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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
Luigi Capozza, Institutsseminar - 6.2.2006 2/38
Outline
Theory
Measurement principle
Physical processes
Detector response
Some results
Luigi Capozza, Institutsseminar - 6.2.2006 3/38
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
Luigi Capozza, Institutsseminar - 6.2.2006 4/38
Theory
N → ∆ transition: only isovector
ARL = AresRL + Anon-res
RL
Non resonant asymmetry Anon-resRL : model dependent
phenomenological effective interaction lagrangians:
Luigi Capozza, Institutsseminar - 6.2.2006 5/38
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)
]
Luigi Capozza, Institutsseminar - 6.2.2006 6/38
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
Luigi Capozza, Institutsseminar - 6.2.2006 6/38
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
]
Luigi Capozza, Institutsseminar - 6.2.2006 6/38
Outline
Theory
Measurement principleThe A4 experimentEnergy spectrumProblem: Handling the background
Physical processes
Detector response
Some results
Luigi Capozza, Institutsseminar - 6.2.2006 7/38
The A4 experiment
longitudinally polarisedelectron beam
unpolarised ℓ-H2 target counting of scattered
particles measurement of scattered
particle energy
Luigi Capozza, Institutsseminar - 6.2.2006 8/38
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-
Luigi Capozza, Institutsseminar - 6.2.2006 9/38
A4 experimental setup
Lead fluoride Cherenkovcalorimeter:
1022 crystals
7 rings
146 frames
θ ∈ (30, 40), ϕ ∈ (0, 2π)
Readout electronics:
sum of 9 neighbouringcrystals
Luigi Capozza, Institutsseminar - 6.2.2006 10/38
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
Luigi Capozza, Institutsseminar - 6.2.2006 11/38
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√
Luigi Capozza, Institutsseminar - 6.2.2006 12/38
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
Luigi Capozza, Institutsseminar - 6.2.2006 13/38
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∆
Elastic peakElastic cut Elastic cut
︸ ︷︷ ︸
Monte Carlo simulations
Luigi Capozza, Institutsseminar - 6.2.2006 14/38
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∆
Elastic peakElastic cut Elastic cut
︸ ︷︷ ︸
Monte Carlo simulations
Event generator GEANT4 simulations
Luigi Capozza, Institutsseminar - 6.2.2006 14/38
Outline
Theory
Measurement principle
Physical processesElastic e-p scatteringEnergy straggling in the targetInelastic e-p scattering
Detector response
Some results
Luigi Capozza, Institutsseminar - 6.2.2006 15/38
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′)
Luigi Capozza, Institutsseminar - 6.2.2006 16/38
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
Luigi Capozza, Institutsseminar - 6.2.2006 17/38
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′
Luigi Capozza, Institutsseminar - 6.2.2006 18/38
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)
Luigi Capozza, Institutsseminar - 6.2.2006 20/38
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
Luigi Capozza, Institutsseminar - 6.2.2006 21/38
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)
Luigi Capozza, Institutsseminar - 6.2.2006 21/38
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
Luigi Capozza, Institutsseminar - 6.2.2006 22/38
Outline
Theory
Measurement principle
Physical processes
Detector responseSimulation of the A4 detectorParticle tracking with GEANT4Production and detection of Cherenkov lightParameterisation of the photoelectron emission
Some results
Luigi Capozza, Institutsseminar - 6.2.2006 23/38
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
Luigi Capozza, Institutsseminar - 6.2.2006 25/38
Simulation of the A4 detector
Definition of the detector geometry: Volumes (shape, dimentions, position) Materials (composition, ρ, Z, A)
Luigi Capozza, Institutsseminar - 6.2.2006 26/38
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
Luigi Capozza, Institutsseminar - 6.2.2006 27/38
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)
Luigi Capozza, Institutsseminar - 6.2.2006 28/38
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
Luigi Capozza, Institutsseminar - 6.2.2006 29/38
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
)
%
Luigi Capozza, Institutsseminar - 6.2.2006 30/38
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
Luigi Capozza, Institutsseminar - 6.2.2006 31/38
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
Luigi Capozza, Institutsseminar - 6.2.2006 32/38
Outline
Theory
Measurement principle
Physical processes
Detector response
Some results
Luigi Capozza, Institutsseminar - 6.2.2006 33/38
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
Luigi Capozza, Institutsseminar - 6.2.2006 34/38
Result for electrons
Input information: from the spectrum itself: scattering processes
detector physics
position of the peak
Luigi Capozza, Institutsseminar - 6.2.2006 35/38
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
Luigi Capozza, Institutsseminar - 6.2.2006 36/38
Result for backward scattering
ADC channel0 10 20 30 40 50 60 70
3co
unts
/ 10
0
5
10
15
20
25
30
35
40
background is dominant
it is neutral particles ⇒ γ’s
Luigi Capozza, Institutsseminar - 6.2.2006 36/38
Result for backward scattering
ADC channel0 10 20 30 40 50 60 70
3co
unts
/ 10
01
2
34
567
89
background is dominant
it is neutral particles ⇒ γ’s
coincidence spectrum reproduced by simulation
Luigi Capozza, Institutsseminar - 6.2.2006 36/38
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
Luigi Capozza, Institutsseminar - 6.2.2006 37/38
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
Luigi Capozza, Institutsseminar - 6.2.2006 38/38
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