0 + - decays in a factorization approach Analysis done in - - PowerPoint PPT Presentation
Dalitz plot analysis of D 0 K S 0 + - decays in a factorization approach Analysis done in collaboration with Robert Kamiski (Institute of Nuclear Physics PAS, Krakw, Poland), Jean-Pierre Dedonder and Benoit Loiseau (LPNHE, Paris,
Analysis done in collaboration with Robert Kamiński
(Institute of Nuclear Physics PAS, Kraków, Poland),
Jean-Pierre Dedonder and Benoit Loiseau
(LPNHE, Paris, France) published recently in Physical Review D 89, 094018 (2014), arXiv: 1403.2971 [hep-ph].
0 + -
0 + -,
0 + - reaction are useful in:
s du c
Transition
c d u W+ s
doubly Cabibbo suppressed
A V A V us cd F
s u c d V V G O
) ( ) ( 2
* 2
D0
u
-
u
- Transition
c u W+ s
allowed
d d
d
D0 + K0
d d
+ K0
225 . sin , ,
C us cd
V V
C ud cs
V V cos
A V A V ud cs F
d u c s V V G O
) ( ) ( 2
* 1
C= Cabibbo angle
c s c d d d
d d d
s
u u
u u
D0 D0
u u
K
+ + - - K0 W+ W+
Transition Transition
s du c
allowed doubly Cabibbo suppressed
main part of the effective Hamiltonian:
2 1 *
2 / j j V V G H
ud cs F
Quark currents:
, , ,
A V A V A V A V
d s j c u j d u j c s j
) ( ' ) ( ' ) ( ) (
2 1 2 1
Factorization:
| | | | | |
2 1 2 1
j D j K D j j K
| ' | | ' |
2 1
j K D j
| ' | | ' |
2 1
j K D j
p if j
| |
2 K K p
if j K | ' |
2 D D p
if D j
1 |
' |
f - pion decay constant fK - kaon decay constant fD - D decay constant
Seven partial wave amplitudes:
including in addition the ω + - P- wave transition . 27 amplitudes for the D0 KS
0 + - decay:
a) 7 allowed tree amplitudes, b) 6 doubly Cabibbo suppressed tree amplitudes, c) 14 annihilation (W-exchange) amplitudes (7 allowed and 7 doubly Cabibbo suppressed).
Channel: wave: name:
* *
* * *
* 2
same list as above but with pion charge +
) 1400 ( ), 980 ( , ) 500 ( f f σ f
2
Very rich resonance spectrum complexity of final state interactions
S
K D
) | (| 2 1 | K K KS
Allowed transitions with
ud csV
V *
1
S
K
final state interactions S-wave:
) ( ) ( ] ) )( ( [ 2
2 1 2 2 2 2 2 2 2 2 1 1 1
*
m F m A m m m m m m m f f a G A
K DK K D F P
P-wave:
) ( ) ( )) ( 2
2 2 2 2 1 1 1
*
m F m F m m f a G A
π K π DK π D π F S
m eff. masses of
,
S
K
a1 - effective Wilson coefficient
) (
2
*
π DK
m F
* transition scalar form factor
m
) (
2
m
F
π K
scalar form factor
) (
2
*
π DK
m A
* transition vector form factor
) (
2 1
m
F
π K
vector form factor
2 2
) (
K π
p p m
2 2
) (
K π
p p m
2 2
) (
π π
p p m
2 2 2 2 Br τ D
Data for:
0 + - decays, A. Poluektov et al. (Belle Coll.),
0 - decays, D. Epifanov et al. (Belle Coll.),
Number of degrees of freedom: ndf= 6321 + 89 + 1 – 33 free model param.= 6378. Result: 2 = 9451 which gives 2/ ndf = 1.48.
