Proton decay

This article is about the hypothetical decay of nucleons (protons or neutrons) into other subatomic particles. For the type of radioactive decay in which a nucleus ejects a proton, seeProton emission.For the radioactive decay where a proton within a nucleus converts to a neutron, seepositron emission.

"Nucleon decay" redirects here. For decay of neutrons, seeneutron decay.

The pattern ofweak isospins,weak hypercharges,andcolor chargesfor particles in theGeorgi–Glashow model.Here, a proton, consisting of two up quarks and a down, decays into a pion, consisting of an up and anti-up, and a positron, via an X boson with electric charge −⁠4/3⁠e.

Inparticle physics,proton decayis ahypotheticalform ofparticle decayin which theprotondecays into lightersubatomic particles,such as a neutralpionand apositron.The proton decay hypothesis was first formulated byAndrei Sakharovin 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 least1.67×10³⁴years.

According to theStandard Model,the proton, a type ofbaryon,is stable becausebaryon number(quark number) isconserved(under normal circumstances; seeChiral anomalyfor an exception). Therefore, protons will not decay into other particles on their own, because they are the lightest (and therefore least energetic) baryon.Positron emissionandelectron capture—forms ofradioactive decayin 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 bosonswith a half-life of 10³¹to 10³⁶years. For comparison, theuniverse is roughly1.38×10¹⁰years old.To date, all attempts to observe new phenomena predicted by GUTs (like proton decay or the existence ofmagnetic monopoles) have failed.

Quantum tunnellingmay be one of the mechanisms of proton decay.

Quantum gravity(viavirtual black holesandHawking 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.

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 includedBand/orLviolations of 2, 3, or other numbers, orB−Lviolation. Such examples include neutron oscillations and the electroweaksphaleronanomalyat high energies and temperatures that can result between the collision of protons into antileptonsor vice versa (a key factor inleptogenesisand non-GUT baryogenesis).

Baryogenesis

Main article:Baryogenesis

Unsolved problem in physics:

Do protonsdecay?If so, then what is thehalf-life?Cannuclear binding energyaffect this?

(more unsolved problems in physics)

One of the outstanding problems in modern physics is the predominance ofmatteroverantimatterin 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 incosmologythat 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 breakingthat 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 10¹⁰particles 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 intermediate
X
or
H⁰
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.

Experimental evidence

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 major experimental 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. Currently, the most precise results come from theSuper-KamiokandewaterCherenkov radiationdetector in Japan: a lower bound on the proton's half-life of2.4×10³⁴yearsvia positron decay, and similarly,1.6×10³⁴yearsviaantimuondecay, close to a supersymmetry (SUSY) prediction of 10³⁴–10³⁶years.An upgraded version,Hyper-Kamiokande,probably will have sensitivity 5–10 times better than Super-Kamiokande.

Theoretical motivation

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-lifeof about 10³¹~10³⁶years and decays into apositronand a neutralpionthat itself immediately decays into twogamma rayphotons:

$${\begin{aligned}{\rm {p^{+}\longrightarrow e^{+}+}}&\ \pi ^{0}\\&\downarrow \\&2\gamma \end{aligned}}$$

Since a positron is anantileptonthis decay preservesB − Lnumber, 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.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 least10³¹years.As further experiments and calculations were performed in the 1990s, it became clear that the proton half-life could not lie below10³²years.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 10³⁴–10³⁵years, 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 at6×10³⁹years,a bound applicable to SUSY models,with a maximum for (minimal) non-SUSY GUTs at1.4×10³⁶years.

Although the phenomenon is referred to as "proton decay", the effect would also be seen inneutronsbound inside atomic 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)due to theweak interaction.Neutrons bound inside a nucleus have an immensely longer half-life – apparently as great as that of the proton.

Projected proton lifetimes

Theory class	Proton lifetime (years)	Ruled out experimentally?
Minimal SU(5) (Georgi–Glashow)	1030–1031	Yes
MinimalSUSYSU(5)	1028–1032	Yes
SUGRASU(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${\textstyle \tau _{p}\sim M_{X}^{4}/m_{p}^{5}}$.Supersymmetric GUTs with reunification scales aroundµ ~2×10¹⁶GeV/c²yield a lifetime of around10³⁴yr,roughly the current experimental lower bound.

