Proton decay from quark and lepton compositeness

Within a chiral $SU(15)$ gauge theory in which the Standard Model fermions are bound states of massless preons, we show that proton-decay operators are likely induced at the compositeness scale, $\Lambda_{\rm pre}$. Our estimate of the limit imposed by searches for proton decays is $\Lambda_{\rm pre} > 10^4 \, {\rm TeV}^{1/2} \, C_8^{1/4} \, m_{\cal Q}^{1/2}$, where $C_8$ is a rescaled coefficient of an 8-prebaryon operator induced by $SU(15)$ dynamics, and $m_{\cal Q}$ is the mass of a composite vectorlike quark. The latter has a lower limit related to the mass of a composite vectorlike lepton, which in turn is required by LHC searches to be above 1 TeV. For $C_8$ in the $10^{-5} - 1$ range, the lower limit on $\Lambda_{\rm pre}$ varies between $3 \times 10^3$ TeV and $5 \times 10^4$ TeV. We point out that exotic proton decay modes, into a $\pi^+$ and a heavy right-handed neutrino, could be observed using the Super-Kamiokande or DUNE detectors.