  The search for baryon-number-violating (BNV) nucleon decay is an intriguing
probe of new physics beyond the SM in future neutrino experiments with enhanced
sensitivity. The dark sector states such as an axion or axion-like particle
(ALP) can induce nucleon decays with distinct signature and kinematics from the
conventional nucleon decays. In this work, we study the ALP effective field
theories (EFTs) with baryon number violation and the impact of light ALP on BNV
nucleon decays. We revisit the dimension-8 BNV operators in the extended EFTs
with an ALP field $a$ respecting shift symmetry. The low-energy EFT operators
with $|\Delta (B-L)|=2$ and $|\Delta (B-L)|=0$ are matched to the baryon chiral
perturbation theory. We obtain the effective chiral Lagrangian and the BNV
interactions between ALP and baryons/mesons. The ALP interactions lead to
two-body baryon decays $B\to \ell~({\rm or}~\nu)~a$ and three-body nucleon
decays $N\to M~\ell~({\rm or}~\nu)~a$. We obtain the constraints on the UV
scale from the invisible $\Lambda^0$ decay search at BESIII, the invisible
neutron decay search at KamLAND and proton decay search at Super-K. We also
show the projections of some other baryon/nucleon decays and present the
distinct distributions of kinematic observable.
