investigating lepton universality via a...

Investigating Lepton Universalityvia a Measurement of the

Positronic Pion Decay Branching Ratio

Anthony PalladinoAdvisor: Dinko Pocanic

Ph.D. Dissertation DefenseCharlottesville, Virginia, USA

06 December 2011

Anthony Palladino (UVa) Investigating Lepton Universality with PEN 06 Dec ’11 1 / 37

Outline

IntroductionTheory of Pion Decay

Review of Helicity Suppresion

Physics MotivationLepton Universality

PEN ExperimentPrevious Measurements

TRIUMF and PSI

PEN Detector

AnalysisWaveform Fitting

Pulse Shaping and the Modified χ2 Objective Function

Maximum Likelihood AnalysisObservables, Processes, and Probability Distribution Functions

Conclusions


Introduction Theory of Pion Decay

Theory of π+ Decay

Quark Content: π+ = ud

Mass: mπ+ = 139.6 MeV

Lifetime: τπ+ = 26.03 ns

Decay Mode Branching Fraction

π+ → µ+νµ(γ) 0.9998770(4)π+ → µ+νµγ(Eγ>1MeV) 2.00(25)× 10−4

Bressi et al. ’98

π+ → e+νe(γ) 1.230(4)× 10−4Czapek et al. ’93, Britton et al. ’92, Bryman et al. ’86

π+ → e+νeγ(Eγ>10MeV) 7.386(54)× 10−7Bychkov et al. ’09

π+ → π0e+νe 1.036(6)× 10−8Pocanic et al. ’04

π+ → e+νee+e− 3.2(5)× 10−9Egli et al. ’89



Theory of π+ DecayWhy is π+ → e+νe a rare decay? Helicity Suppression

Conservation of Angular Momentum:In π rest frame, the π has S = 0.The outgoing lepton pair (each spin 1/2) must combine to give S = 0

• both Right-Handed (Positive Helicity), or

• both Left-Handed (Negative Helicity)

Property that if m = 0:

• All S = 1/2 particles are Left-Handed (Negative Helicity)

• All S = 1/2 antiparticles are Right-Handed (Positive Helicity)

⇒ The negative helicity νe (νµ) forces the e+ (µ+) into a negativehelicity state. But,

me+ � mµ+ (mµ+ ' 200me+ )



Theory of π+ Decay

Helicity: For v = c , fraction “violating” = 0.

For a given E , ve > vµ ⇒ e is less likely to have wrong helicity.

“Helicity Conservation” ⇐⇒ 12 + 1

2vc

. .

“Helicity Violation” ⇐⇒ 12 −

12vc

”HelicityViolation”(e+)”HelicityViolation”(µ+) ≈ 3.2× 10−5

π Decay Phase Space:Since the e+ is lighter, the π+ → e+νe decay has a larger phasespace than the π+ → µ+νµ decay. ⇒ gives a factor ∼ 3.3

Γ(π+→e+νe)Γ(π+→µ+νµ) ≈ 3.3 ×( 3.2× 10−5 ) ≈ 10−4



Theory of π+ Decay

π+ → e+νe2-body decay⇒ Ee+ = 69.8 MeV

π+ → µ+νµ followed byµ+ → e+νe νµsequential decay⇒ Emax

e+ = 52.5 MeV

Total Positron Energy (MeV)

Arb

itrar

y N

orm

aliz

atio

n

10-6

10-5

10-4

10-3

10-2

10 20 30 40 50 60 70 80 90 100


Introduction Physics Motivation

The PEN Experiment

• Precision Measurement of the π+ → e+νe branching ratio.

