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the_nu_wgv [2014/06/09 16:53]
gastis created
the_nu_wgv [2014/07/01 14:24]
vassh
Line 1: Line 1:
-[[Don Willcox]] +===== The $\nu$ WGV Group Members ===== 
-[[Nicole Vassh]] + 
-[[Panos Gastis]]+  ​* 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]]
the_nu_wgv.txt · Last modified: 2014/07/01 14:24 by vassh