Write to the Jira Audit Log

import com.atlassian.jira.auditing.*
import com.atlassian.jira.component.ComponentAccessor

final customFieldName = 'GroupPicker'

def auditingManager = ComponentAccessor.getComponent(AuditingManager)
def fields = ComponentAccessor.customFieldManager.getCustomFieldObjectsByName(customFieldName)

assert fields // Failed to find any fields with this name

def field = fields.first()

def record = new RecordRequest(AuditingCategory.FIELDS, 'Foo bar...')
    .withChangedValues(
        new ChangedValueImpl('A Name', 'Previous value', 'New value'),
        new ChangedValueImpl('Another name', 'I used to be...', 'And I\'m now...'),
    )
    .forObject(AssociatedItem.Type.CUSTOM_FIELD, field.name, field.id) // adding an object is optional...

auditingManager.store(record)