Results for D0- D0 Mixing:
World Averages

 

People working on this:   Alan Schwartz, Bostjan Golob
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 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 measurements and their world averages are presented here:

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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 (click on for high resolution):

 

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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
2009 Belle
y CP = (0.11 ± 0.61 ± 0.52)%
673 fb−1 near Υ(4S) resonance, D → (K+K) K0 decays
2012 LHCb y CP = (0.55 ± 0.63 ± 0.41)% 29 pb−1 at √s = 7 TeV (LHC 2010)
2012 BaBar
y CP = (0.72 ± 0.18 ± 0.12)%
A Γ = (0.09 ± 0.26 ± 0.06)%
468 fb−1 near Υ(4S) resonance
2012 Belle
y CP = (1.11 ± 0.22 ± 0.11 )%
A Γ = (−0.03 ± 0.20 ± 0.08 )%
976 fb−1 (full Belle data set)
2013 LHCb
A Γ (K+K) = (−0.035 ± 0.062 ± 0.012)%
A Γ +π) = (0.033 ± 0.106 ± 0.014)%
1 fb−1 at √s = 7 TeV (LHC 2011)
  COMBOS average
y CP = (0.866 ± 0.155 )%
CL = 0.464
A Γ = (−0.014 ± 0.052 )%
CL = 0.927
( output for y CP )   ( output for A Γ )
symmetrized statistical and systematic errors;
stat. errors for two Belle analyses have correl.= 0.0165.

            Plot of y CP average (click on for high resolution):                                     Plot of A Γ average (click on for high resolution):

               

 

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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 )% 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
2013 Belle RB(K + π π + π ) = (0.324 ± 0.008 ± 0.007)% 791 fb−1 near Υ(4S) resonance

 

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D0 → K0S π+ π and D0 → K0S K+ K Dalitz plot 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
2010 BaBar
x = (0.16 ± 0.23 ± 0.12 ± 0.08)%
y = (0.57 ± 0.20 ± 0.13 ± 0.07)%
468.5 fb−1 near Υ(4S) resonance
  COMBOS average
x = (0.419 ± 0.211 )%   CL = 0.30
y = (0.456 ± 0.186 )%   CL = 0.63
(output for x)   (output for y)
symmetrized statistical, systematic errors;
stat. and syst. errors assumed uncorrelated

            Plot of x average (click on for high resolution):                                           Plot of y average (click on for high resolution):

               

 

 

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Ψ(3770) → D0-D0 results, using correlations. These results are from CLEO-c's 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, yCP, x'2, y' etc. (as measured by other experiments) are used in the fit. HFAG does not use the Extended results.


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
818 pb−1 at Ψ(3770) resonance

 

 


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