Physics 233A Homework #1.
Spring 2012
Due: Mon. 13th Feb.
1) Muon Decay Rate
(a) Starting with the 4fermion eective charged current Lagrangian of the standard model
(Peskin and Schroeder eq. 20.90, extended to three generations, with eq. 20.91 for the
co
Physics 233B (Murayama)
HW #2, due Sep 28, 2012
1. Conrm the following expressions for the twobody phase space in the centerofmomentum frame.
s
m2 m2
1+ 1 2 ,
(1)
E1 =
2
s
s
m2 m2
s
1 1 + 2 ,
(2)
E2 =
2
s
s
2
2
2
2 2
s
= 1 2(m1 + m2 ) + m1 m2
p1 = p2 =
Physics 233B (Murayama)
HW #5, due Dec 12, 5:00 pm
The CP quantum number of the Higgslike particle can be determined
from the fourlepton nal state. Consider the following three operators separately,
hZ Z ,
hZ Z ,
aZ Z .
(1)
Compute the azimuthal correla
Physics 233B (Murayama)
HW #1, due Sep 14, 2012
1. The synchrotron radiation loss is given by
P =
1 e 2 a2 4
,
6 0 c3
a=
v2
,
R
(1)
where R is the radius of curvature. The formula for the instantaneous luminosity is
N+ N
L = fc
S
(2)
4x y
with S 1. Dete
233B HW #2
1. twobody phase space
Just follow the lecture notes.
2. pseudoscalar meson leptonic decays
The operator is
G
O = F Vq1 q2 q1 g m H1  g5 L q2 n g m H1  g5 L l
2
The matrix element is
m
X0 q1 g m g5 q2 P\ = fP pP .
The amplitude is
G
m
i M =
233B HW #1
1. Synchrotron radiation loss
According to the formula (1), the synchrotron radiation loss scales as E4 R2 , once v c. However, in order to compensate for
the falling cross section s 1 E2 , we need to increase L E2 , which requires N E accordin
Physics 233B (Murayama)
HW #4, due Oct 26, 5:00 pm
The process e+ e q q g has the dierential cross section
1 d2
s
x2 + x2
1
2
= CF
,
0 dx1 dx2
2 (1 x1 )(1 x2 )
(1)
2
where 0 = 4 3 q Q2 is the lowest order e+ e q q cross section. For
q
3s
scalar gluons, h
233B HW #3
1.Nonrelativistic quark model
We make use of the relationship P = H1LL+1
Charmed mesons c u, c d (obviously I = 1 )
2
state
D H1870L
JP L S
0 0 0
D0 H1865L
0
0 0
*
0
1

0 1
*
D H2010L
1

0 1
D*
0
D*
0
0
0
+
1 1
H2400L 0+
1 1
D1 H2420L0 1+
Notes on Phase Space
Fall 2012, Physics 233B, Hitoshi Murayama
1
TwoBody Phase Space
The twobody phase is the basis of computing higher body phase spaces.
We compute it in the rest frame of the twobody system, P = p1 + p2 =
( s, 0, 0, 0).
d3 p1
d3 p2
d
Physics 233B (Murayama)
HW #3, due Oct 12, 2012
1. In the particle listing of Particle Data Group, explain the quantum numbers I(J P ) of charmed mesons, charmed, strange mesons, and I G (J P C )
of c mesons using the nonrelativistic quark model.
c
2. In
Physics 233A Homework 3:
Electroweak Physics/Perturbative QCD
Spring 2012
Due: Fri. 6th April.
1) Electroweak Unication into SU (3)
The electroweak theory, based on the gauge group SU (2) U (1)Y , is sometimes said
to unify electromagnetism with the weak
Physics 233A Homework 2:
W Production; Extra Gauge/Higgs bosons
Spring 2012
Due: Friday March 9th
1) Transverse Mass of the W Boson
I will not spent much time discussing high energy physics experiments in this course.
This is covered in detail in Physics
Physics 233A TakeHome Final
Spring 2012
Due: 5 pm Thur. 10th May.
1) H W W, ZZ using the Equivalence Theorem
In the standard model, with a single Higgs doublet, two important decay modes of the
Higgs Boson, if heavy enough, are W + W and ZZ. Use the Gold
Physics 233A Homework # 4
QCD: Mesons and their interactions
Spring 2012
Due: Fri. 27th April.
1) Pseudoscalar meson transformations
The nonlinear chiral Lagrangian can be written in terms of the eld = e(2i/f ) , where
are the pion, eta and kaon elds w
I.
LIE GROUPS: NOTES BY Y. GROSSMAN AND Y. NIR
As we will later see, a crucial role in model building is played by symmetries. You
are already familiar with symmetries and with some of their consequences. For example,
Nature seems to have the symmetry of
Classical theory
Rutherford scattering
H=
p2

2m
Z e2
r
HamiltonJacobi equation
1
2m
S 2
JI r M +
1
r
2
S 2
S 2
1
I q M +
J f N N 
2
2
r sin q
Z e2
r
S
=  t
Separation of variables
S 2
S
S 2
1
E =  t , L2 = I q M +
J f N
2
sin q
Then using new