Dalitz analysis of the decay * B + →π + π - π +

Richard Kass HADRON09 Tallahassee FL 1

Dalitz analysis of the decay* B+→π+π-π+

Outline of Talk*Introduction*Analysis technique*Results*Summary & Conclusions

Richard Kass for the BaBar Collaboration* charged conjugate states implied throughout talk


Why study charmless 3-body B decays?

Interference from both penguin & tree amplitudes can give direct CP violation.

Time-dependent measurements & interferences between intermediate states can allow measurement of all three CKM angles.

Can search for signs of new physics such as enhanced branching fractions or CP asymmetries – new physics particles can enter in the loop diagrams

Can improve understanding of the nature of some intermediate resonances, i.e. hadronic physics.

B+→π+π-π+ is a charmless 3-body B decay


Dalitz-plot Analysis

Dalitz plot is a representation of e.g. the B→PPP phase space. In our case P=pseudoscalar=charged pion.The invariant masses are constrained by

mB2+mi

2+mj2+mk

2=mij2+mik

2+mjk2

Make a 2D scatter plot in mij2 and mjk

2

Our case: mij=low mass π+π- combo, mjk=high mass π+π- combo Structure in the DP gives information on resonance masses,

widths and spins, relative phases, interference etc.Model each contribution to the DP as a separate amplitude with a

complex coefficient (isobar model).

Red points show a spin 0 resonance

Green points show spin 1 resonance

Purple points show spin 2 resonance

Each of these has a different mass, width & composition.

example

mlow2

mhi2


Dalitz-plot analysis of

B+→π+π-π+

In principle can extract the CKM angle from the interference between B+→ c0+ & other modes such as B+→ 0+

This mode also provides important information to improve the DP model in B0→ +0, which is used to measure the CKM angle

BF & ACP measurements used to test factorisation and other effective theories

Light meson spectroscopy aided by information from as many different final states as possible


PRD 72, 052002 (2005) used 232x106 BB events (~half of this analysis)Prominent ρ(770) and 3σ evidence for f2(1270)

Previous BaBar Results


PEP-II at SLAC asymmetric e+e− collider: 9 GeV (e-)/3.1 GeV (e+)

PEP-II Peak Luminosity 1.2 x 1034 cm-2s-1

BaBar recorded 424 fb-1 at Y(4S)4.65 x 108 (4S)→BB events


1.5 T Solenoid Electromagnetic Calorimeter

(EMC)Detector of Internally

Recflected Cherenkov

Light (DIRC)

Instrumented Flux Return

(IFR)Silicon Vertex Tracker (SVT)

Drift Chamber (DCH)e- (9 GeV)

e+ (3.1 GeV)

BaBar BaBar DetectorDetector

SVT, DCH: charged particle tracking: vertex & mom. resolution, K0

s/ΛEMC: electromagnetic calorimeter: /e/π0/ηDIRC, IFR, DCH: charged particle ID: π/μ/K/pHighly efficient trigger for B mesons


Threshold kinematics: we know the initial energy (E*beam) of the Y(4S) system Therefore we know the energy & magnitude of momentum of each B meson

Background Background

(spherical)

(jet-structure)

Signal Signal

Analysis Technique

Also, use neural networks + unbinned maximum likelihood fits

2*2*BbeamES pEm **

beamB EEE Event topology


BackgroundsB MesonsExplicitly veto 2-body states that can mimic B+→π+π-π+

B+→D0π+ with D0→π+π- and/or mis-ID’s D0→π+K-/K+K-

B+→Ksπ+ with Ks→π+π-

B+→[J/Ψ, Ψ(2S)]π+ with Ψ→l+l- with mis-ID’s l’s as π’sEstimate background due to other B meson decays Number of events estimated from MC and used in ML fit I) 2-body with extra track: B0→π+π- plus π+ (11 events) II) 3-body with mis-ID track(s): B+→K+π-π+ (199 events) III) B0→π+π-π0 with π- substituted for π0 (120 events) IV) B combinatorial backgrounds (495 events)Continuum: e+e-→uu, dd, ss, cc modeled using MC and below-Y(4S) data


Amplitude Formalism-IThe total signal amplitudes for B+ and B- decays are:

jjj

jjj

mmFcmmAA

mmFcmmAA

),(),(

),(),(

2min

2max

2min

2max

2min

2max

2min

2max

The F’s contain the strong force dynamics: Fj=Fj

Fj(m2max, m2

min)Rj(m)Xj(p*)Xj(q)Tj(m) j=spin of resonance, m=mass of resonance q=momentum of daughter in rest frame of resonance p*=momentum of bachelor pion in B rest frame Xj= Blatt-Weisskopf barrier form factors Rj(m)= resonance line shapes ρ’s use Gounaris-Sakurai parameterization, others relativistic BWs Tj(m)=angular distribution (use Zemach tensor formulism)The c’s contain the weak force dynamics: cj=(xj+Δxj)+i(yj+Δyj) & cj=(xj-Δxj)+i(yj-Δyj) Δxj & Δyj are CP violating components

