Contents

# Contents

## Idea

In the present standard model of particle physics the proton is a stable bound state (of quarks). But in some hypothetical extensions of the standard model, notably in many GUT models, the proton would be unstable, albeit with an extremely long decay time, and hence could decay (e.g. Kolešová-Malinský 14).

Experimental searches for rare proton decay show that the minimum mean lifetime of the proton is at least on the order of $10^{31}$ years (e.g. Super-Kamiokande 15), probably higher.

Since the age of the observable universe is about $1.3 \cdot 10^{10}$ years, this translates to saying that on average at most one proton in 10 kilotons of protons (essentially 10 kilotons of hydrogen atoms) decays per year.

More recently it has been claimed that GUT models may entirely avoid proton decay after all (Mütter-Ratz-Vaudrevange 16, Fornal-Grinstein 17), in particular in gauge-Higgs grand unification such as Spin(11)- (“SO(11)”-) and Spin(12)- (“SO(12)”-) models: (Hosotani-Yamatsu 15, Furui-Hosotani-Yamatsu 16, Sec. 2.6 Hosotani 17, Section 6)

## References

### General

• Jogesh Pati, Discovery of Proton Decay: A Must for Theory, a Challenge for Experiment (arXiv:hep-ph/0005095)

• Helena Kolešová, Michal Malinský, Proton lifetime in the minimal $SO(10)$ GUT and its implications for the LHC, Phys. Rev. D 90, 115001 (2014) (arXiv:1409.4961)

### Experimental constraints

Experimental results include

• Super-Kamiokande, Search for Nucleon and Dinucleon Decays with an Invisible Particle and a Charged Lepton in the Final State at the Super-Kamiokande Experiment (arXiv:1508.05530)

### Proton stability in GUTs

Claims that proton decay may be entirely avoided in GUTs after all are discussed in:

• Andreas Mütter, Michael Ratz, Patrick K.S. Vaudrevange, Grand Unification without Proton Decay (arXiv:1606.02303)

(claims that many string theory and supergravity models have this property)

• Bartosz Fornal, Benjamin Grinstein, $SU(5)$ Unification without Proton Decay, Phys. Rev. Lett. 119, 241801 (2017) (arXiv:1706.08535)

and in particular in gauge-Higgs grand unification (such as Spin(11)- (“SO(11)”-) and Spin(12)- (“SO(12)”-) models):

• Yutaka Hosotani, Naoki Yamatsu, Gauge–Higgs grand unification, Progress of Theoretical and Experimental Physics, Volume 2015, Issue 11, November 2015 (arXiv:1504.03817, doi:10.1093/ptep/ptw116)

• Atsushi Furui, Yutaka Hosotani, Naoki Yamatsu, Toward Realistic Gauge-Higgs Grand Unification, Progress of Theoretical and Experimental Physics, Volume 2016, Issue 9, September 2016, 093B01 (arXiv:1606.07222)

• Yutaka Hosotani, Gauge-Higgs EW and Grand Unification, International Journal of Modern Physics AVol. 31, No. 20n21, 1630031 (2016) (arXiv:1606.08108)

Discussion in SemiSpin(32)-heterotic string phenomenology:

• Saul Ramos-Sanchez, Section 5.4 of Towards Low Energy Physics from the Heterotic String, Fortsch. Phys. 10:907-1036, 2009 (arXiv:0812.3560)

• Yuta Hamada, Masahiro Ibe, Yu Muramatsu, Kin-ya Oda, Norimi Yokozaki, Proton Decay and Axion Dark Matter in $SO(10)$ Grand Unification via Minimal Left-Right Symmetry (arXiv:2001.05235)