status report on parity violation in the (1232) · pdf fileoutline theory measurement...

Status report on parity violation in the∆(1232) resonance

Luigi Capozza

A4 CollaborationInstitut für Kernphysik

Johannes Gutenberg Universität Mainz

Institutsseminar - 6.2.2006

Luigi Capozza, Institutsseminar - 6.2.2006 1/38

Outline

Theory

Measurement principle

Physical processes

Detector response

Some results


Outline

Theory


Physical processes

Detector response

Some results


Theory

Parity violation asymmetry in ep → eNπ:

ARL =σR − σL

σR + σL=

GF Q2

2√

2πα

WPV

WEM

At Tree level:

WEM: unpolarised electromagnetic

WPV : helicity dependent interference of EM and NC transitionamplitudes

Flavor-SU(3) and isospin:

JEMµ

= JEMµ

(T = 1) + JEMµ

(T = 0)

JNCµ

= ξT=1V JEM

µ(T = 1) + ξT=0

V JEMµ

(T = 0) + ξ(0)V V(s)

µ

JNC5µ

= ξT=1A A(3)

µ+ ξT=0

A A(8)µ

+ ξ(0)A A(s)

µ


Theory

N → ∆ transition: only isovector

ARL = AresRL + Anon-res

RL

Non resonant asymmetry Anon-resRL : model dependent

phenomenological effective interaction lagrangians:


Theory

JEMµ

= JEMµ

(T = 1) + JEMµ

(T = 0)

JNCµ

= ξT=1V JEM

µ(T = 1) + ξT=0

V JEMµ

(T = 0) + ξ(0)V V(s)

µ

JNC5µ

= ξT=1A A(3)

µ + ξT=0A A(8)

µ+ ξ

(0)A A(s)

µ

Resonant asymmetry:

AresRL = − GF Q2

4√

2πα

[ge

AξT=1V + ge

VξT=1A F(Q2, s)

]


Theory

Resonant amplitudes:˙

∆(p′)˛

˛JEMµ

˛

˛N(p)¸

= uλ(p′)

»„

Cγ3

Mγ

ν +Cγ

4

M2p′ν +

Cγ5

M2pν

«

(gλµgρν − gλρgµν)qργ5

–

u(p)

D

∆(p′)˛

˛

˛JNCµ + JNC

5µ

˛

˛

˛N(p)

E

=

uλ(p′)

"

CZ3V

Mγ

ν +CZ

4V

M2p′ν +

CZ5V

M2pν

!

(gλµgρν − gλρgµν)qργ5 + CZ

6V gλµγ5

CZ3A

Mγ

ν +CZ

4A

M2p′ν!

(gλµgρν − gλρgµν)qρ + CZ5Agλµ + CZ

6Apλqµ

#

u(p)

Considering:

isospin symmetry

conservation of vector current

spin and parity of the ∆(1232) (Jπ = 3/2+)

dominance of magnetic dipole amplitude


Theory

Resonant asymmetry:

AresRL = − GF Q2

4√

2πα

[ge

AξT=1V + ge

VξT=1A F(Q2, s)

]

Axial response function of p → ∆ transition:

F(Q2, s) = P CA5

CV3

[

1 +W2 − Q2 − M2

2M2

CA4

CA5

]


Outline

Theory

Measurement principleThe A4 experimentEnergy spectrumProblem: Handling the background

Physical processes

Detector response

Some results


The A4 experiment

longitudinally polarisedelectron beam

unpolarised ℓ-H2 target counting of scattered

particles measurement of scattered

particle energy


A4 experimental setup

MAMIE=855 MeV or E=570 MeV

I=20 A, P= 80 %µ

Comptonlaserback scatterpolarimeter

Hydrogentarget

PbF

Calorimeter2

Luminosity

TransmissionCompton PolarimeterBeam Dump

e-

e-

e-

e-


A4 experimental setup

Lead fluoride Cherenkovcalorimeter:

1022 crystals

7 rings

146 frames

θ ∈ (30, 40), ϕ ∈ (0, 2π)

Readout electronics:

sum of 9 neighbouringcrystals


Energy spectrum

ADC Channel60 80 100 120 140 160 180 200 220

coun

ts

0

20

40

60

80

100

310× E’(MeV)300 400 500 600 700 800

W(MeV)1100.01150.01200.01250.01300.01350.0

th0πpeak∆

Elastic peakElastic cut Elastic cut


Extraction of the physical asymmetry

Aexp =

N+

ρ+ − N−

ρ−

N+

ρ+ + N−

ρ−

= P · Aphys + Ainst

• extraction of counts√

• normalisation on target density√

• correction of helicity correlated instrumental effects√


Problem: Handling the background

First step: Identification of the contributing physical processes Estimation of their contribution to the spectrum

