Step 1: Identification of the cranial nerve. The cranial nerve responsible for regulating the heartbeat is the vagus nerve, also known as cranial nerve \( X \).
Step 2: Function of the vagus nerve. The vagus nerve is a mixed nerve that plays a significant role in parasympathetic control over the heart. It helps decrease the heart rate by releasing acetylcholine, which slows down the electrical impulses in the sinoatrial (SA) node of the heart.
Step 3: Comparison with other options. - Option \( (A) \): Cranial nerve IX (glossopharyngeal nerve) is involved in taste and the gag reflex, not heartbeat regulation.
- Option \( (B) \): Cranial nerve VII (facial nerve) controls facial expressions and salivary glands.
- Option \( (D) \): Cranial nerve VIII (vestibulocochlear nerve) is responsible for balance and hearing.
Conclusion: The correct answer is \( (C) \ \text{X (vagus nerve)} \).