### Has dark matter been observed?

The group of G. Cantatore has reported an optical rotation of a laser beam in a magnetic field (hep-exp/0507107). The experimental arrangement involves a magnetic field of strength B=5 Tesla. Laser beam travels 22000 times forth and back in a direction orthogonal to the magnetic field travelling 1 m during each pass through the magnet. The wavelength of the laser light is 1064 nm. A rotation of (3.9+/-.5)× 10

^{-12}rad/pass is observed.

A possible interpretation for the rotation would be that the component of photon having polarization parallel to the magnetic field mixes with QCD axion, one of the many candidates for dark matter. The mass of the axion would be about 1 meV. Mixing would imply a reduction of the corresponding polarization component and thus in the generic case induce a rotation of the polarization direction. Note that the laser beam could partially transform to axions, travel through a non-transparent wall, and appear again as ordinary photons.

The disturbing finding is that the rate for the rotation is by a factor 2.8× 10^{4} higher than predicted. This would have catastrophic astrophysical implications since stars would rapidly lose their energy via axion radiation.

The motivation for introducing axion was the large CP breaking predicted by the standard QCD. No experimental evidence has been found has been found for this breaking. The idea is to introduce a new broken U(1) gauge symmetry such that is arranged to cancel the CP violating terms predicted by QCD. Because axions interact very weakly with the ordinary matter they have been also identified as candidates for dark matter particles.

In TGD framework there is special reason to expect large CP violation analogous to that in QCD although one cannot completely exclude it. Axions are however definitely excluded. TGD predicts a hierarchy of scaled up variants of QCD and entire standard model plus their dark variants corresponding to some preferred p-adic length scales, and these scaled up variants play a key role in TGD based view about nuclear strong force (see this and this), in the explanation of the anomalous production of e^{+}e^{-} pairs in heavy nucleus collisions near Coulomb wall (this), high T_{c} superconductivity (see this, this, and this), and also in the TGD based model of EEG (see this). Therefore a natural question is whether the particle in question could be a pion of some scaled down variant of QCD having similar coupling to electromagnetic field. Also dark variants of this pion could be considered.

What raises optimism is that the Compton length of the scaled down quarks is of the same order as cyclotron wavelength of electron in the magnetic field in question. For the ordinary value of Planck constant this option however predicts quite too high mixing rate. This suggests that dark matter has been indeed observed in the sense that the pion corresponds to a large value of Planck constant. Here the encouraging observation is that the ratio λ_{c}/λ of wavelength of cyclotron photon and laser photon is n=2^{11}, which corresponds to the lowest level of the biological dark matter hierarchy with levels characterized the value hbar= 2^{11k}hbar_{0}, k=1,2,....

The most plausible model is following.

- Suppose that the photon transform first to a dark cyclotron photon associated with electron at the lowest n=2
^{11}level of the biological dark matter hierarchy. Suppose that the coupling of laser photon to dark photon can be modelled as a coefficient of the usual amplitude apart from a numerical factor of order one equal to α_{em}(n) propto 1/n. - Suppose that the coupling g
_{πNN}for the scaled down hadrons is proportional to α_{s}^{4}(n) propto 1/n^{4}as suggested by a simple model for what happens for the nucleon and pion at quark level in the emission of pion.

_{c}/λ must correspond to preferred values of n characterizing Fermat polygons constructible using only ruler and compass, and that the rate for the rotation of polarization depends on photon frequency and magnetic field strength in a manner not explained by the model based on the photon-axion mixing.

The chapter Does TGD Predict the Spectrum of Planck Constants? of "Towards S-Matrix" contains the detailed calculations.

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