Results for D⁰- D⁰ Mixing: World Averages
(through 25 July 2020)

People working on this:   Alan Schwartz
For a complete list of references click here
For results of the global fit to all observables, 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 measurements and their world averages are presented here:

• 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 cos φ − (1/2)(|q/p| − |p/q|) x sin φ, and
                                              A _Γ = (1/2)(|q/p|−|p/q|) y cos φ −(1/2)(|q/p|+|p/q|) x sin φ     (here)
• D⁰ → K⁰_S ω, D⁰ → K⁺ K⁻ K⁰ :   constraint on y _CP     (here)
• D⁰ → K⁺ π ⁻ π ⁰ and K⁺ π ⁻ π ⁺ π ⁻ :
    constraints on R _B, R _M, <R _D>, α<y'>, x" ≡ x cos δ_Kππ + y sin δ_Kππ, and y" ≡ y cos δ_Kππ - x sin δ_Kππ     (here)
• Ψ(3770) → D⁰-D⁰ reactions :   constraints on R_D, x², y, cos δ, and sin 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 (click on for high resolution):

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
2009	Belle	y CP = (0.11 ± 0.61 ± 0.52)%	673 fb−1, D0 → (K+K−) K0 decays
2012	BaBar	y CP = (0.72 ± 0.18 ± 0.12)% A Γ = (0.09 ± 0.26 ± 0.06)%	468 fb−1, D0 → K+K−, π+π− decays
2014	CDF	A Γ (K+K−) = (−0.19 ± 0.15 ± 0.04)% A Γ (π+π−) = (−0.01 ± 0.18 ± 0.03)% A Γ (combined) = (−0.12 ± 0.12)%	9.7 fb−1 at √s = 1.96 TeV
2015	BESIII	y CP = (−2.0 ± 1.3 ± 0.7)%	2.92 fb−1 at √s = 3.773 GeV
2016	Belle	y CP = (1.11 ± 0.22 ± 0.09 )% A Γ = (−0.03 ± 0.20 ± 0.07 )%	976 fb−1, D0 → K+K−, π+π− decays
2019	LHCb	y CP = (0.57 ± 0.13 ± 0.09)%	3.0 fb−1 at √s = 7, 8 TeV
2020	LHCb	A Γ (K+K−) = (−0.044 ± 0.023 ± 0.006)% A Γ (π+π−) = (0.025 ± 0.043 ± 0.007)% A Γ (combined) = (−0.029 ± 0.020 ± 0.006)%	8.4 fb−1 pp collisions at √s = 7, 8, 13 TeV D*+ → D0π+ flavor tag + B → D0μ− X flavor tag
2020	Belle	y CP = (0.96 ± 0.91 ± 0.61 +0.17−0.00)%	976 fb−1, D0 → K0S ω decays
	COMBOS average	y CP = (0.719 ± 0.113 )% CL = 0.21 A Γ = (−0.0309 ± 0.0204 )% CL = 0.86	( output for y CP )   ( output for A Γ ) symmetrized statistical and systematic errors;

            Plot of y _CP average (click on for high resolution):                                     Plot of A _Γ average (click on for high resolution):

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	RWS(K + π − π 0) = (0.229 ± 0.015 +0.013 −0.009 )%	281 fb−1 near Υ(4S) resonance
2006	BaBar	RWS(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
2013	Belle	RWS(K + π − π + π− ) = (0.324 ± 0.008 ± 0.007)%	791 fb−1 near Υ(4S) resonance
2016	LHCb	RM(K + π − π + π− )/2 = (0.0048 ± 0.0018)%	3.0 fb−1 pp collisions at √s = 7, 8 TeV

Ψ(3770) → D⁰-D⁰ results, using correlations:
The CLEO-c results are from their Standard fit, in which no external constraints are used in the fit. CLEO-c also quotes results from an Extended fit, in which external constraints for x, y, y_CP, x'², y' etc. (as measured by other experiments) are used in the fit. HFLAV does not use the Extended results.

The BESIII result uses external constraints for r², R_M, and y (as measured by other experiments), and thus HFLAV does not use this result in its global fit.

Year	Experiment	Parameter	Fit Result	Comment
2012	CLEO-c	R D x 2 y cos δ sin δ	(0.533 ± 0.107 ± 0.045)% (0.06 ± 0.23 ± 0.11)% (4.2 ± 2.0 ± 1.0)% 0.81 +0.22−0.18 +0.07−0.05 −0.01 ± 0.41 ± 0.04	0.82 fb−1 at Ψ(3770) resonance
2014	BESIII	cos δ	1.02 ± 0.11 ± 0.06 ± 0.01	2.92 fb−1 at Ψ(3770) resonance