Flavor and Strong Dynamics

This week i cannot report on any of the regular CERN seminars (meaning, i understood nothing or didn't even dare to walk in). Salvation came from the phenomenology journal club which hosted a short, informal talk by Roberto Contino. Roberto was talking about partial compositeness, reviewing a partly forgotten work on fermion masses in technicolor.

The common lore about technicolor is that it faces two serious problems. One is the difficulty to comply with the electroweak precision tests, in particular with the notorious S parameter. The other is the flavour problem: it is tough to generate the observed fermion mass pattern without producing excessive flavour-changing neutral currents.

Typically, technicolor models generate the fermion masses as follows. First, at some high scale, one introduces a four-fermion operator that marries two standard model fermions and two technifermions. The technifermions condense, breaking the electroweak symmetry and giving mass to the W and Z bosons. When this happens, thanks to four-fermion operators like the one above we also get mass terms for the standard model fermions. Parametrically, the fermion masses are given by

where is the technicolor scale of order TeV and d is the dimension of the technifermion bilinear. The classical dimensions is of course d=3 but in a strongly interacting theory renormalization effects may lead to a different, anomalous dimension. The problem is that in calculable setups d >= 2. This leads to an unpleasent tension. On one hand, to obtain the large top quark mass we need to be rather close to . On the other hand we would like to be as high as possible because in generic technicolor models we also generate unwelcome operators with 4 standard model fermions: . If is too low, this leads to excessive flavor violation that is inconsistent with, for example, the kaon mixing experiments.

Though these problems could be overcome by labourious model-building, there exists in fact a simple solution proposed long ago by David B. Kaplan. All the problems mentioned above just disappear without a trace when the standard model fermions couple linearly to technicolor operators: . The fermion masses are now set by the anomalous dimension of the coupling . If is postive, the coupling gets suppressed at low energies and one gets

which is appropriate for light fermions of the first and second generation. When is negative, the coupling goes to an IR fixed point and one finds

which is appropriate for the top quark. In this scenario, can be even as high as the Planck scale. No flavor problem! It turns out that technicolor has "only" one serious problem, that with the electroweak precision tests.

One practical consequence of this scenario is that the standard model fermions mix with composite states from the technicolor sector, hence the name partial compositeness. This could show up as deviations of the fermionic interactions from the standard model predictions. For example, if the b quark has sizable admixture of composite states, the Z->bb branching ratio will be modified. In fact, the mixing with the technicolor sector is expected to be strongest for heavy fermions. Thus, the top quark should be mostly composite. Recall that top couplings have been very poorly measured so far...

Another nice thing about this mechanism is that it can be trivially implemented in 5D holographic models. This is the connection to Roberto's present research. But that's a longer story. If you want to know more about it, i recommend to start with a short review article by Roberto himself.

PS. As you may have noticed, this post contains a number of equations. Equations are an efficient tool to reduce the number of readers. For that, my eternal gratitude to the author of the script which enables LaTeX embeddings :-)
But the boundig boxes around the equations should not be there. Heeeelp!