Proton decay

Despite significant experimental effort, proton decay has never been observed. The current experimental lower bound on the proton lifetime (${\displaystyle {\tau }_p}$) is 2.4×10³⁴ years (in the decay channel into a positron and a neutral pion: p → e⁺ + π⁰).

According to the Standard Model, the proton, a type of baryon, is stable because baryon number is conserved. Since protons are the lightest baryons in the model, they cannot decay into other particles on their own and are therefore stable. However, baryon number conservation is an accidental global symmetry of the Standard Model, not associated with any fundamental gauge symmetry, slightly violated by non-perturbative SU(2)_L sphaleron effects, negligible at low temperatures but relevant in the early Universe.

Positron emission and electron capture—forms of radioactive decay in which a proton becomes a neutron—are not proton decay, because in these processes the proton interacts with other particles within the atom.

Grand Unified Theories (GUTs) explicitly break the baryon number symmetry, allowing protons to decay via the Higgs particle, magnetic monopoles, or new X bosons with a half-life in the range 10³¹ to 10³⁶ years. For comparison, the universe is roughly 1.4×10¹⁰ (14 billion) years old, which is at least twenty orders of magnitude lower. Although at first glance it may seem nearly impossible to explore such long lifetimes, it is sufficient to monitor 10³⁴ protons per year (with efficiency = 1) to be sensitive to average lifetimes of 10³⁴ years. About 10³⁴ protons are contained in approximately 30 kton of water, slightly more than the fiducial volume of the most sensitive experiment currently in operation, Super-Kamiokande.

The easiest decay channel to detect is the one into a positron and a neutral pion, ${\displaystyle p\to e^{+}{\pi }^0}$, a common prediction of many GUT models. This channel has a very clean signature, with no invisible particles in the final state. This allows for full reconstruction of the proton mass from the decay products, and, since it is a two-body decay, the total recoil momentum is expected to be small.

Supersymmetric extensions of GUT models favor the ${\displaystyle p\to {\overline{\nu }}_{\mu }{K}^{+}}$decay channel, which is more difficult to detect in water Cherenkov detectors because the antineutrino leaves the detector undisturbed and the kaon momentum is below the Cherenkov-light production threshold in water. The process can be identified by detecting the muons produced by kaon decays at rest, as well as the gamma rays emitted when a nucleon decays within the oxygen nucleus. The nucleus may remain in an excited state following this decay, from which it rapidly relaxes by emitting gamma rays.

Other processes can enable experiments to test the baryon number conservation, such as neutron-antineutron oscillations and specific nucleon–antinucleon conversion processes, accessible through electron–deuteron scattering.

History

In the Standard Model (SM), matter stability is described by assigning a baryon number B=+1 to the proton (lightest baryon), following Hermann Weyl's 1929 proposed conservation principle. Ernst Stueckelberg formally postulated the baryon number (heavy charge at the time) conservation law in 1939.

In the 1950s it was realized that limits on proton decay were exceedingly long. The very existence of advanced life forms on Earth implied ${\displaystyle {\tau }_p\gtrsim {10}^{16}}$ yr, in the same paper was quoted a limit ${\displaystyle {\tau }_p\gtrsim {10}^{21}}$ yr from absent spontaneous ²³²Th fission induced by nucleon decay. More refined geochemical limits from searches in muscovite for tracks left in geological times by pions from nucleon decay, derived a lower limit ${\displaystyle {\tau }_p\gtrsim 2\times {10}^{27}}$ yr. Radiochemical experiments using 1710 kg of underground potassium acetate (KC₂H₃O₂) set a similar limit (${\displaystyle {\tau }_p\gtrsim {10}^{26}}$ yr) by detecting the ³⁹K→³⁸Ar→³⁷Ar decay chain.

