Baryon Number and Lepton Number Non-Conservation

Baryon number conservation is a pretty simple thing. It states that the number calculated by subtracting the number of anti-quarks in a system from the number of quarks in a system is conserved.

The Standard Model allows certain interactions that do not conserve baryon number to take place. Indeed, while possibility of baryon number non-conservation is pretty much irrelevant to ordinary Standard Model physics in anything remotely resembling ordinary temperatures, where the Standard Model suppresses the behavior to undetectable rarity, baryon number non-conservation at the kind of temperatures assumed to exist by cosmologists in the moments after the Big Bang to produce the mix of particles we see today in cosmologies based on the Standard Model.

In the Standard Model baryon number non-conservation is associated with chiral anomalies and in particular with a process called a sphaleron that cannot be represented by a Feynman diagram.

This particular nuance of the Standard Model has a big problem. It is a feature of the Standard Model, like the potential for CP violation in strong interactions, which has never been observed, even though a modified conservation law (B-L conservation where B standard for baryon number and L stands for lepton number) is ready and waiting to explain it and constrain it theoretically, if it were ever observed. As of a 2006 paper discussing the experimental evidence for baryon number non-conservation (and citing S. Eidelman et al. (Particle Data Group), Phys. Lett. B592 (2004) 1): "No baryon number violating processes have yet been observed." Some of the processes that B-L conservation might make possible in some beyond the standard model theories, such as proton decay, are also not observed.

Thus, while most beyond the standard model physics propose B-L conservation compliant processes that violate baryon conservation number, beyond the standard model physics that prohibit baryon conservation are not prohibited by experimental evidence, although they would require significant revisions in cosmologies based on the Standard Model at unobservable moments in the history of the universe. Still, the cosmology problems associated with absolute baryon conservation don't pose nearly the problem for quantum gravity theories that, for example, propose a "big bounce" as loop quantum gravity does, as opposed to a pure "big bang."

A similar notion called lepton number also exists, and there are also subconcepts of lepton number for the electron, muon and tau generations of leptons called leptonic family number. Lepton family number is apparently violated in neutrino oscillation. But, while lepton number violation is permitted in cases of chiral anomalies, just as baryon number violation is within the context of the Standard Model, it isn't clear from experimental evidence if this ever actually happens. (One-loop Feynman diagrams like the triangle diagram do involve a chiral anomaly, and clearly are necessary to include in calculations that produce the right answers for pion decay, but it isn't obvious to me that these involve lepton number violations, and, if they do, it may be the lepton number violation definition rather than the existence of such a rule that is at fault.)

Lepton number conservation is closely related to a deep issue concerning the nature of neutrino mass (Dirac or Majorana):

Dirac neutrino masses can be generated by the standard Higgs mechanism. Majorana neutrino masses require a new mechanism of neutrino mass generation that is beyond the Standard Model. One of the most popular mechanisms of neutrino mass generation is the see-saw mechanism [51, 52, 53]. This mechanism is based on the assumption that the law of conservation of lepton number is violated at a scale that is much larger then the scale of violation of the electroweak symmetry. The see-saw mechanism allows to connect the smallness of neutrino masses with a large physical scale that characterizes the violation of the lepton number conservation law.

If neutrino masses are Dirac just as all other particle masses in the Standard Model are, then lepton number non-conservation is not necessary. If they have Majorana masses, then lepton number non-conservation is necessary. Neutrinoless double beta decay, which violated lepton number conservation and is also associated with Majorana masses for neutrinos, has not been observed (see also here (2010)). This places significant limits on the nature of Majorana mass if it exists, and is also notable because it is one of the few areas of fundamental particle physics that can be examined experimentally with great precision without the immensely expensive particle accelerators (such as the LHC).

Thus, baryon number non-conservation and lepton number non-conservation, while well motivated theoretically, like SUSY and various grand unified theories, are mere possibilities that experiments continue to offer absolutely no evidence to substantiate. It might be fruitful to focus on theories that instead conserve both baryon number and lepton number because these are completely consistent with experiment and the exercise of developing equations and quantum mechanical rules that observe these symmetries might provide additional useful insights for new beyond the standard model investigations.