VT College of Science presents Breakthrough - A Student Research Magazine Vol. 1 No. 1 | Page 10

10 BREAKTHROUGH MAGAZINE | 2014

simply does not have a well-defined flavor state, which is to say a neutrino’s flavor state is dependent on a combination of mass states.
Allowing for non-zero rest mass of neutrinos, we can thusly produce expressions for the probability of neutrino oscillations.
P(v�
P(ve
P(ve

vƮ ) = 4|U33|2|U23|2 sin( Δm L )2 (2)
4E
2

Δm2L 2
v�) = 4|U13|2|U23|2 sin(
) (3)
4E

Δm2L 2
vƮ) = 4|U33|2|U13|2 sin(
) (4)
4E

Where v� is a muon neutrino, ve is an electron neutrino, vƮ is a tau neutrino, Δm2L is the difference in the squares of the neutrino mass
eigenstates, L is the distance traveled by neutrino, E is the energy of the neutrino, and U is the mixing matrix. In these equations the

dimensions of E and L are related, kilometers correspond to gigaelectronvolts and meters correspond to megaelectronvolts. The matrix
U is known as the Pontecorvo-Maki-Nakagawa-Sakata matrix [6], PMNS, and is represented by,

( )
( )
( )

U = [A][B][C] ( 5)
with A, B, and C being the matrices,

cosθ12 sinθ12 0
A = (6)
- sinθ
cosθ 0

0

12

0

12

1

cosθ13
0
e-ircp sinθ13
B= (7)
0
1
0
e-ircp sinθ13 0
cosθ13

1

0

0

0

-sinθ23

cosθ23

0
cosθ23 sinθ23

C= (8)

The various angles involved in the matrices A, B, and C are known as the mixing angles, and each matrix is used to describe the mixing
to atmospheric neutrinos. It is the angle, θ13, that has been the subject of much study recently, as it’s value has recently been probed

of neutrinos from different sources. A corresponds solar neutrinos, B corresponds to nuclear reactor neutrinos, and C corresponds
by reactor and accelerator based experiments, including T2K, Double Chooz, RENO, and Daya Bay. The discovery of the value of this
angle opens research into CP violation of neutrinos, and could even potentially help to explain why our universe is matter dominated, as
opposed to being annihilated after the big bang by anti-matter. A vast majority of neutrino experiments actively researching the topics
discussed utilize scintillation events created in detectors from the inverse beta decay process to detect neutrinos, which makes them
extremely sensitive to muons.
Muons were discovered by Carl D. Anderson and Seth Neddermeyer in 1936 while studying cosmic rays. They noticed a particle that
curved less sharply than electrons but more sharply than protons while traveling through a magnetic field. Anderson and Neddermeyer
noted that the particle also had the same charge as an electron. It soon became apparent that this was an as of yet unclassified particle,
and the muon was discovered. The muon together with the electron, tau, and the neutrinos discussed previously make up a class of
particles known as leptons, a group of elementary particles that do not undergo strong interactions. A strong interaction is an interaction [