A MONTE CARLO STUDY

μ μ

μ

DETECTING COPLANAR CHARGED TRACKS IN MUON DECAY

^-

A MONTE CARLO STUDY

1,2

Wan Ahmad Tajuddin Wan Abdullah and 1Janatul Firdaus Solehan

'Department

of

Physics, Faculty

of

^Science, Universiti Malaya, 50603Kualal Lumpur, Malaysia

3Faculty

of

Computer Science and

Information

Technology, Universiti Malaya.50603KualaLumpur, Malaysia

ABSTRACT

Inparticle detector, muon decay

u+

-A

e+ e+

e~ simulation teas use to study

of

^{muon particles}

bombardment to solid

surface .

^{Inthis paper the muon decay was simulated by using Monte Carlo}

method. The result showstree tracks charge must be incoplanar position with the

surface.

ABSTRAK

Dalam.pengesanzarah, Muon pereputanu

+ ^—>

^e

+

^e

+

e-simulasi adalah digunakan untuk mengkaji zarah Muon pengeboman ke permukaan pepejal. Dalam. kertas ini pereputan Muon telah disimulasikan dengan menggunakan kaedah Monte Carlo. Hasilnya menunjukkan pokok menjejaki caj mesti berada dalam kedudukan sesatah dengan permukaan.

Keywords:muon,MonteCarlo,detector

INTRODUCTION

The existence of muon was first identified in cosmic ray experiments in 1936.The muon is an elementary particle similar to the ^electron, with a unitary negativeelectric charge and a spin of lh. It isclassified as a lepton, together with theelectron,the tau,and the threeneutrinos.Itisanunstable subatomic particle with a mean lifetime of 2.2 ps.Like all elementary particles, the muonhas a correspondingantiparticle of opposite charge but equal massand spin: the antimuon (also called a positive muon).Muonsare denoted by ^" and antimuonsby

+.

Muons havea massof 105.7

MeV/c2,

whichisabout 200 timesthemassofanelectron.

CHARGED LEPTON FLAVOUR VIOLATION

Charged-lepton flavour violation (CLFV) isdefined by all charged-leptonprocessesthat violate lepton-flavour number.Inthe minimal standard modelneutrinosare massless and lepton flavour isconserved separately for each generation. The muonsystem is one of the best places to search for lepton-flavour-violating (LFV). In Table 1, the upper limits of variouslepton-flavour-violating decays arelisted. Inthis researchwe select ^+—

>

e+ e+

e"ascandidate.

The event signature ofthe decay p+H>

e+

^e"

e+

iskinematically well

constrained,

sinceallparticles in the final state are detectable. The decay width of p+H>e+

e+

^e" is determined from the

Effective

Lagrangian. In

μ

μ

μ γ

μ μ

μ μ

τ γ

τ μ γ τ μ μ μ τ

π μ

𝐾_𝐿⁰ μ π μ 𝐾_𝐿⁰ π μ

μ τ τ μ

μ

μ

θ ϕ

experimental for search ^+—

> e+e+e~

have been carried out after the pioneeringmeasurement in 1976 usinga

cylindrical spectrometer. Table 2 willshow the historicalprogress and summary of searches for ^+—

> e+e+e~

decay.

Table 1. Experimental limits for the lepton-flavour-violating decays ofmuon,tau, pion,kaon,andZ boson.

Reaction Present limit Reference

+-a

e+ <1.2

x

10"11 Brooks

et

al. (1999)

+-a

e+ e+

e"

<1.0

x

1012 Bellgardt.

et

al (1988)

-

Ti -<

^e

Ti <6.1

x

10"13 Wintz (1998)

+

e~

^—

»

^"

e+ <8.3

x

1011 Willmann

et al.

(1999)

-a- e

<2.7

x

10-6 Edwards

et

al. (1997)

-a

<3.0

x

10-6 Edwards

et

al (1997)

-A

<1.9

x

10"6 Bliss

et

al. (1998)

-a e e e

<2.9

x

10"6 Bliss

etat.

