**Core Concept**
The Hertwig's epithelial root sheath (HERS) is a critical structure in the development of the tooth root. It is a band of epithelial cells that guides the formation of the tooth root by regulating the proliferation and differentiation of odontoblasts. Proper formation of the HERS is essential for the normal development of the tooth root.

**Why the Correct Answer is Right**
The failure of Hertwig's epithelial sheath diaphragm to investigate the proper horizontal level leads to an abnormal tooth root morphology, specifically a **supernumerary root**. This occurs due to the incomplete or distorted formation of the tooth root, resulting in an extra root or an abnormal root morphology. The HERS diaphragm is responsible for regulating the horizontal growth of the tooth root, and any disruption in this process can lead to supernumerary roots.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because a **supernumerary tooth** is a tooth in addition to the normal complement of teeth, not an abnormal root morphology. While both are developmental anomalies, they are distinct entities.
**Option B:** This option is incorrect because a **pegged tooth** is a tooth with a small, pointed cusp, but it is not directly related to the failure of Hertwig's epithelial sheath diaphragm.
**Option C:** This option is incorrect because a **dilated odontoblast process** is a histopathological feature of certain dental caries, but it is not a direct consequence of the failure of Hertwig's epithelial sheath diaphragm.

**Clinical Pearl / High-Yield Fact**
The Hertwig's epithelial root sheath is a key structure in tooth development, and its proper formation is essential for normal tooth root morphology. Understanding the role of the HERS in tooth development can help clinicians diagnose and manage various dental anomalies.

**Correct Answer: A. Supernumerary root**