"He is wearing a hat today."
Here, I think, 了 is necessary. It'd still be okay without, but its clearer that he doesn't usually wear a hat and he did today, for instance.
In my personal and humble opinion, the Chinese sentence does not seem to be the corresponding translation. 了 is a very flexible particle and can be used in many instances. If you look at this link:
you will see that "modal 了" can be used when a situation has changed or when informing someone about a new situation. The problem with this Chinese sentence is that "modal 了" always goes at the end of the sentence. On the other hand, "aspectual 了" always follows the verb.
So maybe to actually convey the novelty they should placed the "modal 了" at the end of the sentence like so: 他今天戴帽子了。 This sentence conveys more meaning than the actual translation. Beside "wearing a hat today", the guy in the sentence probably does not usually wear hats (maybe because he has a majestic lion like mane that would be such a shame to hide) and this could be considered as a "changed or new situation". Therefore I think that the issue is with the Chinese sentence.
I rest my case!
P.S. If I am incorrect please let me know and show me some sources if possible :) Thanks!!
The nuance that you mentioned in given sentence isn't fully translated in English, but it is still acceptable. On the other hand, putting 了 at the end has a past tense implication to it, so that it can be translated as "He wore a hat today". Please note that there is, in most cases and in this case as well, no error in the Chinese sentence.
The fact that "戴" means "put on" as well as "wear", which have different aspects in English, makes this a little confusing, but the grammar explanations Andrea links to do seem to support her interpretation. However, I appreciate your native ear.
I tried the neutral "他今天戴帽子", but it wasn't accepted.
Maybe 'dai' means more of 'to put on' in this case: i.e. He put on a hat this morning and therefore... he is wearing a hat today?
According to my girlfriend: 他今天戴帽子 is a neutral statement meaning "He is wearing a hat today." 他今天戴了帽子 puts a slight emphasis on the fact that he usually does not wear a hat, and could maybe best be translated with "Today he is wearing a hat." 他今天戴帽子了 expresses strongly that a change has happened. This could be translated in English with "Today, he is wearing a hat." or "Finally, he is wearing a hat today". 他今天戴了帽子 cannot mean "He wore a hat today" because the particle 了 does not signify past tense when in combination with a present time indicator like 今天. One could for example say 他今天早上戴了帽子: "He wore a hat this morning."
Great explanation. Note that while the translation "He wore a hat today" leaves much to be desired in both languages, it cannot be said to be unacceptable per se.
To add to what has been said, 他今天带了帽子