2
) (
π K
p p s
S
2
) (
π K
p p s
S
0 - effective mass
0 + and + - effective
0 +
0 - decay
mK (GeV)
[KS
0 - ]S + 25.0 3.6 8.2 0.1 7.9 0.1
KS
0 [ - + ]S 16.9 1.3 14.7 0.2 2.9 0.1
[KS
0 - ]P + 62.7 4.5 24.7 5.7 8.7 3.0
KS
0 [ - + ]P 22.0 1.6 4.4 0.1 6.7 0.04
Channel Br (%) Br (tree) Annihil. low. limit Br (KS
0) = (21.2 0.5) %
Br (K*(892)+-) = (62.9 0.8) %
0 + - decays are analysed using the factorization
approximation.
weak-decay tree amplitudes.
the S-, P- states are described in terms of the corresponding form
using unitarity, analyticity and chiral symmetry and by the present Dalitz plot analysis.
distributions and with the - KS
0 - decay data is achieved.
amplitudes are significant.
10 1 i i i
M M M A T ;
i i
Ti – tree ampl. Ai – annihilation ampl.
e ampl. fitted ;
i
ρ i i i i
M M M c M c ds ds Br d
2 2 2
| | |
2 . 2 2 2
| | ; | |
i ann i i tree i
A c ds ds Br d T c ds ds Br d
i i ρ i i
. i i tree i i low ann i
= phase of the KS
0 amplitude
Two mesons form a resonance R=h2h3
3 2 23 3 3 2 2
3 2
D h Rh D
Example:
) ( ) ( ) ( ) (
3 2 1
p p K p p D
D
*
) 892 ( K K R
,
2 2 A V D
c s j m p p p s p p p p
) ( ,
1 2 3 2 23 3 2 1
terms
3
) ( 2 ) ( | | ) (
2 1 2 1 * 3 2
* *
π DK μ D K D
m A p p p ε m i p D j p p R ) (
2
*
m ADK
Vertex function:
) ( 1 ) ( ) (
23 1 3 2 23
* * *
s F f m p p s G
K K K K K
*
K
polarization
1
D to K* transition form factor
| ' | ) ( ) ( ) ( | ' | ) ( ) ( ) (
3 2 1 1 23 3 3 2 2 1 1
3 2
j p p R p h s G j p h p h p h
h Rh
Example:
1
, f R K h
,
A V D
d s j p p s p p p p
) ( ' ,
2 3 2 23 3 2 1
2 2 23 2 3 2 1
| ' | ) ( ) (
D f K D D K
m F p p s m i j p p f p K
2 D f K
2nd term
) ( ) (
23 2 23
s F s G f
) ( 23 s F
S
K D
) | (| 2 1 | K K KS
Allowed transitions with
ud csV
V *
1
S
K
final state interactions S-wave:
) ( ) ( ] ) )( ( [ 2
2 1 2 2 2 2 2 2 2 2 1 1 1
*
m F m A m m m m m m m f f a G A
K DK K D F P
P-wave:
) ( ) ( )) ( 2
2 2 2 2 1 1 1
*
m F m F m m f a G A
K DK D F S
D- wave:
* 2 * 2 * 2 * 2 * 2
2 2 2 2 2 1 1 1
) , ( ) ( 2
K K K K K DK F D
im m m m m D G m F f a G A
S
) (
2
* 2
m
F DK
) 1430 (
* 2
K transition form factors
* 2 S
K K
G
) , (
2 2 m
m D
= D-wave angular distribution function
m eff. masses of
,
S
K
a1 - effective Wilson coefficient
) (
2
*
m F DK
* transition scalar form factor
m
S-wave:
) ( ) ( ) ( 2
2 1 2 2 2 2 1 2
m F m A m m f f a G An
D K D F P
P-wave:
) ( ) ( ) ( 2
2 2 2 2 2 2 1 2
m F m F m m f a G An
D f K K D F S
D-wave: ) ( ) , ( ) ( 2
2 2 2 2 2 2 2 1 2
2 2 2 2 2
m im m m m m D G m F f a G An
f f f f Df D F D
) (
2
2 m
F Df
) 1270 (
2
f transition form factors ) , (
2 2 m
m D
m
effective mass
Annihilation ( W-exchange) transitions with
final state interactions
) (
2 D f K
m F
a2 - effective Wilson coefficient
) (
2 D K
m A
2
f
G
0 + - decay
a) A. Poluektov et al. (Belle Coll.), Phys. Rev. D 81, 112002 b) P. del Amo Sanchez et al. (BaBar Coll.),
2
) (
p p s
S
K 2
) (
p p s
S
K 2
) (
p p s