Fludarabine and Intermediate-dose TBI Followed by PTCy in Patients Undergoing Allo Transplant for Heme Malignancies

Inclusion Criteria: * Patients ages 18-65 years. * Patients with a diagnosis of one of the following hematologic malignancies: * Acute myeloid leukemia or chronic myeloid leukemia with no circulating blasts and less than 5% blasts in the bone marrow; * Myelodysplastic syndrome with less than 5% blasts in the bone marrow by IHC or flow cytometry whichever is highest; * Myeloproliferative neoplasms with less than 5% blast in the marrow and peripheral blood; * Acute lymphoblastic leukemia in CR (CIBMTR criteria); or Lymphoma in CR (CIBMTR criteria). * Patients who are eligible for allogeneic stem cell transplant per Transplant Program SOPs. * Patients with a Karnofsky performance status (KPS) of ≥60%. * Patients with adequate organ function defined by: * Cardiac: LVEF ≥50% * Pulmonary: DLCO ≥50% of predicted * Hepatic: Bilirubin ≤1.5x ULN, ALT/AST ≤2.5x ULN * Renal: Creatinine clearance ≥50 mL/min * All participants of reproductive potential must use effective contraception following allogeneic hematopoietic stem cell transplantation (allo-HSCT), in accordance with guidelines from the American Society for Transplantation and Cellular Therapy (ASTCT), the FDA, and other expert bodies. * For Male Participants: ○ Male participants must use effective contraception for at least 12 months after transplant, and longer if receiving immunosuppressive or cytotoxic medications. Chemotherapy and radiation can cause DNA damage to sperm, and even if fertility returns, mutations m…