September 18, 2012
Cornell University, Department of Physics
PHYS 7646, Elementary particle II, HW # 1, due: 9/6/12
General remark: This homework is more a review of topics that we just touched upon.
The rst two questions are more directly related to what
Michael Savastio
BSM: Homework 9
1
1.1
When we take the limit of m1 , m2 small the fermions become centered at x5 = 0. For m1 , m2
the
2
2
wavefunction overlap becomes e(m1 m2 ) /2 so that the Yukawa coupling approaches 1 (m1 m2 )/
1).
(Is this what you
Michael Savastio
Physics 7646: Homework 8
1
To construct this theory, we will rst need the kinetic terms for each eld. These come from the Kahler
potential terms of the form . For simplicity I will ignore gauge symmetries (non were specied anyway).
We hav
Michael Savastio
Physics 7646: Homework 7
1
1.1
The renormalization group equations for a general Yang-Mills gauge theory to 1 loop order are
d
1 11
4
1
1 =
C2 (G) Tf T
d log()
2 3
3
6
where C2 (G) is the Casimir invariant C2 (SU (N ) = N , C2 (U (1) = 0
Michael Savastio
Physics 7646: Homework 6
1
1.1
Freeze out occurs roughly when H (for some process with a conversion rate ). For neutron proton
conversion G2 T 5 . From the Friedmann equation H g T 2 . Therefore, if we increase g , then freeze
F
out will
Michael Savastio
Physics 7646: Homework 5
1
1.1
We want to nd the probability for one avor of neutrino to oscillate into another. For this well need
eiHt | =
eiEi t Ui |i
i
So
eiEi t Ui Uj ij
| =
i,j
and
eiEi t Ui Ui
| | |2 =
i
j
eiEi t Uj Uj
To simplif
Michael Savastio
Physics 7646: Homework 4
1
1.1
Remember that
yK :=
K S K L
=
K S + K L
2
KS and hence yK 1 results from which decay modes are available to which kaon.
The fact that KL
The KS is approximately CP even, so it can decay into 2 , which is als
Michael Savastio
BSM: Homework 3
1
1.1
As noted in lecture, neither gluons nor photons can give rise to tree-level FCNCs in any theory when U (1)EM
and SU (3)C are unbroken symmetries of the theory (certainly the case here). The reason is that the photon
Michael Savastio
Physics 7646: Homework 2
1
1.1
The statement that the Higgs contributes at one loop order to the EWP diagrams in the limit of vanishing
light fermion masses is rather trivial. Since at tree level the only participants in these diagrams ar
I.
INTRODUCTION
During the course we will try to answer the question: What are the basic laws of physics?
Namely, we will try to nd out what the basic constituents of matter and what their fundamental interactions are. While we cannot fully answer the que