## Friday, October 7, 2011

### Quark Paper of the Day

Luckily I was browsing hep-ph again, and saw this paper by Fermilab scientists Marcela Carena and Wolfgang Altmannshofer, confirming the possibility of a certain non standard prediction for the $B_d$ mixing phase in quark mixing. From the abstract:
Taking into account the stringent bounds on the branching ratio of the rare $B_s \rightarrow$ $\mu^{+} \mu^{-}$ decay, we investigate to which extent the framework allows to address the observed $2$-$3$ sigma discrepancies in fits of the unitarity triangle. We find that a non standard $B_d$ mixing phase, that is in agreement with the current bounds on CP violation in $B_s$ mixing, requires the presence of higher dimensional operators both in the Kahler potential and the superpotential ...

1. So, Mitchell, where was that paper on tachyonic Poincare reps, with the statement about keeping unitary operators but giving up unitarity?

2. Oh, here it is. See the table on page 48. Nice link, Mitchell.

3. You want links? I've got links... Tachyonic representation theory for the braid group in 3 dimensions and the loop braid group in 4 dimensions. Functors for braiding 1-dimensional defects bound by tachyons. Seiberg duality from braiding of sheaves - this last one goes back to the (p,q) webs. I'm guessing that braiding the external legs of the diagram has a meaning. As you recall, the tachyons show up when the legs cross, and that is normally interpreted as a recombination of branes into a planar web. Also Urs Schreiber's K-theory dictionary mapping tachyons to Dirac operators (!).

4. And I should probably mention the tachyonic electroweak half-knots (talk), though these "half-knots" aren't anything as topologically well-defined as a braid or a knot; they are field configurations over a finite region of space, defined by the behavior of the Chern-Simons number of the SU(2) field and winding number of the Higgs field. If you check the paper, it starts out by talking about the CP violating phase in the CKM matrix (in the context of primordial baryogenesis). So maybe you can get your non-standard mixing phase, from a tachyonic phase transition in a condensate of mirror neutrinos (rather than in an elementary Higgs field).

5. Good, Mitchell, more and more evidence against fairies. Thanks for the reading material. The LHCb experiment will probably tell us next year whether or not the non standard phase works, by confirming or refuting the D0 dimuon anomaly.

6. Don't forget that the symmetric and braid groups are linked by the theory of the field with one element. This is crucial to understanding Fourier supersymmetry, although this needs more work.