## March 14, 2012

### Spring Break

I could be back in Austin, chillin’ at SXSW. Instead, I’m here in College Station, at a workshop on higher-dimensional CFTs.

I’ll be giving a talk, on Thursday, which will be a lot like the one I gave in Munich, two weeks ago. The only advantage will be that the paper, that I alluded to previously, is finally be out.

There are, I’ll admit, some compensations. Andreas Stergiou gave a very nice talk, today, about his work with Ben Grinstein and Jean-François Fortin on theories with scale but not conformal invariance. They have to work in $4-\epsilon$ dimensions, and need to go to 3 loops to find a violation of conformal invariance. Aside from their complexity, (interacting, unitary and Poincaré-invariant) scale invariant QFTs are *weird*. They are manifested as Renormalization Group limit cycles (or, even crazier, quasi-periodic motion on a torus), rather than fixed points. Fixed-point theories really *are* conformally-invariant.

## March 8, 2012

### Daya Bay

Congratulations to the Daya Bay Experiment for their announcement of the first measurement of a non-zero value of the neutrino mixing angle, $\theta_{1,3}$ $\sin^2(2 \theta_{1,3}) = 0.092 \pm 0.017.$ which is $5.2\sigma$ away from zero. Since there was no good theoretical reason to expect this mixing angle to vanish, it’s pleasing to see the first definitive experimental results on its value.

One thing, though, that annoys me about the coverage that I’ve seen is the *blithe* assertion that neutrino masses (and mixing angles) are now “part of the Standard Model.” That is an *incredibly dumb* thing to say. Yes, it’s true that one can write down a dimension-5 operator, using only Standard Model fields, which gives neutrinos a mass (and which, if non-diagonal in the flavour eigenstate basis, leads to neutrino mixing, too). That operator looks like

where $h$ is the Higgs doublet, $\psi^i$ are the lepton doublets, and $(\cdot,\cdot)$ is the skew-symmetric bilinear form on the fundamental representation of $SU(2)$. The complex symmetric $3\times3$ matrix, $c_{ij}$, is dimensionless. If we assume that its entries are $O(1)$, then the mass scale, $M$, suppressing this operator, is enormous, $M\sim 10^{15} \text{GeV}$. This operator is no more a “part of the Standard Model” than is the dimension-6 operator (also expressible, *purely* in terms of Standard Model fields) which mediates proton decay. Both are suppressed by GUT-scale masses, indicating that have to do with short-distance physics, well beyond the Standard Model’s $M_{EW}\sim 250 \text{GeV}$.