Baryon Number: a Key to Physics Beyond the Standard Model

Baryon number, one of the accidental global symmetries of the Standard Model, can act as a key to open the door to new physic. After a recap of the history of theories for baryon number, I will show that interesting implications arise from writing down a consistent gauge theory for baryon number. This gauge symmetry can be broken at a low scale without introducing dangerous baryon number non-conserving operators inducing proton decay, obviating the need to postulate the existence of a large desert to suppress this process. Besides that, anomaly cancellation demands the introduction of additional fermions, and I will discuss two possible implications of this: I will present models where the dark matter candidate carries baryon number, and I will show that one can find sets of fermions that nicely implement a KSVZ sector for the QCD axion with a Peccei-Quinn symmetry protected from Planck-scale physics