Transcript QCD - Istituto Nazionale di Fisica Nucleare

Recent Results from FOCUS
Sandra Malvezzi
I.N.F.N. Milano
QCD 2005
Conversano 16 -20 June 2005
How charm can still be charming
• Charm physics is a paradigm of how
– precise measurements have led to a revival of the sector
• New Physics search: Mixing, CPV, rare and forbidden decays
• Spectroscopy of high-mass states (“the renaissance of spectroscopy”)
– sophisticated investigations
(typical of a mature field, under study over various decades)
• Dalitz plot analyses, Semileptonic Form-Factor measurements...
have revealed limits in the “standard” approach
precisely
• QCD effects in charm weak decays can complicate the analysis
and the phenomenological interpretation of the results requiring
a new direction/approach in the decay dynamics investigation
–
What experimentalists have learnt so far
• Goals:
– Proper tools for present/future precise high-statistics studies of
charm and beauty hadrons
– coherent description of FSI in Beauty - Charm decays and &
Light hadron sector (hopefully)
– Synergy between experimentalists and theorists
• FOCUS has played a pioneering role in various analyses
FOCUS role
• Lifetime hep-ex/0504056 A Measurement of the Ds+ Lifetime
• Mixing hep-ex/0501006 D0-D0 hadronic mixing and DCS decays
(the best charm mixing limit from a fixed-target exp)
•
•
•
•
•
•
•
Pentaquark hep-ex/0506013 Pentaquark search (Null) 0c  D(*) p
Rare & forbidden decays
Semileptonic
Hadronic decays (Dalitz plot)
Multi-body channels (4,5,6 bodies)
Charm Baryons
D* spectroscopy hep-ex/0406044- hep-ex/0312060
Charm lifetimes
Ds 0.5074  0.0055  0.0051
 ( Ds )
 1.239  0.014  0.009
 ( D0 )
Bigi Uraltsev
1.00-1.07 (no WA/WX)
0.8-1.27 (different process
interference)


(
D
)
(*) FOCUS
 2.54  0.02
0
(○) PDG 2002  ( D )
1
1

 ( )   ( D )   ( c )
15
3
0
c
Charm mixing circa 2000
Time evolution
of wrong-sign
D* decay
2 sigma hints of
mixing at few
percent level!
D*    D 0
    K   
d
(K) =
409.4  1.34 ps
CP lifetime
comparisons
(KK) =
395.4  5.5 ps
Some intriguing results.....not conclusive!
Mixing circa 2003
Things have come a long way
since those heady days...
B-factories are leading the game
It will be
interesting to see
if mixing does
occur at the
percent level.
2004-2005: data continue....
Belle : hep-ex/0408125
FOCUS
hep-ex/0501006
Phys. Lett. B 618 - 23
....agrees better with
BaBar & Belle
than with the
old CLEO contour
More and more
stringent limits!
The best mixing limit from a
fixed-target experiment:
a valuable check
FOCUS has the world’s most accurate lifetime
measurements and excellent lifetime-resolution.
Decay dynamics investigation
• .....The semileptonic sector
New results on D  K

Our K spectrum looks
like 100% K*(892)
This has been
known for about
20 years
...but a funny thing happened when we tried to measure the form factor ratios
by fitting the angular distributions
Decay is very accessible to theory
Assuming the K spectrum contains nothing but K*, the decay rate
is straight-foreward
An unexpected asymmetry in the K* decay
A 4-body decay requires
5 kinematics variables: 3 angles
and 2 masses
2
MW 2  q  t
M K
-15 % F-B
asymmetry
matches
model
d
 1  cos 2 V
d
forward-backward
asymmetry in
cos V below the K*
pole but almost none
above the pole
Sounds like
QM interference
Try an interfering spin-0 amplitude
Phys.Lett.B535,43,2002
2
(1  cos l ) sin V i 
e BH 
2 2
(1  cos l ) sin V  i
2
2
(plus mass terms)
M  (t  m  ) 
e BH 
2 2
 sin l (cos V B  Aeiδ ) H 0

2
m0
Aeid will produce
B 2
3 interference terms
m  m2  im 
0
H0(q2), H+(q2), H-(q2) are helicity-basis form factors computable by LQCD...
0
F-B asymmetry
M K
• K*  interferes with S- wave K and creates a forwardbackward asymmetry in the K* decay angle with a mass variation
due to the varying BW phase
•The S-wave amplitude is about 7% of the K* BW with a
45o relative phase
•D+ K is the natural place to study the K system in the absence
of interactions with other hadrons. Due to Watson’s theorem the
observed K phase shift should be the same as those measured in
elastic scattering
The S & P waves from LASS

