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

               

 

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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)%
<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

 

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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. 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

 

 


This page is maintained by A. Schwartz and was last updated