Results for D⁰- D⁰ Mixing: World Averages
(through 24 September 2023)

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 → 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	Belle	y CP = (0.96 ± 0.91 ± 0.61 +0.17−0.00)%	976 fb−1, D0 → K0S ω decays
2021	LHCb	A Γ (K+K−) = (0.003 ± 0.013 ± 0.003)% A Γ (π+π−) = (0.036 ± 0.024 ± 0.004)% A Γ (combined) = (0.010 ± 0.011 ± 0.003)%	8.4 fb−1 pp collisions at √s = 7, 8, 13 TeV D*+ → D0π+ flavor tag + B → D0μ− X flavor tag
2022	LHCb	y CP (K+K−) − y CP (Kπ) = (0.708 ± 0.030 ± 0.014)% y CP (π+π−) − y CP (Kπ) = (0.657 ± 0.053 ± 0.016)% y CP − y CP (Kπ) (combined) = (0.696 ± 0.026 ± 0.013)%	6 fb−1 pp collisions at √s = 13 TeV D*+ → D0π+ flavor tag
	Weighted average	y CP − y CP (Kπ) = (0.697 ± 0.028 )% A Γ = (0.0089 ± 0.0113 )%	( COMBOS output for A Γ ) symmetrized statistical and systematic errors