The theory of proton decay is based on the idea that protons, one of the building blocks of atoms, are not actually fundamental particles but are composed of smaller particles called quarks. According to the Standard Model of particle physics, protons are made up of two "up" quarks and one "down" quark. However, some theories propose that protons can decay into other particles, such as a positron and a neutral pion.
One of the main reasons we expect protons to decay is because of the idea of symmetry in physics. The laws of physics are believed to be symmetrical, meaning that they should be the same for all particles and interactions. However, the fact that protons are stable while other particles, such as neutrons, can decay, breaks this symmetry. Therefore, it is theorized that protons should also be able to decay.
In terms of the expected half-life of protons, it is difficult to predict as it depends on the specific theory being tested. Some theories propose a half-life of around 10^32 years, which is much longer than the age of the universe. This is why it is challenging to detect proton decay in experiments.
In terms of what protons should decay into, as mentioned earlier, some theories propose that they decay into a positron and a neutral pion. However, there are also other proposed decay modes, such as a neutrino and a meson. The exact decay products depend on the specific theory being tested.
The current state of experiments and theory in relation to proton decay is still ongoing. Many experiments, such as the Super-Kamiokande experiment in Japan and the Deep Underground Neutrino Experiment (DUNE) in the US, are searching for evidence of proton decay. However, so far, no definitive evidence has been found. Theories continue to be developed and tested, and further experiments are being planned to explore this phenomenon.
In conclusion, the expectation of proton decay is based on the idea of symmetry in physics and the possibility that protons are not fundamental particles. The exact half-life and decay products are dependent on the specific theory being tested. While experiments and theories are ongoing, no definitive evidence of proton decay has been found yet.