Proton decay is the hypotheticaldecay of aproton into lightersubatomic particles, such as a neutralpion and apositron.[1] The proton decay hypothesis was first formulated byAndrei Sakharov in 1967. Despite significant experimental effort, proton decay has never been observed. If it does decay via a positron, the proton's half-life is constrained to be at least1.67×1034 years.[2]
According to theStandard Model, the proton, a type ofbaryon, is stable becausebaryon number (quark number) isconserved (under normal circumstances; seeChiral anomaly for an exception). Therefore, protons will not decay into other particles on their own, because they are the lightest (and therefore least energetic) baryon.Positron emission andelectron capture—forms ofradioactive 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-Modelgrand unified theories (GUTs) explicitly break the baryon number symmetry, allowing protons to decay via theHiggs particle,magnetic monopoles, or newX bosons with a half-life of 1031 to 1036 years. For comparison, theuniverse is roughly1.4×1010 (14 billion) years old.[3] To date, all attempts to observe new phenomena predicted by GUTs (like proton decay or the existence ofmagnetic monopoles) have failed.
Quantum gravity[4] (viavirtual black holes andHawking radiation) 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 insupersymmetry.[5][6][7][8]
There are theoretical methods of baryon violation other than proton decay including interactions with changes of baryon and/or lepton number other than 1 (as required in proton decay). These includedB and/orL violations of 2, 3, or other numbers, orB − L violation. Such examples include neutron oscillations and the electroweaksphaleronanomaly at high energies and temperatures that can result between the collision of protons into antileptons[9] or vice versa (a key factor inleptogenesis and non-GUTbaryogenesis).
One of the outstanding problems in modern physics is the predominance ofmatter overantimatter in theuniverse. 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 incosmology 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 forsymmetry breaking that favour the creation of normal matter (as opposed to antimatter) 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 ofbosons.
Most grand unified theories explicitly break the baryon number symmetry, which would account for this discrepancy, typically invoking reactions mediated by very massiveX bosons(X) or massiveHiggs bosons (H0
). The rate at which these events occur is governed largely by the mass of the intermediateX orH0
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.
Proton decay is one of the key predictions of the various grand unified theories (GUTs) proposed in the 1970s, another major one being the existence ofmagnetic monopoles. Both concepts have been the focus of majorexperimental 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 theSuper-Kamiokande detector in Japan gave lower limits for protonmean lifetime of6.6×1034 years for decay to anantimuon and a neutralpion, and1.67×1034 years for decay to apositron and a neutral pion, close to a supersymmetry (SUSY) prediction of 1034–1036 years.[10] An upgraded version,Hyper-Kamiokande, probably will have sensitivity 5–10 times better than Super-Kamiokande.[11]
Despite the lack of observational evidence for proton decay, somegrand unification theories, such as theSU(5) Georgi–Glashow model andSO(10), along with their supersymmetric variants, require it. According to such theories, the proton has ahalf-life of about 1031~1036 years and decays into apositron and a neutralpion that itself immediately decays into twogamma rayphotons:
Since a positron is anantilepton this decay preservesB − L number, which is conserved in mostGUTs.
Additional decay modes are available (e.g.:p+
→μ+
+π0
), both directly and when catalyzed via interaction withGUT-predictedmagnetic monopoles.[12] 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 theHyper-Kamiokande.
Earlygrand unification theories (GUTs) 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 least1031 years. As further experiments and calculations were performed in the 1990s, it became clear that the proton half-life could not lie below1032 years. 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 1034–1035 years, ruling out the simpler GUTs (including minimal SU(5) / Georgi–Glashow) and most non-SUSY models. The maximum upper limit on proton lifetime (if unstable), is calculated at6×1039 years, a bound applicable to SUSY models,[13] with a maximum for (minimal) non-SUSY GUTs at1.4×1036 years.[13](part 5.6)
Although the phenomenon is referred to as "proton decay", the effect would also be seen inneutrons bound insideatomic nuclei. Free neutrons—those not inside an atomic nucleus—are already known to decay into protons (and an electron and an antineutrino) in a process calledbeta decay. Free neutrons have a half-life of 10 minutes (610.2±0.8 s)[14] due to theweak interaction. Neutrons bound inside a nucleus have an immensely longer half-life – apparently as great as that of the proton.
| Theory class | Proton lifetime (years)[15] | Ruled out experimentally? |
|---|---|---|
| Minimal SU(5) (Georgi–Glashow) | 1030–1031 | Yes |
| MinimalSUSY SU(5) | 1028–1032 | Yes |
| SUGRA SU(5) | 1032–1034 | Yes |
| SUSYSO(10) | 1032–1035 | Partially |
| SUSY SU(5) (MSSM) | ~1034 | Partially |
| SUSY SU(5) – 5 dimensions | 1034–1035 | Partially |
| SUSY SO(10) MSSM G(224) | 2×1034 | No |
| Minimal (Basic) SO(10) – Non-SUSY | < ~1035 (maximum range) | No |
| Flipped SU(5) (MSSM) | 1035–1036 | No |
The lifetime of the proton in vanilla SU(5) can be naively estimated as.[16] Supersymmetric GUTs with reunification scales aroundµ ~ 2×1016 GeV/c2 yield a lifetime of around1034 yr, roughly the current experimental lower bound.
Thedimension-6 proton decay operators are and where is thecutoff scale for theStandard Model. All of these operators violate both baryon number (B) andlepton number (L) conservation but not the combinationB − L.
InGUT models, the exchange of anX or Y boson with the massΛGUT can lead to the last two operators suppressed by. The exchange of a triplet Higgs with massM can lead to all of the operators suppressed by. SeeDoublet–triplet splitting problem.
In supersymmetric extensions (such as theMSSM), we can also have dimension-5 operators involving two fermions and twosfermions caused by the exchange of a tripletino of massM. The sfermions will then exchange agaugino orHiggsino orgravitino leaving two fermions. The overallFeynman diagram has a loop (and other complications due tostrong interaction physics). This decay rate is suppressed by whereMSUSY is the mass scale of thesuperpartners.
In the absence ofmatter parity, supersymmetric extensions of the Standard Model can give rise to the last operator suppressed by the inverse square ofsdown quark mass. This is due to the dimension-4 operatorsqℓd͂c anducdcd͂c.
The proton decay rate is only suppressed by which is far too fast unless the couplings are very small.
