Talent

This page is read only. You can view the source, but not change it. Ask your administrator if you think this is wrong.
===== The $\nu$ WGV Group Members =====

  * Don Willcox (code/parameters)
  * Nicole Vassh (parameters/analysis)
  * Panos Gastis (code/analysis)

===== Project Goal =====

To examine the effect of the neutrino magnetic moment on the primordial abundances. This will be done by considering the magnetic moment as a free parameter (presumably larger than the standard model prediction). This additional magnetic moment coupling will then keep the neutrinos coupled to the electrons past the traditional $\sim 1$ MeV temperature. Here we preliminarily consider the effect on primordial abundances when the magnetic pair-production process $e^{+}+e^{-}\leftrightarrow \nu +\bar{\nu}$ is included into the big bang nucleosynthesis code of F. Timmes.

===== Decoupling Temperature Calculation =====


We would like to find the decoupling temperature, such that:
$$\Gamma= G_F^2T^5 + \mu_\nu^2T^3 \sim H = \frac{T^2}{M_{pl}} $$

Let's replace with some more illustrative constants:
$$\Gamma = \frac{T^5}{M_W^4} + g_\nu^2\frac{T^3}{m_p^2} \sim H = \frac{T^2}{M_{pl}} $$

For $g_\nu\equiv 0$, we have:
$$ T_0^3 = \frac{M_W^4}{M_{pl}} $$

We can use this to rewrite the cubic equation, in dimensionless form:
$$\left(\frac{T}{T_0}\right)^3 = 1 - g_\nu^2 \frac{M_{pl}^{2/3}M_W^{4/3}}{m_p^2}\frac{T}{T_0}$$
 
We can see that the last term is of order unity when $g_\nu\sim \frac{m_p}{M_{pl}^{1/3}M_W^{2/3}}\sim 10^{-8}$, allowing us to rewrite the equation as:
$$\left(\frac{T}{T_0}\right)^3 = 1 - \left(\frac{g_\nu}{10^{-8}}\right)^2 \frac{T}{T_0}$$

===== Preliminary Results and Presentation =====

{{:bbnnmm.pdf|}}

===== Revised Results and Conclusions =====

{{:nmmabundtalent.pdf|}}


===== Source Code on Git Repository =====

  * [[https://github.com/dwillcox/bbn-numu]]
Talent

User Tools

Site Tools

Page Tools
