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