The PRIMEX Experiment: A Fundamental Test of the Chiral

Anomaly Prediction in QCD

Erik Minges

April 23rd, 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

Rotational Symmetry

Symmetry Breaking

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 π0 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 ChiralAnomaly 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.

– High precision measurement of decay rate, dominated by axial anomaly.

0

0

Chiral Anomaly• Axial symmetry of the Classical Lagrangian of

Quantum Chromodynamics is broken in the Chirallimit.

– 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

– Where is the number of quark colors in QCD and is the Pion decay constant.

• Precise predicted decay width

• Number of quark colors will be directly measured by this experiment

– Number colors most fundamental parameter in Physics

1210513.2)3(

GeVf

NA C

MeVf 42.92

3CN

eV

Am725.7

64

23

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

Electron beam passing through

nucleus field and change momentum,

produce Bremsstrahlung radiation

Measure energy and momentum

of scattered electrons yield energy

and momentum of gamma produced

Radiator

Physics target

(Primakoff)

Magnet measure pair production to monitor

photon flux and sweep out charged particles

Helium bag less particle interaction

than air and cheaper than vacuum

Status of PRIMEX

PrimEx-I

() = 7.82eV2.2%2.1%

Leading Order

Chiral Anomaly

Next toLeading Order

Chiral Anomaly

Analysis Results for the 6x6PbWO4 Crystal Prototype

Detector Beam Test

Center Crystals PbWO4

Surrounding Lead Glass

My Project for PRIMEX

• What is the need for an energy calibration?– 36 PbWO4 crystals detect incident beam energy via ADC

– Meaningful average pulse height signal from ADC requires calibration of each crystal using known incident beam energies

• How is the incident beam energy found?– 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

e

36241 1011645.0*1046112.0*1015153.05004.3 XXXXEbeam

Relative Energy Calibration• 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

Ebeam=A*(mean ADC)

i.e. For run 435 (centered on crystal 26)

Ebeam = E(29) = 3.98145729105

(mean ADC) = 5413

... so A = 7.35536171E-04!!!

adc(1) for run 435 cut at (X=29) and (Y=31)

mean ADC = 5413

Global Energy Calibration• Absolute scale from 5x5 cluster size

• Shower interacts in several crystal– Sum all deposited energy in surrounding crystals to account for leakage

Ebeam = B*[ ∑ Ai * (mean ADC)i ]

419

i.e. For run 419 (centered on crystal 15)

Ebeam = E(29) = 3.98145729105

∑ Ai * (mean ADC)I = 5.095

... so B = .781444021796 !!!

with σ/Ere = .018637880275

Now just take the average value ofthe four center crystals

Bavg = .781858818128

ResultsError bars for (Ere/Ebeam)associated with run 413

21 22 23

- Ratio of Energies Deposited in a single module

Minimum deposited energy is at boundary of crystal. (As expected)

Maximum deposited energy is at center of crystal.

Results

21 22 23

Error bars for (σ/Ere)associated with run 413

21 22 23

- Energy Resolution of the Prototype

Energy resolution at center is greater than at boundaries of crystal. (As expected)

Results - Shower ProfileThe shower profile measures the dependence of the

average pulse-height ratio for different crystal channels

1.) Adjacent Channel ratio

Ai/Ai+1

2.) Adjacent Row ratio

Aj/Aj+1

3.) Separated Channel ratio

Ai+1/Ai-1

Results - Adjacent Channel Ratio

Run 435 for E26/E27

2726

1

Boundary

Results - Adjacent Row Ratio Run 422 E3,9,15/E4,10,16

3, 9, 15 4, 10, 16

1

Boundary

Results - Separated Channels Ratio Run 435 for E28/E26

26 27

Center: 27

28

1

Reconstructed Position Method

• Center of Gravity Method

Weight factor for cell

• Linear Weight

where,

• Logarithmic Weight

)(

*)(

i

N

i

i

ii

N

i

i

cal

E

xE

x

)( ii E

T

iii

E

EE )(

N

i

iT EE

T

iii

E

EWE ln,0max 0

thi

Linear - Reconstructed Position

3x3 – run 389 3x3 – run 422

8

9

10

9

10

11

Linear - Reconstructed Position5x5 – run 413

21

22

S shape indicates some systematic shift from the method incorporated.

Linear Position Resolution

3x3 – run 389 3x3 – run 422

8 9 10

9 10 11

Linear Position Resolution5x5 – run 413

21 22Position resolution worst at boundaries and best at center

Logarithmic Reconstructed Position

3x3 – run 389 3x3 – run 422

8

9

10

9

10

11~ %3 error (leakage)

~ %3 error (leakage)

Logarithmic Reconstructed Position5x5 – run 413

21

22

(No systematic shift)

Logarithmic Position Resolution

3x3 – run 389 3x3 – run 422

8 9 10 9 10 11

3% error

Logarithmic Position Resolution5x5 – run 413

21 22

1% error

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

Thank You PrimEx!… 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 derive Newton’s second law of motion, .

• Forces are hard to find.

– Lagrangian utilizes conservation of energy

• , where is a generalized coordinate system

• Lagrangian equation of motion:

– Conservation Law

• If , where C is a constant.

amF

0

ii x

L

dt

d

x

L

Cx

L

x

L

ii

0

ix txUtxxTxxL iiiii ,,,,

Conservation Law second example

• Parity Violation

– Flip either one, or all spatial variable signs.

– Parity

• Example

– A mirror flips the original object by the vertical

• Parity of mirror = -1.

• Discontinuous symmetry –> No conservation law .

),,(),,(,1

),,(),,(,1

zyxzyx

zyxzyx

Cross Section• Cross section in particle physics expresses the likelihood

of interaction between two particles.

– Differential cross section, is the probability to observe a scattered particle per unit solid angle.

_ # Particles detected per second_______ _____

(Flux of incident particles)(# target particles)(detector area)

dFN

dN

d

d

t

S

d

d