B and L violation by non-perturbative electroweak effects

Question

I was reading about the definition of R-parity on this paper http://arxiv.org/abs/hep-ph/9709356 (pg. 53 54). The author says that postulating B and L numbers conservation in the MSSM is sub-optimal as

1. In the SM their conservation is not postulated but arises from the absence of any renormalisable term in the Lagrangian associated to their violation
2. B and L violation can occur in small amounts due to the presence of non-perturbative electroweak effects anyway

About reason 2, the author references a paper by t'Hooft which, unfortunately, I cannot download. My question is: what are these non-perturbative effects?

I have seen that there are other questions and answers here related to this topic but I was looking for some less technical, general, or even qualitative answer.

Thank you!

Answer 1

The baryon non-conservation in the quantum theory is caused by the chiral anomaly, which leads to the baryon current $j_B^\mu = \sum_i \bar q_i \gamma^\mu q_i$ being not conserved as $$ \partial_\mu j_B^\mu \propto F\wedge F$$ where $F$ is the field strength tensor of the electroweak field. Now, $\int \partial_\mu j_B^\mu \propto \int F\wedge F$ is a topological invariant, associated to the instanton (see also) sector we're in. The instanton is essentially the classical solution - the vacuum - we're basing our quantum field theoretic perturbative expansion around (see also this and this post of mine). This means instantons are invisible from the perturbative viewpoint - you have to fix one to do perturbation theory.

Furthermore, if one expands the partition function as a Taylor series around vanishing coupling constant, which essentially defines the perturbative approach, the instanton contributions vanish because they are suppressed with a factor $\mathrm{e}^{-1/g}$ whose Taylor expansion at vanishing coupling is identically zero, and hence doesn't appear in the perturbation series (cf. nLab).

Graphically, the anomaly and hence the non-conservation is associated to the triangle diagrams

see "Lectures on Anomalies" by Bilal.