In $\beta^-$ decay, a neutron transforms into a proton within the nucleus according to the equation: neutron $\to$ proton + $\beta^-$ + $x$ In this equation the particle represented by 'x' is
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$\beta^-$ decay produces an antineutrino. $\beta^+$ decay produces a neutrino.
Step 1: Conservation Laws:
In beta decay (specifically $\beta^-$ decay), a neutron turns into a proton and an electron (beta particle).
To conserve spin and lepton number, another particle is emitted.
$n \to p + e^- + \bar{\nu}_e$
The electron has lepton number +1. To keep total lepton number zero (as for neutron), the emitted particle must have lepton number -1. This is the antineutrino ($\bar{\nu}_e$).