# Combination of Direct and Indirect CP Violation (updated 8 August 2011)

People working on this:   Marco Gersabeck

Notation: This combination uses measurements of direct and indirect CP violation to extract the level of agreement for a no-CP-violation hypothesis. The observables are:

A Γ ≡ [τ(D0 → K+ K) − τ(D0 → K+ K )] / [τ(D0 → K+ K) + τ(D0 → K+ K )]

to constrain indirect CP violation via A Γ = -aCPind, and
ΔACP ≡ ACP(KK) - ACP(ππ)

to constrain direct CP violation (aCPdir) via ΔACP = ΔaCPdir + Δ〈t〉/τ aCPind, where Δ〈t〉 is the difference of the average proper time of the KK and ππ modes. A χ2 fit is performed in the plane ΔaCPdir vs. aCPind. For cases where an experiment does not directly quote a value for ΔACP, the difference of the quoted values for ACP(KK) and ACP(ππ) is calculated, adding all uncertainties in quadrature. This may overestimate the systematic uncertainty for the difference as it neglects correlated errors; however, the result is conservative and the effect is small as all measurements are statistically limited. For all measurements, statistical and systematic uncertainties are added in quadrature when calculating the χ2.

Year Experiment Results Δ〈t〉/τ Comment Reference
2008 BaBar ACP(KK) = (0.00 ±0.34 (stat.) ±0.13 (syst.))%
ACP(ππ) = (-0.24 ±0.52 (stat.) ±0.22 (syst.))%
0.00 385.8 fb−1 near Υ(4S) resonance B. Aubert et al. (BABAR Collab.), Phys. Rev. Lett. 100, 061803 (2008).
2008 Belle ΔACP = (-0.86 ±0.60 (stat.) ±0.07 (syst.))% 0.00 540 fb−1 near Υ(4S) resonance M. Staric et al. (BELLE Collab.), Phys. Lett. B 670, 190 2008).
2011 CDF ACP(KK) = (-0.24 ±0.22 (stat.) ±0.10 (syst.))%
ACP(ππ) = (0.22 ±0.24 (stat.) ±0.11 (syst.))%
0.25 5.94 fb−1 s  = 1.96 TeV p p  collisions A. Di Canto (CDF Collab.), Preprint (BEAUTY 2011).
M.J. Morello (CDF Collab.), Preprint (CHARM 2010).
2011 LHCb Preliminary ΔACP = (-0.28 ±0.70 (stat.) ±0.25 (syst.))% 0.10 37 pb−1 s  = 7 TeV pp collisions R. Aaij et al. (LHCb Collab.), CERN-LHCb-CONF-2011-023 (2011).
2007 Belle AΓ = (0.01 ±0.30 (stat.) ±0.15 (syst.))% - 540 fb−1 near Υ(4S) resonance M. Staric et al. (Belle Collab.), Phys. Rev. Lett. 98, 211803 (2007).
2008 BaBar AΓ = (0.26 ±0.36 (stat.) ±0.08 (syst.))% - 384 fb−1 near Υ(4S) resonance B. Aubert et al. (BaBar Collab.), Phys. Rev. D 78, 011105(R) (2008).
2011 LHCb Preliminary AΓ = (-0.59 ±0.59 (stat.) ±0.21 (syst.))% - 28 pb−1 s  = 7 TeV pp collisions R. Aaij et al. (LHCb Collab.), CERN-LHCb-CONF-2011-046 (2011).
Fit Result
 Agreement with no CP violation CL = 0.200

Combination Plot: The combination plot shows the measurements listed in the Table above for ΔACP and AΓ, where the bands represent ±1σ intervals. The point of no CP violation (0,0) is shown as a filled circle, and two-dimensional 68% CL, 95% CL, and 99.7% CL regions are plotted as ellipses.

From the fit, the change in χ2 from the minimum value for the no-CPV point (0,0) is 3.222; this corresponds to a CL of 0.200 for two degrees of freedom. Thus the data is consistent with no CP violation at 20.0% CL. The central values and ± 1σ errors for the individual parameters are:

aCPind = (−0.023 ± 0.232 )%

ΔaCPdir = (−0.477 ± 0.270 )%