Monday, Nov. 20, 2006PHYS 3446, Fall 2006 Jae Yu 1 PHYS 3446 – Lecture #20 Monday, Nov. 20, 2006...

Monday, Nov. 20, 2006 PHYS 3446, Fall 2006Jae Yu

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PHYS 3446 – Lecture #20Monday, Nov. 20, 2006

Dr. Jae Yu

1. Parity• Properties of Parity• Determination of Parity• Conservation and violation of parity

2. Time Reversal and Charge Conjugation

3. The Standard Model Quarks and LeptonsGauge BosonsSymmetry Breaking and the Higgs particle


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• 2nd term exam– In class, this Wednesday, Nov. 22– Covers: Ch 4 – CH11

• Workshop on Saturday, Dec. 2– 10am – 5pm– CPB 303 and other HEP areas

• Write up due: Before class Wednesday, Dec. 6

Announcements


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• Due date: Prior to class on Wednesday, Dec. 6• Requirements

– Need to put the name(s) of the person(s) who wrote the given sections– Professionally prepared in MS words

• No spelling or grammar mistakes• The style of the write up should be unified so that it looks like written by one person

– All contents on the template and more should be contained in the write up– Pictures, diagrams and photos should be added w/ appropriate figure captions

numbered in order of appearance. The captions should go at the bottom of the figure.

– References must be indicated throughout the text in order of appearance. They must be properly matched in the list of bibliography at the end of the document.

– Tables must be added and numbered in order of appearance. The caption should go on top of the table.

• Key evaluation points – Quality of the document – 30%– Content and organization of the document – 20 %– Satisfaction of the above requirements – 25%– Thoughtfulness, usefulness and relevance of contents of the document – 25%

• E.g. The contact information of vendors must be usable for the construction

Write Up Requirements and Evaluation


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• Requirements– Professionally prepared using power points

• Need your presentations 30 min prior to the class– Each presentation must be 10min (presentation) + 2min (question and

answer)– Must have the following components:

• General Introduction• Motivation• Design considerations and requirements• Design features• Test of design and its functionality• Conclusions and future improvements

• Key evaluation points – 25% each– Quality of the slides – Content and organization of the slides– Knowledge on presentation material – answers to questions– Manner of presentation

Presentation Requirements


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• Monday, Dec. 4:1. Shane2. Daniel3. Heather4. Justin5. Cassie6. Layne

• Wednesday, Dec. 6:1. Pierce2. Jessica3. James4. Matt5. Lauren

Presentation Schedule


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• To keep local gauge invariance, new particles had to be introduced in gauge theories– U(1) gauge introduced a new field (particle) that mediates the

electromagnetic force: Photon– SU(2) gauge introduces three new fields that mediate weak force

• Charged current mediator: W+ and W- • Neutral current: Z0

– SU(3) gauge introduces 8 mediators (gluons) for the strong force• Unification of electromagnetic and weak force SU(2)xU(1)

gauge introduces a total of four mediators– Neutral current: Photon, Z0

– Charged current: W+ and W-

Gauge Fields and Mediators


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• The space inversion transformation (mirror image) Switch right- handed coordinate system to left-handed

• How is this different than normal spatial rotation?– Rotation is continuous in a given coordinate system

• Quantum numbers related to rotational transformation are continuous – Space inversion cannot be obtained through any set of rotational

transformation• Quantum numbers related to space inversion is discrete

• Parity is an example of the discrete transformation

Parity

ct

x

y

z

Parity��

ct

x

y

z


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• Position and momentum vectors change sign under space inversion

• Where as their magnitudes do not change signs

• Vectors (particles w/ JP=1-) change signs under space-inversion while the scalars (particles w/ JP=0+) do not.

Properties of Parity

r

r r r

p mr

P�� r

P�� mr p

p p p

P�� r r r r r

P�� p p p p p


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• Some vectors, however, behave like a scalar– Angular momentum

– These are called pseudo-vectors or axial vectors (particles w/ JP=1+)• Likewise some scalars behave like vectors

– These are called pseudo-scalars (particles w/ JP=0-)• Two successive application of parity operations must turn the

coordinates back to original– – The possible values (eigen values) of parity, P, are +1 (even) or -1

(odd).• Parity is a multiplicative quantum number

Properties of Parity

L r p

a b c

P�� r p r p L

P�� a b c a b c

2P P P P


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• Two parity quantum numbers– Intrinsic parity: Bosons have the same intrinsic parities as their

anti-particles while fermions have opposite parity than its anti-particle (odd) Why?

