## Thursday, 25 June 2009

### Angles and Demons

Since writing down the standard model back in the summer of love the only progress in particle theory has been the discovery that neutrinos have masses. This fact makes the leptons similar in spirit to the quarks in the sense that transitions between different flavors are possible. In both cases the flavor eigenstates, that is the states to which the W bosons couple, are not the same as the mass eigenstates but linear combinations thereof. This fact opens the door to a fascinating endeavor of measuring the angles in the unitary matrix that relates the flavor and the mass eigenstates.

The angles in the quark sector have been measured from every angle. The final conclusion is that what they taught at school was right: the sum of the angles in a (unitarity) triangle is equal to 180 degrees. In the lepton sector, experiment is lagging behind: so far we know only two of the angles. The one known as the atmospheric or $\theta_{23}$ angle (responsible in particular for the transitions of atmospheric muon neutrinos into tau ones) is close to 45 degrees. The solar or $\theta_{12}$ angle (responsible for the vanishing of electron neutrinos produced in the Sun) turned out to be a bit smaller, about 30 degrees. For the last angle, at the moment we have only an upper bound from the CHOOZ reactor experiment: $\theta_{13} < 11$ degrees at 90 percent C.L.

Now what have demons to do with it? I recently came across a talk from the MINOS collaboration a few month ago in Fermilab. MINOS, when on leave from Hades, studies the muon neutrino beam sent over the distance of 735 kilometers from Fermilab to a far detector located in the Soudan mine in Minnesota. One reason to bother (just imagine what it takes to dig such a long tunnel to send the neutrino beam over several states) is a precise measurement of the angle $\theta_{23}$ which controls the fraction of muon neutrinos that disappear on the way. But there may be more fun than that. Most of the muon neutrinos that vanish turn into tau neutrinos who escape detection. However, if $\theta_{13}$ is non-zero then a small fraction of the muon neutrinos should turn into electron neutrinos, and those receive a warm welcome in Soudan. Thus, MINOS is one in a long queue of experiments trying to pinpoint $\theta_{13}$.

In February this year MÌNOS announced their first results concerning the electron neutrino appearance. They see 35 electron event, roughly 1.5 sigma above the expected background of $27$ events. Not too significant, but already tantalizing. Moreover, if the MINOS data are combined with all available neutrino data the hint for a non-zero $\theta_{13}$ is strengthened to 2 sigma. The central value for $\theta_{13}$ inferred from the overall fit is 8 degrees (plus minus 4) - just below the CHOOZ limit.

If the current hints converge to a full-fledged measurement of $\theta_{13}$ in the 5-10 degrees ballpark then there are some far reaching consequences. First of all, measuring the $\theta_{13}$ angle paves the way to measuring yet another angle (isn't particle physics exciting?), more precisely the CP violating phase in the neutrino mixing matrix. Secondly, it would appear that the mixing angles in the lepton sector are pretty random numbers with no structure, in stark contrast to the quark sector where the CKM matrix displays a very hierarchical structure. In other words, neutrinos would prove to be anarchic. That would mean that anarchy is at rule, at least in the lepton sector, for the first time since Barcelona'36.

Anonymous said...

Umm... There's no tunnel. The neutrinos travel through solid rock from FNAL to Soudan.

Nice post though. NOvA, which is run by mostly the same people as MINOS, should have an even better shot at pinning down theta 13.

Jester said...

No tunnel? So disappointing :-)

Anonymous said...

Jester, stay cool with the phrasing. the way the first two paragraphs are written will lead your average crackpot to conclude that \theta_{12}+\theta_{23}+\theta_{31} \neq 180 degrees \Rightarrow my specific TOE involving Illuminated LHC black holes explains why Barcelona sadly ended up in the hands of stalinists...

good entry anyway. I'd heard about the \sim 8 degrees estimate... it's always a bit depressing to realise that 1.5 sigma stuff makes the news nowadays. more gossip from LHC please!!! (well, I'll be able to get some of that first hand in a week from now...)

CarlBrannen said...

Funny, I just sent an article into PRD (coauthored with Marnni Sheppeard) giving a new parameterization of 3x3 unitary matrices (based on the discrete Fourier transform) that happens to make the lepton mixing matrix very natural.

The usual parameterizations are basically products of 1-parameter groups, that is, they are based on Lie algebra / Lie group theory (which is very generic) rather than the discrete Fourier transform.

Jester said...

Anon, yeah it's not super clear from the text that the angles I'm talking about are not the same as the angles in the unitarity triangle, and that they dont have to add up to 180 degrees...let's hope that nobody gets fooled.

Anonymous said...

Please somebody tell me that the very first comment is a joke. Or at least that "there's no tunnel" is meant as something like "there's no spoon".

Anonymous said...

Of course it was a joke, only unintended :)