Which theory can explains or predicts conservation of nucleons? Number of nucleons are conserved in a nuclear reaction and decays. Is there a theory which predicts that?
 A: Baryon conservation is part of the Standard Model. At the quark level, it comes down to the fact that neither electromagnetism nor quantum chromodynamics (photon or gluon exchange, respectively), change the properties of the participating quarks. (Anti)quarks carry a baryon number of $\pm \frac 1 3$, and that, with any new quarks occurring via (at the vertex level):
$$ \gamma^* \rightarrow q\bar q$$
$$ g \rightarrow q\bar q$$
meanwhile, quarks disappear via annihilation:
$$ q\bar q \rightarrow \gamma^*$$
$$ q\bar q \rightarrow g$$
Both processes conserve quark flavor, while gluon emission does change quark color.
The weak interaction can change flavors, e.g.:
$$ d \rightarrow u+ W^- $$
$$ u \rightarrow d+ W^+ $$
$$ s \rightarrow u+ W^- $$
$$ c \rightarrow s+ W^+ $$
$$ b \rightarrow c+ W^- $$
$$ t \rightarrow b+ W^+ $$
and their $C$ conjugates. The details of these couplings are captured in the CKM matrix. Since (anti)quarks all carry $\pm\frac 1 3$ baryon number, it is conserved. (Note: without the flavor changing weak interaction, all quarks would stable).
Perhaps the most famous flavor changing reaction is beta decay:
$$ n \rightarrow p + e^- +\bar{\nu}_e $$
which proceeds via $d\rightarrow u+W^-$ and the often ignored $W^+ + d \rightarrow u$ where the $W^+$ arises off-shell with an on shell $e\bar{\nu}_e$ pair.
In standard theories of electroweak unifications (GUTs), the electroweak bosons ($\gamma, W^{\pm},Z^0$) are unified with the gluons, leading to heavier bosons (sometimes called $X$ and $Y$) which would act as operators linking quarks and leptons. The experimental signature of that is proton decay:
$$ p \rightarrow e^+ +\pi^0 $$
which looks like:

So far proton-decay searches have come up empty.
In these theories, so-called $B-L$ conservation applies. That is, baryon number minus electron number is conserved.
