Global Fit of Neutrino Oscillation Parameters. Student: Wei- Jiun Tsai Supervisor: Melin Huang, Pisin Chen. Part 1 Neutrino Oscillation. In this part, I just give a global picture about how to calculate the transition probability from one neutrino flavor to another .
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Student: Wei-Jiun Tsai
Supervisor: Melin Huang, Pisin Chen
(1) Neutrinos travel from the source (atmospheric layer) to the earth
surface( propagation in vacuum).
(2) Neutrinos travel from the earth surface to the detector
(propagation in matter).
, δ is the CP-violating phase, and U is a unitary matrix,
Now we solve the time-evolution equation of three-flavor neutrinos.
The wave function of a neutrino propagating through a medium obeys
(1) In vacuum :
In the flavor eigenstate basis, (1.2) can be rewritten as
Hamiltonian for a neutrino propagating in vacuum, expressed in mass eigenstate basis, and
(2) In matter
Because of weak interaction between neutrinos and matter, the Hamiltonian should
be modified by including such a effect.
By (1.5), (1.4) becomes
The modified term from weak interaction for a neutrino propagating in matter, expressed in flavor eigenstate basis.
, Veis the potential for the charged-current interaction.
Gf is Fermi’s constant, Ne is the electron number density
Solving equation (1.4) and (1.7) computationally, one can get
after neutrino travel through a certain distance.
general is expressed as
and rate is defined by
Variables in equation (2.1) and (2.2) are explained in detail on next page
Some certain incident zenith angle of ν
Function of neutrino oscillation parameters
For SNO and Super-K atmospheric neutrino,
Φν : SNO uses Bartolνatmos flux distribution.
Super-K uses Honda νatmos flux distribution.
Pαβ : include ① ν propagation from atmosphere to the earth surface
and ② ν propagation from the earth surface to detector
For ① : Need to calculate
For ② : Melin has the code
I have to do.
(C) ϵ : detection efficiency, can be found from published papers.
(D) : total number of target nucleon.
(E) tlive: total livetime.
All are involved in
SNO and Super-K
Single meson production
Coherent π production
(F) : differential cross section
Quantities needed to check:
Quantities needed to calculate:
Pαβ , theoretical yield or rate as functions
of neutrino oscillation parameters
n : Eν energy bin.
m : neutrino zenith angle bin.
Depending on data distribution, we have two methods
Dnmis measured yield.
Ynmis theoretical yield.
If the data behave like a Gaussian distribution.
σnmis standard deviation.
If the data behave like a Poisson distribution.
By minimizing , one can find the best fit of neutrino
Combine together for
global fit of neutrino
SNO on going
Super-K on going
I have to deal with them.