How can I hire a professor to write a research paper?

Yes, some professors are available for consultancy work. Find one or two in your specialty, and approach them: some universities have directories of experts listed by subject, to help you identify suitable researchers. You'll find they're typically lower-priced than the equivalent grade of management consultant, as well as doing better work.

However.

Though you're paying the piper, you won't be calling the tune (with the exception of a handful of rogues).

Which means that they'll publish what they find. It is highly likely that there will be some of it you don't like, which will mean you won't want to publicise the final report. They will write one or more papers based on what they've found, and if the university's legal team has done its job properly, you'll have no say in the content of those papers, nor how the university promotes them, so it will be out of your control.

If you want to learn something about your industry from an academic angle, you will get your money's worth, subject to real data being available. Academics are sometimes able to get access to information that others could not, precisely because of the pressures on them to remain independent and treat data impartially. However, the fact that you're funding them may impair their access.

Do bear in mind that an academic will typically put a lot of work into describing the uncertainties: so on first skim, the impression you'll get from the report is that it mostly says "we don't know this, and we can't know that; there are indications of those. More research is required". The report may take some digesting, as a lot of academics are very experienced at writing, but surprisingly few write lucidly and accessibly.

If you're looking for promotional material, this really is the wrong tack.