Physics 489 (Fall 2013) Assignment #2
Due Wednesday Oct. 23, 2013
Do all problems. They are of equal value. As usual the policy on late assignments (and
other assignment related issues) can be found on the course website.
1. Griffiths 3.27 (for more pract
Phy489 Lecture 2
Standard Model Particle Masses
0.511 MeV/c2
Fermions
( spin )
Matter particles
106 MeV/c2
e
e
e L
ue L
~150 MeV/c
u L
d
d L
~150 MeV/c
, Z 0
W
0
W gZ
,
2
2
Bosons
( spin 1 )
Force carriers
g
L
L
c
~1.5 GeV/c
c L
s
s L
2
~
PHY489/1489 (2013) Assignment #1 Solutions (Oct. 15, 2013)
I have some comments on the answers to the first problem on the assignment.
1) The problem stated that you had to draw a diagram for all allowed processes,
exce
Phy489 Lecture 2122
0
Chiral Fermion States & Electroweak UnicaBon
QuesBon: how can we contemplate unifying two forces that appear to have couplings
that are very dierent in form (not just in apparent magnitudes since
Phy489 Lecture 20
Neutral Weak Interactions
Unification of the electromagnetic and weak interactions (Glashow, Weinberg, Salam) is
discussed in 9.7. We will cover some of this, but only briefly
Discussion (to follow) of the neutral weak interaction is bas
Phy489 Lecture 3
1
So far
Fundamental interactions in the Standard Model (SM)
Mediated by particle exchange
Three fundamental forces
have different effective strengths
act over different timescales
These two statements are correlated
Particle conte
Phy489 Lecture 4
1
Special Relativity: Lorentz Transformations
not accelerating
y
S
y'
S'
v
x
Consider two inertial reference frames S
and S' having a relative velocity v (which
we will align along the x axis). If an event
occurs in S at space-time coordi
PHY489 Lecture 18
Electrodynamics of Quarks and Hadrons
Here we wont discuss contribution from the weak interaction (yet). Note that QED
describes the interaction of the photon with charged spin-1/2 fermions. We just discussed
electron-muon scattering. Ca
Phy489 Lecture 19
Charged Weak Interactions
Fundamental charged weak interaction leptonic vertex:
Here, a lepton emits (absorbs) a W- (W+) and transforms into neutrino
of the same lepton species.
W
Here, a neutrino absorbs (emits) a W- (W+) and transforms
Phy489 Lecture 9
Discussion is of baryon wavefunctions because baryons are
made up of three quarks (which are treated here as identical)
while mesons consist of distinguishable particles since they are
made of quark-antiquark pairs.
0
Slide from Lecture 2
Phy489 Lecture 6
Reminder about invariant mass:
2
A system of n particles has a mass defined by M INV c 2 = PTOT PTOT where PTOT
is the total four momentum of the system PTOT = p1 + p2 + p3 + . + pn
2
2
2
! E1 + E 2 + . + E n ! !
! $ ! E TOT ! $
E TOT !
2
Phy489 Lecture 7
0
Clebsch-Gordan Coefficients
| j1m1 > | j2 m2 > =
j1 + j2
j =| j1 j2 |
C
j j1 j2
m m1 m 2
| jm > m = m1 + m2
Two systems with spin j1 and j2 and z components m1 and m2 can combine to
give a system which (quantum-mechanically) is a linear
PHY489 Lecture 13
Feynman Rules for Fundamental Processes
So far we have learned about:
particle content
interactions (allowed vertices)
conservation laws
relativistic kinematics
Fermis golden rule for scattering and decays
Two-body decay rates, dif
Phy489 Lecture 11
Question
Why are
(
K *0 K *0 oscillations not observed experimentally ?
K *0 is the same as K 0 but with spin-1 instead of spin-0. )
K0
sd
spin 0 M (K 0 ) 498 MeV / c 2
K *0
sd
spin 1 M (K *0 ) 892 MeV / c 2
The mixing process is a secon
PHY489 Lecture 14
The Dirac Equation
First a reminder (hopefully) from non-relativistic quantum mechanics:
E=
2
p
2m
+V
To express this in the form of a wave equation we make the operator
substitutions
p i
E i
t
and allow these to act on a wavefunction
2
PHY489 Lecture 12
Fermis Golden Rule for Transitions
transition probability
W=
Mif
matrix element
2
2
2
Mif f E
()
= f Vif i
2
Density of final states
available for energy E.
Matrix element contains the
fundamental physics (e.g. the
dynamics).
There are c
PHY489 Lecture 15
Solutions to the Dirac Equation
(
)
=
here the matrices are 4x4 and is a 4-component Dirac spinor
Still need to discuss the form of the spinor :
We had i mc = 0 :
1
2
3
4
Consider first the case in which is stationary (independent o
Phy489 Lecture 9
1
CP Violation
Standard Model contains only left-handed neutrinos and right-handed anti-neutrinos
C L = L
charge conjugation not a symmetry of the weak interaction
P L = R
parity also not conserved in weak interactions
CP L = R
what about
PHY489 Lecture 16
0
Quantum Electrodynamics
Follow Griffiths sections 7.5-7.7 + example 7.7 from section 7.8, using
the e- e- scattering as an example.
Feynman rules for Quantum Electrodynamics
e- e- scattering
Spin-averaging of amplitudes
Scattering of
PHY489/1489 (Fall 2013) Assignment 1
Due Wednesday Oct. 2, 2013
There are 7 problems on the following two pages. Do all of them. Total points = 60.
Please take note of the following:
When comparing to experimental data (here or in future assignments) plea
Phy489 Lecture 8
0
Discrete Transformations: Parity
Parity operation inverts the sign of all spatial coordinates:
Position vector (x, y, z) goes to (-x, -y, -z)
(eg P(r) = -r )
Clearly P2 = I (so eigenvalues are 1)
Regular (polar) vectors transform in thi