Most information on K-+ scattering comes from the
LASS experiment (SLAC, E135) Aston et al., Nucl. Phys. B296 (1988) 493
PWA
by LASS
892 MeV/c2
The phase difference between S & P wave at K*(892) pole from LASS
is ~ 45 degrees!.
A broad Breit-Wigner amplitude ( the controversial k(900))?
4000
mK
k(900) with no fsi phase shift
and with a 100 degree phase
shift.
2000
0
-2000
-4000
FOCUS fit
LASS Scaled fit
Kappa
Kappa
-6000
0.8 0.82 0.84 0.86 0.88 0.9 0.92 0.94 0.96 0.98
1
cos v weighted M(K), GeV/c2
hep-ex/0503043 Hadronic Mass Spectrum Analysis of D+ K Decay
and Measurementof the K*(892)0 Mass and Width in FOCUS
Additional checks: k(900) is not required
D  K Form Factors

d 5
 f (H  , H0 , Ht )
2
dmK dq d cos V d cos  d 
H  ,0,t (q 2 )  g  A1,2,3 (q 2 ),V (q 2 )) 
The vector and axial form factors are generally
parametrized by a pole dominance form
D+
Ai (0)
V (0)
2
Ai (q ) 
1  q 2 M 2 A V (q )  1  q 2 M 2
d
2
V
Two numbers
parameterize
the decay
rv  V (0) A1 (0)
r2  A2 (0) A1 (0)
s
u
u
d
M A  2.5
GeV / c 2
MV  2.1 GeV / c 2
Nominal spectroscopic
pole masses
Group
rv
r2
Phys.Lett.B 544(2002) 89
FOCUS
1.504  0.057  0.039 0.875  0.049  0.064
BEATRICE
1.45  0.23  0.07
1.00  0.15  0.03
E 791(e)
1.90  0.11  0.09
0.71  0.08  0.09
E 791(  )
1.84  0.11  0.09
0.75  0.08  0.09
E 687
1.74  0.27  0.28
0.78  0.18  0.11
E 653
2.00  0.33  0.16
0.82  0.22  0.11
E 691
2.0  0.6  0.3
0.0  0.5  0.2
•Our analysis is the first to include the effects on the acceptance due to changes in
the angular distribution brought about by the S-wave interference
•The inclusion of the S-wave amplitude dramatically improved the quality of the
Form-Factor Fit
• Form -factor lattice calculation (Damir Becirevic ICHEP02) RV = 1.55  0.11
is remarkably close to the FOCUS result.
Decay dynamics investigation ..cont’d
• .....The hadronic sector
– Dalitz-plot analysis of D decays
Dalitz Analysis of Heavy Flavour Decays
• Powerful tool!
– It provides a “complete observation” of the decay
– Everything could be in principle measured
• from the dynamical features of the HF decay mechanism
– Relative importance of non-spectator processes
• up to the CP-violating phases, mixing, etc
– Just recall  from Bo and gf3 from B   D(*)K
• We have already learnt a lot about charm
Recent articles (the Dalitz-plot revenge)
• hep-ex/0503052 Searches for CP violation and  S-wave in
the Dalitz Plot analysis of D0++0 (CLEO)
• hep-ex/0503045 Search for D0 - D0 Mixing in the Dalitz Plot
Analysis of D0 KS0 + - (CLEO)
• hep-ex/0504039 Measurement of g in B  D(*)K decays
with a Dalitz analysis of D  KS0 + - (BaBar)
• hep-ex/0504013 Measurement of f3 with Dalitz Plot
Analysis of B   D(*)K Decay (Belle)
• hep-ex/0408099 Measurement of CP-Violating Asymmetries
in B0 ()0 Using a Time-Dependent Dalitz Plot Analysis
( BaBar)
Sophisticated studies both in charm & beauty
I will
• Address key issues of the Heavy Flavour Dalitz analysis
– Formalization problems
• Failure of the traditional “isobar” model
• Need for the K-matrix approach
– Implications for the future Dalitz analyses in the B-sector
• Discuss these issues in the context of the recent Ds+,
D++-+ Dalitz analysis we performed in FOCUS
Formalization Problems
Dr 3
|
12
2
3
r
1
• The problem is to write the propagator for the
resonance r
– For a well-defined wave with specific isospin and
spin (IJ) characterized by narrow and wellisolated resonances, we know how.
•the propagator is of the simple Breit-Wigner type
•the decay amplitude is
A  FD Fr  p1
J
p3
J
PJ (cos 13r ) 
F 1
F  (1  R 2 p 2 ) 
1
2
F  (9  3R 2 p 2  3R 4 p 4 ) 
1
2
mr2  m12 2  imr r
Spin 0
PJ  1
Spin 1
PJ  (2 p3  p1 )
Spin 2
PJ  2( p3 p1 ) 2 (3 cos 2 13  1)
•the decay matrix element
M   a je A j
id j
j
1
In contrast
when the specific IJ–wave is characterized by large and heavily
overlapping resonances (just as the scalars!), the problem is not
that simple.
Indeed, it is very easy to realize that the propagation is no longer
dominated by a single resonance but is the result of a complicated
interplay among resonances.
In this case, it can be demonstrated on very general grounds that the
propagator may be written in the context of the K-matrix approach as
( I  iK   )1
where K is the matrix for the scattering of particles 1 and 2.
i.e., to write down the propagator we need to know the related
scattering K-matrix
E.P.Wigner,
What is K-matrix? Phys. Rev.
70 (1946) 15
S.U. Chung et al.
Ann. Physik 4 (1995) 404
• It follows from S-matrix and, because of S-matrix
unitarity, it is real
S  I  2i  T 
1/ 2
K  T  i
1
1
1/ 2
T  ( I  iK   ) K
1
• Viceversa, any real K-matrix would generate an unitary
S-matrix
• This is the real advantage of the K-matrix approach:
– It (heavily) simplifies the formalization of any scattering
problem since the unitarity of S is automatically
respected.
From Scattering to Production
• Thanks to I.J.R. Aitchison (Nucl. Phys. A189 (1972) 514), the
K-matrix approach can be extended to production processes
• In technical language,
– From
T  ( I  iK   ) K
– To
F  ( I  iK   ) P
1
1
• The P-vector describes the coupling at the production with
each channel involved in the process
– In our case the production is the D decay
K-Matrix Picture of D++-+


