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CPV in three-body decays: the Dalitz plot analysis. DIF06 LNF - February 28 –March 3. Sandra Malvezzi INFN Milano. Outline. The power of the Dalitz plot analysis CPV and Dalitz plot Recent applications of the Dalitz technique in the beauty sector Results - PowerPoint PPT Presentation
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CPV in three-body decays: the Dalitz plot analysis
DIF06
LNF - February 28 –March 3
Sandra Malvezzi INFN Milano
Outline
• The power of the Dalitz plot analysis – CPV and Dalitz plot
• Recent applications of the Dalitz technique in the beauty sector– Results– Problems/complications
• Some guidance from charm – D mesons and FSI– A pioneering anlysis in D
• Conclusions
• SPIRES search for “Dalitz and date after 1999Dalitz and date after 1999” 91 entries
after 2004after 2004 29 entries
• Experiments: FOCUS, E791, CLEO, BaBar-Belle
• From D to B decays
• From decay dynamics to CPV to New From decay dynamics to CPV to New PhysicsPhysics
Dalitz plot in the last few years
new millennium
Dalitz plot: the revenge
• The experimentalist’s struggle!
“When the going gets tough, the tough get going”– for the younger in the auditurium:
the analysis is certainly complex but not impossible
– if you survive, you might understand how QM works!
The power of the Dalitz plot
• Dalitz plot analysis allows for determination of a complete set of decay parameters, i.e. amplitudes and phases
• CP is a matter of phase• Exploit interference and make use of formalisms
with explicit CKM phases.– B angle– B D(*)K (*) angle
...promising
CPV and Dalitz plot
• Promising and complementary approach
• Independent measurements to over determine the unitarity triangle provide a non-trivial test of the Standard Model.
• Comparing the results in various channels and
via different analysis techniques will allow us to find possible inconsistency...
the way to New Physics.
Results and complications
Some pilot Dalitz-plot analyses in the beauty sector
• A theoretically clean way to extract is via atime-dependent Dalitz plot analysis of B – Snyder - Quinn formalism Phys. Rev. D48, 2139 (1993) – from the operative point of view B all charge
combinationswith all possible resonant structures and interferences.
• A full Dalitz analysis from BaBar= (113+27
-17 ± 6)° – 213 ML BB hep-ex/0408099 (ICHEP04)
• A “partial’’ Dalitz analysis from Belle – Selecting distinct bands in the Dalitz Plot
= (102 ± 11 ± 15)°– 152 ML BB hep-ex/0408003
Phys. Rev. Lett. 94, 121801 (2005)
B
B not Dalitz• This decay has recently received attention: small
theoretical uncertainty– Potentially highly complicated
• Three possible helicity states for the decay– Helicity 0 is CP-even– Helicity ±1 are not CP eigenstates
• BaBar =(100 ± 13)° fL = 0.978 ± 0.014+0.021
-0.029 – 232 ML BB hep-ex/0503049
Phys. Rev. Lett. 95, 041805 (2005)
• Belle= (88 ± 17)° fL = 0.941+0.034
-0.040 ± 0.030 – 275 ML BB hep-ex/0601024
Some complicationsto gofromto
fromtomeans selecting and filtering the desired states among the
possible contributions, e.g. f,
• How to deal with the underlying strong dynamics effects?– The Swave is characterized by broad, overlapping
states: unitarity is not explicitly guaranteed by a simple sum of Breit -Wigner (BW) functions
– Independently of the nature of (genuine resonance or a strong dynamics structure), it is not a simple BW
– f0(980) is a Flatté-like function, coupling to KK and
• Possibility of observing CP violation in BDK decays – B+ D(*)K(*)+ can produce neutral D mesons of both
flavors– D0 and D0 mesons can decay into a common final state
BDK
B+
b
u
u
sc
u
K(*)+
D(*)0
u
cs
uu
b
B+
K(*)+
D(*)0
Relative phase= is the sum of strong and weak interaction phases
= for charge conjugate mode
Dalitz plot andthe angle
Dalitz plot analysis to extract • Originally: interference of Cabibbo-favored D0 K+
and doubly Cabibbo-suppressed D0 K+
• Recently: interference D0, D0 KSboth CF decays)
• Belle - 275 ML BB
=(64 ±15)° for B± DK ± ( 137 – 139 events )
=(75 ±25)° for B± D*K ± ( 34 - 35 events )
combined samples14
15(68 13 11)
hep-ex 0506033
Dalitz plot andthe angle (II)
• BaBar - 227 ML BB
Phys. Rev. Lett. 95 (2005) 121802
• A model for D0 decay is needed
– Dominating source of systematic error
hep-ex/050403912 1410 1170 31
Somecomplications
• Model assumptions .... • Set of 15 two-body amplitudes
( K*(892K*(1430K2*(1430K*(1680
plus doubly Cabibbo-suppressed partners for each of these states)
Ks() KsKsKsf0(980), Ksf2(1270), Ksf0(1370), KS1,
KS2
1 and 2 are “ad hoc” resonances introduced to describe excess of events at threshold and at 1.1 GeV2
M1 = 539 ± 9 MeV 1= 453 ± 16 MeV
M = 1048 ± 7 MeV 1= 109 ± 11 MeV
A word of caution• Some questions
– Do wereally understandthe systematics?
