mathit CP$ INVARIANCE

References:

AAIJ 2021AI PR D104 072010 Search for time-dependent $CP$ violation in $D^0 \to K^+ K^-$ and $D^0 \to \pi^+ \pi^-$ decays AAIJ 2020 PR D101 012005 Updated measurement of decay-time-dependent CP asymmetries in $D^0 \to K^+K^-$ and $D^0 \to \pi^+\pi^-$ decays AAIJ 2017AK PRL 118 261803 Measurement of the $\mathit CP$ Violation Parameter $\mathit A_{\Gamma }$ in ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ and ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Decays STARIC 2016 PL B753 412 Measurement of ${{\mathit D}^{0}}-{{\overline{\mathit D}}^{0}}$ Mixing and Search for $\mathit CP$ Violation in ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ , ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Decays with the Full Belle Data Set AAIJ 2015AA JHEP 1504 043 Measurement of Indirect $\mathit CP$ Asymmetries in ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit K}^{+}}$ and ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$ Decays using Semileptonic ${{\mathit B}}$ Decays AAIJ 2014AL PRL 112 041801 Measurements of Indirect $\mathit CP$ Asymmetries in ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit K}^{+}}$ and ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$ Decays AALTONEN 2014Q PR D90 111103 Measurement of Indirect $\mathit CP$-Violating Asymmetries in ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{+}}{{\mathit K}^{-}}$ and ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit \pi}^{+}}{{\mathit \pi}^{-}}$ Decays at CDF LEES 2013 PR D87 012004 Measurement of ${{\mathit D}^{0}}−{{\overline{\mathit D}}^{0}}$ Mixing and $\mathit CP$ Violation in Two-Body ${{\mathit D}^{0}}$ Decays AAIJ 2012K JHEP 1204 129 Measurement of Mixing and $\mathit CP$ Violation Parameters in Two-Body Charm Decays AUBERT 2008U PR D78 011105 Measurement of ${{\mathit D}^{0}}−{{\overline{\mathit D}}^{0}}$ Mixing using the Ratio of Lifetimes for the Decays ${{\mathit D}^{0}}$ $\rightarrow$ ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ , ${{\mathit K}^{-}}{{\mathit K}^{+}}$ , and ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$ STARIC 2007 PRL 98 211803 Evidence for ${{\mathit D}^{0}}−{{\overline{\mathit D}}^{0}}$ Mixing AUBERT 2003P PRL 91 121801 Limits on ${{\mathit D}^{0}}{{\overline{\mathit D}}^{0}}$ Mixing and $\mathit CP$ Violation from the Ratio of Lifetimes for Decay to ${{\mathit K}^{-}}{{\mathit \pi}^{+}}$ , ${{\mathit K}^{-}}{{\mathit K}^{+}}$ and ${{\mathit \pi}^{-}}{{\mathit \pi}^{+}}$