Exercise to treat spin-dependent decays

I. Goal:– Study the relationship between momentum pe

accuracy/precision and a, Analyzing power <A>.

– Estimate the required performance of the detector.

Tool: GEANT4

1

II. Exercise to check basic kinetics:1. Energy and momentum conservation,2. 2D event yield distribution as functions of y and cmS

y = pcme/pmax

cmS is an angle between spin-axis and momentum direction of

decay-e+ at the center-of-mass system. ( see next page)

III. Check wiggle plots:“usual” wiggle plot,“Beam-loss free” wiggle plot.

Today’s contents

0,tsin,tcosS aa

Center-of-Mass system

taX,

Y

Z

Momentum

sinsin,cossin,cosp

p mcm

mcm

mcm

e

eDirection of decay-positron

mcm

ZB,0,0B

Magnetic field

Spin-direction

mcm

mcmm

Lab cos1

coscos

,mLabWe measure . Lorentz boost

2

tcoscostsincossinSp

pcos a

mcma

mcm

e

eScm

Scm

Angle between spin-axis and momentum direction of decay-e+ at the center-of-mass system:

2

mp

ppy

maxe

maxee

.y23

1y2yA ,y23yyn

,sincosyA1yn2

1

dyd

dP

2

Monte Carlo

Expected 2D event yield distribution as functions of y and cmS

3

Monte Carlo

4

P=300MeV/c , =3,Tc =7.4nsec, R=333mm,Ta=2/a=2.2sec.

Positron energies28 ~191 MeV

GEANT4B3 T

Condition:

5

8.6MeV positron

50.4MeV positron

GEANT4

102MeV positron

B ＝ 3T

6

II. Check basic kinetic values from GEANT4

7

Probing Spin-dependent Decay Info.

I. To be more simple, I set 100% ! II. Probe “decay process” information in the lab frame

directly. (I use “UserSteppingAction”.) Spin vector, momentum of at previous step of decay

process. Momentum and energies of daughters.

III. Check momentum/energy conservation. Within few eV at =1, within few keV at =3. why?

IV. Apply Lorentz transformation to get values in the center-of-mass system.

V. Cook values as I want!!

ee

8

2

mp

ppy

maxe

maxee

GEANT4

XL

2Z

2YT

pp

ppp

2Z

2Y

2Xe pppp

X axis is always -momentum direction.

9

Monte Carlo vs. GEANT4

y = pcme/pmax

is an angle between spin-axis and momentum direction of decay-e+ at the center-of-mass system.

10

Monte Carlo

GEANT4

11

III. Wiggle plots made by GEANT4

12

“Usual” wiggle plot and “Beam-loss free” wiggle plot

tcosA1t

expNtF a

4 free parametersCovariant matrix is OK.9.5 105 , E> 200 MeV 1.3105e+

13

tcoscosA12

N

tcoscostdydsinyayndyyn2

1tN

tcoscosya12

yn

dydsin

dP

dyd

dP

.tcoscostsincossincos ,here

,cosya1yn4

1

dyd

dP

amcm

amomcm

y

Scm

Scm

y

amomcmS

cmScmcm

amomcma

momcm

Scm

Scm

cm

Scm

tcosAtRtL

tRtLtAsym

,tcosA12

NtR ,tcosA1

2

NtL

a

aa

“Beam loss free” wiggle plot by knowing

momcm

Measure!

An angle between + and e+ momentum direction in the center-of-mass system.

No exponential term! 14

LEFT RIGHT

tcosAtAsym a

No worry about -beam loss! But, need to handle left-right

detector asymmetry.

9.5 105 , 1.9 105 e+ y> 0.6 , LEFT: 1 cos 0.7RIGHT:1 cos 1 0.7

15

A big advantage to measure

.y

Ecos

,cosddyyn

cosdydcosyayn

A

thLabS

cm

cos

Scm

y

y cos

Scm

Scm

LAB

Scm

Scm

.

dyyn

dyyayn

A

y

yCM

Lab-frame

Center-of-mass frame

”Effective Analyzing Power” is smeared by cos cm S

If we can measure cm S event-by-

event, ”Effective Analyzing Power” is NOT smeared by cos cm

S!

Spincm

We have bigger effective Analyzing Power 16

Next things….

I. Study the relationship between measured momentum accuracy/precision and a, Analyzing power <A>.

II. Estimate the required performance of the detector.

Now, I am ready to think about detector performance.

I, also, will play with G4-beamline to think about -beam line. (Need a time to learn it, though.)

17

18

How many positrons we need for EDM ?Value [e cm] statistics comment

Exp. results

( 3.7 3.4 ) 1019

(0.04 1.6 0.17) 1019

( 0.1 0.2 1.07 )1019

11.4106 e+, e

9.4106 e+

975 106 e

CERN (1974~76)E821 (1999, 2000, Trace back detector, Fig .7)*E821 （ 2001, PSD1-5, Tbl. IV)*

Predic-tion

(1.4 1.5 ) 1025 　 Mass scale of lepton EDMs

> 10 -23 Extended SM model

Our goal

1022 level 1024 level

~1013 @ magic=29.3

~1017@ magic=29.3

~ 31014 @ =3~ 31018@ =3

cme107.4cm2

e

2EDM 14

e

m

Bt

2 t

0

e

t

0e

sume

sume1

0e1

NtexpN~N

,N2AA

1

N2AA

1

EDM sensitivity:

m2

eBA1

“Improved Limit on the Muon Electric Dipole Moment “ 2EAPS/123-QCD

y vs. cos

.y23

1y2yA ,y23yyn

cosyA1yn2

1

cosdyd

dP

2

y

cos

19

20

a

0

0

etotal

a0e

AN

21

NdttNN

,tcost

expNtN

*a

*a

*

20

*2*0

**a

0**0

**00total

,AN

21

AN

21

,NN

,NNN

ミュービーム強度はによらず、一定だとし、(Ntotal=const.)

I checked with Toy Monte Carlo

Relationship between a and