CPV in threebody decays: the Dalitz plot analysis

1
CPV in three-body decays the Dalitz plot
analysis

• DIF06
• LNF - February 28 March 3

Sandra Malvezzi INFN Milano
2
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 ?ppp
• Conclusions

3
Dalitz plot in the last few years

• SPIRES search for Dalitz and date after 1999
• 91 entries
• 
  after 2004
• 29 entries
• Experiments
• FOCUS, E791, CLEO, BaBar-Belle
• From D to B decays
• From decay dynamics to CPV to New Physics

new millennium
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Dalitz plot the revenge

• The experimentalists 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!

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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 ? rp a angle
• B ? D()K () g angle
• ...promising

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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.

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Some pilot Dalitz-plot analyses in the beauty
sector

• Results and complications

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B ? rp

• A theoretically clean way to extract a is via a
  time-dependent Dalitz plot analysis of B ? rp
• Snyder - Quinn formalism Phys. Rev. D48,
  2139 (1993)
• from the operative point of view B ? pp-p0
  (all charge combinations) with all possible
  resonant structures and interferences.
• A full Dalitz analysis from BaBar
• a (11327-17 6)
• 213 ML BB
  hep-ex/0408099 (ICHEP04)
• A partial Dalitz analysis from Belle
• Selecting distinct bands in the pp-p0 Dalitz
  Plot
• a (102 11 15)
• 152 ML BB
  hep-ex/0408003
• Phys. Rev. Lett. 94, 121801 (2005)
  

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B ? rr (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
• a(100 13) fL 0.978
  0.0140.021-0.029
• 232 ML BB hep-ex/0503049 Phys. Rev.
  Lett. 95, 041805 (2005)
• Belle
• a (88 17) fL
  0.9410.034-0.040 0.030
• 275 ML BB hep-ex/0601024

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Some complications

• to go from B?ppp to B ? rp
• from B?pppp to B ? rr
• means selecting and filtering the desired states
  among the possible contributions, e.g. sp,
  f0(980)p, sr, ss, rpp...
• How to deal with the underlying strong dynamics
  effects?
• The pp S-wave 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 s (genuine
  resonance or a strong dynamics structure), it is
  not a simple BW
• f0(980) is a Flatté-like function, coupling to KK
  and pp

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B?DK

• Possibility of observing CP violation in B?DK
  decays
• B? D()K() can produce neutral D mesons of
  both flavors
• D0 and D0 mesons can decay into a common final
  state

u
u
b
K()
s
D()0
c
b
c
B
s
B
D()0
K()
u
u
u
u
Relative phase qdg is the sum of strong and
weak interaction phases q-d-g for
charge conjugate mode
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Dalitz plot and the g angle

• Dalitz plot analysis to extract g
• Originally interference of Cabibbo-favored D0 ?
  Kp-p0 and doubly Cabibbo-suppressed D0 ? Kp-p0
  
• Recently interference D0, D0 ? KSpp- (both CF
  decays)
• Belle - 275 ML BB
• g(64 15) for B ?DK ( 137 139
  events )
• g(75 25) for B ?DK ( 34 - 35 events
  )
• combined samples

hep-ex 0506033
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Dalitz plot and the g 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/0504039
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Some complications

• Model assumptions ....
• Set of 15 two-body amplitudes
• (Kp)p K(892)p, K(1430)p, K2(1430)p,
  K(1680)p
• (plus doubly Cabibbo-suppressed partners for each
  of these states)
• Ks(pp) Ksr, Ksv, Ksf0(980), Ksf2(1270),
  Ksf0(1370), KSs1, KSs2
• s1 and s2 are ad hoc resonances introduced to
  describe excess of events at pp threshold and at
  1.1 GeV2
• Ms1 539 9 MeV Gs1 453 16 MeV
• Ms2 1048 7 MeV Gs1 109 11 MeV

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A word of caution

• Some questions
• Do we really understand the 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

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A way to proceed ...

• BaBar
• Implemented the K-matrix formalism to describe
  the pp S-wave component in D0, D0 ?KSpp-
• 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 g angle ?3
  (hep-ex/0507101)
• The right track to pursue ... promising!

