Neutrino Oscillations and Fugacity in the Early Universe

Speaker : Chun-Yen Chen (National Taiwan University)Advisor : Pisin Chen (National Taiwan University, LeCosPA Center)

Copyright 2015 Symmetry Magazine, Artwork by Sandbox Studio, Chicago with Ana Kova

Co-Author : Cristopher Gauthier

Introduction : Neutrino Oscillation & Fugacity We all now know that neutrinos has non-zero mass

and so will oscillate, mainly having two types 1. between active and sterile ν => Planck’s data for suggested no sterile neutrinos2. between different flavors

Birrell et al. have suggested that we should consider an additional cosmic parameter – the primordial neutrino fugacity, which will change the primordial neutrino distribution and also affect BBN and CMB.

Birrell, Jeremiah et al. Mod.Phys.Lett. A28 (2013) 1350188 arXiv:1303.2583 [astro-ph.CO]

Dolgov, A.D. et al. Nucl.Phys. B632 (2002) 363-382 hep-ph/0201287 MPI-PHT-2001-52

Introduction : Fugacity of Neutrinos

For Gibbs free energy of neutrinos:

In general, we can have independent chemical potential for neutrino and anti-neutrino

where and Therefore the Fermi-Dirac distribution can be rewrite as

And the and can be rewritten as

degeneracy fugacity

Introduction : Big Bang Nucleosynthesis About 3min after the Big Bang, many light

elements were created by the Big Bang Nucleosynthesis (BBN).

BBN is affected by two key parameters:1. Baryon-photon ratio η2. Neutron-proton ratio

The larger n/p+ ratio is, the more 4He would be created

Quantum kinetic equation of neutrinos

Using Boltzmann equation to get the quantum kinetic equation of neutrino, which is so called as “spin-precession formula”

where the and are defined in the SU(2) space with two-flavor model

and similar for anti-neutrinos.

Dolgov, A.D. et al. Nucl.Phys. B632 (2002) 363-382 hep-ph/0201287 MPI-PHT-2001-52

Vacuum oscillation

MSW effect forward scatteringCollisional decoherence

Approximation To analysis the QKE of neutrino we solve it from

where ,and and are new angular variables defined by

By solving the approximate eigenvalues and eigenvectors to 1st order in D ,

Approximation Including only the relevant non-oscillation term, and

taking the thermal average of the difference between the neutrino and anti-neutrino, we get a linear approximation solution

whereand and

with

Approx. Result : D = 0

The solid lines assume a non-zero fugacity and the dashed lines assume zero fugacity for both flavor.

Approx. Result : With D

The solid lines assume a non-zero fugacity and the dashed lines assume zero fugacity for both flavor.

Numerical Result

Conclusion and Future Work Including the freedom of fugacity of neutrinos and

anti-neutrinos will affect the magnitude of the lepton asymmetry for each flavor in the early universe.

And this will also affect the BBN and so the abundance of the light elements.

On the other hand, we can give a constraint for the primordial neutrino fugacity by the observation data of the light elements abundance and know the evolution of neutrinos and anti-neutrinos before the decoupling.

Thank You For Listening

Speaker : Chun-Yen ChenEmail : u02222076@ntu.edu.tw

Introduction : Big Bang Nucleosynthesis About 3min after the Big Bang, many light

elements were created by the Big Bang Nucleosynthesis (BBN).

BBN is affected by two key parameters:1. Baryon-photon ratio η2. Neutron-proton ratio

The larger n/p+ ratio is, the more 4He would be created