Proton decay

One of the outstanding problems in modern physics is the predominance of matter over antimatter in the universe. 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 in cosmology that 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 for symmetry breaking that 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 10¹⁰ particles 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 of bosons.

Most grand unified theories explicitly break the baryon number symmetry, which would account for this discrepancy, typically invoking reactions mediated by very massive X bosons (
X
) or massive Higgs 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.

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 of magnetic 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 the Super-Kamiokande water Cherenkov radiation detector in Japan:^[13] a lower bound on the proton's half-life of 2.4×10³⁴ years via positron decay, and similarly, 1.6×10³⁴ years via antimuon decay, close to a supersymmetry (SUSY) prediction of 10³⁴–10³⁶ years.^[14] An upgraded version, Hyper-Kamiokande, probably will have sensitivity 5–10 times better than Super-Kamiokande.

Despite the lack of observational evidence for proton decay, some grand unification theories, such as the SU(5) Georgi–Glashow model and SO(10), along with their supersymmetric variants, require it. According to such theories, the proton has a half-life of about 10³¹~10³⁶ years and decays into a positron and a neutral pion that itself immediately decays into two gamma ray photons:

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

Since a positron is an antilepton this decay preserves B − L number, which is conserved in most GUTs.

Additional decay modes are available (e.g.:
p⁺
→
μ⁺
+
π⁰
), both directly and when catalyzed via interaction with GUT-predicted magnetic monopoles.^[15] 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 the Hyper-Kamiokande.

Early grand 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 least 10³¹ years. As further experiments and calculations were performed in the 1990s, it became clear that the proton half-life could not lie below 10³² years. 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 10³⁴–10³⁵ years, 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 at 6×10³⁹ years, a bound applicable to SUSY models,^[16] with a maximum for (minimal) non-SUSY GUTs at 1.4×10³⁶ years.^{[16](part 5.6)}

Although the phenomenon is referred to as "proton decay", the effect would also be seen in neutrons bound 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 called beta decay. Free neutrons have a half-life of 10 minutes (610.2±0.8 s)^[17] due to the weak interaction. Neutrons bound inside a nucleus have an immensely longer half-life – apparently as great as that of the proton.

The lifetime of the proton in vanilla SU(5) can be naively estimated as ${\textstyle \tau _{p}\sim M_{X}^{4}/m_{p}^{5}}$ .^[19] Supersymmetric GUTs with reunification scales around µ ~ 2×10¹⁶ GeV/c² yield a lifetime of around 10³⁴ yr, roughly the current experimental lower bound.

The dimension-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 ${\displaystyle \Lambda }$  is the cutoff scale for the Standard Model. All of these operators violate both baryon number (B) and lepton number (L) conservation but not the combination B − L.

In GUT models, the exchange of an X or Y boson with the mass Λ_GUT can lead to the last two operators suppressed by ${\textstyle 1/\Lambda _{\text{GUT}}^{2}}$ . The exchange of a triplet Higgs with mass M can lead to all of the operators suppressed by ${\textstyle 1/M^{2}}$ . See Doublet–triplet splitting problem.

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

In supersymmetric extensions (such as the MSSM), we can also have dimension-5 operators involving two fermions and two sfermions caused by the exchange of a tripletino of mass M. The sfermions will then exchange a gaugino or Higgsino or gravitino leaving two fermions. The overall Feynman diagram has a loop (and other complications due to strong interaction physics). This decay rate is suppressed by ${\textstyle 1/MM_{\text{SUSY}}}$  where M_SUSY is the mass scale of the superpartners.

 

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

ℓ

d͂
^c and
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.

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

• Amsler, C.; et al. (Particle Data Group) (September 2008). "Review of Particle Physics – N Baryons" (PDF). Physics Letters B. 667 (1–5): 1–6. Bibcode:2008PhLB..667....1A. doi:10.1016/j.physletb.2008.07.018. hdl:1854/LU-685594. S2CID 227119789.
• Hagiwara, K.; et al. (Particle Data Group) (July 2002). "Review of Particle Physics – N Baryons" (PDF). Physical Review D. 66 (1): 010001. Bibcode:2002PhRvD..66a0001H. doi:10.1103/PhysRevD.66.010001. ISSN 0556-2821.
• Adams, Fred; Laughlin, Greg (2000). The five ages of the universe: inside the physics of eternity. London: Touchstone Books. ISBN 978-0-684-86576-8.
• Krauss, Lawrence Maxwell (2001). Atom: an odyssey from the big bang to life on earth-- and beyond. Boston: Little Brown & Company. ISBN 978-0-316-49946-0.
• Wu, Dan-di; Li, Tie-zhong (1985). "Proton decay, annihilation or fusion?". Zeitschrift für Physik. 27 (2): 321–323. Bibcode:1985ZPhyC..27..321W. doi:10.1007/BF01556623. ISSN 0170-9739. S2CID 121868029.
• Nath, Pran; Fileviez Pérez, Pavel (April 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. S2CID 119542637.

 

Wikiquote has quotations related to Proton decay.

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• Luciano Maiani (8 February 2006). The problem of proton decay (PDF). Third NO-VE International Workshop on Neutrino Oscillations in Venice. Venice.