Above the electroweak scale Λ_EW (corresponding to the vacuum expectation value of the Higgs field, around 246 GeV), where Standard Model unification occurs, the three fundamental forces have comparable couplings, suggesting unification in Grand Unified Theories (GUTs). Historical models like Pati–Salam model (1973), unifying quarks/leptons and Georgi–Glashow model (1974), unifying all forces and particles/antiparticles, predict B violation via superheavy gauge bosons M_X. The natural GUT energy scale Λ_GUT is where SM gauge couplings converge, ~10¹⁵ GeV. This value is approximately thirteen orders of magnitude higher than the electroweak scale, or more than eleven orders of magnitude higher than the energy achievable in experiments conducted at particle accelerators. However, at these energies the estimation of proton decay lifetime is around 10²⁹–10³¹ yr, within reach of dedicated experiments: when GUTs were proposed, the experimental limits were around 10³⁰ yr (for decay modes which produce 𝜇 →𝑒 decays). These considerations strongly motivated proton decay searches.

In 1981 was published the first limit by a water Cherenkov detector at the Homestake gold mine, looking for the production and detection of a decaying muon following a nucleon decay event: ${\displaystyle {\tau }_p\gtrsim 3\times {10}^{31}{B}_{\mu }}$ yr, where ${\displaystyle B_{\mu }}$ is the model-dependent probability for this particular decay channel (or branching ratio). In the early 80s several experiments started. Some were based on calorimeter-type detectors, including the particle experiments at Kolar Gold Fields (India), NUSEX (Mont Blanc Tunnel, Italy), Fréjus (Fréjus Road Tunnel, France), Soudan (Minnesota, US); while other were water Cherenkov detectors: IMB (Ohio, US), HPW (Utah, US), KamiokaNDE (Japan).

The IMB experiment published a remarkable limit for the p → e⁺π⁰ decay channel ${\displaystyle {\tau }_p\ge 6.5\times {10}^{31}}$ yr (1983) (from now on the branching ratio term is omitted) and provided the first limit for ${\displaystyle p\to {\overline{\nu }}_{\mu }{K}^{+}}$: ${\displaystyle {\tau }_p\ge {10}^{31}}$yr, but in the past 40 years, the experimental scene has been dominated by the KamiokaNDE experiment and its successor Super-Kamiokande.

The construction of KamiokaNDE experiment under the direction of Masatoshi Koshiba was completed in 1983. The detector was a cylindrical tank (16 m in height and 15.6 m in diameter) containing 3,000 tons of pure water, equipped with about 1,000 photomultiplier tubes (PMTs) arranged on the lateral surface. It was located in the Kamioka zinc mine (near the city of Hida, Gifu Prefecture, Japan). The photomultipliers detected Cherenkov light, emitted by charged particles traversing the water at speeds greater than the speed of light in the medium.

KamiokaNDE was able to set stringent lower limits on the proton lifetime (${\displaystyle {\tau }_p}$ > 2.6 × 10³² years at 90% confidence level for the p → e⁺ + π⁰ decay channel), thereby ruling out all the simplest Grand Unified Models of elementary particles.

The great success of KamiokaNDE, motivated the collaboration to propose a gigantic upgrade of the detector: Super-Kamiokande, a cylinder 41.4 m tall and 39.3 m in diameter holding 50,220 tonnes of ultrapure water, 17 times more massive than KamiokaNDE. Super-Kamiokande construction began in 1991 and was completed in 1996.

The most updated limits of Super-Kamiokande, still operational, are

• 2.4×10³⁴ years for decay to a positron and a neutral pion (p → e⁺ + π⁰),
• 1.6×10³⁴ years for decay to an antimuon and a neutral pion (p → μ⁺K⁰),
• 0.59×10³⁴ years for decay to an muon antineutrino and a positive kaon (p → ν̄K⁺).

Two Nobel prizes for neutrino physics were awarded to scientists based on work using experimental facilities originally designed to detect proton decay. In 2002, Masatoshi Koshiba was awarded "for pioneering contributions to astrophysics, in particular for the detection of cosmic neutrinos", by upgrading the KamiokaNDE experiment. (sharing half prize with Raymond Davis Jr. for the same motivations).T. Kajita of the Super-Kamiokane collaboration was awarded the 2015 Nobel Prize "for the discovery of neutrino oscillations, which shows that neutrinos have mass", jointly to Art McDonald of the SNO experiment.