Proton decay

Proton decay is a hypothetical form of particle decay in which a proton transforms into lighter subatomic particles such as a positron and a neutral pion. Although extensively investigated, proton decay has never been observed, and the proton is experimentally known to be extraordinarily long-lived. The concept is of great theoretical importance in particle physics because proton decay is predicted by many grand unified theories (GUTs), which seek to unify the strong, weak and electromagnetic interactions. Proton decay is also closely tied to cosmological questions such as baryon asymmetry and the origin of matter in the universe.

Stability in the Standard Model

Within the Standard Model of particle physics the proton is considered stable. This stability arises from the conservation of baryon number, a quantum number assigned to quarks and baryons. As the lightest baryon, the proton cannot decay into any lighter baryonic state without violating baryon number conservation. Standard weak processes that convert protons into neutrons, such as positron emission or electron capture, are not examples of proton decay, because the proton participates as part of an atomic nucleus and baryon number is conserved.
Although baryon number conservation is an empirical rule rather than a fundamental symmetry, the Standard Model contains no mechanism for proton decay except through non-perturbative effects such as sphaleron processes at extremely high energies.

Proton Decay in Grand Unified Theories

Many GUTs, including the early SU(5) Georgi–Glashow model and SO(10) theories, do not conserve baryon number. These theories often predict that protons can decay through the exchange of massive gauge bosons known as X and Y bosons, or via heavy Higgs fields. Representative decay signatures include:

• p → e⁺ + π⁰, with the pion promptly decaying to two gamma photons,
• p → μ⁺ + π⁰,
• modes involving kaons or neutrinos in supersymmetric extensions.

The predicted lifetimes in minimal SU(5) are of order 10³⁰–10³¹ years, but experimental limits now far exceed these values, ruling out the simplest models. Supersymmetric GUTs typically predict longer lifetimes, around 10³⁴–10³⁶ years, compatible with current limits.
Proton decay lifetimes are generally controlled by the mass scale of the underlying GUT particles, with heavier mediators causing slower decay. A common dimensional estimate for the proton lifetime in SU(5) theories is:
τₚ ∼ Mₓ⁴ / mₚ⁵,
where Mₓ is the GUT boson mass and mₚ is the proton mass.

Beyond GUT Mechanisms

Several additional theoretical frameworks allow proton instability:

• Quantum gravity effects, including virtual black holes and Hawking radiation, may lead to baryon number violation on extremely long timescales beyond GUT predictions.
• Models with large extra dimensions can modify baryon number violation pathways.
• Higher-dimensional operators in effective field theories can break baryon and lepton number through processes that need not resemble traditional GUT decay channels.

Other processes involving baryon-number violation include neutron–antineutron oscillations, sphaleron transitions and mechanisms generating B − L violation.

Baryogenesis and Matter–Antimatter Asymmetry

A central problem in cosmology is explaining why the observable universe contains more matter than antimatter. The net baryon number density is positive, indicating a fundamental asymmetry that must have arisen in the early universe. GUTs naturally include baryon-number-violating reactions mediated by heavy bosons, which could generate a small initial imbalance of around one extra matter particle per 10¹⁰ particle–antiparticle pairs shortly after the Big Bang. When matter and antimatter annihilated, the tiny surplus of baryons remained and now constitutes ordinary matter.
GUT-based baryogenesis is one proposed mechanism, though other models such as leptogenesis also rely on related symmetry-breaking processes.

Experimental Searches

Since the early 1980s, large underground detectors have searched for the characteristic signatures of proton decay. The most sensitive facility to date is Super-Kamiokande in Japan, a vast water Cherenkov detector. Its results place extremely high lower bounds on proton lifetimes:

• Greater than roughly 10³⁴ years for the decay p → e⁺ + π⁰,
• and a similar bound for p → μ⁺ + π⁰.

These limits are already strong enough to exclude many classical GUTs. Future detectors such as Hyper-Kamiokande, with volumes five to ten times larger, are expected to improve sensitivity significantly and may probe supersymmetric GUT predictions.
Although free neutrons undergo well-known beta decay with a half-life of about ten minutes, bound neutrons within nuclei show no such instability and appear to have lifetimes comparable to or exceeding the proton’s stability.

Decay Operators

Proton decay can be described mathematically by effective operators in quantum field theory.

• Dimension-6 operators, such as qqqℓ / Λ², arise from the exchange of heavy GUT bosons and violate baryon number B and lepton number L but preserve B − L.
• Dimension-5 operators appear in supersymmetric frameworks and involve sfermions and heavy tripletinos. These can induce proton decay through loop diagrams after further exchange of gauginos or Higgsinos.

The suppression scale Λ—often taken to be the GUT or Planck scale—determines the decay rate. Theoretical consistency requires strong suppression, consistent with the enormous experimental bounds.