Dalitz analysis of the decay * B + →π + π - π +
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Transcript of 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
Richard Kass HADRON09 Tallahassee FL 2
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
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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
Richard Kass HADRON09 Tallahassee FL 4
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
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PRD 72, 052002 (2005) used 232x106 BB events (~half of this analysis)Prominent ρ(770) and 3σ evidence for f2(1270)
Previous BaBar Results
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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
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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
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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
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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
Richard Kass HADRON09 Tallahassee FL 10
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
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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
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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
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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)
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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)
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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
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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
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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
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Extra slides
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BaBar DIRC
BaBar K/BaBar K/IDID
D*+ → D0+ D0→ K+ -
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Dalitz Plot, DataDalitz Plot, Data
D0
J/Ψ & Ψ(2S)
Background subtracted Dalitz plot exclude charm and charmonia regions
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Best & 2Best & 2ndnd Best Fit Results Best Fit Results
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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
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PredictionsPredictionsLi and Yang, PRD 73, 114027 (2006).
Chiang and Zhou, J High Energy Phys. 03 (2009) 055.
Scheme B2
Scheme A2