Second step: Estimation of their asymmetry Calculation of a dilution factor


Knowledge of the background

physicalprocessesinside the

target

+response

of theapparatus

⇒

ADC Channel60 80 100 120 140 160 180 200 220

coun

ts

0

20

40

60

80

100

310× E’(MeV)300 400 500 600 700 800

W(MeV)1100.01150.01200.01250.01300.01350.0

th0πpeak∆


︸︷︷︸

Monte Carlo simulations


Knowledge of the background

physicalprocessesinside the

target

+response

of theapparatus

⇒

ADC Channel60 80 100 120 140 160 180 200 220

coun

ts

0

20

40

60

80

100

310× E’(MeV)300 400 500 600 700 800

W(MeV)1100.01150.01200.01250.01300.01350.0

th0πpeak∆


︸︷︷︸

Monte Carlo simulations

Event generator GEANT4 simulations


Outline

Theory


Physical processesElastic e-p scatteringEnergy straggling in the targetInelastic e-p scattering

Detector response

Some results


Event generator

Variables to be generated:

• x : position of the scattering

• θ : polar scattering angle

• E′: final electron energy

Needed:

• ranges: (xmin, xmax), ∆Ω, (E′

min, E′

max)

• differential cross sections: dσ(x, θ, E′)


Elastic e-p scattering

Rosenbluth cross section:

d2σ

dΩ

∣∣∣∣Ros(E, θ) (dipole fit for GE and GM )

Radiative corrections to the elastic scattering:

_e

_e

ip

fp

= _e

_e

ip

fp

+ _e

_e

ip

fp

+ _e

_e

ip

fp

+ _e

_e

ip

fp

+ _e

_e

ip

fp


Radiative corrections to the elastic scattering

Two kinematical regions:

radiative tail from the elastic peak (E′ < E′

el − ∆Er)

d3σ

dΩdE′

∣∣∣∣tail

(E, E′, θ)

elastic peak (E′ > E′

el − ∆Er)

d2σ

dΩ

∣∣∣∣peak

(E, θ) = (1 + δ(∆Er, E, θ))d2σ

dΩ

∣∣∣∣Ros

(E, θ)

Peaking approximation ⇒ Mo and Tsai’s formulae

for δ andd3σ

dΩdE′


Energy straggling in the target

Energy losses given by: Radiation Collisions

E [MeV]∆10 20 30 40 100 200 300

]-1

[M

eVeI

-610

-510

-410

-310

-210 Mo and Tsai

Landau

Moller/

Large energy losses mainly due to BremsstrahlungLuigi Capozza, Institutsseminar - 6.2.2006 19/38

Straggling function

Formula of Mo and Tsai:

Ie(E0, E, t) =bt

E0 − E

[

EE0

+34

(E0 − E

E0

)2] (

lnE0

E

)bt

for Bremsstrahlung using peaking approximation valid up to a cut E < E0 − ∆Es

for E > E0 − ∆Es

J∆Ese (E0, t) = 1 −

∫ E0−∆Es

0dE · Ie(E0, E, t)


Generation of ep→ep(γ) events

Energystraggling

+ radiativecorrections

⇒ 4 kinematical regions

E500 1000 1500 2000 2500 3000 3500 4000 4500 5000

E’

500

1000

1500

2000

2500

sE∆

elE’

rE∆ - elE’

0E


Generation of ep→ep(γ) events

Region Cross section

I d2σ

dΩ

∣∣∣∣I

= Jed2σ

dΩ

∣∣∣∣peak

(E0)

II d3σ

dΩdE′

∣∣∣∣II

= Ie(E0, E)dEdE′

d2σ

dΩ

∣∣∣∣peak

(E)

III d3σ

dΩdE′

∣∣∣∣III

= Jed3σ

dΩdE′

∣∣∣∣tail

(E0)

IV d3σ

dΩdE′

∣∣∣∣IV

=

∫ Emax

Emin

dE Ie(E0, E)d3σ

dΩdE′

∣∣∣∣tail

(E)


Inelastic e-p scattering

Processes: e + p → e + p + π0

e + p → e + n + π+

Inclusive cross section:

d3σ

dΩedE′=

∫

dΩπ

d5σ

dΩedE′dΩπ

E’[MeV]200 300 400 500 600

MeV

srnb

dE’

Ωdσ3 d

0.0

0.2

0.4

0.6

0.8


Outline

Theory


Physical processes

Detector responseSimulation of the A4 detectorParticle tracking with GEANT4Production and detection of Cherenkov lightParameterisation of the photoelectron emission

Some results


The A4 detector

PbF2 Cherenkovcalorimeter

ℓ-H2 target

1022 crystals ordered in 7 ringsLuigi Capozza, Institutsseminar - 6.2.2006 24/38

The response of the A4 detector

What happens between scattering and the energy spectrum?

