# Results for D0- D0 Mixing: World Averages (assuming CP conservation)

People working on this:   David Asner, Bostjan Golob, Alan Schwartz

Notation: the mass eigenstates are denoted D 1 ≡ p|D0> + q|D0> and D 2 ≡ p|D0> − q|D0>; R D is the ratio of magnitudes of D0 → f and D0 → f amplitudes; δ and δKππ are strong phase differences between D0 → f and D0 → f amplitudes, and φ is a weak phase difference. The mixing parameters are defined as x ≡ (m2 − m1)/Γ and y ≡ (Γ2 − Γ1)/(2Γ), where Γ = (Γ1 + Γ2)/2. In the absence of CP violation, our convention is x = (mCP+ − mCP−)/Γ, y = (ΓCP+ − ΓCP−)/(2Γ), and δ = δ D0 → K+n(π) − δ D0 → K+n(π) .

The following "pure" measurements and their world averages are presented:

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D0 → K+l ν results for R M ≡ (x2+y2)/2.

Year Experiment Result Comment
1996 FNAL E791 R M = (0.11 +0.30 −0.27 +0.00 −0.014 )% 500 GeV πN interactions (2 × 1010 events)
2005 CLEO II.V R M = (0.16 ± 0.29 ± 0.29 )% 9.0 fb−1 near Υ(4S) resonance
2004 BaBar R M = (0.23 ± 0.12 ± 0.04 )% 87 fb−1 near Υ(4S) resonance
2007 BaBar R M = (0.004 +0.070 −0.060 )%
 344 fb−1 near Υ(4S) resonance; decays are "double-tagged" (tag side is fully reconstructed)
2008 Belle R M = (0.013 ± 0.022 ± 0.020 )% 492 fb−1 near Υ(4S) resonance
COMBOS average
 R M = (0.0130 ± 0.0269 )% CL = 0.967
 (output)   stat. and syst. errors assumed uncorrelated; BaBar 2004 result not included as correlation with BaBar 2007 not determined

Plot of average:

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D0 → K+ K, π+ π, K+ K K0 results for: y CP ≡ [Γ(CP+)/<Γ>]−1 = (1/2)(|q/p| + |p/q|) y cosφ − (1/2)(|q/p| − |p/q|) x sin φ, and A Γ ≡ [τ(D0 → K+ K) − τ(D0 → K+ K )] / [τ(D0 → K+ K) + τ(D0 → K+ K )] = (1/2)(|q/p|−|p/q|) y cosφ −(1/2)(|q/p|+|p/q|) x sin φ .

Year Experiment Result Comment
1999 FNAL E791 ΔΓ = (0.04 ± 0.14 ± 0.05 ) ps −1 500 GeV πN interactions (2 × 1010 events)
2000 FOCUS y CP = (3.42 ± 1.39 ± 0.74 )% γN interactions (1 × 106 reconstr. D → K n(π) decays)
2002 CLEO II.V y CP = (−1.2 ± 2.5 ± 1.4 )% 9.0 fb−1 near Υ(4S) resonance
2002 Belle y CP = (−0.5 ± 1.0 +0.7 −0.8 )% 23.4 fb−1 near Υ(4S) resonance; no D* tag
2007 Belle
 y CP = (1.31 ± 0.32 ± 0.25 )% A Γ = (0.01 ± 0.30 ± 0.15 )%
540 fb−1 near Υ(4S) resonance
2008 BaBar
 y CP = (1.03 ± 0.33 ± 0.19)% A Γ = (0.26 ± 0.36 ± 0.08 )%
 384 fb−1 near Υ(4S) resonance; D*+ → D0 π+ -tagged analysis
2009 BaBar
 y CP = (1.12 ± 0.26 ± 0.22)% y CP = (1.16 ± 0.22 ± 0.18)%
 384 fb−1 near Υ(4S) resonance; untagged analysis The second value of yCP is tagged+untagged combined
2009 Belle
 y CP = (0.11 ± 0.61 ± 0.52)%
673 fb−1 near Υ(4S) resonance, D → (K+K) K0 decays
COMBOS average
 y CP = (1.107 ± 0.217 )% CL = 0.397 A Γ = (0.123 ± 0.248 )% CL = 0.616
 ( output for y CP )   ( output for A Γ ) symmetrized statistical, systematic errors; stat. errors for two Belle analyses have correl.= 0.0165; common syst. errors for two Babar analyses have correl.= 1.0

Plot of y CP average:                                                                   Plot of A Γ average:

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D0 → K+ π results for: R D, x' ≡ x cosδ + y sin δ, y' ≡ y cosδ - x sin δ, and R B ≡ R D + y' √ R D + (x2+y2)/2 . These results assume no CPV; for results allowing for CPV click here

