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Global Fit of Neutrino Oscillation Parameters

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Global Fit of Neutrino Oscillation Parameters

Student: Wei-Jiun Tsai

Supervisor: Melin Huang, Pisin Chen

- In this part, I just give a global picture about how to calculate the transition probability from one neutrino flavor to another.
- The state of a neutrino can be expressed either in the flavor eigenstate basis or in the mass eigenstate basis. The transformation between the two bases is
- Because what I study is atmospheric neutrinos, this part is divided into two portions :
(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).

(1.1)

flavor

basis

mass

basis

, 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

Schrodinger equation

(1) In vacuum :

In the flavor eigenstate basis, (1.2) can be rewritten as

(1.2)

where

Hamiltonian

(1.3)

where

and

Hamiltonian for a neutrino propagating in vacuum, expressed in mass eigenstate basis, and

(1.4)

(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

(1.5)

where

The modified term from weak interaction for a neutrino propagating in matter, expressed in flavor eigenstate basis.

(1.6)

, Veis the potential for the charged-current interaction.

Gf is Fermi’s constant, Ne is the electron number density

and

(1.7)

Solving equation (1.4) and (1.7) computationally, one can get

after neutrino travel through a certain distance.

Function of

(1.8)

- Yield is the number of events that are detected. The theoretical yield formula in
general is expressed as

and rate is defined by

Variables in equation (2.1) and (2.2) are explained in detail on next page

(2.1)

Some certain incident zenith angle of ν

(2.2)

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

atmospheric

neutrino analysis

Quasi-Elastic Scattering

Deep-Inelastic Scattering

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.

(1)

If the data behave like a Gaussian distribution.

σnmis standard deviation.

(2)

If the data behave like a Poisson distribution.

By minimizing , one can find the best fit of neutrino

oscillation parameters.

SNO done

Solar experiments

Super-K done

Homestake done

GNO done

Rate experiments

Gallex done

SAGE done

Combine together for

global fit of neutrino

oscillation parameters

Brexino done

CHOOZ done

Reactor experiments

KamLAND done

Accelerator νμ

MINOS done

K2K done

Atmospheric νμ

SNO on going

Super-K on going

I have to deal with them.