section_path: Stability
section_name: Stability
paragraph_text: Stability
  
  The spontaneous decay of free protons has never been observed, and protons are therefore considered stable particles according to the Standard Model. However, some grand unified theories (GUTs) of particle physics predict that proton decay should take place with lifetimes between 10 and 10 years. Experimental searches have established lower bounds on the mean lifetime of a proton for various assumed decay products.
  
  Experiments at the Super-Kamiokande detector in Japan gave lower limits for proton mean lifetime of 6.6 × 10 years for decay to an antimuon and a neutral pion, and 8.2 × 10 years for decay to a positron and a neutral pion. Another experiment at the Sudbury Neutrino Observatory in Canada searched for gamma rays resulting from residual nuclei resulting from the decay of a proton from oxygen-16. This experiment was designed to detect decay to any product, and established a lower limit to a proton lifetime of 2.1 × 10 years.
  
  However, protons are known to transform into neutrons through the process of electron capture (also called inverse beta decay). For free protons, this process does not occur spontaneously but only when energy is supplied. The equation is:
  
  The process is reversible; neutrons can convert back to protons through beta decay, a common form of radioactive decay. In fact, a free neutron decays this way, with a mean lifetime of about 15 minutes. A proton can also transform into a neutron through beta plus decay (β+ decay).
  
  According to quantum field theory, the mean proper lifetime of protons τ p {\displaystyle \tau _{\mathrm {p} }} becomes finite when they are accelerating with proper acceleration a {\displaystyle a}, and τ p {\displaystyle \tau _{\mathrm {p} }} decreases with increasing a {\displaystyle a}. Acceleration gives rise to a non-vanishing probability for the transition p → n + e + ν. This was a matter of concern in the later 1990s because τ p {\displaystyle \tau _{\mathrm {p} }} is a scalar that can be measured by the inertial and coaccelerated observers. In the inertial frame, the accelerating proton should decay according to the formula above. However, according to the coaccelerated observer the proton is at rest and hence should not decay. This puzzle is solved by realizing that in the coaccelerated frame there is a thermal bath due to Fulling–Davies–Unruh effect, an intrinsic effect of quantum field theory. In this thermal bath, experienced by the proton, there are electrons and antineutrinos with which the proton may interact according to the processes:
  
  Adding the contributions of each of these processes, one should obtain τ p {\displaystyle \tau _{\mathrm {p} }}.