Post on 03-Feb-2016
description
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