The PRIMEX Experiment: A
Fundamental Test of the Chiral
Anomaly Prediction in QCD
Erik Minges
April 23 rd , 2010

Outline
• Symmetry and conservation Laws
– Overview and examples
• PRIMEX physics motivation
– The Chiral Anomaly
• Experimental Setup
• PRIMEX first run results
• Prototype detector beamtest
– Energy calibration, shower profile, position resolution
– Conclusion

Symmetry – What is it?
• Generalized to mean invariance
– A system which remains unchanged under a certain kind of transformation.
• Rotational symmetry of a pencil
Symmetry Breaking
Rotational Symmetry

Symmetry cont.
• Powerful tool in physics
– In 1905, Amalie Noether determined the connection between symmetry and conservation laws
• Noether’s theorem – For every continuous mathematical symmetry, there is a corresponding conservation law.
• “it is only slightly overstating that physics is the study of symmetry.” – Philip Warren Anderson
– American Physicist and Nobel Laureate
• Contributions to theories of localization, antiferromagnetism, and high-temperature superconductivity

PRIMEX Experiment
• The PRIMEX experiment at Thomas Jefferson National Lab is to measure the lifetime of the π 0 particle with high precision.
This experiment is a very important test of Quantum
Chromodynamics (the theory to describe the strong interaction).

PRIMEX Physics Motivation
• Prediction of the decay width in Chiral
Anomaly is exact in the Chiral limit.
– However quarks have mass.
– Leads to correction in theory.
• Neutral Pion decay measured to test fundamental prediction of low energy QCD.
–    dominated by axial anomaly.

Chiral Anomaly
• Axial symmetry of the Classical Lagrangian of
Quantum Chromodynamics is broken in the Chiral limit.
– Chiral limit is when the up, down quark masses vanish.
• This symmetry breaking is of pure Quantum mechanical origin due to quantization.
• The Lagrangian has continuous symmetry, but no conservation law associated with it
– i.e. - no conserved current

Confirmation of Quark Color
• In the chiral limit, the predicted decay amplitude
A



N
( 3
 f

C
)

2 .
513

10

2
GeV

1
– Where is the number of quark colors in QCD
C and is the Pion decay constant.
• Precise predicted decay width
  m
3


A

64
 
2

7 .
725 eV
• Number of quark colors will be directly measured by this experiment
– Number colors most fundamental parameter in Physics

Primakoff Effect
• Virtual photon from nucleus of target interacts with tagged photon from incident photon beam.
– Virtual photon and tagged photon create neutral Pi meson
• Photopion production from Coulomb field of nucleus.
• Pion decay in forward direction, so need good central resolution.
– Pi zero has high branching ratio to decay into 2 gamma rays, which HYCAL can detect.

Experimental Setup
Helium bag less particle interaction than air and cheaper than vacuum
Magnet measure pair production to monitor photon flux and sweep out charged particles
Electron beam passing through nucleus field and change momentum, produce Bremsstrahlung radiation
Radiator
Physics target
(Primakoff)
Measure energy and momentum of scattered electrons yield energy and momentum of gamma produced

Status of PRIMEX
PrimEx-I

(

) = 7.82eV

2.2%

2.1%
Next toLeading Order
Chiral Anomaly
Leading Order
Chiral Anomaly

4
Center Crystals PbWO4
Surrounding Lead Glass

• What is the need for an energy calibration?
– 36 PbWO
4 e
– Meaningful average pulse height signal from ADC requires calibration of each crystal using known incident beam energies
• e
– x-y coordinate detector with 60 scintillating fibers on each axis
• Detects position of incident electrons.
• Each fiber approximately 2 mm in diameter
– Dipole magnet’s field yields incident energy of electrons
• Incident electron beam energy as a function of X – fiber number is
E beam

3 .
5004

0 .
15153

10

1
*

0 .
46112

10

4
*

0 .
11645

10

6

• Alignment
– Each crystal needs to have the same response
– Align each individual crystal center
• Assume all incident energy is deposited at center of crystal
• Assume no energy is lost due to leakage into surrounding crystals
• Find mean ADC at center of crystal, divide by known incident energy adc(1) for run 435 cut at (X=29) and (Y=31)
E beam
=A*(mean ADC) mean ADC = 5413 i.e. For run 435 (centered on crystal 26)
E beam
= E(29) = 3.98145729105
(mean ADC) = 5413
... so A = 7.35536171E-04!!!