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What is the K-matrix?
E.P.Wigner, Phys. Rev. 70 (1946) 15
S.U. Chung et al. Ann. Physik 4 (1995) 404

• 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.

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• 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

• Adding BWs a la traditional Isobar Model
• Breaks Unitarity
• Heavily modify the phase motion!

Add K
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FOCUS D? p p p - analysis
Yield D 1527 ?51 S/N D 3.64
Sideband
Signal
PLB 585 (2004) 200
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K-matrix fit results
C.L fit 7.7
High mass projection
Low mass projection
Reasonable fit with no retuning of the AS
K-matrix. No new ingredients (resonances), not
present in the scattering, required !
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Isobar analysis of D? p p p would instead
require An ad hoc scalar meson s
m 442.6 27.0 MeV/c G 340.4 65.5 MeV/c
With s
Without s
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FOCUS D s ?? p p p - analysis
Yield Ds 1475 ?50 S/N Ds 3.41
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K-matrix fit results
C.L fit 3
No three-body non-resonant contribution
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The effort continues, grows and matures....
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B ? ? DK?

• Statistical accuracy of the g 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? g ( 112 ? 35 ? 9 ? 11 ? 8 )
• BaBar
• B ? ? DK? and B ? ? D()K?
  (hep-ex/0507101)
• g ( 67 ? 28 ? 13 ?
  11 )

(D ?Kspp-)
non-resonant B ? ? DKSp?
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Dalitz Analysis of B ? Khh

• Belle hep-ex/05100059
• 140 fb-1 B? Kpp- and B? KKK-
• 357 fb-1 B0? K0pp-
• Already mentioned complications due to pp states
• KK final state can come from f0(980), f0(1300),
  f0(1500) coupled-channel parametrization
• CP asymmetry is predicted very small in B?
  K0(892) p
• window to NP
• Kp model is needed.

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Dalitz Analysis of B ? hhh

• BaBar
• 210 fb-1 B? ppp hep-ex/0507025
• Phys. Rev. D72, 052002 (2005)
• 205.4 fb-1 B? Kpp hep-ex/0507004
• Phys. Rev. D72, 072003 (2005)
• 230 fb-1 B0? KK-KS0 hep-ex/0507094

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Dalitz plot and B ? fKs

• Promising way to search for New Physics
• A reliable SM prediction exists for
• sin2b(Bd ?J/yKs) ? sin2b(Bd ?fKs)
• BaBar/Belle average for 2005
• sin2b(Bd ?J/yKs) 0.685 0.032
• sin2b(Bd ?fKs)
• 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 f affect
  the measurement?
• It is mandatory to measure various contributions
  and related interference via a Dalitz plot
  analysis.

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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..

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Beauty and charm relationship...

• B ?rp
• B ??ppp D ??ppp
• B ?D()K()
• ?Kspp
• ? Kpp0
• B ? Kpp D ??Kpp
• from charm we can learn something for beauty
  .... but not only ...

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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??K?K p? )
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Dalitz plot analysis and CPV in the charm sector

• FOCUS D?KK p (ICHEP 02)
• BaBar D0 ??K0KK hep-ex/050702
• Phys. Rev. D72, 052008 (2005)
• CLEO
• D0 ? p p- p0 hep-ex/0503052
• Phys. Rev. D70, 031102 (2005)
• D0 ? KS p p- hep-ex/0311033
• Phys.Rev. D70, 091101 (2004)
• No statistically significant asymmetries reported
  ...
• improve accuracy!

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D?KKp is (would be) a good candidate

• Two amplitudes (spectator CSD - penguin)
• Good yield and S/N ratio
• Strong phases present

D , Ds ?KK?
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Simple idea ... look at D/D

• Measure coefficient and phase for each amplitude
• Look for possible local asymmetry in D/D
  parametrs
• Complications in the final state (KK) (Kp)
  treatment
• f0(980)/a0(980) coupled-channel lineshape
• Higher mass f0(1370)-f0(1500) ...
• Broad K0(1430) ...

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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)

ICHEP2002
Coefficients D, D, D-
Phases D, D, D-
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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. ...

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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 ? Kpp, Bs ? KKp)
• 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