– Are we confident of controlling strong dynamics effects in the analysis?
• Where can we look for directions?
– Charm: we have already come across parametrization and formalism issues
– Low and intermediate energy processes
• Hadron spectroscopy
• Scattering
A way to proceed ...
• BaBar– Implemented the K-matrix formalism to describe
the S-wave component in D0, D0 KS• Benefiting from charm expertise and work
– FOCUS three-pion Dalitz plot analysis
• No ad “ad hoc” resonances needed
• tried to quote a preliminary, reliable, systematic error on the angle: 3°hep-ex/0507101
– The right track to pursue ... promising!
What is the K-matrix?
• It follows from the S-matrix and, because of S-matrix unitarity, it is real
• Vice versa, any real K-matrix will generate a unitary S-matrix
• This is the real advantage of the K-matrix approach:– It (drastically) simplifies the formalization of any
scattering problem since the unitarity of S is automatically respected.
1/ 2 1/ 22S I i T 1 1K T i 1( )T I iK K
E.P.Wigner,Phys. Rev. 70 (1946) 15
S.U. Chung et al.Ann. Physik 4 (1995) 404
• For a single-pole problem, far away from any threshold, a K-matrix amplitude reduces to the standard BW formula
• The two descriptions are equivalent
• In all the other cases, the BW representation is no longer valid
• The most severe problem is that it does not respect unitarity
Add BW
Add K
Add BW Add K
The Unitarity circle
Adding BWs a la “traditional Isobar Model”
– Breaks Unitarity
– Heavily modify the phase motion!
Yield DYield D++ = 1527 = 1527 5151
S/N DS/N D++ = 3.64 = 3.64
FOCUS D+ ++- analysis
Sideband Signal
PLB 585 (2004) 200
2lowm
2highm
D
C.L fit 7.7 %
K-matrix fit results
Low mass projection High mass projection
18 11.7
+
+2
0 +
(S - wave)π 56.00 ± 3.24 ± 2.08 0(fixed)
f (1275)π 11.74 1.90 0.23 -47.5 .7
ρ (770)π 30.82 ± 3.14 ± 2.29 -139.4 ±16.5 ± 9.9
decay channel phase (deg)fit fractions (%)
Reasonable fit with no retuning of the A&S K-matrix. No new ingredients (resonances),not present in the scattering, required !
r
j
2iδ 2 2r r 12 13
r 2iδ 2 2j j 12 13j
a e A dm dmf =
a e A dm dm
With
Without
C.L. ~ 7.5%
Isobar analysis of D+ ++would instead require An “ad hoc” scalar meson:
C.L. ~ 10-6
m = 442.6 ± 27.0 MeV/c = 340.4 ± 65.5 MeV/c
FOCUS D s+
++- analysis
Observe:
•f0(980)
•f2(1270)
•f0(1500) Sideband
Signal
Yield Ds+ = 1475 50
S/N Ds+ = 3.41
C.L fit 3 %
sD
Low mass projection High mass projection
+
+20 +
(S - wave)π 87.04 ± 5.60 ± 4.17 0(fixed)
f (1275)π 9.74 4.49 2.63 168.0 18.7 2.5
ρ (1450)π 6.56 ± 3.43 ± 3.31 234.9 ±19.5 ±13.3
decay channel phase (deg)fit fractions (%)
No three-body non-resonant contribution
sD K-matrix fit results
The effort continues, grows and matures....
B DK*
• Statistical accuracy of the extraction can be improved by adding excited K states to the analysis
Belle – B DK* (hep-ex/0504013) – 253 fb-1 56 signal candidates B DK*
= ( 112 35 9 11 8 )°
BaBar
– B DK* and B D(*)K* (hep-ex/0507101)
= ( 67 28 13 11 )°
non-resonant B DKS(D Ks+-)
Dalitz Analysis of B Khh
Belle hep-ex/05100059
• 140 fb-1 B+ K++- and B+ K++-
• 357 fb-1 B0 K0+
– Already mentioned complications due to states
– KK final state can come from f0(980), f0(1300), f0(1500) – coupled-channel parametrization
• CP asymmetry is predicted very small in B+ K*0(892) +
– window to NP
– K model is needed.