1  
D
2  KK
P
3  Multi  body
4 = 
(1  iK  )1

5   '
F  ( I  iK   ) P
1
Describes coupling
of resonances to D
Known from Scattering Data
Beside restoring the proper dynamical features of the resonances, it allows for the
inclusion of all the knowledge coming from scattering experiments: enormous
amount of results and science!
• For a single pole problem, far away of any threshold,
K-matrix amplitude reduces to the standard BW formula
• The two descriptions are equivalent
• In all the other cases, the BW representation is not any
more valid (limit of the traditional isobar model!!!)
• The most severe problem is that it does not respect
unitarity
Add BW
Add BW
Add K
Adding BWs ala
“traditional Isobar Model”
–Breaks the Unitarity
Add K
–Heavily modify the
phase motion!
The Unitarity circle
Summarizing
The decay amplitude may be written, in general, as a coherent sum
of BW terms for waves with well-isolated resonances plus
K-matrix terms for waves with overlapping resonances.
A( D)  a0e
id 0
m
  ai e Fi
i 1
id i
BW

n
 ae
i  m 1
i
id i
Fi
K
Can safely say that in general K-matrix formalization is just
K
required by scalars (J=0), whose general Fi form is

2



g
1

s
(
s

s
m


 j
K
1
0
A  / 2)(1  s A 0 )
Fk  ( I  iK   ) kj  2
 fj

s  s0 
( s  s A0 )

  m  s

Where can we get a reliable  S-wave
scattering parametrization from?
• In other words, we need to know K to proceed.
• A global fit to (all) the available data has been performed
“K-matrix analysis of the 00++-wave in the mass region below 1900 MeV’’
V.V Anisovich and A.V.Sarantsev Eur.Phys.J.A16 (2003) 229
p00n,n, ’n, |t|0.2 (GeV/c2)
p00n, 0.30|t|1.0 (GeV/c2)
p-  KKn
:
*
*
*
*
*
*
*
*
*
GAMS
GAMS
BNL
CERN-Munich
Crystal Barrel
Crystal Barrel
Crystal Barrel
Crystal Barrel
E852
  
pp  000, 00 , 0
pp  000, 00
pp  0, K+K-0, KsKs0, K+Ks
np  00-, , KsK-0, KsKs-p00n, 0|t|1.5 (GeV/c2)
H2
At rest, from gaseous H 2
At rest, from liquid H 2
At rest, from liquid D2
At rest, from liquid
An impressive amount of data is well described in terms of 5 poles
( )
( )
scatt

g
g
1

s
i
j
0
Kij00 ( s)    2
 fijscatt
scatt
  m s
s

s

0

KijIJ
 ( s  s A m2 2)(1  s A0 )

