Transcript Monday, Nov. 20, 2006

PHYS 3446 – Lecture #20
Monday, Nov. 20, 2006
Dr. Jae Yu
1. Parity
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Properties of Parity
Determination of Parity
Conservation and violation of parity
2. Time Reversal and Charge
Conjugation
3. The Standard Model
Monday, Nov. 20, 2006
Quarks and Leptons
Gauge Bosons
Symmetry Breaking and the Higgs
PHYS 3446, Fall 2006
particle
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Announcements
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2nd term exam
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Workshop on Saturday, Dec. 2
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In class, this Wednesday, Nov. 22
Covers: Ch 4 – CH11
10am – 5pm
CPB 303 and other HEP areas
Write up due: Before class Wednesday, Dec. 6
Monday, Nov. 20, 2006
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Write Up Requirements and Evaluation
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Due date: Prior to class on Wednesday, Dec. 6
Requirements
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Need to put the name(s) of the person(s) who wrote the given sections
Professionally prepared in MS words
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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.
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No spelling or grammar mistakes
The style of the write up should be unified so that it looks like written by one person
Key evaluation points
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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%
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E.g. The contact information of vendors must be usable for the construction
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Presentation Requirements
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Requirements
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Professionally prepared using power points
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Each presentation must be 10min (presentation) + 2min (question and
answer)
Must have the following components:
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Need your presentations 30 min prior to the class
General Introduction
Motivation
Design considerations and requirements
Design features
Test of design and its functionality
Conclusions and future improvements
Key evaluation points – 25% each
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Quality of the slides
Content and organization of the slides
Knowledge on presentation material – answers to questions
Manner of presentation
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Presentation Schedule
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Monday, Dec. 4:
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Wednesday, Dec. 6:
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5.
Monday, Nov. 20, 2006
Shane
Daniel
Heather
Justin
Cassie
Layne
Pierce
Jessica
James
Matt
Lauren
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Gauge Fields and Mediators
• 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 WMonday, Nov. 20, 2006
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Parity
• The space inversion transformation (mirror image) Switch
right- handed coordinate system to left-handed
 ct

x
 y

z






Parity
 ct 



x


y


 z 
• 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
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Properties of Parity
• Position and momentum vectors change sign under
space inversion
r P r
p  mr P mr   p
• Where as their magnitudes do not change signs
r  r r
P
 r    r  
r r  r
p
P
 p   p 
p p  p
p p
• Vectors (particles w/ JP=1-) change signs under
space-inversion while the scalars (particles w/ JP=0+)
do not.
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Properties of Parity
• Some vectors, however, behave like a scalar
– Angular momentum
L  r  p P  r     p   r  p  L
– These are called pseudo-vectors or axial vectors (particles w/ JP=1+)
• Likewise some scalars behave like vectors
a  b  c P  a   b   c   a  b  c
 
 


– These are called pseudo-scalars (particles w/ J =0 )


P
-
• Two successive application of parity operations must turn the
coordinates back to original
2
–
P   P P    P    
– The possible values (eigen values) of parity, P, are +1 (even) or -1
(odd).
• Parity is a multiplicative quantum number
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Parity
• Two parity quantum numbers
– Intrinsic parity: Bosons have the same intrinsic parities as their
anti-particles while fermions have opposite parity than its antiparticle (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?
2
d
– Newton’s equation of motion for a point-like particle m r  F
dt 2
– For electromagnetic
and gravitational forces we can write the
2
forces m d r  F  C rˆ , and thus are invariant under parity.
dt 2
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r2
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Determination of Parity Quantum Numbers
• 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 L hyperon.
• The parities of other particles are determined relative to these
assignments through the analysis of parity conserving
interactions involving these particles.
• L hyperon is always produced with a K in pair. So one can
only determine parity of K if parity of L is fixed.
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Parity Determination
• When the parity is conserved, it can restrict decay
processes that can take place.
• Consider a parity conserving decay: AB+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
l
J
 A  BC  1  BC  1
– If the decay products have spin zero, for the reaction to
take place we must have  A   BC between the intrinsic
parities
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Parity Determination
• Therefore, the allowed decays must have
0  0   0 
0  0   0 
0  0   0 
– Where the spin intrinsic parity of the particles are
expressed as JP
• Are the following decays allowed under parity
conservation? 0   0   0 
0  0  0
0  0  0
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Example 1, p- parity
• Consider the absorption of low energy p- in
deuterium nuclei

p  d nn
• The conservation of parity would require
p d  1  nn  1
li
lf
• What are the intrinsic parity of deuteron and of the
two neutrons?
– Deuteron: +1; Neutrons: +1
p    1l f li   1l f li
• This capture process is known to proceed
from
an
l
li=0 state, thus we obtain p   1

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Example 1, p- parity, cont’d
• Since spin of the deuteron Jd=1, only a few possible
states are allowed for the final state neutrons
1)
nn  J  1, s  1, l f  0 or 2
2)
nn  J  1, s  1, l f  1
3)
nn  J  1, s  0, l f  1
or
• 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 p  1

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Parity Violation
• Until the observation of “tq” puzzle in cosmic ray
decays late 1950’s, parity was thought to be
conserved in (symmetry of) all fundamental
interactions
• The t and q particles seem to have identical mass,
lifetimes, and spin (J=0) but decay differently
2


0






1
q  p p
 q p p    1

t  p p p






0

t   p p p    1  1
3
• These seem to be identical particles. Then, how
could the same particle decay in two different
manner, violating parity?
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Parity Violation
• 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
 Kp 2 
K   p   p   p   Kp 3 
K  p  p 0
• Parity is conserved in strong and EM interactions but
not in weak interactions w/ very little degree of violation
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Time Reversal
• Invert time from t  - t .
t T t
r T r
p  mr T mr   p
L  r  p T  r     p   r  p   L
• How about Newton’s equation of motion?
d 2r
C
m 2  F  2 rˆ
dt
r
2
2
d
r
d
T m  1 2  m 2r  F  C2 rˆ
dt
dt
r
2
– Invariant under time reversal
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Charge Conjugate
• Conversion of charge from Q  - Q .
Q C Q
q
q
E  c 2 rˆ C c 2 rˆ   E
r
r
ds  rˆ
ds  rˆ
B  cI
C c  I 
 B
2
2
r
r


• Under this operation, particles become antiparticles
• What happens to the Newton’s equation of motion?
d 2r
C
m 2  F  2 rˆ
dt
r
C
d 2r q2
2
m 2  2  1 rˆ  F
dt
r
– Invariant under charge conjugate
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