How Long Could We Live?

Abstract

We investigate model independent upper bounds on total proton lifetime in the context of Grand Unified Theories with the Standard Model matter content. We find them to be $\tau_p \leq 1.5^{+0.5}_{-0.3} \times 10^{39} \ \frac{(M_X/10^{16} \textrm{GeV})^4}{\alpha_{GUT}^2} (0.003 \textrm{GeV}^3 / \alpha)^2 \textrm{years}$ and $\tau_p \leq 7.1^{+0.0}_{-0.0} \times 10^{36} \ \frac{(M_X/10^{16} \textrm{GeV})^4}{\alpha_{GUT}^2} (0.003 \textrm{GeV}^3 / \alpha)^2 \textrm{years}$ in the Majorana and Dirac neutrino case, respectively. These bounds, in conjunction with experimental limits, put lower limit on the mass $M_X$ of gauge bosons responsible for the proton and bound-neutron decay processes. For central values of relevant input parameters we obtain $M_X \geq 4.3 \times 10^{14} \sqrt{\alpha_{GUT}} \textrm{GeV}$. Our result implies that a large class of non-supersymmetric Grand Unified models, with typical values $\alpha_{GUT} \sim 1/39$, still satisfies experimental constraints on proton lifetime. Our result is independent on any CP violating phase and the only significant source of uncertainty is associated with imprecise knowledge of $\alpha$--the nucleon decay matrix element.