(1998)

0 -a e

<8.6

x

10"9 Krolak

et

al. (1994)

-a e

<4.7

x

10"12 Ambrose

et

al. (1998)

K+

-a ⁺

+e <2.1

x

10"10 Lee

et al.

(1990)

->

⁰

+e <3.1

x

10"9 Arisaka

et

al (1998)

Z°ÿ e

<1.7

x

10-6 Akers

et

al. (1995)

Z°ÿ e

<9.8

x

lO

⁶

Akers

et

al. (1995)

Z° <1.2

x

10-5 Akers

et

al. (1997)

Candidate: ^+—>ÿ

e+

e"

e+

Table2. The historicalprogressandsummaryofsearches for ^+—

> e+e+e

decay.

Place Year 90%-C.L.

upper

limit Reference

JINR 1976 < ^1.9

^x

^10"9 Korenchenko

et

al. (1976)

LANL 1984 < ^1.3

^x

^{1010 Bolton}

^et

^{al. (1984)}

SIN 1984 < ^1.6

^x

^{1010 Bertl}

^et

^{al. (1984)}

SIN 1985 < ^2.4

^x

^{1012 Bertl}

^et

^{al. (1985)}

LANL 1988 < ^3.5

^x

¹⁰

ⁿ

^Bolton

^et

^{al. (1988)}

SIN 1988 < ^1.0

^x

^{1012 Bellgardt}

^et

^{al. (1988)}

JINR 1991 < ^3.6

^x

^{1011 Baranov}

^et

^{al. (1991)}

Duringthe muondecay, tree charged particle willproduce. Figurel gives configuration ofmuondecay inxyz plane,wheretheta ( ) isacolatitudethe angle betweenthez-axis and the positionvector ofpipoandp3.The Phi( ) ismeasured from thex-axisthesameazimuthal angle.

Muon decays at rest has been used in all past experiments. In this case, the conservation of momentum

μ

μ

∑

e+'s

andonee-,wherepi and Ei(i=l-3),respectively, themomentumandenergyofeach of the e's. Kinematics of the ⁺ -A

e+ e+

e" decay in the muon center ofmass system, in which Pi,Po and

P3

are the momentum vector respectivelytothe 2 positron and 1electron.

z

Pi

Pi

Figure1. Kinematic variables of +—te+

e+

^e".

Pi

2

Figure 2. Theconservationofmomentum =

(| iPi|=0)

SIGNATURE: 3 CHARGED TRACKS IN MUON DECAY COPLANAR

In particle physics there two ways used to reveal the inner structure of atom. First method we look at smashingbeams of particleinto target in the lab. Secondway welookup at collision of beamwith fixed solid target. To observemuonparticle, we assume that the muonwilldecay treeparticle charge. This tree charge particle will be detected in coplanar. For simulation we use scalar triple product to make sure that tree charged tracks decay in coplanar position.Insimulation the value of [(vixvo)

• V3]

^{must bezero. Zeromeansits} perpendicular andwe cansay that thetreesubparticle chargewasincoplanar.

μ

μ

θ π

ϕ π

ѱ π π

μ μ μ

θ ϕ θ ϕ θ

σ θ ϕ σ ѱ θ ϕ σ ѱ ϕ

σ θ ϕ σ ѱ θ ϕ σ ѱ ϕ

MONTE CARLO STUDY

A Monte Carlousesrandomnumbersto modelsomesort ofaprocess.Inparticle physicsweused MonteCarlo methodtofindthe pprobability of particle interacting with matter and surviving the nuclear.Inthis research a Monte Carlo simulationwas to generate the random of data to useinmuondecay.Fromthe random data wewillgeneratethe simulation oftreechargedtracks in coplanar position.

SIMULATION

Firsly,we needgeneraterandom data for themuondecay ( +—te+e+e~). We needto decide the rangevalue of thecomponent inmuondecay.So that data wasselected in this range.The rangevalue of thecomponent for eachparticle charged tracks show in Table 3.

Figure 3. Figurationoftreechargedtracks inmudecay incoplanar.