( s  s A0 )

is a 5x5 matrix (i,j=1,2,3,4,5)
A&S
1=, 2=K K 3=4 4=  5=  '
gi ( ) is the coupling constant of the bare state  to the meson channel
fijscatt and
s0 describe a smooth part of the K-matrix elements
(s  sAm2 2)(1  sA0 ) (s  sA0 )
suppresses the false kinematical singularity
at s = 0 near the  threshold
A&S T-matrix poles and couplings
(m ,  / 2)
g
g KK
(1.019, 0.038) 0.415 e i 13.1 0.580 e i 96.5
(1.306, 0.167) 0.406 e i 116.8 0.105 e i 100.2
g 4
0.1482 e i 80.9
0.8912 ei 61.9
g
g '
0.484 e i 98.6 0.401 e i 102.1
0.142 e i 140.0 0.225 e i 133.0
(1.470, 0.960) 0.758 e i 97.8 0.844 e i 97.4 1.681 e i 91.1 0.431 e i 115.5 0.175 e i 152.4
(1.489, 0.058) 0.246 e i 151.5 0.134 e i 149.6 0.4867 ei 123.3 0.100 ei 170.6 0.115 ei 133.9
(1.749, 0.165) 0.536 e i 0. 0.072 e i 3. 0.33 e i 3.6 0.160 e i 126.7 0.313 e i 101.1
•This set of poles and couplings coherently describes the  scattering.
a s object is already included ....as very well known it is not a simple
narrow BW
Can we fit our D data??
FOCUS D+  + + - analysis
Yield D+ = 1527 51
S/N D+ = 3.64
Sideband
Signal
PLB 585 (2004) 200
D   




K-matrix fit results
2
mhigh
Low mass projection
decay channel
(S - wave)π +
f 2 (1275)π +
ρ0 (770)π +
fr =


High mass projection
fit fractions (%)
phase (deg)
56.00 ± 3.24 ± 2.08
0(fixed)
11.74  1.90  0.23 -47.5  18.7  11.7
30.82 ± 3.14 ± 2.29 -139.4 ± 16.5 ± 9.9
ar e iδr A r
a je
j
iδ j
2
2
2
dm12
dm13
2
Aj
2
2
dm12
dm13
C.L fit 7.7 %
2
mlow
Reasonable fit with no retuning
of the A&S K-matrix.
No new ingredient (resonance)
required not present in the
scattering!
Isobar analysis of D+  + + would instead require
a new scalar meson: s m = 442.6± 27.0 MeV/c
 = 340.4 ± 65.5 MeV/c
With s
Without s
C.L. ~ 7.5%
C.L. ~ 10-6
What about s-meson then?
• Can conclude that
– Do not need anything more than what is already in the  S-wave phaseshift to explain the main feature of D  3  Dalitz plot
Or, if you prefer,
– Any s-like object in the D decay should be consistent with the same slike object measured in the  scattering.
• Note: B  D(*)K Dalitz plot analysis
– The model used for the D0 Ks+- decay is one of the main sources of
systematics
– Two “ad hoc” scalar states s1and s2 to describe excess of events not
reproduced by “established” resonances.
FOCUS D s+   + + - analysis
Yield Ds+ = 1475 50
S/N Ds+ = 3.41
Observe:
•f0(980)
•f2(1270)
Sideband
Signal
•f0(1500)
PLB 585 (2004) 200
D     K-matrix fit results