Passage through material layers

Physics of the detector

Electromagnetic showerCherenkov effect


Simulation of the A4 detector

Definition of the detector geometry: Volumes (shape, dimentions, position) Materials (composition, ρ, Z, A)


Simulation of the A4 detector

Definition of particles and processes γ:

Compton scattering pair production photoelectric effect

e− and e+: ionisation Bremsstrahlung multiple scattering

only for e+: annihilation


Particle tracking with GEANT4

mean free path (MFP)

σ’s

continuous (CP)

discrete (DP)

materialsprocessescuts

particle tracking

stepping 5. calculate effect of CP’s4. sample position3. choose DP by MC2. calculate probabilities1. choose shortest MFP

6. sample final state of DP’s(step ∋ only 1 DP)


Production and detection of Cherenkov light

More geometry and materialproperties:

refractive indexes absorption lengths optical surfaces

More particles and processes:

optical photons Cherenkov effect absorption boundary process

Wavelenght [nm]300 400 500 600 700 800

Wavelenght [nm]300 400 500 600 700 800

abso

rptio

n le

ngth

[m

]

0.0

0.5

1.0

1.5

2.0

Wavelenght [nm]300 400 500 600 700 800

Wavelenght [nm]300 400 500 600 700 800

refr

activ

e in

dex

1.70

1.75

1.80

1.85

1.90

⇒ tracking of optical photons


Production and detection of Cherenkov light

Spectral sensitivity characteristic:

input window

photocathode sensitivity

Wavelenght [nm]250 300 350 400 450 500 550 600 650

Wavelenght [nm]250 300 350 400 450 500 550 600 650

WmA

esk

1

10

210

Quantum efficiency:

QE(λ) ≃(

124 nmλ

· ske(λ)W

mA

)

%


Parameterisation of the photoelectron emission

Simulating the whole electromagnetic shower is possible

Tracking all Cherenkov photons takes too long

Parameterisation needed:

deposited energyin one crystal

⇒Photoelectrons

in the respectivePMT


Parameterisation of the photoelectron emission

Ansatz: gaussian fluctuations of Npe

[MeV]dE0 100 200 300 400 500 600 700

peN

0

200

400

600

800

1000

1200

1400

1600

strong linear correlationr = 0.997

mean Npe lineardependent on Ed

(MeV)dE0 100 200 300 400 500 600 700

peva

rian

ce o

f N

0

2000

4000

6000

8000

10000

σ2Npe

also linear in Ed


Outline

Theory


Physical processes

Detector response

Some results


Comparison with the experimental spectrum

1. “Calibration”: Npe → ADC channel

knowledge of offset and peak position linearity

2. Scaling factor ξ

ξ =L σ · ∆t

Nevt

L : luminosity (ρ I ℓ)

σ : total cross section

∆t : run duration

Nevt: simulated events


Result for electrons

Input information: from the spectrum itself: scattering processes

detector physics

position of the peak


Result for backward scattering

ADC channel0 10 20 30 40 50 60 70

3co

unts

/ 10

5

10

15

20

25

30

35

40

background is dominant



ADC channel0 10 20 30 40 50 60 70

3co

unts

/ 10

0

5

10

15

20

25

30

35

40


it is neutral particles ⇒ γ’s



ADC channel0 10 20 30 40 50 60 70

3co

unts

/ 10

01

2

34

567

89


it is neutral particles ⇒ γ’s

coincidence spectrum reproduced by simulation


Work in progress

Contribution of γ’s?(at backward angle important!)

Processes

e + p → e + p + π0 → (e + p) + γ + γ

e + p → (e + p) + γ

Detector response very similar to e−

conversion (dominant) Compton


Summary

Parity violation in the ∆(1232) interesting for hadronstructure

Possibility of measuring the PV asymmetry within the A4experiment

Large background: understanding of energy spectrumneeded

Study of scattering processes detector response

Detector response under control Electron contribution well understood Working on contribution of γ’s


status report on parity violation in the (1232) · pdf fileoutline theory measurement...

Documents