Table3. Rangevalue of kinematic variable of +—te+e+e~

Variable Range value

Theta( )

^0ÿ2

Phi( )

^0ÿ2

Psi( )

^-

/2

^-a

/2

Pi 0

-a mass

of +(105.7 MeV/r)

P2 0

-a mass

of +-

pi

P.3 Mass of +- (Pi + ^P2)

After we generate the random data from range value of above variable we can construct momentum of each Pi,

P2

^and

P3.

The reconstructedmomentumofthesetreechargedtracksas

(Pl.Pix,

Ply.Piz) =(Pi,picos sin

,

picos cos

,

pisin )

(P2,

P2x, P2y,P2z)=

Pox

⁼

-P2

^{cos 3 cos cos}

+ ^P2

^{sin 3 sin sin cos -}

^P2

^{sin 3cos sin}

P2y

-P2

^{cos 3cos sin}

+

^{Posin 3sin sin sin}

+

^{Posin 3cos cos}

σ σ

θ ϕ

(P3,P3x, P3y,P3z)=

P3x^=0-

Plx

^-

P2x P3.V

^=0-Ply-P2y

P3Z=0

For component Piwe used normal trigonometry and for component P2we used transformation translationon origin. After weget thevalueofPiand P2we can get the value of P3.For component P2westart when pion thex-axis.

Refer tothe Figure 4,A show the origin of kinematic variable ofmuondecay. Bshow when thetaiszero and Cshows thepionthe x-axisthat meansthe phiiszero.Whenpiisonthex-axis,^tofindthe P2we canlookup at xy plane,we canstart looking for theP2at this point.ForP2component weneed another variable, 3 this isanangle betweenx-axis and y-axis. For 3, we cangeneratethis from the cosinelaw. So start at this point wedotreetimestransformation011thecomponent p2we usethe last transformationas acomponent p2

1

A B C

Figure4. A:Originofthe kinematic ofmuondecay,B:theta, =0,C:phi, =0.

v

> ^Vin-ffij

PI*

Figure5.Treecharged tracksonxy plan

μ

μ

PI

A.

o3

\

/\ol /\

*

^pj

Figure 6.Cosinelaw tofind the angle between

Pi

^{and Po}

RESULTS

Figure7,show us the distribution of each kinematicsvariablein the ⁺-A

e+ e+

e".This data was generating random number byMonte Carlo simulation. Fromthisdatawe cancomputethevalueofdata for treecharged tracks.InFigure 8.A,the value of coplanarityiszeroshow usthe tree charged track wasincoplanar. The rest of the graph shows the efficiency vs angular resolution. This efficiency show when we put some error in calculation. Figure8.B show the efficiency when it has 0.005 error, FigureS.C show the efficiency when it has 0.010error and lastly Figure 8.D show the efficiency whenithas 0.015error.

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Figure7. Distribution of random number of kinematic variable in

e+ e+

e"

I ^{rtkrcfoli )}

-

^a

-

S»

i«e

o

-»

:

—

-_»

m

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a:

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m

-

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^. -•

IE LM UE ka uz ^{ib (SB} U» 1X4: MB

* .

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U1 US OS US ID GOB Ml OH OK

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9m LME!1

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cabu«r*!nir(i1) B

~s fail

"l tod ^in.Rn.nn _"

ⁿ

U1 US Ott US Ul COS LM OH OK

c

D

FigureB.Efficiencyvsangular resolution

CONCLUSION

The simulationof themuondecay needsto be in coplanar. The purposeof this simulation we canexpand to the detector inmuondetector for the future research.

REFERENCES

Yoshitaka Kuno, Yasuhiro Okada,Muon Decay and Physics Beyond the Standard Model,Reviews of Modern Physics. Volume 73.Nol,Jan2001.

Mattew E. Thrasher, The Measurement,

Simulation,

and Interoretation of the Lifetime of Cosmic Muons, August 1998.

IzyanHazwani Hasyim, Development of Novel Particle Detector With Pixel Photon Counter Readout,May 2010.

Frank Close,Particle PhysicsA Very Short Introduction,2004.