s



Ds     
Low mass projection
decay channel
(S - wave)π +
f 2 (1275)π +
ρ0 (1450)π +
High mass projection
fit fractions (%)
87.04 ± 5.60 ± 4.17
9.74  4.49  2.63
6.56 ± 3.43 ± 3.31
phase (deg)
0(fixed)
168.0  18.7  2.5
234.9 ± 19.5 ± 13.3
C.L fit 3 %
No three-body non-resonant contribution
Even more: from P to Q-vector
• Just by a simple insertion of KK-1 in the decay
amplitude F
F  ( I  iK  )1 P  ( I  iK  )1 KK 1P  TK 1P  TQ
• We can view the decay as consisting of an initial
production of the five virtual states , KK, ,
’ and 4, which then scatter via the physical
T-matrix into the final state.
• The Q-vector contains the production amplitude
of each virtual channel in the decay
Q-vector for Ds
• S-wave dominated by an initial production of , 
and KK-bar states
Ratio of moduli of
Q-vector amplitudes
The normalizing
 modulus
The two peaks of the ratios correspond to the two dips of the  normalizing
modulus, while the two peaks due to the K-matrix singularities, visible in the
normalization plot, cancel out in the ratios.
Q-vector for D+
• The same!
– s-wave dominated by an initial production of ,
 and KK-bar states
The resulting picture
• The S-wave decay amplitude primarily arises from a
ss-bar contribution such as that produced by
– Cabibbo favored weak diagram for Ds
– One of the two possible singly Cabibbo suppressed
diagram for D+. For the D+. the ss-bar contribution
competes with a dd-bar contribution..
• The measured fit fractions seems to confirm this
picture
– S-wave decay fraction, 87% for Ds and only 56% for D+
– The dd-bar contribution in D+ case evidently prefers to
couple to a vector state like (770), that alone accounts
for about 30% of the decay.
Conclusions
• Systematic investigation of charm decay dynamics is giving
interesting results in both semileptonic and hadronic sectors
• Dalitz plot analysis is and will be a crucial tool to extract physics
from the HF decays
– Nevertheless, to fully exploit this unlimited potential a
systematic revision of the amplitude formalization is required
• FOCUS has applied the K-matrix approach for the first
time to the HF sector
– Its application has been decisive in clearing up a situation which
recently became quite fuzzy and confusing: new “ad hoc”
resonances were required to understand data
• K-matrix allows for a rigorous coupled-channel analysis
– This will be the further step in the Dalitz analysis of HF decays
• D+, D+s f0 amplitudes can feed both 3 and KK
Conclusions...cont’d
• Strong dynamics effects in D-decays now seem under control and
fully consistent with those measured by light-quark experiments.
• The new scenario is very promising for the future measurements of
the CP violating phases in the B sector, where a proper description of
the different amplitudes is essential.
• FOCUS is now sudying the D+K-++
– High statistics sample –Test of the model
– Quasi two-body process or multi-body process ?
High momentum  combination
FOCUS D+K-
50000 events
The first charm Dalitz
analysis – MK1 (1977)
D+K
Low momentum  combination
(GeV2)
“...consistent with a phase
space Dalitz distribution.”
The future
B  D  
B  D *   
2
nodes!
1 node
D2* and D*0
We can learn even
about D* states !!
D1 , D1' and D*2
BACKUP SLIDES
• My backup
What do you learn from Dalitz plots?
•Bands indicate resonance
contributions
2
mKK
f
f
D  KK
D  KK

s
broad
states
•For spinless parents, the
number of nodes in the band
give you the resonance spin
mK2 
K *K
•Look at the f band
K *K
2
mKK
•Interference pattern gives
relative phases and
amplitudes
•Look at the D+ K* band
pattern of asymmetry
Nearly all charm
analyses use the
isobar model:
Isobar model: Add up BW’s with angular factors
M   ame Am
id m
m
A
p1
J
p3
J
PJ (cos 13r )
mr2  m12 2  imr r
CP violation on the Dalitz plot
• For a two-body decay
Atot = g1M1eid1 + g2M2eid2
CP conjugate
di = strong phase
Atot = g*1M1eid1 + g*2M2eid2
CP asymmetry:
aCP=
|Atot|2- |Atot|2
|Atot
|2+
|Atot
|2
=
2Im(g2 g1*) sin(d1-d2)M1M2
|g1|2M12+|g2|2M22+2Re(g2 g1*)cos(d1-d2)M1M2
2 different amplitudes
strong phase-shift
CP violation & Dalitz analysis
Dalitz plot = FULL OBSERVATION of the decay
COEFFICIENTS and PHASES for each amplitude
Measured phase:
=d+f
CP conserving
CP conjugate
f = -f
=d-f
aCP=0.006±0.011±0.005
Measure of direct CP violation:
asymmetrys in decay rates of DKK 