Dalitz Analysis of B hhh
BaBar• 210 fb-1 B± ±±hep-ex/0507025
Phys. Rev. D72, 052002 (2005)
• 205.4 fb-1 B± ±±hep-ex/0507004
Phys. Rev. D72, 072003 (2005)
• 230 fb-1 B0 +Shep-ex/0507094
Dalitz plot and B Ks
Promising way to search for New Physics• A reliable SM prediction exists for
sin2(Bd J/Ks) sin2(Bd Ks)
• BaBar/Belle average for 2005– sin2(Bd J/Ks) = 0.685 ± 0.032
• sin2(Bd Ks) == 0.50 ± 0.25 +0.07 –0.04 BaBar= 0.44 ± 0.27 ± 0.05 Belle– How do other resonant (e.g. f0(980)) and non-resonant KK
components underneath affect the measurement? – It is mandatory to measure various contributions and
related interference via a Dalitz plot analysis.
First set of conclusions • Dalitz plot analysis represents a powerful, unique
and promising tool to study CP violation in the beauty sector
• The analysis is challenging but there are no shortcuts to perform precise studies (New Physics)
• There is a new vigorous effort to perform amplitude analyses – more robust formalism implemented– many different channels analysed – beauty community can benefit from charm
experience and expertise
but need to go on..
Beauty and charm relationship...
• B – B D
• B D(*)K(*)
Ks K0
• B KD
from charm we can learn something for beauty .... but not only ...
CPV in charm • In the SM, the D system is not as sensitive to CP as the K
and B mesons. • The small effects predicted could leave open a window onto
NP • Charm is unique (I. Bigi):
– non-Standard-Model effects might exhibit very different patterns for the up and down classes of quarks
– Charm decays are the only up-type decays that afford a probe of such physics
• Important to measure it! – Asymmetry in decay rates are already measured, also
in three-body decays
– Alternative approaches are worth being exploited ...
(D(DKKK K ))
Dalitz plot analysis and CPV in the charm sector
• FOCUS D+K+K– + (ICHEP 02) • BaBar D0 K0K+K– hep-ex/050702
Phys. Rev. D72, 052008 (2005)
• CLEO – D0 hep-ex/0503052
Phys. Rev. D70, 031102 (2005)
– D0 KS hep-ex/0311033
Phys.Rev. D70, 091101 (2004)No statistically significant asymmetries reported ...
improve accuracy!
D+K–K++ is (would be) a good candidate
– Two amplitudes (spectator CSD - penguin)
– Good yield and S/N ratio
– Strong phases present
Yield D+ = 7106 92
1.7 1.8 1.9 2.0
GeV
2.1
1250
1750
0250
500750
1000
1500
20002250
+ -2
K Km
- +2
K πm
1 1.5 2 2.5 3 3.5
m(KK)(GeV)2 2
2 m(K)
(GeV
)2
0.20.40.60.8
11.21.41.6
1.82
D+ , Ds KK
• Measure coefficient and phase for each amplitude
• Look for possible local asymmetry in D+/D– parametrs • Complications in the final state (KK) (K) treatment
– f0(980)/a0(980) coupled-channel lineshape– Higher mass f0(1370)-f0(1500) ...– Broad K*0(1430) ...
Simple idea ... look at D+/D–
=+
Measured phase:
=-
CP conjugate
CP conserving
=
CP violating
=-
D+/D- split samples
• Fit based on BW formalism– preliminary and tentative
– No CPV but a more reliable parametrization needed
– Start studying scattering S-matrix (K-matrix)
Coefficients: D±,, DD++,, DD--
Phases: DD±±,, DD++,, DD--
ICHEP2002
Hadronic physics
• The other perspective The hadronic physics challenge ...– very clean samples of HF decays offer an
unprecedented opportunity to investigate light meson physics
• enriching, testing and finding consistency with the already available measurements from low-intermediate energy experiments ...
– BES, BaBar, Belle, Cleo-c have (and/or) will have clean, high-statistics samples to provide phase-shift behaviour, measuring resonance parameters ... etc. ...
Conclusions• Dalitz plot analysis will definitely keep us company over the
next few years • Some complications have already emerged
– expecially in the charm field
others (unexpected) will only become clearer when we delve deeper into the beauty sector– Bs will be a new chapter (hep-ph/0602207 Bs K, Bs KK)
• There will be a lot of work for both theorists and experimentalists – Synergy invaluable!
The are no shortcuts toward ambitious and
high-precision studies and NP search