How Long Could We Live?
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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 $τ_p \leq 1.5^{+0.5}_{-0.3} \times 10^{39} \ \frac{(M_X/10^{16} \textrm{GeV})^4}{α_{GUT}^2} (0.003 \textrm{GeV}^3 / α)^2 \textrm{years}$ and $τ_p \leq 7.1^{+0.0}_{-0.0} \times 10^{36} \ \frac{(M_X/10^{16} \textrm{GeV})^4}{α_{GUT}^2} (0.003 \textrm{GeV}^3 / α)^2 \textrm{years}$ 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 $M_X \geq 4.3 \times 10^{14} \sqrt{α_{GUT}} \textrm{GeV}$. Our result implies that a large class of non-supersymmetric Grand Unified models, with typical values $α_{GUT} \sim 1/39$, 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 $α$--the nucleon decay matrix element.
13 pages, 2 figures. Few corrections, new references
13 pages, 2 figures. Few corrections, new references