The new_cluster field is mandatory in the payload when creating a job through the Databricks REST API because it specifies the cluster configuration on which the job will run. This includes details like the instance type and number of instances, which are crucial for the job's execution. While fields like job_name, notebook_task, and email_notifications are useful for job management and execution details, they are not mandatory. The job_name helps in identifying the job, notebook_task defines the task the job will execute, and email_notifications are for setting up alerts, but none of these are required for the job creation process.