Additionally, from the religious point of view, Jewish doesn't even necessarily have a "racial" origin. The Aramaeans were a Semitic people who began to settle in large numbers in Mesopotamia in the period just before the Medean-Persian conquest, and quickly gained a reputation as crafty and successful merchants (which identity was transferred to the Jews as a pejorative--see below). The conquest of Babylon and its hegemonic cities and tribes by the Medes and Persians, and the rise of the Persian empire gave greater scope to the Aramaeans' mercantile activities. They were so successful that Aramaic became the lingua franca
of the Middle East long before the Hellenistic period, and remained the most commonly spoken language even after the Greco-Macedonian conquest gave rise to the Hellenistic era.
The Aramaeans were impressed with the religion of the Hebrews and became what properly is called confessional Jews--i.e., Jews in a religious and cultural sense. They spread Judaism throughout the Middle East just as they spread their language. The Arabs of the Arabian peninsula in the lifetime of Mohammed who espoused a religious belief from an organized religion were overwhelmingly confessional Jews. The Aramaean merchants spread Judaism as far east as China, and Marco Polo notes the presence of "Jews" throughout the Mongol Empire of Kublai.
Later, many Aramaeans converted to Christianity, in early days, and Nestorian Christianity was spread by them just as Judaism had been. Polo also records the presence of Christians throughout Kublai's Sino-Mongolian empire, and this refers to the Nestorian Christians produced by the spread of the religion by Aramaean merchants.
So in fact, it would be very difficult to identify the "racial" antecedents of Jews around the world. Given that the concept of human races is only slightly over a century old, it is all rather an anachronistic exercise in any event.