Write down the given nuclear reaction.

The reaction is:

The sum of the mass numbers (superscripts) on the reactant side must equal the sum of the mass numbers on the product side.
For the reactants: $14 + 1 = 15$
For the products: $14 + A_X$
So, $15 = 14 + A_X$
$A_X = 15 - 14 = 1$

The sum of the atomic numbers (subscripts) on the reactant side must equal the sum of the atomic numbers on the product side.
For the reactants: $7 + 0 = 7$
For the products: $6 + Z_X$
So, $7 = 6 + Z_X$
$Z_X = 7 - 6 = 1$

Particle X has a mass number $A_X = 1$ and an atomic number $Z_X = 1$.
This corresponds to a proton, which is represented as $^{1}_{1}p$ or $^{1}_{1}H$.

A: an electron ($^{0}_{-1}e$)
B: a proton ($^{1}_{1}p$)
C: a neutron ($^{1}_{0}n$)
D: $\gamma$-radiation ($^{0}_{0}\gamma$)

The particle with $A=1$ and $Z=1$ is a proton.

The final answer is $\text{B: a proton}$.