b Polarization Measurement at ATLAS

b Polarization Measurement at ATLAS

Michela Biglietti1

on behalf of the ATLAS b working group:Eduard De La Cruz Burelo2,

Claudio Ferretti2,Homer A Neal2, Natalia Panikashvili2,4 Mária

Smizanská3, Shlomit Tarem4

1. INFN Naples, Italy2. University of Michigan, USA3. University of Lancaster, UK

4. Technion Institute of Technology, Israel

Beauty 2005 - 10th International Conference on B-Physics at Hadron Machines - June 20 - 24 2005, Assisi, Italy.

2

b Production at LHC

Due to the parity conservation in the strong interactions, at LHC b can be produced with polarization orthogonal to the production plane

... but why polarization ? Large number of unanswered

questions about the role of spin in production of hyperons at high energies which we wish to explore

hyperon (uds)Why is the polarization is so

large ?Why is the shape so unusual ?

bhyperon (udb)Are the mechanisms of and b

polarization different ?Are the s and b production

mechanisms similar ? Does the polarization depend on

quark mass?K. Heller, Procedings of the 9th International Symposium

on High Energy Physics, Bonn (1990)

3

b Decay

The considered decay, b J/pis characterizes by 4 helicity amplitudes and the asymmetry parameter b caused by the parity non conservation of the weak interactions 1/21/2 +1

Α(1/2,1)b

1)1/2,Α(b

1/2,0)Α(a

Α(1/2,0)a

2222

2222

bbbaa

bbaa

helicity amplitudes and asymmetry parameter b not yet measured

they can, in principle, be predicted using PQCD, and thus be a tool to test theoretical models and to search for new physics

Other interesting studies for this decay channel Lifetime of b hyperon

CP violation in baryons

4

b in ATLAS

For Low luminosity operations

L= 1033 cm-2 s-1

∫L= 10fb -1 O(1012) b

per year

In the first 3 years O(105) b J/p

(ATLAS TDR estimation)

The world’s biggest sample so far is ~ O(102) bJp

p(7 TeV)

p(7 TeV)

b

J/

p

5

Measurement of b J/

The b polarization (Pb) and decay parameters can be determined from the angular distributions p.d.f. of the cascade decay

bJ/()(p) p.d.f. depends on 5 angles + 6 parameters of 4 complex helicity amplitudes and polarization Pb ( 7

unknowns).

6

What angular distributions do we expect?

P = 0%

P = -40%

P = 40%

Cos() Cos() Cos()

Probability distributions:

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A Model for b Decay

The general amplitude for the decay b J/ is given by:

* - polarization vector of the vector meson (J/)

A1, A2, B1, B2 - complex decay amplitudes are calculable within the framework of PQCD models using factorization theorems (Phys. Rev. D65:074030, 2002, hep-ph/0112145) Helicity amplitudes related to A1, A2, B1, B2:

,215251 )(pΛm

pBγBγ

m

pAγγA)(p)ε(pΛM

b

b

b

b

b

ΛbΛ

μΛμ

Λ

μΛμ

ψJ

*μΛ

Units x10-

10

b = - 0.457a+ = -0.0176 - 0.4290ia- = 0.0867 + 0.2454ib+ = -0.0810 - 0.2837ib- = 0.0296 + 0.8124i

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Generation of Polarized b

In order to study the feasibility of measuring b polarization in ATLAS we have developed a way to make polarized b in EvtGen

EvtGen: originally written in BaBar and CLEO, now also in MC/LCG project

package providing a framework for implementation of processes relevant to B physicsuses spinor algebra and helicity amplitudes

it’s possible to set the polarization of the particle before the particle is decayed .. and obtain the correct angular distributions

PythiaPythia

HepMCHepMC

EvtGen uses spinor algebra and helicity amplitudesEvtGen uses spinor algebra and helicity amplitudes

1. Set polarization

2. Two body decay by specifying the helicity amplitudes for the final state particles

b-Baryons

First ever adaptation of EvtGen as a generator of polarized baryons

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EvtGen Cross Check

5 angular distributions are generated using both the probability function and using the full amplitude feature in EvtGen

cos()Slope~0

cos()

HelAmpProb

cos()Slope~b∙P

Blue squares are events generated according to probability function

Red circles are events generated with helicity amplitudes in EvtGen

Very good agreement between the angular Very good agreement between the angular distributions generated with EvtGen and the distributions generated with EvtGen and the

probability density function!probability density function!