Decay operators

Dimension-6 proton decay operators

Thedimension-6 proton decay operators are${\textstyle qqq\ell /\Lambda ^{2},}$${\textstyle d^{c}u^{c}u^{c}e^{c}/\Lambda ^{2},}$${\textstyle {\overline {e^{c}}}{\overline {u^{c}}}qq/\Lambda ^{2},}$and${\textstyle {\overline {d^{c}}}{\overline {u^{c}}}q\ell /\Lambda ^{2},}$where$\Lambda$is thecutoff scalefor theStandard Model.All of these operators violate both baryon number (B) andlepton number(L) conservation but not the combinationB−L.

InGUTmodels, the exchange of anX or Y bosonwith the massΛ_GUTcan lead to the last two operators suppressed by${\textstyle 1/\Lambda _{\text{GUT}}^{2}}$.The exchange of a triplet Higgs with massMcan lead to all of the operators suppressed by${\textstyle 1/M^{2}}$.SeeDoublet–triplet splitting problem.

• Proton decay. These graphics refer to theX bosonsandHiggs bosons.
• 
  Dimension-6 proton decay mediated by theX boson (3,2)
  _−5⁄6in SU(5) GUT
• 
  Dimension-6 proton decay mediated by the
  X boson (3,2)
  _1⁄6in flipped SU(5) GUT
• 
  Dimension-6 proton decay mediated by the
  triplet Higgs T (3,1)
  _−1⁄3and the
  anti-triplet HiggsT(3,1)
  _1⁄3in SU(5) GUT

Dimension-5 proton decay operators

In supersymmetric extensions (such as theMSSM), we can also have dimension-5 operators involving two fermions and twosfermionscaused by the exchange of a tripletino of massM.The sfermions will then exchange agauginoorHiggsinoorgravitinoleaving two fermions. The overallFeynman diagramhas a loop (and other complications due to strong interaction physics). This decay rate is suppressed by${\textstyle 1/MM_{\text{SUSY}}}$whereM_SUSYis the mass scale of thesuperpartners.

Dimension-4 proton decay operators

In the absence ofmatter parity,supersymmetric extensions of the Standard Model can give rise to the last operator suppressed by the inverse square ofsdownquark mass. This is due to the dimension-4 operators
q

ℓ

d͂
^cand
u
^c
d
^c
d͂
^c.

The proton decay rate is only suppressed by${\textstyle 1/M_{\text{SUSY}}^{2}}$which is far too fast unless the couplings are very small.

See also

• Age of the universe
• B − L
• Virtual black hole
• Weak hypercharge
• X and Y bosons
• Iron star

Further reading

• C. Amsler;Particle Data Group(2008)."Review of Particle Physics –NBaryons "(PDF).Physics Letters B.667(1): 1–6.Bibcode:2008PhLB..667....1A.doi:10.1016/j.physletb.2008.07.018.hdl:1854/LU-685594.S2CID227119789.
• K. Hagiwara;Particle Data Group(2002)."Review of Particle Physics –NBaryons "(PDF).Physical Review D.66(1): 010001.Bibcode:2002PhRvD..66a0001H.doi:10.1103/PhysRevD.66.010001.
• F. Adams; G. Laughlin (2000-06-19).The Five Ages of the Universe: Inside the Physics of Eternity.Simon and Schuster.ISBN978-0-684-86576-8.
• L.M. Krauss (2001).Atom: An Odyssey from the Big Bang to Life on Earth.Little Brown.ISBN978-0-316-49946-0.
• D.-D. Wu; T.-Z. Li (1985). "Proton decay, annihilation or fusion?".Zeitschrift für Physik C.27(2): 321–323.Bibcode:1985ZPhyC..27..321W.doi:10.1007/BF01556623.S2CID121868029.
• P. Nath; P. Fileviez Perez (2007). "Proton stability in grand unified theories, in strings and in branes".Physics Reports.441(5–6): 191–317.arXiv:hep-ph/0601023.Bibcode:2007PhR...441..191N.doi:10.1016/j.physrep.2007.02.010.S2CID119542637.

External links

• Proton decay at Super-Kamiokande
• Pictorial history of the IMB experiment
• Luciano Maiani(8 February 2006).The problem of proton decay(PDF).Third NO-VE International Workshop on Neutrino Oscillations in Venice.Venice.