Mitchell Naisbit University of Manchester

o

A study of the decay

using the BaBar detector

Mitchell Naisbit – Elba

Mitchell Naisbit University of Manchester--o

1 - Contents

• Motivation for study

• Event selection

• Models of the Hadronic Current

• Smearing

• Results

• Conclusions

Mitchell Naisbit University of Manchester--o

2 - Motivation• Important uncertainty in calculations of (gμ-2) arises from

hadronic loop corrections:

• Experimentally determined spectral functions allow us to calculate these corrections

• CMD-2 experiment measured e+e- +- cross section. ALEPH, CLEO and OPAL gave data on --o spectral function CVC allows us to relate the two results

• After corrections made for isospin symmetry breaking effects the two data sets were seen to disagree below and around the mass peak BaBar’s high statistics make it ideal for studying data

Mitchell Naisbit University of Manchester--o

3 - Event Selection• Use 1-1 topology in CoM

• Require signal in one hemisphere of event and tag in other:

SIGNAL TAG

Decay Cuts:

Event Cuts:

- track ID - single o

- e or track ID - no o

o

ee

- 0.85 < Thrust < 0.985 (uds, bhabhas)

- ECM(π) + ECM(πo)<5.29GeV (beam bckgnds)

- CMS Tag track momentum<4GeV/c ( bckgnds)

- No unused neutrals with lab energy>0.3GeV (a1 tau bckgnds)

- ECM(π) +ECM(πo)>0.75GeV ( bckgnds)

Mitchell Naisbit University of Manchester--o

4 - Invariant Mass Spectrum• Form invariant mass of -o:

Electron Tag

= 1.22%

Mitchell Naisbit University of Manchester--o

Muon Tag

5 - Spectrum II

= 1.13%

Mitchell Naisbit University of Manchester--o

6 - Tag comparison

Peak normalised overlay

ratio as function of mass

Mitchell Naisbit University of Manchester--o

7 - --o

• Main contribution to -o lineshape is from (770)

(1450) and (1700) resonances included in PDG but not precisely measured

• Many theoretical models available allowing fits to -o partial width to determine contribution from each resonance

2223

2

22

2

2

2

2

|)m(F|mm41

Mm1

Mm21Nm

dmdn

Perform fit to mass spectrum:

phase space pion form factor

c

Mitchell Naisbit University of Manchester--o

8 - Spectral Function

• Model form factor (F) with Breit-Wigner functions:

b)1(

|AeBWeBWeBW||)m(F| 2

2iii

22

• Use various models for the Breit-Wigners:

)m(mi)mM(

MBW

2222

2

)m(mi)m(f)mM(

dMMBW

22222

2

Kuhn and Santamaria (KS):

Gounaris and Sakurai (GS):

Mitchell Naisbit University of Manchester--o

9 - Smearing• The data invariant mass spectrum will be smeared by the

detector resolution- migration or loss of events

• To account for this smearing use a smeared fit function in the process of making the fit

• Use Monte Carlo to determine the amount of smearing:

For each bin, i, in generator level MC distribution fill a histogram, Hij, with the reconstructed mass of the ni entries

Mitchell Naisbit University of Manchester--o

10 - Smearing II• Fit Gaussian to each histogram and plot sigma as a function of mass

low mass

rho mass

high mass

- low tail

Mitchell Naisbit University of Manchester--o

• Allow amount of smearing to vary in fit using a floating scale factor

0.00857m)0.00814)(s1()m(

• Extract (m) using a linear fit

0.00857m0.00814)m(

11 - Smearing III

Mitchell Naisbit University of Manchester--o

12 - Smearing IV• Convolve fit function with a mass dependent Gaussian

2

2

)m(2)mm(

e)m(2

1

• All parameters allowed to float in turnNorm. = N

masses = M M’ M’’ widths = ’ ’’ phases = ’ ’’

couplings = A

Smearing scale factor = s Bkgnd = b

Mass dependent width exponent =

Calculate unsmeared fit function, multiply each bin by mass dependent Gaussian and re-sum to give smeared function

Mitchell Naisbit University of Manchester--o

13 – KS FitN 20297 49.423_________________________________________________________ M

0.75539 0.00039053M’ 1.2964 0.0059416M’’ 1.6402 0.0074653 _________________________________________________________

0.14287 0.00018715’ 0.52167 0.0052295’’ 0.18733 0.0047002_________________________________________________________

0.21593 0.0010583 -0.0534 0.00131A -0.13386 0.0059447_________________________________________________________

’ 181.55 0.55545’’ 166.60 3.1724 -137.97 0.038500_________________________________________________________

2.3396 0.028196s 0.14956 0.021997b 2.6797 5.4526

2 = 1.814N

m( o) /GeV

Fit range (0.4,2)

Mitchell Naisbit University of Manchester--o

14 – KS Fit IIN 16900 45.196 _________________________________________________________ M

0.74359 0.00017781 M’ 1.1060 0.0063427 M’’ 1.5673 0.0047170 _________________________________________________________

0.15825 0.00025341 ’ 0.83960 0.013740 ’’ 0.49216 0.010036 _________________________________________________________

0.22196 0.0011434 -0.22577 0.0010546 A -0.22146 0.0057674 _________________________________________________________

’ 103.19 2.9447 ’’ 109.66 0.68011 -137.97 0.069106 _________________________________________________________

3.1479 0.0086927 s -0.017598 0.021912 b -2.8277 7.2601

2 = 1.383N

m( o) /GeV

Fit range (0.3,2)

Mitchell Naisbit University of Manchester--o

15 – Comments on fit• KS model fits well to spectrum, but it is only a

parameterisation

- don’t expect a perfect fit to this high precision data over so many orders of magnitude.

• Scale factor to smearing is around 15%

- parameters are correlated so fit can favour narrow resonances with higher smearing scale, or the opposite

- this scale factor is just a temporary measure - not claiming MC smearing is 15% too low, just that our parameterisation of the smearing histograms needs to be improved = double Gaussian?

• Problems with fits - some convergence problems, and inconsistent fit parameters with unreliable errors.

Mitchell Naisbit University of Manchester--o

16 - Conclusions

• Selection procedure developed to give high purity sample of --o candidates

• Smearing technique developed to account for detector resolution effects and integrated into fitting procedure

• Invariant mass spectrum fitting procedure implemented giving good fit over 5 orders of magnitude

• Ongoing work to improve fits and determine , ’ etc. parameters

- validating smearing technique and testing different fit functions

Mitchell Naisbit University of Manchester--o

Mitchell Naisbit University of Manchester--o

Extra Slides

Mitchell Naisbit University of Manchester--o

1 - AWG Pi0 Selection

• pi0AllLoose• No merged 0s• No dead/noisy channels• Photon energy deposited in 2 crystals• Lat 0.0010.05• E50 MeV• Split-off energy cut: 110 MeV• Split-off distance cut: 25 cm• Fit probability: 2 5.0• Combinatorics: keep best fit 0

Mitchell Naisbit University of Manchester--o

FCN= 68.92403num fit points = 54Num fit params = 16DOF = 54 – 16 =38 CHISQUARE = 1.814