Proton decay

Proton decay is the hypothetical decay of a proton into lighter subatomic particles, such as a neutral pion and a positron. The proton decay hypothesis was first formulated by Andrei Sakharov in 1967. Despite significant experimental effort, proton decay has never been observed. The current experimental lower bound on the proton lifetime is.
According to the Standard Model, the proton, a type of baryon, is stable because baryon number is conserved. Therefore, protons will not decay into other particles on their own, because they are the lightest baryon. Positron emission and electron capture—forms of radioactive decay in which a proton becomes a neutron—are not proton decay, since the proton interacts with other particles within the atom.
Some beyond-the-Standard-Model grand unified theories explicitly break the baryon number symmetry, allowing protons to decay via the Higgs particle, magnetic monopoles, or new X bosons with a half-life of 10 to 10 years. For comparison, the universe is roughly years old. To date, all attempts to observe new phenomena predicted by GUTs have failed.
Quantum gravity may also provide a venue of proton decay at magnitudes or lifetimes well beyond the GUT scale decay range above, as well as extra dimensions in supersymmetry.Black Holes, and Large Extra Dimensions - NASA/ADS">
There are theoretical methods of baryon violation other than proton decay including interactions with changes of baryon and/or lepton number other than 1. These included B and/or L violations of 2, 3, or other numbers, or B − L violation. Such examples include neutron oscillations and the electroweak sphaleron anomaly at high energies and temperatures that can result between the collision of protons into antileptons or vice versa.

Baryogenesis

One of the outstanding problems in modern physics is the predominance of matter over antimatter in the universe. The universe, as a whole, seems to have a nonzero positive baryon number density - that is, there is more matter than antimatter. Since it is assumed in cosmology that the particles we see were created using the same physics we measure today, it would normally be expected that the overall baryon number should be zero, as matter and antimatter should have been created in equal amounts. This has led to a number of proposed mechanisms for symmetry breaking that favour the creation of normal matter under certain conditions. This imbalance would have been exceptionally small, on the order of 1 in every 10¹⁰ particles a small fraction of a second after the Big Bang, but after most of the matter and antimatter annihilated, what was left over was all the baryonic matter in the current universe, along with a much greater number of bosons.
Most grand unified theories explicitly break the baryon number symmetry, which would account for this discrepancy, typically invoking reactions mediated by very massive X bosons or massive Higgs bosons. The rate at which these events occur is governed largely by the mass of the intermediate or particles, so by assuming these reactions are responsible for the majority of the baryon number seen today, a maximum mass can be calculated above which the rate would be too slow to explain the presence of matter today. These estimates predict that a large volume of material will occasionally exhibit a spontaneous proton decay.

Experimental evidence

Proton decay is one of the key predictions of the various grand unified theories proposed in the 1970s, another major one being the existence of magnetic monopoles. Both concepts have been the focus of major experimental physics efforts since the early 1980s. To date, all attempts to observe these events have failed; however, these experiments have been able to establish lower bounds on the half-life of the proton. Experiments at the Super-Kamiokande detector in Japan gave lower limits for proton mean lifetime of for decay to an antimuon and a neutral pion, and for decay to a positron and a neutral pion, close to a supersymmetry prediction of 10³⁴–10³⁶ years. An upgraded version, Hyper-Kamiokande, will have sensitivity 5–10 times better than Super-Kamiokande.

Theoretical motivation

Despite the lack of observational evidence for proton decay, some grand unification theories, such as the SU Georgi–Glashow model and SO, along with their supersymmetric variants, require it. According to such theories, the proton has a half-life of about ~ years and decays into a positron and a neutral pion that itself immediately decays into two gamma ray photons:
Since a positron is an antilepton this decay preserves number, which is conserved in most GUTs.
Additional decay modes are available, both directly and when catalyzed via interaction with GUT-predicted magnetic monopoles. Though this process has not been observed experimentally, it is within the realm of experimental testability for future planned very large-scale detectors on the megaton scale. Such detectors include the Hyper-Kamiokande.
Early grand unification theories such as the Georgi–Glashow model, which were the first consistent theories to suggest proton decay, postulated that the proton's half-life would be at least. As further experiments and calculations were performed in the 1990s, it became clear that the proton half-life could not lie below. Many books from that period refer to this figure for the possible decay time for baryonic matter. More recent findings have pushed the minimum proton half-life to at least – years, ruling out the simpler GUTs and most non-SUSY models. The maximum upper limit on proton lifetime, is calculated at, a bound applicable to SUSY models, with a maximum for non-SUSY GUTs at.
Although the phenomenon is referred to as "proton decay", the effect would also be seen in neutrons bound inside atomic nuclei. Free neutrons—those not inside an atomic nucleus—are already known to decay into protons in a process called beta decay. Free neutrons have a half-life of 10 minutes due to the weak interaction. Neutrons bound inside a nucleus have an immensely longer half-life – apparently as great as that of the proton.

Projected proton lifetimes

The lifetime of the proton in vanilla SU can be naively estimated as. Supersymmetric GUTs with reunification scales around yield a lifetime of around, roughly the current experimental lower bound.

Decay operators

Dimension-6 proton decay operators

The dimension-6 proton decay operators are and where is the cutoff scale for the Standard Model. All of these operators violate both baryon number and lepton number conservation but not the combination − .
In GUT models, the exchange of an X or Y boson with the mass can lead to the last two operators suppressed by. The exchange of a triplet Higgs with mass can lead to all of the operators suppressed by. See Doublet–triplet splitting problem.

Dimension-5 proton decay operators

In supersymmetric extensions, we can also have dimension-5 operators involving two fermions and two sfermions caused by the exchange of a tripletino of mass. The sfermions will then exchange a gaugino or Higgsino or gravitino leaving two fermions. The overall Feynman diagram has a loop. This decay rate is suppressed by where is the mass scale of the superpartners.

Dimension-4 proton decay operators

In the absence of matter parity, supersymmetric extensions of the Standard Model can give rise to the last operator suppressed by the inverse square of sdown quark mass. This is due to the dimension-4 operators and.
The proton decay rate is only suppressed by which is far too fast unless the couplings are very small.