Pb=-40%

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Data Simulation, Reconstruction and Analysis

Events generated with Pythia/EvtGenseveral input modelsProduction cuts:

pT() > 2.5GeV, pT() > 4.0GeV,

pT (/p) > 0.5 GeV, ||< 2.7

Full simulation in ATLAS detector with Geant4 Recostruction

Dedicated algorithm for low pT muons developed Better efficiency for J/ identification

Inner Detector tracking and vertexing algorithms for and b identificationAngular distributions determination

AnalysisMC toy for "fast" predictionsMaximum Likehood method to measure Pb and b decay parameters

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Event Reconstruction J/mass

mass

b mass

= 80% = 40.5 MeV

= 40% = 2.8 MeV

= 28% = 21.5 MeV

= rec efficiency from Gaussian fits = rec efficiency from Gaussian fits

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Angular distributions in ATLAS detector

Cos() Cos() Cos()

Reconstructed anglevsGenerated angle

P=-100%

ATLAS acceptance modifies the angular distributions and increases the difficulty of the measurement

ATLAS acceptance modifies the angular distributions and increases the difficulty of the measurement

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Angular Resolutions

Cos(rec)-Cos(gen)

AnglesGaussian fit

mrad

cos 2

cos 21

32

cos 3

13

14

Maximum Likelihood (ML) Method

')',(),,(

)',(),,(),,'(

ddTAw

dTAwAwobs

where:

P

b

b

a

a

A

,,

2

2

1

1

θ’: Measured anglesθ : Generated angles

)',()',()',(

RT

R(θ,θ’) is the resolutionε(θ,θ’) is the acceptance correction

ML Mehod :

dFi )()(Acceptance correction normalization : i=0...19

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The ML results (Toy MC sample + angular resolution from reconstruction + detector acceptance)

only statistical uncertainties are shown

Pb = - 20%

b,Pχ,φ,φ,,r,rα 10b

Pb = - 40%

b,Pχ,φ,φ,,r,rα 10b

Parameter PullsParameter Pulls Parameter PullsParameter Pulls

Maximum Likelihood Results

b

22

1

22

0b P;ββχ;βαφ;βαφ;aar;aar;α

In the problem we have 9 parameters: P and four complex amplitudes

The normalization + global phase constraint 7 independent parameters

iβiβiαiα ebb,ebb,eaa,eaa

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Decoupling P and b

bPcos() – dominant term The 5 angle method allows to

decouple P and b.

Estimating the statistical uncertainties

b can be measured with good precision even if P~0.

2) Small uncertainty (P), even for P~0.

statistical uncertainty of bstatistical uncertainty of bstatistical uncertainty of Pstatistical uncertainty of P

P P

correletion of b and Pcorreletion of b and P

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Summary and OutlookWe have done an extensive study of the feasibility of measuring b parameters in ATLAS:

Generator model in EvtGen for producing polarized b in ATLAS

b reconstruction from their decay into ’s and J/

Polarization and amplitudes extraction from the decay anglesEffects of angular resolution on the determination of the parameters Correlations between b and polarization

Future plansmake background studies continue to develop likelihood fitting proceduresincorporate trigger in analysismake Lifetime feasibility studiesdevelop plans for CP studies

18

Backup...

19

Acceptance Effects

ATLAS acceptance modifies the angular distributions

ATLAS acceptance modifies the angular distributions

It’s possible to correct distorted angular distributions with weight factors

generated distributionsgenerated after cutsafter corrections

cos() cos()cos()

Cuts @ Generator Level:

pT(p,)>0.5 GeV

pT()>2.5, 4 GeV

||<2.7

To calculate the corrections, phase space events (without any model or cuts) are used

pro

ton p

t (M

eV

)

cos()

cut

20

Backgrounds

Dominated by J/from b-hadrons + from heavier hadrons and fragmentation

fake and combinatorial background found negligible in similar topologies (B0 J/ Ks)

real J/ from cascade decay estimated at percent level (ex. Ξb

-,0 Ξ-,0 J/-,0J/)

B0 J/ Ks where a proton mass is given to a p rejected with mass constraints

for non direct b from b; try to reconstructb to reduce the diluition of polarization