  In this paper we systematically consider the baryon ($B$) and lepton ($L$)
number violating dinucleon to dilepton decays ($pp\to \ell^+\ell^{\prime+},
pn\to \ell^+\bar\nu^\prime, nn\to \bar\nu\bar\nu^\prime$) with $\Delta B=\Delta
L=-2$ in the framework of effective field theory. We start by constructing a
basis of dimension-12 (dim-12) operators mediating such processes in the low
energy effective field theory (LEFT) below the electroweak scale. Then we
consider their standard model effective field theory (SMEFT) completions
upwards and their chiral realizations in baryon chiral perturbation theory
(B$\chi$PT) downwards. We work to the first nontrivial orders in each effective
field theory, collect along the way the matching conditions, and express the
decay rates in terms of the Wilson coefficients associated with the dim-12
operators in SMEFT and the low energy constants pertinent to B$\chi$PT. We find
the current experimental limits push the associated new physics scale larger
than $1-3$ TeV, which is still accessible to the future collider searches.
Through weak isospin symmetry, we find the current experimental limits on the
partial lifetimes of transitions $pp\to \ell^+\ell^{\prime+}, pn\to
\ell^+\bar\nu^\prime$ imply stronger limits on $nn\to\bar\nu\bar\nu^\prime$
than their existing lower bounds, which are improved by $2-3$ orders of
magnitude. Furthermore, assuming charged mode transitions are also dominantly
generated by the similar dim-12 SMEFT interactions, the experimental limits on
$pp\to e^+e^+,e^+\mu^+,\mu^+\mu^+$ lead to stronger limits on $pn\to
\ell^+_\alpha\bar\nu_\beta$ with $\alpha,\beta=e,\mu$ than their existing
bounds. Conversely, the same assumptions help us to set a lower bound on the
lifetime of the experimentally unsearched mode $pp\to e^+\tau^+$ from that of
$pn\to e^+\bar\nu_\tau$, i.e., $\Gamma^{-1}_{pp\to e^+\tau^+}\gtrsim 2\times
10^{34}~\rm yrs$.
