1. Our Parametrization of D0K-K+0 Dalitz Plot
D0 decay three-body amplitude
 (1020) 
A =  
m2(K+0) (GeV2/c4)
ar, δr : Free parameters of fit 
K*+
Angular distribution
Blatt-Weisskopf form factors
K*-
m2(K-0) (GeV2/c4)
Define amplitude for the D0K-K+0 decay as:
Relativistic
Breit-Wigner
PDF for signal events = | f |2
Flatte: f0 / a0(980)
Kalanand Mishra

2. I=1/2 K S-wave Parameterization
Nucl. Phys. B296, 493 (1988);
LASS Amplitude for K-+ K-+ scattering.
K-+ amplitude extracted from a model-independent partial-wave   analysis of D+K-++ decay by the E791 collaboration.
Phys. Rev. D73, (2006);
Normalized to arbitrary scale for m(K)>1.15 Gev/c2 for easy comparison.   
- 800
E-791
LASS
Kalanand Mishra

3. LASS I=1/2 K S-wave Parameterization
Kπ S-wave amplitude is described by the coherent sum of an effective range term and the K*0(1430) resonance:
S(s) = (√s/ p). sin . ei
 = cot-1 [ 1/ap + rp/2 ] cot -1 [ (m2R-s)/(mR R ) ]
Effective Range (NR) term K*0(1430) resonance term
a = scat. length, r = eff. range, mR = mass of K*0(1430), R= width
p = momentum of either daughter in the Kπ rest frame.
Phase
space
factor
For K scattering, S-wave is elastic up to K' threshold (1.45 GeV).
Kalanand Mishra

4. [ E791 Collaboration, slide from Brian Meadow’s Moriond 2005 talk ]
K S-wave from D0K-++ DP
[ E791 Collaboration, slide from Brian Meadow’s Moriond 2005 talk ]
Divide m2(K-+) into slices
Find s–wave amplitude in each slice (two parameters)
Use remainder of Dalitz plot as an interferometer
For s-wave:
- Interpolate between (ck,k).
Model P and D waves.
Phys. Rev. D73, (2006); hep-ex/
S (“partial wave”)
Kalanand Mishra

5. FOCUS Parametrization of D+K-++ Dalitz Plot
D+ decay three-body amplitude
Relativistic
Breit-Wigner
aj, δj : Free parameters of fit
K S-wave: I =1/2, 3/2
Production Vector
K-Matrix formulation
K-Matrix parameters
are derived from scattering data and Chiral Perturbation Theory (ChPT). 
Kalanand Mishra

6. K-Matrix Parametrization
g1, g2 are coupling constants for K and K’ channels
Normalization constant
Adler pole for I=1/2
Fit LASS and Kscattering data (from SLAC, 1978) simultaneously for 12 parameters: c11i, c12i, c22i, d12i, where i = 0, 1, 2.
Expansion variable
Adler pole for I=3/2
Kalanand Mishra

7. Use LASS data to get K S-wave Parameters
Extends down to threshold using ChPT
Kalanand Mishra

8. Parametrization of Production vector “P”
Fit the FOCUS data for 9 parameters: c1i , c2i , c3i , where i = 0, 1, 2
Kalanand Mishra