Fit results for D0- D0 Mixing
(allowing for CP violation)

 

People working on this:   David Asner, Bostjan Golob, Brian Petersen, Milind Purohit, Alan Schwartz
For a complete list of references click here
For world average values of measured observables (used below) 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 δ2 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 → Kn(π) − δ D0 → Kn(π) .


Allowing for CP violation, there are a total of 8 underlying parameters:   x, y, δ, δ 2 , R D, A D, |q/p|, and φ From all experiments, there are currently 26 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 ,   (x) K+ π π 0 ,   (y) K+ π π 0 ,   (R M ) K+ π π + π ,   (R M ) Ψ(3770) ,   (y) Ψ(3770) ,   (R D ) Ψ(3770) ,   (R D 1/2 cos δ) 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 in blue (on the left sides of the equations), the underlying parameters in magenta (on the right sides), and intermediate variables in black.

 

Observables used:


Index Observable Value Source
1 y CP (1.132 ± 0.266)% World average (COMBOS combination)   of D0 → K+ K / π+ π results
2 A Γ (0.123 ± 0.248)% World average (COMBOS combination)   of D0 → K+ K / π+ π results
(3-5)
6
x (no CPV)
y (no CPV)
|q/p| (no dCPV)
Arg(q/p)=φ (no dCPV)
 
 
x
y
|q/p|
φ
(0.811 ± 0.334)%
(0.309 ± 0.281)%
0.95 ± 0.22 +0.10 −0.09
(−0.035 ± 0.19 ± 0.09) radians
 
(0.81 ± 0.30 +0.13 −0.17 )%
(0.37 ± 0.25 +0.10 −0.15 )%
0.86 ± 0.30 +0.10 −0.09
(−0.244 ± 0.31 ± 0.09) radians
  No CPV:   World average (COMBOS combination)   of D0 → K0 π+π results  

CPV-allowed:   Belle   D0 → K0 S π+ π results; correlation coefficients:
1   −0.007   −0.255α   +0.216
−0.007   1   −0.019α   −0.280
−0.255α   −0.019α   1   −0.128α
+0.216   −0.280   −0.128α   1
(Note: α = (|q/p|+1)2/2 is a variable transformation factor)

7 R M (0.0173 ± 0.0387)% World average (COMBOS combination)   of D0 → K+l ν results
8
x"
y"
(2.39 ± 0.61 ± 0.32)%
(−0.14 ± 0.60 ± 0.40)%
BaBar   K+ π π 0 result; correlation coefficient = −0.34.
Note: x" = x cos δ2 + y sin δ2,   y" = y cos δ2 − x sin δ2.
9 R M (0.019 ± 0.0161)% BaBar   K+ π π + π result
10
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)%
CLEOc   Ψ(3770) results; correlation coefficients:
1   −0.0644   0.0072   0.0607
−0.0644   1   −0.3172   −0.8331
0.0072   −0.3172   1   +0.3893
0.0607   −0.8331   +0.3893   1
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, δ2, 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 = (0.97 +0.27 −0.29 )%,                     y = (0.78 +0.18 −0.19 )%,

                                                    δ = (0.38 +0.20 −0.22 ) radian,         δ2 = (0.57 +0.44 −0.45 ) radian,

                                                    R D = (0.335 ± 0.009)%,                     A D = (−2.2 ± 2.5)%,

                                                    |q/p| = 0.86 +0.18 −0.15   ,                     φ = (−0.17 +0.14 −0.16 ) radians.

MIGRAD correlation coefficients:

χ 2 contributions:

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MNCONTOUR-like 2-d plots:

 

           

 

 

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

 

           

 

           

 

           

 

 


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