Rπe2 = Γ(π+→e+νe(γ))Γ(π+→µ+νµ(γ)) =

(gegµ

)2 (memµ

)2 (1−m2e/m

2µ)

2

(1−m2µ/m

2π)

2 (1 + δRπe2)

Rcalcπe2

=

(1.2352± 0.0005)× 10−4

Marciano & Sirlin, [PRL 71, 3629 (1993)]

(1.2354± 0.0002)× 10−4Finkemeier, [Phys. Lett. B 387, 391 (1996)]

(1.2352± 0.0001)× 10−4Cirigliano & Rosel, [PRL 99, 231801 (2007)]

Rexpπe2 = (1.230± 0.004)× 10−4

Experiment World Average (Current PDG)

Our Goal: ∆Rexp

Rexp ≤ 5× 10−4 PDG: ∆Rexp

Rexp ∼ 3.3× 10−3

Lepton Universality: W. Loinaz, et. al., Phys. Rev. D 65, 113004 (2004) [hep-ph/0403306](gegµ

)π

= 1.0021± 0.0016



Lepton Universality

From Loinaz et al.,PRD 70 (2004) 113004

∆` `′ = ε` − ε`′

where g`g`′

= 1 +ε`−ε`′

2

g`W +

ν`

`+u

d

π+{



Deviations from SM Prediction

A Branching Ratio that is different from the SM prediction could becaused by:

• lepton non-universality,

• charged Higgs particles in theories with more Higgs than SM,

• pseudoscalar leptoquarks in theories with dynamical symmetrybreaking,

• vector leptoquarks in GUTs,

• SUSY partner particles appearing in loop diagrams,

• non-zero neutrino masses,

• Majorons.



Mass Limits on Leptoquark and Supersymmetric Particles

A measurable deviation in Rπe2 from the SM prediction is clear evidence ofphysics beyond the SM, sensitive to mass scales of many TeV.

Particle Current Bounds Projected Mass Sensitivity

Charged Higgs Boson mH > 2 TeV > 6.9 TeV

Pseudoscalar Leptoquark mp > 1.3 TeV > 3.8 TeV

Vector Leptoquark MG > 220 TeV > 630 TeV

Following the calculations in Shanker, NP B204 (82) 375


PEN Experiment Previous Measurements

History of the Measurement

Branching Ratio0.0001 0.00011 0.00012 0.00013 0.00014

Branching Ratio0.0001 0.00011 0.00012 0.00013 0.00014

)1993Czapek (

)1992Britton (

)1986Bryman (

)1964DiCapua (

)1960Anderson (


PEN Experiment PEN Detector

Paul Scherrer InstituteVilligen, Aargau, Switzerland



The PEN Apparatus◦ stopped π+ beam◦ active target counter◦ 240-det. pure CsI calo.◦ central tracking◦ digitized PMT signals◦ stable temp./humidity

ATPMTvac.

MWPC1

MWPC2

PH

wAD

BC

CsIpure

π+beam

10 cm

PEN Detector 2008

wAD

(x4)



PEN Detector



Beam Counter, Focusing Magnets, and Detectors



The PEN Apparatus: 2008

◦ stopped π+ beam◦ active target counter◦ 240-det. pure CsI calo.◦ central tracking◦ digitized PMT signals◦ stable temp./humidity

ATPMTvac.

MWPC1

MWPC2

PH

wAD

BC

CsIpure

π+beam

10 cm

PEN Detector 2008

wAD

(x4)



The PEN Apparatus: 2008Novel, low cost, four-piece, Wedged Degrader. (UZh: P. Robmann)

Pros:

• x,y position sensitivity of beam π+

Cons due to thicker degrader (13mm as opposed to 5mm):

• higher beam momentum required ⇒ more nuclear reactions in target.

• more material increases multiple scattering ⇒ π position resolutionsuffers.



The PEN Apparatus: 2008

CsIpure

PV

MWPC1

MWPC2

Detector2008Ver9.xxx

Universität Zürich

Allgemeintoleranz DIN 7168-f

Physik-Institut

Bearb.

der

POS.