– Parity under spatial transformation that follows the rule: P=(-1)l

• l is the orbital angular momentum quantum number

• Are electromagnetic and gravitational forces invariant under parity operation or space inversion?– Newton’s equation of motion for a point-like particle

– For electromagnetic and gravitational forces we can write the forces , and thus are invariant under parity.

Parity

2

2

d rm Fdt

2

2 2ˆ

d r Cm F rdt r


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• How do we find out the intrinsic parity of particles?– Use observation of decays and production processes– Absolute determination of parity is not possible, just like

electrical charge or other quantum numbers.– Thus the accepted convention is to assign +1 intrinsic

parity to proton, neutron and the hyperon.• The parities of other particles are determined relative to these

assignments through the analysis of parity conserving interactions involving these particles.

• hyperon is always produced with a K in pair. So one can only determine parity of K if parity of is fixed.

Determination of Parity Quantum Numbers


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• When the parity is conserved, it can restrict decay processes that can take place.

• Consider a parity conserving decay: AB+C– Conservation of angular momentum requires both sides

to have the same total angular momentum J.– If B and C are spinless, their relative orbital angular

momentum ( l ) must be the same as J(=l+s).– Thus conservation of parity implies that

– If the decay products have spin zero, for the reaction to take place we must have between the intrinsic parities

Parity Determination

1l

A B C

A B C

1J

B C


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• Therefore, the allowed decays must have

– Where the spin intrinsic parity of the particles are expressed as JP

• Are the following decays allowed under parity conservation?

Parity Determination

0

0 0 0

0

0

0 0

0 0

0 0

0 0 0

0 0 0


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• Consider the absorption of low energy - in deuterium nuclei

• The conservation of parity would require

• What are the intrinsic parity of deuteron and of the two neutrons? – Deuteron: +1; Neutrons: +1

• This capture process is known to proceed from an li=0 state, thus we obtain

Example 1, - parity

d

1 ild

1 fl

1 fln n

1 1f i f il l l l

n n


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• Since spin of the deuteron Jd=1, only a few possible states are allowed for the final state neutrons

• Since the two neutrons are identical fermions, their overall wave functions must be anti-symmetric due to Pauli’s exclusion principle leaves only (3) as the possible solution

• Making pion a pseudo-scalar w/ intrinsic parity

Example 1, - parity, cont’d

1) 1, 1, 0 or 2fnn J s l

1

2) 1, 1, 1fnn J s l

3) 1, 0, 1fnn J s l

or


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• Until the observation of “” puzzle in cosmic ray decays late 1950’s, parity was thought to be conserved in (symmetry of) all fundamental interactions

• The and particles seem to have identical mass, lifetimes, and spin (J=0) but decay differently

• These seem to be identical particles. Then, how could the same particle decay in two different manner, violating parity?

Parity Violation

31 1

0

21 1

0


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• T.D. Lee and C.N. Yang studied all known weak decays and concluded that there were no evidences of parity conservation in weak decays– Postulated that weak interactions violate parity– See, http://ccreweb.org/documents/parity/parity.html for more

interesting readings• These turned out to be

• Parity is conserved in strong and EM interactions but not in weak interactions w/ very little degree of violation

Parity Violation

K

K

0 2K

3K

http://ccreweb.org/documents/parity/parity.html


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• Invert time from t - t .

• How about Newton’s equation of motion?

– Invariant under time reversal

Time Reversal

r

p mr

T �� r

T �� mr p

L r p

t T �� t

2

2 2ˆ

d r Cm F rdt r

2 2

2

2 2 2ˆ1

d r d r Cm m F r

dt dt r

T ��

T �� r p r p L


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• Conversion of charge from Q - Q .

• Under this operation, particles become antiparticles• What happens to the Newton’s equation of motion?

– Invariant under charge conjugate

Charge Conjugate

2ˆ

qE c r

r

C �� 2

ˆq

c r Er

Q C �� Q

2

2 2ˆ

d r Cm F rdt r

2 2

2

2 2ˆ1

d r qm r Fdt r

C ��

2

ˆds rB cI

r

C �� 2

ˆds rc I B

r

Monday, Nov. 20, 2006PHYS 3446, Fall 2006 Jae Yu 1 PHYS 3446 – Lecture #20 Monday, Nov. 20, 2006...

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