Some grand unification theories suggest that the decay \(p \rightarrow \pi^{0}+e^{+}\) may be possible, in which case all matter may eventually become radiation. Are (a) baryon number and (b) electric charge conserved in this hypothetical proton decay?

Baryon number conservation is a fundamental principle in particle physics that states the total baryon number—the sum of the number of baryons or heavy particles such as protons and neutrons—must remain constant in an isolated system. According to our current understanding of the Standard Model, processes such as nuclear reactions and particle decays should always maintain this conservation rule.

However, the exercise discussing the hypothetical proton decay into a neutral pion and a positron introduces a scenario where this conservation law appears to be violated. The proton, being a baryon, carries a baryon number of +1, while the pion and positron, being non-baryonic, both carry a baryon number of 0. In the decay process of p \rightarrow \(pi^{0}\) + \(e^{+}\), the initial baryon number is +1 and the final baryon number is 0, indicating a discrepancy.

Such a violation of baryon number conservation suggests new physics beyond the Standard Model. In fact, several grand unification theories, which aim to unify the fundamental forces, predict that baryon number can be violated under certain conditions, meaning that protons could potentially decay. Nevertheless, proton decay has never been observed, and it remains one of the unsolved mysteries in particle physics.

Electric charge conservation is another law in particle physics that, unlike baryon number conservation, is observed to be upheld strictly in all known processes. This law states that the total electric charge of an isolated system remains constant over time. Charges can be transferred between particles, but the total amount of charge does not change.

In the reaction p \rightarrow \(pi^{0}\) + \(e^{+}\), if we look at the charges of the individual particles, we see that the proton has a charge of +1. The decay products consist of a neutral pion, with a charge of 0, and a positron, with a charge of +1. The overall charge before decay is +1, and after decay, it remains +1, perfectly obeying the conservation of electric charge. This adherence to charge conservation in the proposed decay supports the idea that charge conservation is an unbroken symmetry in the universe.

Grand unification theories (GUTs) represent attempts within the field of theoretical physics to unify the three fundamental forces of the Standard Model: electromagnetism, the strong nuclear force, and the weak nuclear force. The hope is to achieve this unification at energy levels much higher than those currently achievable by experimental physics. A successful GUT would also integrate the force-carrying particles with baryons and leptons (like protons and electrons) into a single framework.

GUTs often predict phenomena that challenge established conservation laws, such as proton decay. While electric charge seems unchangeable, baryon and lepton numbers might not be as sacrosanct as once thought. These theories suggest proton decay is possible and could be a process through which matter eventually converts to radiation over immense time spans. This hypothesized decay, if observed, would provide evidence for GUTs and have profound implications for our understanding of the universe. It would imply that matter is not eternally stable and make us reconsider the long-term fate of the universe. Currently, ongoing experiments aim to detect proton decay to either confirm or constrain the parameters of GUTs.