Datum

ZEICH_Nr. ANZ. MATERIAL

MASSTAB:

FILE:

PROJEKT/TITEL:

BESCHREIBUNG

(±0.1)

Detector 2008Setup with wedge degrader

BLATT:

Robmann october 2008

PeterPro

π+Beam

Photomultiplier ModuleHamamatsu H2431-50

TargetCounter

20 mm

30 mm

DistanceDegrader - Target

Target(Diameter 30 mm)

10 cm

y

z



Acqiris Digitizer

Acqiris High Speed 10-bit PXI/CompactPCI Digitizer, Model DC2824 Channels, each with 2 GS/s

Digitized PMT waveforms from three beamline detectors:

• Upstream Beam Counter

• Active Degrader

• Active Target



Fwd Beam Counter

Degrader Top & Bottom

Degrader Left & Right

Target

0 100 200 300 400 500 600 700 800 900 1000

0

10000

20000

30000

40000

50000

B0 Waveform

0 100 200 300 400 500 600 700 800 900 1000

0

5000

10000

15000

20000

25000

30000

35000

DEGLR Waveform

0 100 200 300 400 500 600 700 800 900 1000

0

10000

20000

30000

40000

50000

60000

DEGTB Waveform

0 100 200 300 400 500 600 700 800 900 1000

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

TGT Waveform


Analysis Waveform Fitting

Target Waveform Analysis

• Calibrate target energy to monoenergetic muon.

• Provide cuts, useful for distinguishing the various processes.

Channel Number (ns*2)0 100 200 300 400 500 600 700 800

Dig

itize

r A

mpl

itude

0

5000

10000

15000

20000

25000

30000

35000

TGT Waveform

π+ → µ+ → e+ Event.

Channel Number (ns*2)0 100 200 300 400 500 600 700 800

Dig

itize

r A

mpl

itude

0

5000

10000

15000

20000

25000

30000

35000

TGT Waveform

π+ → e+ Event.



Pulse ShapingDeveloped an iterative program to create a digital adaptive filter.

Input:

• Averaged systemresponse waveformarray, wi

• Desired waveformarray, wi

Output:

• Shaping array(”Filter“), si

-50 0 50 100 150 200 250 300

Nor

mal

ized

Am

plitu

de

0

0.2

0.4

0.6

0.8

1

Waveform Bin (0.5ns)-50 0 50 100 150 200 250 300

00.005

0.010.0150.02

0.0250.03

Pulse Shaping: wi =kmax∑

k=kmin

skwj where k ≡ i − j



Pulse Shaping

(0.5 ns)n

0 50 100 150 200 250 300 350 400

Filt

er A

mpl

itude

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

50 55 60 65 70 75 80 85 90 95

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

(0.5 ns)n

550 600 650

Am

plitu

de (

Arb

itrar

y U

nits

)

0

0.2

0.4

0.6

0.8

1

1.2 +π

+µ +e

Target Waveform

WaveformFiltered Target

• Filtering (Shaping) isolates the monoenergetic muon for energycalibration.

F A. Palladino, A. van der Schaaf, D. Pocanic,“Reconstructing Detector Waveforms with Overlapping Pulses”,to be submitted 2011.



Target Waveform Fit Parameters

Pulse Position in time Amplitude

π+ Known (from Degrader) Known (from TOF and EB0 +∑

Edeg )

σ ∼ 65 ps σ ∼ 716 keV (5.5%)

µ+ Unknown Known (monoenergetic)

σ ∼ 200 keV (4.8%)

e+ Known (from Plastic Hod.) Known (from tracking)

σ ∼ 492 ps σ ∼ 878 keV (29.2%)



π+ → µ+ → e+ Event Fit

(0.5 ns)n

600 610 620 630 640 650 660 670 680

Am

plitu

de (

Arb

itrar

y U

nits

)

0

0.5

1

1.5

2

2.5+π +µ

+e

WaveformRaw Target


(0.5 ns)n

600 610 620 630 640 650 660 670 680

Am

plitu

de (

Arb

itrar

y U

nits

)

0

0.5

1

1.5

2

2.5+π

+µ

+e


WaveformSubtracted Target

(0.5 ns)n

600 610 620 630 640 650 660 670 680

Am

plitu

de (

Arb

itrar

y U

nits

)

0

0.5

1

1.5

2

2.5+π

+µ

+e


Fit Result3-peak

Fit Prediction3-peak

Fit Result2-peak


π+ → e+ Event Fit

(0.5 ns)n

600 610 620 630 640 650 660 670 680

Am

plitu

de (

Arb

itrar

y U

nits

)

