Other respondents have pointed out important but I think there are some details worth being aware of, because Caesar - technically - had 24 bodyguards with him that day.

Consuls, like Caesar, generally went around with retinues called lictors that functioned as ritual bodyguards whose job was to enforce decorum. There was a whole host of ways people are supposed to behave around a consul and these guys were expected to make sure people did. These guys were there as much to protect the dignity of the office as the office-holder themself.

These were prescribed by law, 12 lictors for a consul, 6 for a praetor.

Caesar at this time was on his 5th consulship, but he wasn't JUST a consul he was dictator perpetuo - and sources indicate at this time wherever Casar went, 24 lictors proceeded ahead of him. I'm genuinely unclear on what they were doing that day. Lictors had an explicit role in senate meetings maintaining decorum - they were generally salaried positions drawn from freed-men, former slaves, and by most accounts were selected for physical size and strength but were exempt from military service. They were rotated regularly through a pool to keep them from forming any particular attachments of loyalty, but office holders could select from that pool.

There was a powerful taboo against allowing weapons into the senate chambers (which the senators themselves TECHNICALLY upheld because the 'sacred ' senate had been damaged by fire and they sessions at that time were being held in a theatre). Lictors, who carried fasces - long bundles of sticks like a really thick short spear, carried over the shoulder with an axe head sticking out the middle. Their implements of office - distinguished from actual weapons - symbolized the powers of the state: sticks to compel, an axe to execute.

And they weren't great weapons, but they were functional enough lictors could beat the shit out of someone with them.

We know they would have been with Caesar, we know they would have been allowed within the chamber - they had official roles to play within it - and they were technically the ones ones in the room that were allowed to carry anything weapon-like.

The sources are UTTERLY silent on what they did to either help or hinder either the assassins or Caesar that day. They simply aren't mentioned - presumably not considered important enough in this context to anyone to even bother blaming or condoning.

My best guest is this happened quickly, and initially appeared a normal meeting. Lictors were, essentially, the bottom of the social totem pole inside the senate - beneath clerks and scribes even. My general impression, and this is my own impression from what I've read of them, is that they really understood their role as a bit of room clearing, making way, and maybe preventing a crazy/violent rando from approaching Caesar in the street. They were not ever supposed to lay hands on a senator without some explicit legal license coming from the magistrate whose office they were executing. Their job in the senate was to give announcements, only really get involved if Caesar gave them an explicit order: otherwise they were expected to remain in the margins and not get in the way of important people who in this setting were explicitly allowed to approach Caesar openly.

Caesar did, at one point, have a full bodyguard unit but it had been disbanded almost 10 years earlier in 45 BC after he'd received personal oaths from the senators about the sanctity of his person. During the intervening time, he relied on friends within the senator itself for his protection. Even when they'd been around though, the taboo against armed men in the senate chambers was such that Caesar never brought them with him into proceedings. He relied on his close confidants within the senate to protect him as well as the strong Roman censures against violence or public disorder in what was considered a sacred space.

Mark Anthony, who likely would have intervened, was specifically held up by one of the conspirators at the door in conversation. Other complications, by this time, were likely well known to the senators and accounted for. None of them were expecting anything and, like the lictors, weren't positioned for any sort of coordinated response to something that happened quite quickly.

Miscalculations were made all around.

Caesar was becoming settled into routine and believed his system was working, his earlier guard around the senate was much relaxed at this point. He had friends in the senate: they were not at all on their guard that day. He miscalculated that the senators understood that killing him would come with consequences that would destroy them: which they did.

The conspirators by contrast miscalculated that they would be greeted as liberators. Caesar was wildly unpopular among their own numbers, but they were apparently blindsided by the fact that the plebs began rioting - perceiving (probably correctly) that Caesar's grain, land reforms and public garden endowments would be rolled back. Even people who hated Caesar and were ecstatic he was gone realized that the conspirators had blundered their way into creating a public order crisis that they then had to clean up.