Intensity-Modulated Proton Beam Therapy or Intensity-Modulated Photon Therapy in Treating Patients With Stage III-IVB Oropharyngeal Cancer

Inclusion Criteria: * Histologically documented squamous cell carcinoma of the oropharynx (American Joint Committee on Cancer \[AJCC\] version \[v\]7 stage III-IV A,B) * Tumor tissue (primary or cervical metastasis) available for human papilloma virus (HPV) and/or p16 (in situ hybridization \[ISH\], immunohistochemistry \[IHC\] or genotyping testing); if you do not have enough leftover tumor tissue available, you will have a tumor biopsy for tumor marker testing * Eastern Cooperative Oncology Group (ECOG) performance status = 0, 1, or 2 * Negative pregnancy test for women of child bearing potential * Concurrent chemotherapy * Bilateral neck radiation Exclusion Criteria: * Previous radiation treatment for head and neck mucosal primary cancers within the past 5 years (i.e. oropharynx, nasopharynx, hypopharynx, larynx, and oral cavity) * Pregnant or breast-feeding females * Clinically significant uncontrolled major cardiac, respiratory, renal, hepatic, gastrointestinal or hematologic disease but not limited to: * Symptomatic congestive heart failure, unstable angina, or cardiac dysrhythmia not controlled by pacer device * Myocardial infarction within 3 months of registration * Distant metastases (stage IV C, any T, any N and M1) * Previous surgical resection or neck dissection for oropharyngeal cancer, administered with therapeutic intent