0

0.5

1

1.5

2

2.5

+π

+e

WaveformRaw Target


(0.5 ns)n

600 610 620 630 640 650 660 670 680

Am

plitu

de (

Arb

itrar

y U

nits

)

0

0.5

1

1.5

2

2.5

+π

+e


WaveformSubtracted Target

(0.5 ns)n

600 610 620 630 640 650 660 670 680A

mpl

itude

(A

rbitr

ary

Uni

ts)

0

0.5

1

1.5

2

2.5

+π

+µ+e


Fit Result3-peak


Fit Result2-peak




Waveform FittingModified χ2 Function:

χ2 = 1nd.o.f.

n∑i=1

(wFiti − wi

σw

)2

+ λ1

(EFitπ+ − EPred

π+

σEπ+

)2

+ λ2

(EFite+ − EPred

e+

σEe+

)2

t (0.5 ns / bin)600 605 610 615 620 625 630 635 640 645

w[

t ]

0

0.5

1

1.5

2

Shaped Target Waveform

2 Peak Fit Prediction

2 Peak Fit


3 Peak Fit

Figure: Waveform fit with both hypotheses.Anthony Palladino (UVa) Investigating Lepton Universality with PEN 06 Dec ’11 27 / 37


Waveform FittingModified χ2 Function:

χ2 = 1nd.o.f.

n∑i=1

(wFiti − wi

σw

)2

+ λ1

(EFitπ+ − EPred

π+

σEπ+

)2

+ λ2

(EFite+ − EPred

e+

σEe+

)2

t (0.5 ns / bin)550 560 570 580 590 600 610 620 630 640

w[

t ]

0

0.2

0.4

0.6

0.8

1

1.2

1.4Shaped Target Waveform


2 Peak Fit


3 Peak Fit

Figure: Waveform fit with both hypotheses.Anthony Palladino (UVa) Investigating Lepton Universality with PEN 06 Dec ’11 28 / 37


Waveform Fitting Results

Eve

nts

per

Cel

l

0

50

100

150

200

250

300

350

400

3 peak2χ

0 5 10 15 20 25 30 35

2 pe

ak2 χ

0

5

10

15

20

25

30

35

+ e→ +π

+ e→ +µ → +π

(MeV)+eE0 10 20 30 40 50 60 70 80

2 pe

ak2 χ

-

3 pe

ak2 χ

=

2 χ∆

-40

-30

-20

-10

0

10

20

30

40

Eve

nts

per

Cel

l

0

50

100

150

200

250

300

350

400

450

+πt - +et-10 0 10 20 30 40 50 60 70

2 pe

ak2 χ

-

3 pe

ak2 χ

=

2 χ∆

-40

-30

-20

-10

0

10

20

30

40

Eve

nts

per

Cel

l

0

20

40

60

80

100

120

140


Analysis Maximum Likelihood Analysis

PEN Data Analysis

Strategy:

Determine the most likely value of the π+ → e+νe branching ratio using aMaximum Likelihood Analysis.

Benefits:

• Provides a unique, unbiased, minimum variance estimate (for a largeenough sample).

• Practical, tractable approach via product PDFs

• Use as much data as possible to determine Rπe2 ; loose cuts.

Complication:

• Critical dependence on PDF



Maximum Likelihood AnalysisOne likelihood function encompassing many observables and processes.

L(−→xe ; fm

)=N∏e=1

[M∑

m=1

fm Pm

(−→xe

)]where N is the number of events, and

(−→xe ) are the observables

• Time between π+ and e+

• Total Positron Energy

• “Probability” of Pile-up

“P“pile-up = ln

[∑k=1

e−|dtk |/τµ

]• Pion Decay Vertex

• etc.

(fm) fraction of process m

• fπe2 , π+ → e+

• fπµ2 , π+ → µ+ → e+

• fAcc, Accidentals / Pile-up

• fDIF, Pion Decays-in-flight

• fHad, Proton

• f?, etc.