• Absolute scale from 5x5 cluster size
• Shower interacts in several crystal
– Sum all deposited energy in surrounding crystals to account for leakage
E beam
= B*[ ∑ A i
* (mean ADC) i
] i.e. For run 419 (centered on crystal 15)
E beam
= E(29) = 3.98145729105
∑ A i
* (mean ADC)
I
= 5.095
... so B = .781444021796 !!!
with σ/E re
= .018637880275
Now just take the average value of the four center crystals
B avg
= .781858818128
419

- Ratio of Energies Deposited in a single module
Error bars for (E re
/E beam
)associated with run 413
Maximum deposited energy is at center of crystal.
Minimum deposited energy is at boundary of crystal.
(As expected)
21 22 23

- Energy Resolution of the Prototype
Error bars for (σ/E re
)associated with run 413
21 22
21
23
22 23
Energy resolution at center is greater than at boundaries of crystal.
(As expected)

Results - Shower Profile
The shower profile measures the dependence of the average pulse-height ratio for different crystal channels
1.) Adjacent Channel ratio
A i
/A i+1
2.) Adjacent Row ratio
A j
/A j+1
3.) Separated Channel ratio
A i+1
/A i-1

Results - Adjacent Channel Ratio
Run 435 for E
26
/E
27
27
1
26
Boundary

Results - Adjacent Row Ratio
Run 422 E
3,9,15
/E
4,10,16
1
3, 9, 15
Boundary
4, 10, 16

Results - Separated Channels Ratio
Run 435 for E
28
/E
26
1
26
Center: 27
27 28

Reconstructed Position Method
• Center of Gravity Method x cal

N  i
 i
( E i
) * x i
N  i
 i
( E i
)
 i
( E i
)
 i
• Linear Weight
 i
( E i
)

E i
E
T • Logarithmic Weight
 i
  i
 where, max 0 , 


W
0
E
T

 ln


N  i
E i
E i
E
T






8
Linear - Reconstructed Position
3x3 – run 389 3x3 – run 422
11
10
10
9
9

Linear - Reconstructed Position
5x5 – run 413
22
S shape indicates some systematic shift from the method incorporated.
21

Linear Position Resolution
3x3 – run 389 3x3 – run 422
8 9 10
9 10 11

Linear Position Resolution
5x5 – run 413
21 22
Position resolution worst at boundaries and best at center

Logarithmic Reconstructed Position
3x3 – run 389 3x3 – run 422
11
~ %3 error (leakage)
~ %3 error (leakage)
10
9 10
8
9

Logarithmic Reconstructed Position
5x5 – run 413 (No systematic shift)
22
21

Logarithmic Position Resolution
3% error
3x3 – run 389 3x3 – run 422
9 10 11
8 9 10

Logarithmic Position Resolution
5x5 – run 413
1% error
21 22

Linear or Logarithmic Weight?
• Linear weight - large systematic errors
• Radial energy fall off of showers is exponential
• Energy deposited in the module decreases exponentially as a function of the distance from the point of incidence.

Logarithmic Weight
• Ideal weight must employ a logarithmically weighted energy due to the exponential fall off of the shower profile
• The logarithmically weighting of the deposited energy signals produce the best results
• Which is what we were expecting from the results

Conclusion
• PRIMEX Experiment provide precision test on
Chiral Anomaly prediction.
• Energy Resolution
– %1.7 at the center and %2.2 at boundaries
– Worse at edge of crystals
– Due to fluctuation of shower and energy leakage
• Reconstructed Position
– Center of gravity
• Linear has large systematic error
• Logarithmic is almost linear; small systematic shift

… and my mentor: Dr. Gan - UNCW

Conservation Laws
• Symmetries in nature lead to conservation laws
– A particular measurable property of an isolated physical system does not change as the system evolves
– Corresponds to a conserved physical quantity.
• Conservation of energy, linear momentum, angular momentum, electric charge, probability, mass, etc.
• Usually derived from Lagrangian dynamics
– A reformulation of classical mechanics that combines conservation of momentum with conservation of energy.

Lagrangian Dynamics
• Lagrangian of a system is a classical method to
F
 m a
• Forces are hard to find.
– Lagrangian utilizes conservation of energy
• L
 x i
,  i
  x i
,  i
, t
   i x coordinate system
• Lagrangian equation of motion:

L
 x i
 d dt
– Conservation Law
• If , where C is a constant.
 x i
 x  i


 
L
 x  i




0

Conservation Law second example
• Parity Violation
– Flip either one, or all spatial variable signs.
– Parity 


 
1 ,
1 ,




(
( x , x , y , y , z z
)
)




(

(
 x ,
 x ,
 y ,
 y ,
 z ) z )



• Example
– A mirror flips the original object by the vertical
• Parity of mirror = -1.
• Discontinuous symmetry –> No conservation law .

Cross Section
• Cross section in particle physics expresses the likelihood of interaction between two particles.
– d
 scattered particle per unit solid angle.
 d
 d
 d

 dN
FN
S d
 t

_ # Particles detected per second_______ _____
(Flux of incident particles)(# target particles)(detector area)