The nominal model includes:ρ(770), ρ(1450), f2(1270), f0(1370) + non-resonant

PDG

ML fit


Amplitude Formalism-IIThe fit fraction for an individual amplitude is:

2min

2max

22

2min

2max

22

)(

)(

dmdmAA

dmdmFcFcFF JJJJ

J

The CP asymmetry for a contributing resonance is:

)(

)(22

22

,JJ

JJJCP

cc

ccA

The nominal model includes ρ(770), ρ(1450), f2(1270), f0(1370) + non-resonant BUT additional resonance added too,e.g. f0(980).

note: sum of fit fractions can be <1 or >1 due to interference


Maximum Likelihood FitEvent yields are extracted using an unbinned extended maximum likelihood fit.

),,,,( 2min

2max BES

jk

N

j kk

N qEmmmPNeLe

N=∑NK with Nk= event yield for category k. signal, qq, B meson backgrounds (number fixed from MC) Ne= total number of events in data sample qB= charge of the B meson Pk=PDF for category k: P=P(mES)xP(∆E)xP(Dalitz)

The signal reconstruction efficiencies are determined as a function of location in Dalitz plot(m2

max, m2min) for B+ and B- separately using MC.

Procedure is extensively tested with Monte Carlo toy MCs and embedded MCs

our fit has 20 free parameters


Fit to Data

signal signal

qq qq

4335 B± candidates yields 1219±50 signal events

“sPlots”NIM A 555 (2005) 356

__ ML fit __ ML fit

__ ML fit __ ML fit

We calculate a chisq between a model & data: Number of events in a bin vs predicted number The best model is the one with the lowest chisq/dof

PRD 79, 072006 (2009)


Systematic ErrorsMany sources of systematic errors consideredallow BB backgrounds to floatvary the PDF parameterscompare with data/MC control samples: B-→ D0π-, D0→K-π+

tracking efficiency & particle IDmodeling of Neural NetworkDalitz plot model (composition of model & values of masses, widths, etc)


Branching Fraction Results

The decay is dominated by B+→ ρ(770)0π+ and 3π non-resonantThe χc0, χc2, & f0(980) components not statistically significant

PDG: (16.2±1.5)x10-6stat syst model

“Bes

t Fi

t So

luti

on”

f0(1370) mass=1400±50 MeV/c2

f0(1370) width=300±80 MeV

determined from ML fit


CP Asymmetry ResultsAll CP asymmetries are consistent with zero.

Large variation in the ACP’s between best & 2nd best fit:

“Bes

t Fi

t So

luti

on”

best 2nd bestχ2

best/dof =82/84 χ2

2nd/dof= 86/84


B+→π+π-π+ Conclusions●This analysis uses the full BaBar data set Published: PRD 79, 072006 (2009)●Decay is dominated by ρ(770)π & 3π non-resonant No evidence for χc0, χc2, & f0(980) BFs in good agreement with PDG & theories Li and Yang, PRD 73, 114027 (2006), Chiang and Zhou, J. HEP. 03 (2009) 055.●All CP asymmetries consistent with zero Lack of χc0 & χc2 implies this mode is not useful for CKM angle γ measurement with present data samples.●These results will help other analyses Reduce model related errors in determination of CKM angle α from time dependent Dalitz analysis of B0→π+π-π0


Extra slides


BaBar DIRC

BaBar K/BaBar K/IDID

D*+ → D0+ D0→ K+ -


Dalitz Plot, DataDalitz Plot, Data

D0

J/Ψ & Ψ(2S)

Background subtracted Dalitz plot exclude charm and charmonia regions


Best & 2Best & 2ndnd Best Fit Results Best Fit Results


Model ParameterizationBlatt-Weisskopf Barrier Form Factors: rBW=4.0±1.0 (GeV/c)-1

Breit-Wigner line shape: q0=q(m0)

Zemach Tensors:

Gounaris-Sakurai parameterization

Non-resonant:αnr=0.28±0.06(GeV/c2)-2


PredictionsPredictionsLi and Yang, PRD 73, 114027 (2006).

Chiang and Zhou, J High Energy Phys. 03 (2009) 055.

Scheme B2

Scheme A2

Documents

Dalitz analysis of the decay * B + →π + π - π +