Step 1: Recall the HVZ reaction.
The Hell–Volhard–Zelinsky reaction specifically introduces a halogen atom at the \(\alpha\)-carbon of a carboxylic acid.
Step 2: Analyze other reactions.
Gattermann and Sandmeyer reactions involve aromatic diazonium salts, while Riemer–Tiemann reaction introduces a formyl group in phenols.
Step 3: Conclusion.
Therefore, the reaction involving \(\alpha\)-halogenation of carboxylic acids is the Hell–Volhard–Zelinsky reaction.