Model: Probability Distribution Functions, Pm

L(−→

E Total ; fπe2 , fπµ2 , fAcc, fDIF, fHad

)

• πµ2

• πe2

• Accidental Coincidence

• π Decay-in-flight

• Hadronic (proton)

χ2/Ndof = 3.8

10 20 30 40 50 60 70 80 90

-110

1

10

210

310

410

510

610

710

Energy Histograms stacked on top of each otherEnergy Histograms stacked on top of each other

ETotal (MeV)



Model: Probability Distribution Functions, Pm

L(−→

∆t ; fπe2 , fπµ2 , fAcc, fDIF, fHad

)

• πµ2

• πe2

• Accidental Coincidence

• π Decay-in-flight

• Hadronic (proton)

χ2/Ndof = 1.3

(ns)πt - et-5 0 5 10 15 20 25 30 35 40

Eve

nts

per

bin

310

410

510

te − tπ (ns)



Practicality: Negative Log Likelihood

` = −lnL L = e−` Np2e vs. Nmichel

Number of Michel events

19.5619.58 19.619.6219.6419.6619.68 19.7

610×

events

ν e→ π

Number of

3600036500

3700037500

3800038500

39000

-ln(

L)

0

10

20

30

40

50

Number of Michel events

19.5619.58 19.619.6219.6419.6619.68 19.7

610×

events

ν e→ π

Number of

3600036500

3700037500

3800038500

39000

L

0

0.2

0.4

0.6

0.8

1

Number of Michel events19.56 19.58 19.6 19.62 19.64 19.66 19.68 19.7

610×

eve

nts

ν e

→ πN

umbe

r of

36000

36500

37000

37500

38000

38500

39000

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8-310×

C++ code written specifically for this analysis.



Maximum Likelihood Analysis

• Framework complete

◦ Flexible: can add/remove processes and observables◦ Error analysis correct (weighted events)

• Errors comparable to χ2 fit

◦ ∆RR = 0.16% (statistical)

◦ ∆RR ∼ 2% (systematic) → ∆R

R < 0.02%


Conclusions

Conclusion

Year 2006 (Beam Development Phase):• Detector Refurbishment (Same detector from PiBeta Experiment).

Year 2007 (Experiment Development Phase):• More refurbishments / Many new components and upgrades.

Year 2008 (1st Production Phase):• Use of wedged degrader for π tracking.

• Recorded ∼ 5× 106 π+ → e+νe decays

Years 2009 and 2010 (2nd and 3rd Production Phases):• Use of mini-TPC for improved π tracking.

• Recorded ∼ 20× 106 more π+ → e+νe decays

Year 2011 (Data Analysis Phase):• Finalized target waveform analysis

• Developed Maximum Likelihood analysis framework


Conclusions

PEN Experiment Collaboration Members:L.P. Alonzi,a V. A. Baranov,c W. Bertl,b M. Bychkov,a Yu.M. Bystritsky,c

E. Frlez,a V. Kalinnikov,c N.V. Khomutov,c A.S. Korenchenko,c

S.M. Korenchenko,c M. Korolija,f T. Kozlowski,d N.P. Kravchuk,c

N.A. Kuchinsky,c M.C. Lehman,a D. Mekterovic,f D. Mzhavia,c,e A. Palladino,a

D. Pocanic,a? P. Robmann,g O.A. Rondon-Aramayo,a A.M. Rozhdestvensky,c T.Sakhelashvili,b V.V. Sidorkin,c U. Straumann,g I. Supek,f Z. Tsamalaidze,e

A. van der Schaaf,g? E.P. Velicheva,c V.V. Volnykh,c

aDept of Physics, Univ of Virginia, Charlottesville, VA 22904-4714, USAbPaul Scherrer Institut, CH-5232 Villigen PSI, SwitzerlandcJoint Institute for Nuclear Research, RU-141980 Dubna, RussiadInstitute for Nuclear Studies, PL-05-400 Swierk, PolandeIHEP, Tbilisi, State University, GUS-380086 Tbilisi, GeorgiafRudjer Boskovic Institute, HR-10000 Zagreb, CroatiagPhysik Institut der Universitat Zurich, CH-8057 Zurich, Switzerland

blue = Ph.D. Candidate

? = Spokesperson

PEN Web page: http://pen.phys.virginia.edu


investigating lepton universality via a...

Documents