Year Experiment Result Comment
1998 FNAL E791 RB = (0.68 +0.34 −0.33 ± 0.07)% 500 GeV πN interactions (2 × 1010 events)
2000 CLEO II.V
 RB = (0.332 +0.063 −0.065 ± 0.040)% RD = (0.47 +0.11 −0.12 ± 0.04)% x' = (0.0 ± 1.5 ± 0.2)% y' = (− 2.3 +1.3 −1.4 ± 0.3)%
9.0 fb−1 near Υ(4S) resonance
2005 FOCUS
 RB = (0.429 +0.063 − 0.061 ± 0.027)% RD = (0.381 +0.167 − 0.163 ± 0.092)% x' 2 = − 0.059% y' = 1.0%
γN interactions (1 × 106 reconstr. D → K n(π) decays)
2006 Belle
 RB = (0.377 ± 0.008 ± 0.005)% RD = (0.364 ± 0.017)% x' 2 = (0.018 +0.021 −0.023 )% y' = (0.06 +0.40 −0.39 )%
400 fb−1 near Υ(4S) resonance
2007 BaBar
 RD = (0.303 ± 0.016 ± 0.010)% x' 2 = (−0.022 ± 0.030 ± 0.021)% y' = (0.97 ± 0.44 ± 0.31)%
384 fb−1 near Υ(4S) resonance
2007 CDF (Run II)
 RB = (0.415 ± 0.010)% RD = (0.304 ± 0.055)% x' 2 = (−0.012 ± 0.035)% y' = (0.85 ± 0.76)%
1.5 fb−1 at √s = 1.96 TeV (Tevatron)

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D0 → K+ π π 0 and K+ π π + π results for: R B, R M, <R D>, and α<y'>, where <…> denotes a quantity integrated (or averaged) over the selected phase-space region of the Dalitz plot, and α is a suppression factor in the range (0,1) arising from strong phase differences over the Dalitz plot. For D0 → K+ π π 0 there is a strong phase difference δKππ (analogous to δ in D0 → K+ π decays): x" ≡ x cosδKππ + y sin δKππ, y" ≡ y cosδKππ - x sin δKππ. These results assume no CPV.

Year Experiment Result Comment
2005 Belle
 RB(K + π − π 0) = (0.229 ± 0.015 +0.013 −0.009 )% RB(K + π − π + π− ) = (0.320 ± 0.018 +0.018 −0.013 )%
281 fb−1 near Υ(4S) resonance
2006 BaBar
 RB(K + π − π 0) = (0.214 ± 0.008 ± 0.008)% RM = (0.023 +0.018 −0.014 ± 0.004)% = (0.164 +0.026 −0.022 ± 0.012)% α = (−0.012 +0.006 −0.008 ± 0.002)%
230.4 fb−1 near Υ(4S) resonance
2006 BaBar
 RM = (0.019 +0.016 −0.015 ± 0.002)% α = (− 0.6 ± 0.5 ± 0.1)%
230.4 fb−1 near Υ(4S) resonance
2008 BaBar
 x"(K + π − π 0) = (2.61 +0.57 −0.68 ± 0.39)% y"(K + π − π 0) = (−0.06 +0.55 −0.64 ± 0.34)%
384 fb−1 near Υ(4S) resonance

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D0 → K0S π+ π results. These results assume no CPV; for results allowing for CPV click here

Year Experiment Result Comment
2005/2007 CLEO II.V
 x = (1.9 +3.2 −3.3 ± 0.4 ± 0.4)% y = (−1.4 ± 2.4 ± 0.8 ± 0.4)%
 9.0 fb−1 near Υ(4S) resonance; The errors are statistical, experimental systematic, and decay model systematic, respectively.
2007 Belle
 x = (0.80 ± 0.29 ± 0.17)% y = (0.33 ± 0.24 ± 0.15)%
540 fb−1 near Υ(4S) resonance
COMBOS average
 x = (0.811 ± 0.334 )%   CL = 0.74 y = (0.309 ± 0.281 )%   CL = 0.50
 (output for x)   (output for y) symmetrized statistical, systematic errors; stat. and syst. errors assumed uncorrelated

Plot of x average:                                                                                     Plot of y average:

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Ψ(3770) → D0-D0 results, using correlations. The upper measurements are obtained from a fit that uses externally measured branching fractions as input, but no externally measured mixing parameters; the lower measurement is obtained from a fit that uses (in addition to branching fractions) externally measured values of RM and RD.

Year Experiment Result Comment
2008 CLEOc
 R M y R D √RD cos δ
 (0.199 ± 0.173 ± 0)% (−5.207 ± 5.571 ± 2.737)% (−2.395 ± 1.739 ± 0.938)% (8.878 ± 3.369 ± 1.579)%
0.281 fb−1 at Ψ(3770) resonance
cos δ 1.10 ± 0.35 ± 0.07
 Due to external inputs RM and RD, this is not used in HFAG fits