## Sunday, November 21, 2010

### Anti-Hydrogen

At Galaxy Zoo we have been discussing the exciting news that a significant number of anti-hydrogen atoms have been produced at CERN. Given the bound beta decay

$n \rightarrow H + \overline{\nu}$

and its presumably similar looking antimatter reaction, we can conclude that anti-hydrogen will not look exactly like hydrogen. That is, (i) the Particle Data Group informs us of mass differences between neutrons and anti-neutrons and (ii) we know about the mass differences between neutrinos and antineutrinos.

Now if Graham D is correct that the apparent overabundance of galactic neutral hydrogen is due to mirror matter photon emission, then we expect the anti-hydrogen Rydberg constant to be quite close to the hydrogen one. The natural prediction is therefore to restrict energy level differences, between atoms and anti-atoms, to the rest mass energy of the neutrino sector. This leads to a precise small difference in the Rydberg constant, which we use to scale the hypothetical anti-hydrogen spectrum.

1. Hang on a minute ... the mirror Rydberg could be the same as the usual one, with the anti-Rydberg differing significantly. Hmm. So the anti-hydrogen is detected via annihilation, which means $p$ with $\overline{p}$, $e^{-}$ with $e^{+}$ and, if relevant, $(\nu, \overline{\nu})$ with mirror $(\nu, \overline{\nu})$. This makes me think that the masses should be the same ... after all, they annihilate.
But the energy levels? The beta decay suggests some kind of extrapolation from the neutrino scale (delta $m_1$ of $0.0008$ eV) to the neutron scale (delta around $70$ eV). What does this have to do with the $13.6$ eV?