**Core Concept**
The buccinator muscle is a thin, fan-shaped muscle in the cheek that plays a crucial role in mastication, swallowing, and speech. It is pierced by several structures, including blood vessels, nerves, and ducts, which need to pass through this muscle to reach the oral cavity.

**Why the Correct Answer is Right**
The buccinator muscle is pierced by the following structures:
* The buccal branch of the mandibular nerve (Option C) pierces the buccinator muscle to supply the muscles of mastication and the skin of the cheek.
* The buccal branches of the facial artery (Option D) pierce the buccinator muscle to supply the skin and mucous membrane of the cheek.
* The parotid duct (Option B) pierces the buccinator muscle to drain the parotid gland into the oral cavity.
However, the correct answer is not listed among the options provided.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is not provided, so we can skip it.
**Option B:** The parotid duct actually pierces the buccinator muscle, making this option incorrect.
**Option C:** The buccal branch of the mandibular nerve pierces the buccinator muscle, making this option incorrect.
**Option D:** The buccal branches of the facial artery pierce the buccinator muscle, making this option incorrect.

**Clinical Pearl / High-Yield Fact**
To remember the structures that pierce the buccinator muscle, recall the mnemonic "Buccal Branches Pass Through" (BBPT), which stands for the buccal branches of the facial artery and nerve.

**Correct Answer: None**