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CPV in three-body decays: the Dalitz plot analysis DIF06 LNF - February 28 –March 3 Sandra Malvezzi INFN Milano

CPV in three-body decays: the Dalitz plot analysis

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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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Page 1: CPV in three-body decays:   the Dalitz plot analysis

CPV in three-body decays: the Dalitz plot analysis

DIF06

LNF - February 28 –March 3

Sandra Malvezzi INFN Milano

Page 2: CPV in three-body decays:   the Dalitz plot analysis

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

Page 3: CPV in three-body decays:   the Dalitz plot analysis

• 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

Page 4: CPV in three-body decays:   the Dalitz plot analysis

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!

Page 5: CPV in three-body decays:   the Dalitz plot analysis

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

Page 6: CPV in three-body decays:   the Dalitz plot analysis

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.

Page 7: CPV in three-body decays:   the Dalitz plot analysis

Results and complications

Some pilot Dalitz-plot analyses in the beauty sector

Page 8: CPV in three-body decays:   the Dalitz plot analysis

• 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

Page 9: CPV in three-body decays:   the Dalitz plot analysis

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

Page 10: CPV in three-body decays:   the Dalitz plot analysis

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

Page 11: CPV in three-body decays:   the Dalitz plot analysis

• 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

Page 12: CPV in three-body decays:   the Dalitz plot analysis

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

Page 13: CPV in three-body decays:   the Dalitz plot analysis

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

Page 14: CPV in three-body decays:   the Dalitz plot analysis

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

Page 15: CPV in three-body decays:   the Dalitz plot analysis

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

Page 16: CPV in three-body decays:   the Dalitz plot analysis

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!

Page 17: CPV in three-body decays:   the Dalitz plot analysis

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

Page 18: CPV in three-body decays:   the Dalitz plot analysis

• 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!

Page 19: CPV in three-body decays:   the Dalitz plot analysis

Yield DYield D++ = 1527 = 1527 5151

S/N DS/N D++ = 3.64 = 3.64

FOCUS D+ ++- analysis

Sideband Signal

PLB 585 (2004) 200

Page 20: CPV in three-body decays:   the Dalitz plot analysis

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

Page 21: CPV in three-body decays:   the Dalitz plot analysis

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

Page 22: CPV in three-body decays:   the Dalitz plot analysis

FOCUS D s+

++- analysis

Observe:

•f0(980)

•f2(1270)

•f0(1500) Sideband

Signal

Yield Ds+ = 1475 50

S/N Ds+ = 3.41

Page 23: CPV in three-body decays:   the Dalitz plot analysis

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

Page 24: CPV in three-body decays:   the Dalitz plot analysis

The effort continues, grows and matures....

Page 25: CPV in three-body decays:   the Dalitz plot analysis

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+-)

Page 26: CPV in three-body decays:   the Dalitz plot analysis

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.

Page 27: CPV in three-body decays:   the Dalitz plot analysis

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

Page 28: CPV in three-body decays:   the Dalitz plot analysis

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.

Page 29: CPV in three-body decays:   the 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..

Page 30: CPV in three-body decays:   the Dalitz plot analysis

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 ...

Page 31: CPV in three-body decays:   the Dalitz plot analysis

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 ))

Page 32: CPV in three-body decays:   the Dalitz plot analysis

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!

Page 33: CPV in three-body decays:   the Dalitz plot analysis

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

Page 34: CPV in three-body decays:   the Dalitz plot analysis

• 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

=-

Page 35: CPV in three-body decays:   the Dalitz plot analysis

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

Page 36: CPV in three-body decays:   the Dalitz plot analysis

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. ...

Page 37: CPV in three-body decays:   the Dalitz plot analysis

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