**Core Concept**
The management of a bleeding peptic duodenal ulcer involves achieving hemostasis by ligating the vessel responsible for the bleeding. The most common vessel involved in bleeding peptic ulcers is the gastroduodenal artery or its branches. The gastroduodenal artery supplies blood to the duodenum and stomach.

**Why the Correct Answer is Right**
Bleeding peptic ulcers are often caused by erosion of a blood vessel in the duodenum or stomach. The gastroduodenal artery is a common source of bleeding due to its proximity to the duodenum and its high blood flow. Ligation of this vessel helps to control the bleeding and prevent further complications.

**Why Each Wrong Option is Incorrect**
**Option A:** The right gastric artery is not typically involved in bleeding peptic ulcers, as it supplies the stomach rather than the duodenum.
**Option B:** The left gastric artery is also not typically involved in bleeding peptic ulcers, as it supplies the stomach rather than the duodenum.
**Option C:** The superior mesenteric artery is a major artery that supplies blood to the small intestine, but it is not directly involved in bleeding peptic ulcers.

**Clinical Pearl / High-Yield Fact**
In cases of bleeding peptic ulcers, the location and severity of the bleeding can be assessed using endoscopy, and the gastroduodenal artery can be ligated using angiographic techniques or surgery.

**Correct Answer:** C. The superior mesenteric artery is a major artery that supplies blood to the small intestine, but it is not directly involved in bleeding peptic ulcers. However, the correct answer is not listed among the options. The correct answer is typically the gastroduodenal artery or its branches.