Proton Radiotherapy Plus Tremelimumab/Durvalumab for BCLC Stage B and C HCC

Inclusion Criteria: 1. Participants must have diagnosis of HCC that is deemed unsuitable for surgical resection or transplant. Participants may have multiple lesions with a total maximal tumor dimension of \< 20 cm, and no one lesion \> 15 cm. Diagnosis should be confirmed by at least 1 criterion listed below: * Histologically or cytologically proven diagnosis of HCC. * Typical arterial enhancement and delayed washout on multiphasic CT or MRI. 2. Age ≥18 years at the time of signing informed consent document. 3. ECOG performance status 0-1. 4. Barcelona Clinic Liver Cancer (BCLC) stages Intermediate (B) or Advanced (C). 5. Child-Pugh score 5-6 liver function within 28 days of study registration. 6. Documented virology status of hepatitis B virus (HBV), as confirmed by screening HBV serology test. 7. Documented virology status of hepatitis C virus (HCV), as confirmed by screening HCV serology test. 8. Ability to understand and the willingness to sign a written informed consent document 9. Adequate bone marrow, liver, and renal function within 4 weeks before study registration * Hemoglobin ≥ 9.0 g/dL * Absolute neutrophil count (ANC) ≥ 1,000/mm3 * Platelet count ≥ 50,000/μL * Total bilirubin \< 2.5 mg/dL * Serum albumin \>2.8 g/dL * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) ≤ 3 × upper limit of normal (ULN) * Prothrombin time ≤ 6 seconds prolonged * Serum creatinine ≤ 1.5 mg/dL Exclusion Criteria: 1. Prior invasive malignancy unless disease free for a minimum of 2 years 2. Prior radiotherapy to the region of the liver that would result in overlap of radiation therapy fields 3. Prior selective internal radiotherapy/hepatic arterial yttrium therapy, at any time 4. Untreated active hepatitis B or hepatitis C 5. Moderate to severe or intractable ascites 6. Presence of distant metastases that cannot be encompassed by proton radiotherapy 7. Untreated or incomplete treated esophageal or gastric varices 8. Severe, active co-morbidity, defined as follows: * Unstable angina and/or congestive heart failure requiring hospitalization within the last 6 months prior to registration * Myocardial infarction within the last 6 months prior to study entry * Acute bacterial or fungal infection requiring intravenous antibiotics within 28 days prior to study entry * A bleeding episode within 6 months prior to study entry due to any cause. * Thrombolytic therapy within 28 days prior to study entry. * Known bleeding or clotting disorder. * Uncontrolled psychotic disorder 9. Pregnancy or women of childbearing potential and men who are sexually active and not willing/able to use medically acceptable forms of contraception 10. Prior solid organ transplantation. 11. Prior or active autoimmune disease (AID) including autoimmune hepatitis, inflammatory bowel disease, myasthenia gravis, systemic lupus erythematosus, rheumatoid arthritis, antiphospholipid antibody syndrome, Wegener granulomatosis, Sjogren's syndrome, Guillain-Barre syndrome, and multiple sclerosis. 12. Prior or active thrombotic or bleeding disorders, hemoptysis, cerebral vascular accident, significant cardiac disease (ischemic or congestive heart failure), or gastrointestinal perforation. 13. Inability to treat all sites of disease by proton radiotherapy (such as extrahepatic metastases or massive liver tumors whereby the liver constraints cannot be met for covering all sites of liver tumors using proton radiotherapy.) 14. Known HIV infection.