# Proton decay

The standard model of particle physics states that protons are stable, i.e., that the laws of physics do not allow a proton (which is baryonic matter) to spontaneously decay into a positron and photons (non-baryonic matter) because of conservation of the baryon number. However, it has recently been suggested that the predominance of matter over antimatter in the universe is the result of a very slight imbalance in the ratio that occurred very early in its formation. Template:Unsolved This imbalance would have been exceptionally small, on the order of 1 in every 10,000 particles, but after most of the matter and antimatter annihilated, what was left over was all the baryonic matter in our current universe. This means that in essence, rather than breaking the law of conservation of the baryon number, proton decay could actually be the inevitable mechanism for bringing the baryon number back to equilibrium—in a sense correcting the original imbalance that made all current matter in our universe possible.

## 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.

p → e+π0

Though this process has not been observed experimentally, it is within the realm of experimental testability for future planned very large (megaton) scale detectors (eg. Hyper-kamiokande).

Early GUTs (which were in fact the first sound 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 15 minutes, due to the weak interaction.

## Dimension 6 proton decay operators

They are $\displaystyle \frac{qqql}{\Lambda^2}$ , $\displaystyle \frac{d^c d^c u^c e^c}{\Lambda^2}$ , $\displaystyle \frac{\overline{e^c}\overline{u^c}qq}{\Lambda^2}$ and $\displaystyle \frac{\overline{d^c}\overline{u^c}ql}{\Lambda^2}$ 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 ΛGUT can lead to the last two operators suppressed by $\displaystyle \frac{1}{\Lambda_{GUT}^2}$ . 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.

## Dimension 5 proton decay operators

In supersymmetric extensions (e.g. 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 $\displaystyle \frac{1}{M M_{SUSY}}$ where MSUSY 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

$\displaystyle ql\tilde{d^c}$ and $\displaystyle u^c d^c \tilde{d^c}$

The proton decay rate is only suppressed by $\displaystyle \frac{1}{M_{SUSY}^2}$ which is way way way too fast!

## Sphaleron mediated proton decay

At zero temperature, or temperatures significantly below the electroweak temperature, SU(2)W sphalerons are very very rare and their contribution to the proton decay is exponentially suppressed and hence completely negligible. However, at higher temperatures, the density of instantons goes up appreaciably and we can have instanton mediated proton decay. This is due to the anomalous breaking of baryon number by the weak interactions. Of course, at high temperatures (significantly above the mass of the proton) the process goes both ways as a thermodynamical equilibrium is approached. The reverse of this process has been speculated to be the cause of electroweak baryogenesis.