Editing Proton (section)

== Stability ==
{{Main|Proton decay}}
{{unsolved|physics|Are protons fundamentally stable? Or do they decay with a finite lifetime as predicted by some extensions to the standard model?}}
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 theory|grand unified theories]] (GUTs) of particle physics predict that [[proton decay]] should take place with lifetimes between 10<sup>31</sup> and 10<sup>36</sup> years. Experimental searches have established lower bounds on the [[mean lifetime]] of a proton for various assumed decay products.<ref name="Bucella1989" /><ref name="Lee1995" /><ref name="Kamioka" />

Experiments at the [[Super-Kamiokande]] detector in Japan gave lower limits for proton [[mean lifetime]] of {{val|6.6|e=33|u=years}} for decay to an [[antimuon]] and a neutral [[pion]], and {{val|8.2|e=33|u=years}} for decay to a [[positron]] and a neutral pion.<ref name="Nishino2009" />
Another experiment at the [[Sudbury Neutrino Observatory]] in Canada searched for [[gamma ray]]s 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 {{val|2.1|e=29|u=years}}.<ref name="Ahmed2004" />

However, protons are known to transform into [[neutron]]s 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:
: {{SubatomicParticle|Proton+}} + {{SubatomicParticle|Electron|link=yes}} → {{SubatomicParticle|Neutron|link=yes}} + {{SubatomicParticle|Electron neutrino|link=yes}}

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 [[Positron emission|beta plus decay]] (β+ decay).

According to [[quantum field theory]], the mean proper lifetime of protons <math>\tau_\mathrm{p}</math> becomes finite when they are accelerating with [[proper acceleration]] <math>a</math>, and <math>\tau_\mathrm{p}</math> decreases with increasing <math>a</math>. Acceleration gives rise to a [[S-matrix|non-vanishing probability]] for the transition {{nowrap|{{SubatomicParticle|Proton+}} → {{SubatomicParticle|Neutron}} + {{SubatomicParticle|Positron}} + {{SubatomicParticle|Electron neutrino}}}}. This was a matter of concern in the later 1990s because <math>\tau_\mathrm{p}</math> is a scalar that can be measured by the inertial and [[Rindler coordinates|coaccelerated observers]]. In the [[Inertial frame of reference|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 [[Unruh effect|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: 
# {{nowrap|{{SubatomicParticle|Proton+}} + {{SubatomicParticle|Electron}} → {{SubatomicParticle|Neutron}} + {{SubatomicParticle|Neutrino}}}}, 
# {{nowrap|{{SubatomicParticle|Proton+}} + {{SubatomicParticle|Antineutrino}} → {{SubatomicParticle|Neutron}} + {{SubatomicParticle|Positron}}}} and
#  {{nowrap|{{SubatomicParticle|Proton+}} + {{SubatomicParticle|Electron}} + {{SubatomicParticle|Antineutrino}} → {{SubatomicParticle|Neutron}}}}. 
Adding the contributions of each of these processes, one should obtain <math>\tau_\mathrm{p}</math>.<ref>{{Cite journal |last1=Vanzella |first1=Daniel A. T. |last2=Matsas |first2=George E. A. |date=2001-09-25 |title=Decay of Accelerated Protons and the Existence of the Fulling–Davies–Unruh Effect |url=https://link.aps.org/doi/10.1103/PhysRevLett.87.151301 |journal=Physical Review Letters |volume=87 |issue=15 |pages=151301 |doi=10.1103/PhysRevLett.87.151301|pmid=11580689 |arxiv=gr-qc/0104030 |bibcode=2001PhRvL..87o1301V |hdl=11449/66594 |s2cid=3202478 }}</ref><ref>{{Cite journal |last1=Matsas |first1=George E. A. |last2=Vanzella |first2=Daniel A. T. |date=1999-03-16 |title=Decay of protons and neutrons induced by acceleration |url=https://link.aps.org/doi/10.1103/PhysRevD.59.094004 |journal=Physical Review D |volume=59 |issue=9 |pages=094004 |doi=10.1103/PhysRevD.59.094004 |arxiv=gr-qc/9901008 |bibcode=1999PhRvD..59i4004M |hdl=11449/65768 |s2cid=2646123 |access-date=2022-07-24 |archive-date=2023-12-30 |archive-url=https://web.archive.org/web/20231230134640/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.59.094004 |url-status=live }}</ref><ref>{{Cite journal |last1=Vanzella |first1=Daniel A. T. |last2=Matsas |first2=George E. A. |date=2000-12-06 |title=Weak decay of uniformly accelerated protons and related processes |url=https://link.aps.org/doi/10.1103/PhysRevD.63.014010 |journal=Physical Review D |volume=63 |issue=1 |pages=014010 |doi=10.1103/PhysRevD.63.014010 |arxiv=hep-ph/0002010 |bibcode=2000PhRvD..63a4010V |hdl=11449/66417 |s2cid=12735961 |access-date=2022-07-24 |archive-date=2023-12-30 |archive-url=https://web.archive.org/web/20231230134615/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.63.014010 |url-status=live }}</ref><ref>{{Cite journal |last1=Matsas |first1=George E. A. |last2=Vanzella |first2=Daniel a. T. |date=2002-12-01 |title=The fulling–davies–unruh effect is mandatory: the proton's testimony |url=https://www.worldscientific.com/doi/abs/10.1142/S0218271802002918 |journal=International Journal of Modern Physics D |volume=11 |issue=10 |pages=1573–1577 |doi=10.1142/S0218271802002918 |arxiv=gr-qc/0205078 |s2cid=16555072 |issn=0218-2718 |access-date=2022-07-24 |archive-date=2022-07-24 |archive-url=https://web.archive.org/web/20220724015304/https://www.worldscientific.com/doi/abs/10.1142/S0218271802002918 |url-status=live }}</ref>