11

g-2 g-2 phasephase study study from from GEANTGEANT simulation simulation

Qinzeng PengQinzeng Peng

Advisor:Advisor: James Miller James Miller

Boston UniversityBoston University

Sep 28, 2004Sep 28, 2004

Muon g-2 collaboration at BU: Muon g-2 collaboration at BU:

Lee Roberts, Rober Carey, Jon Paley, Xiaobo HuangLee Roberts, Rober Carey, Jon Paley, Xiaobo Huang

Institutes:Institutes:

BU, BNL, UIUC, Univ. of Minnesota, Yale Univ.BU, BNL, UIUC, Univ. of Minnesota, Yale Univ.

22

Outline Outline

I.I. Brief introduction to g-2Brief introduction to g-2

II.II. Experimental set up and simulationExperimental set up and simulation

III.III. Simulation results and analysisSimulation results and analysis

33

What is g-2?What is g-2?

sm

egSS

)

2(

)2

)(1(m

eα

magnetic moment gyromagnetic ratio spin

• Dirac equation predicts g=2• in nature radiative correction makes g≠2

2

2

ga

aμ(SM) = aμ(QED) + aμ(hadronic) + aμ(weak)

aμ(New Physics) = aμ(Measured) − aμ(SM)

where

Studied Muon instead of Electron due to 40000)( 2 em

m

44

Inflector

Kicker Modules

Storagering

Ideal orbitInjection orbit

Pions

Target

Protonsπ

(from AGS) p=3.1GeV/c

Experimental Setup – Muon storage

π μν

S

Polarization

Momentum

B

• Muon polarization• Muon storage ring• injection & kicking• focus by Quadrupoles R=711.2cm

d=9cm

(1.45T)

Electric Quadrupoles

E

55

spin precession and muon decayspin precession and muon decay)()(1()(),( /

0 twCosEAeENEtN t )()(1()(),( /0 twCosEAeENEtN t )()(1()(),( /0 twCosEAeENEtN t

• muons move in circle with constant speed• spin precession (Thomas + Larmor)• electrons decay mostly along the spindirection and boosted by Pmuon

• fitting by 5-parameter function to get

mceB

cs a )1()1(

N(t,E) = N0(E)e-t/τ(1+A(E)Cos(ωat+Φ(E))

mceB

csa a

B

P

S

nscmceB

c 2.149;1

DET

eve

])([1

12 EaBaw mc

ea

magic γ= 29.3

a

66

Phase shift on Phase shift on ωωa a uncertaintyuncertainty

))cos(1()( /0 tAeNtN t

tt 00)(

What if φ is not a constant?

Take an example: if mrad1

And measuring time is about 600 μs, then

00 )()()( tttt t

t/

ppmsrad

smrad

w16.1

/44.1

600/1

77

g2Geant simulationg2Geant simulation

Inflector

Ideal orbit

π

p≈3.1GeV/c B

DET

Beam-line simulation

g2Track

g2GEANT

Simulates nearly all geometric set up in the storage ring

• Inflection• Kicking• scraping

Jon Paley

Hugh Brown

Robert Carey

• Muons generation• Spin polarization

88

Beam-line / Calorimeter alignmentBeam-line / Calorimeter alignment

vertical

horizontal

Radial in Beam

Radial on DET

Vert. in Beam Vert. on DET

Beam in the ringCalorimeter

tdecay-tmeasure=drift time

99

Data selectionData selection

Energy cutEnergy cut : En >1.8GeV: En >1.8GeV Detector dependenceDetector dependence : average over 24 : average over 24

detectorsdetectors Drift timeDrift time : offset of g-2 phase: offset of g-2 phase

)))(cos()(1()(),( /

0 EtEAeENtEN t

dttt measuredecay

nsmraddtperiodgone

timedrift dtdt /44.12 2

1010

Beam

ФФ vs. detector vertical position vs. detector vertical position

• Symmetric about center• Energy dependent• ΔΦ big : -80 ~ +80 mrad• Φ(all) small : about 5 mrad • Φ change sign at 3cm

3cm

DET

ypc1

1111

outward and inward decayoutward and inward decay

outwardoutward Φ < 0< 0 dt longerdt longerinwardinward Φ > 0> 0 dt shorterdt shorter

3cm

outward

inward

1212

ФФ vs. detector radial position vs. detector radial position

• ΔΦ smaller, 30 mrad• Φ ≈0 on outside• Φ >0 on detector

1313

ФФ vs. beam vertical/radial position vs. beam vertical/radial position

• symmetric about center of beam•ΔΦ big• Φ ≈0 at center

• ΔΦ smaller• Φ ≈0 on inside• Φ >0

1414

Beam vertical shiftBeam vertical shift

• ΔΦ ≈0 • Φ is detector dependent, 4 groups --- 4 Quads

1515

Beam width changeBeam width change

idea: change beam vertical distribution by a weighting factor

Result : 1 percent width change / 0.1 mrad phase shift

1616

Beam upper cut – muon lossesBeam upper cut – muon losses

cut at 3cm

vert

ical

• Muon losses: 1.64%• ΔΦ = -0.323 mrad

9cm

1717

Detector gain shiftDetector gain shift

• very small effect

• 10% gain shift /

ΔΦ = 0.014 mrad

DET Vert.E

1.05 E

0.95 E

1818

Beam / detector vertical alignmentBeam / detector vertical alignment

• 0.9mm/1.0mm shift • 0.11%/1.0% width change

1919

CBO modulationCBO modulation

Betatron OscillationBetatron Oscillation

))cos(1()(

))cos(1()(

))cos(1()(

0

0

0

tAt

tAAtA

tANtN

CBO

ACBOA

NCBON

Combine 23 detectors in one CBO periodCombine 23 detectors in one CBO period

Time = MOD ( time - DET# /24*Tcbo, Tcbo)

Coherent Betatron OscillationCoherent Betatron OscillationBOCCBO

n

n

CYBO

CXBO

)1(

2020

Sampling Tcbo=2.4μs

2121

24

;24

1

DETTtt

orCID

Ttt

cbo

cbo

Combine 23 detectors CBO effect

2222

CBO modulation

Number modulation Asymetry modulation, 0.22%

2323

phase modulation, 0.358 mrad dt modulation, 0.175 mrad

2424

conclusionsconclusions

Simulation results consistent with Real datSimulation results consistent with Real data, like FSD studies.a, like FSD studies.

Phase shift due to the geometric set up is Phase shift due to the geometric set up is a small effect on a small effect on ωωa a ..

CBO effect is a small effect.CBO effect is a small effect.