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the_nu_wgv [2014/06/09 16:56] gastis created |
the_nu_wgv [2014/07/01 14:24] (current) vassh |
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- | Members: Don Willcox, Nicole Vassh, Panos Gastis | + | ===== 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]] |