Results for D0- D0 Mixing

(allowing for CP violation)

People working on this:   David Asner, Bostjan Golob, Brian Petersen, Alan Schwartz

For a complete list of references click here

For mixing results assuming no CP violation 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; and δ (φ) is the strong (weak) phase difference between D0 → f and D0 → f amplitudes.

Allowing for CPV, there are a total of 7 underlying parameters:   x, y, δ, R D, A D, |q/p|, and φ

From all experiments, there are currently 22 observables:   y CP ,   A Γ ,   x K0S π+ π ,   y K0S π+ π ,   |q/p| K0S π+ π ,   Arg(q/p) = φ K0S π+ π   (R M ) semileptonic ,   (R M ) K+ π π 0 ,   (R M ) K+ π π + π ,   (R M ) Ψ(3770) ,   (R D) BaBar ,   (A D) BaBar ,   (x'±, y'±) BaBar ,   (R D) Belle ,   (A D) Belle ,   (x'±, y'±) Belle ,

The relationships between these observables and the underlying parameters are given below; the observables appear on the left sides of the equations (in blue), and the underlying parameters on the right sides (in purple).

 

 

Observables used:


Index Observable Value Source
1 y CP (1.12 ± 0.32)% World average (COMBOS combination)   of D0 → K+ K / π+ π results
2 A Γ (−0.17 ± 0.30)% World average (COMBOS combination)   of D0 → K+ K / π+ π results
3 x (0.811 ± 0.334)% World average (COMBOS combination)   of D0 → K0 S π+ π results
4 y (0.309 ± 0.281)% World average (COMBOS combination)   of D0 → K0 S π+ π results
5 |q/p| 0.860 ± 0.316 Belle   D0 → K0 S π+ π results
6 Arg(q/p) (−0.244 ± 0.333) radians Belle   D0 → K0 S π+ π results
7 R M (0.0173 ± 0.0387)% World average (COMBOS combination)   of D0 → K+l ν results
8 R M (0.023 ± 0.01844)% BaBar   K+ π π 0 result
9 R M (0.019 ± 0.0161)% BaBar   K+ π π + π result
10 R M (0.17 ± 0.15)% CLEOc   Ψ(3770) result
11
RD
x' 2+
y' +
(0.303 ± 0.0189)%
(−0.024 ± 0.052)%
(0.98 ± 0.782)%
BaBar   K+ π results; correlation coefficients:
1   +0.77   −0.87
+0.77   1   −0.94
−0.87   −0.94   1
12
A D
x' 2 −
y'
(−2.1 ± 5.4)%
(−0.020 ± 0.050)%
(0.96 ± 0.75)%
BaBar   K+ π results; correlation coefficients same as above.
13
RD
x' 2+
y' +
(0.364 ± 0.018)%
(0.032 ± 0.037)%
(−0.12 ± 0.58)%
Belle   K+ π results; correlation coefficients:
1   +0.655   −0.834
+0.655   1   −0.909
−0.834   −0.909   1
14
A D
x' 2 −
y'
(2.3 ± 4.7)%
(0.006 ± 0.034)%
(0.20 ± 0.54)%
Belle   K+ π results; correlation coefficients same as above.

 

MINUIT fit results: note that x, y, R D, and A D are in percent; δ and φ are in radians.

Fit #1, no CP violation (AD=0, |q/p|=1, φ=0, fixed):

 

Fit #2, no direct CP violation (AD=0, fixed):

 

Fit #3, allowing direct CP violation (i.e., all parameters floated):

 

The final results allowing for CPV are:

                                                    x = (0.84 +0.32 −0.34 )%,         y = (0.69 ± 0.21)%,         δ = (0.38 +0.27 −0.29 ) radians,

                                                    R D = (0.335 ± 0.011)%,         A D = (−0.76 ± 3.10)%,

                                                    |q/p| = 0.88 +0.23 −0.20   ,         φ = (−0.09 +0.17 −0.19 ) radians.

MIGRAD correlation coefficients:

χ 2 contributions:

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MNCONTOUR 2-d plots:   no CPV   plot can be compared with method combining log-likelihood functions (here) , which accounts for non-Gaussian likelihoods.

 

           

 

 

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"MNCONTOUR" 1-d plots:   red dashed horizontal line denotes Δχ 2 = 2.70, corresponding to 90% C.L. Cusp points in φ plot result from multiple solutions.

 

           

 

           

 

 

Last modified 3 December 2007. Send comments to A. Schwartz or M. Purohit