Proton decay

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The decay of a proton, a baryon, into non-baryonic matter, does not occur perturbatively in the Standard Model. The nonperturbative corrections via sphalerons are exponentially suppressed at low temperatures. However, most grand unified theories explicitly break the baryon number symmetry and allow for proton decay mediated by very massive X bosons or massive triplet Higgs fields. This possibility was interesting in cosmology due to the predominance of matter over antimatter in the universe (a nonzero baryon number density), which could be explained as a very slight imbalance in the ratio that occurred very early in its formation. See baryogenesis. Template:Unsolved This imbalance would have been exceptionally small, on the order of 1 in every 10,000,000,000 (10¹⁰) particles a split 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.

Contents 1 Experimental evidence 2 Theoretical motivation 3 Dimension-6 proton decay operators 4 Dimension-5 proton decay operators 5 Dimension-4 proton decay operators 6 Further reading

Experimental evidence

Recent experiments at the Super-Kamiokande water Cherenkov radiation detector in Japan indicate a lower boundary for the proton half-life of 10³⁵ years. Since this is a lower bound, it is consistent with the nonexistence of proton decay.

Theoretical motivation

Despite the lack of observational evidence for proton decay, some grand unification theories require it. According to some such theories, the proton would have a half-life of 10³⁶ years, and would decay into a positron and a pion that itself immediately decays into photons in the range of gamma radiation.

<math> p \longrightarrow e^{+}\pi^{0} </math>

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, 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.

Although the phenomenon is referred to as "proton decay", the effect would also be seen in neutrons bound inside atomic nuclei. A free neutron would of course decay with a half life of about 10 minutes, due to the weak interaction.

Dimension-6 proton decay operators

They are <math>\frac{qqql}{\Lambda^2}</math>, <math>\frac{d^c d^c u^c e^c}{\Lambda^2}</math>, <math>\frac{\overline{e^c}\overline{u^c}qq}{\Lambda^2}</math> and <math>\frac{\overline{d^c}\overline{u^c}ql}{\Lambda^2}</math> where Λ is the cutoff scale for the Standard Model. All of these operators violate both baryon number and lepton number 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 <math>\frac{1}{\Lambda_{GUT}^2}</math>. The exchange of a triplet Higgs with mass M can lead to all of the operators suppressed by 1/M². See doublet-triplet splitting problem.

Image:Proton decay2.png Image:Proton decay3.png Image:Proton decay4.png

Dimension-5 proton decay operators

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 <math>\frac{1}{M M_{SUSY}}</math> where M_SUSY is the mass scale of the superpartners.

Dimension-4 proton decay operators

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

<math>ql\tilde{d^c}</math> and <math>u^c d^c \tilde{d^c}</math>

The proton decay rate is only suppressed by <math>\frac{1}{M_{SUSY}^2}</math> which is far too fast.

Further reading

• Particle Data Group current best estimates of proton lifetime;
  • http://pdg.lbl.gov/2002/bxxxn.pdf - K. Hagiwara et al., Phys. Rev. D 66, 010001 (2002)
• Adams, Fred and Laughlin, Greg The Five Ages of the Universe : Inside the Physics of Eternity ISBN 0684865769
• Krauss, Lawrence M. Atom : An Odyssey from the Big Bang to Life on Earth ISBN 0316499463de:Protonenzerfall

simple:Proton decay ja:陽子崩壊