Well, yes. The Roman legions are pretty famous for using the gladius amongst other things, but you can find "professional" (and the definition of professional varies greatly over time) infantry using all sorts of things.

During the later middle ages, Italian mercenaries were pretty famous and fought broadly throughout Europe, especially favoring the crossbow as the weapon was simple to use and quite effective against advancements in armor technology.

There were also groups of "Vikings" that ended up fighting as professionals in Europe, most famously, the "Varangian Guard" of the Byzantine Empire, who "carry shields and brandish on their shoulders a certain single-edged, heavy-iron weapon" according to one Byzantine source, probably a large axe.

During the end part of the Middle Ages, there were also the famous Swiss mercenaries, the most notable group of whom were the Pontifical Swiss Guard charged specifically with the protection of the Pope. Swiss mercenaries favored dense formations of pikemen and the use of the halberd.

So, in any case, the point I am trying to make is that the weapons that professional infantry used varied based on a lot of factors. Cultural norms, such as the Varangian Guard preferring their axes, were just as important as practical concerns, such as the effectiveness of Italian crossbows against armor or Swiss pikes against the heavy horsemen of the Late Middle Ages.

I can't think of any book that really covers the entirety of this subject, but if you have interest in a particular topic, I probably can recommend some decent sources.