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

People working on this:   David Asner, Bostjan Golob, Alan Schwartz
For a complete list of references click here



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 δ_Kππ 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 = (m_CP+ − m_CP−)/Γ, y = (Γ_CP+ − Γ_CP−)/(2Γ), and δ = δ _{D⁰ → K⁺n(π)} − δ _{D⁰ → K⁺n(π)} .


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

• D⁰ → K⁺l⁻ ν :   constraint on R _M ≡ (x²+y²)/2     (here)
• D⁰ → K⁺ K⁻, π⁺ π⁻ :   constraints on y _CP = (1/2)(|q/p| + |p/q|) y cosφ − (1/2)(|q/p| − |p/q|) x sin φ, and
                                              A _Γ = (1/2)(|q/p|−|p/q|) y cosφ −(1/2)(|q/p|+|p/q|) x sin φ     (here)
• D⁰ → K⁺ K⁻ K⁰ :   constraint on y _CP     (here)
• D⁰ → K⁺ π ⁻ :   constraints on R _D, x' ≡ x cosδ + y sin δ, and y' ≡ y cosδ - x sin δ     (here)
• D⁰ → K⁺ π ⁻ π ⁰ and K⁺ π ⁻ π ⁺ π ⁻ :   constraints on R _B, R _M, <R _D>, α<y'>, x" ≡ x cosδ_Kππ + y sin δ_Kππ, and y" ≡ y cosδ_Kππ - x sin δ_Kππ     (here)
• D⁰ → K⁰_S π⁺ π ⁻ :   constraints on x and y     (here)
• Ψ(3770) → D⁰-D⁰ reactions :   constraints on R _M, y, R_D, and √R_D cos δ; using external input for R_M and R_D, a constraint on cos δ     (here)

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 π −N 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:

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 π −N 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:

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 π −N 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)

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 δ_Kππ (analogous to δ in D⁰ → K⁺ π ⁻ decays): x" ≡ x cosδ_Kππ + y sin δ_Kππ, y" ≡ y cosδ_Kππ - x sin δ_Kππ. 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)% <RD(K + π − π 0) > = (0.164 +0.026 −0.022 ± 0.012)% α<y'(K + π − π 0) > = (−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<y'(K + π − π+ π−)> = (− 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

D⁰ → K⁰_S 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:

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 R_M and R_D.

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