E831
d=d
CP violating
Ds , D+ KK
Ds
D
Ds+  K+ K +
D+  K+ K  +
m2 K
mKK
m2 KK
m2 K
m2 KK
m2K -π+
Decay Fraction and phases
Yield D+ = 7106 92
S/N D+ = 8.62
Preliminary
2
mK + K-
K+ K  projection
K*(892) = 20.7  1.0 %
(0 fixed)
f(1020)
= 27.8  0.7 %
(243.1 5.2)°
K*(1410) = 10.7  1.9 %
(-47.4  4.9) °
K* (1430) = 66.5  6.0 %
(61.8  3.8)°
f0(1370) = 7.0  1.1 %
(60.0  5.3) °
a0(980)
= 27.0  4.8 %
(145.6  4.3)°
f2(1270) = 0.8  0.2 %
(11.6  7.0) °
f(1680)
(-74.3  7.5) °
K   projection
= 1.6  0.4
%
Coefficients: D±, D+, D-




phi(1020) K*(1430)







a0(980) K1(1410) f2(1270)

f0(1370) phi(1680)
Phases: D±, D+, D

phi(1020)



No evidence of CPV



K*(1430) a0(980)

K1(1410)




f2(1270) f0(1370)

phi(1680)
K-matrix approach to improve the quality of the analysis
FSI effect
Watson’s theorem : weak amplitudes are relatively
real; however complex phases can be introduced by
final state interaction
0
Interference term of K * (892) and a nearly constant amplitude
cos d  isenδ
Rare & forbidden decays
D , Ds  h   
Phys.Lett. B572 (2003) 21
(h   , K )
FOCUS improved 8 results by a
factor of 1.7 –14
CDF Br(D0+-)<2.4 x10-6 @ 90% C.L.
is the best limit for this mode (65 pb-1 data)
CDF and D0 can trigger on dimuons promising
Cleo-c sensitivity 10-6
The best mixing limit from a fixed-target experiment,
a valuable check on those results
Phys. Lett. B 618 - 23
•FOCUS has the world’s most accurate lifetime measurements
and excellent ifetime-resolution.
....agrees better with BaBar & Belle
than with the old CLEO contour
( D0  K   )
RD 
( D0  K   )
(0.3810.017+0.008-0.016) %
(0.4290.063-0.061  0.027) % (FOCUS)
Additional more recent studies
hep-ex/0503043
• Search for other resonant contributions in the K spectrum
–
( D  K *(1680)0   )
( D  K     )
–
( D  K *(1680)0   )
( D  K     )
<1.6 % at 90 % C.L
<1.9 % at 90 % C.L
• Deeper investigation of the non-resonant amplitude
– Non-resonant component fitted to an effective range model of the form
• cotdLASS=1/ap*+ bp*/2
a=4.031.72 0.06 GeV-1
b=1.290.63 0.67 GeV-1
• NR contribution of 5.30 0.74 +0.99 – 0.51 %
• angular distribution consistent with the effective-range scalar nonresonant phase shift obtained by LASS
(Watson)
• k excluded from further considerations.
• Hadronic decay D+K-++ will complete the K analysis
( see the end of this talk)
New measurement of the Ds+f ff
hep-ex/0401001
• According to flavor SU(3) symmetry the form factor ratios
rv and r2 describing D+K0* should be close to
Ds+f since the only difference is a spectator quark d
replaced with a s
• Lattice gauge calculations:
max diff= 10%
• Experiment:
– rv OK
– r2 inconsistent (3.3s.
S-wave interference in f?
90
45
0
data
ccbar mc
d  450
events cos V
m0 - G
d  900
m0
m0 + G
events cos V
events
cos V
d  00
f
K*
data
NO evidence for s-wave
interference in Ds f
Ds+f Form Factor results
Group
rv
FOCUS 1.549  0.250  0.145
E 791
2.27  0.35  0.22
CLEO
0.9  0.6  0.3
E 653
2.3  1.0  0.4
r2
0.713  0.202  0.266
1.570  0.250  0.190
1.400  0.500  0.300
2.100  0.550  0.200
1. Most precise measurement to date
2. very consistent with D+K0*
3. very consistent with theoretical expectation
A&S K-matrix poles, couplings etc.
Poles
0.65100
g
g KK
0.24844 0.52523
1.20720
0.91779
0.55427
0
0.38705
0.29448
1.56122
1.21257
0.37024
0.34501
0.23591
0.39642
0.62605
0.97644
0.18409
0.19746
0.18923
0.00357
1.81746
0.15770 0.17915 0.90100 0.00931
s0scatt
f11scatt
3.30564 0.26681
sA
s A0
1.0
0.2
f12scatt
0.16583
g 4
0
f13scatt
0.19840
g
g '
0.38878 0.36397
f14scatt
0.32808
0.20689
f15scatt
0.31193