I'm looking for research papers and studies from disinterested (social) scientists, rather than magazine fluff-pieces or anything funded by the AMI or similar. The trivial google of "Montessori research" doesn't pull up much that passes the sniff-test.
Angeline S. Lillard, PhD is a Professor of Psychology at the University of Virginia with a focus on social and cognitive development including Montessori education. Her book "Montessori: The Science behind the Genius" (now in it's 3rd 2017 Edition) is exceptionally well-researched and written: https://www.montessori-science.org/montessori_science_genius.htm the book provides a balanced review of the literature, also noting where research doesn't support Montessori.
She has published several peer-reviewed papers on the effects of Montessori Education; see Google Scholar: https://scholar.google.com/scholar?hl=en&q=LILLARD (sorted by number of citations).
e.g: The early years: Evaluating Montessori education published in the Journal Science.
A lottery for assigning children to schools was created to control for family income and education. Mainly urban minority children were assigned to either a "normal" or Montessori pre-school.
Benefits of Montessori Education
On several dimensions, children at a public inner city Montessori school had superior outcomes relative to a sample of Montessori applicants who, because of a random lottery, attended other schools. By the end of kindergarten, the Montessori children performed better on standardized tests of reading and math, engaged in more positive interaction on the playground, and showed more advanced social cognition and executive control. They also showed more concern for fairness and justice. At the end of elementary school, Montessori children wrote more creative essays with more complex sentence structures, selected more positive responses to social dilemmas, and reported feeling more of a sense of community at their school.
Note: obviously, the research into Montessori is never "unbiassed" as noted by other comments above because research requires funding. But when research is published in peer-reviewed journals it has a better chance of being refuted/contested and thus we can expect (or hope) that it is more trustworthy.
As a recent parent I've been reading my way through all her work and would recommend others to do the same; it's fascinating! I've learned several counterintuitive things that have forced me to change how I think about child development; specifically around the "Prepared Environment", sensitive periods and never interrupting the child's focus. I'm a software engineer, but have several non-Montessori teachers in the family ... on the back of my reading I've decided to do an AMI certified course to help our child at home and be better informed when it comes to choosing a school. https://montessori-ami.org/training-programmes/ami-teacher-training
Chapter 7 of How To Raise an Adult by Julie Lythcott-Haims refers to a few studies that addresses the unstructured play vs structured play, which Montessori seems to favor more over very rigidly defined activities. Unstructured play (not totally, but within reason) boosts executive brain function which helps them determine which action to take to achieve their goals. (http://journal.frontiersin.org/article/10.3389/fpsyg.2014.00593/full) Kids with better executive brain function generally do better in school and life. http://developingchild.harvard.edu/science/key-concepts/executive-function/
That's what jumped out at me so far having made it to chapter 9. It's a good book so far.
Montessori also teaches social skills, which sure seem to be lacking in many kids today. As someone who hires people, I'd rather hire someone with good social and professional skills.
My son is in a Montessori school now (for two years) and I can see that it doesn't fit well with some kids' temperaments and learning types. I don't think any one-size-fits-all learning approach will work for all kids regardless.
I have done dozens of hours of research on Montessori, but I've never come across any scientific studies, per se, so whether or not what I say is what you're looking for will be up to you. I agree with the previous answer, though, that how to raise your child should not solely be based on research papers, BUT - it should be based on evidence, to a degree. You can search up and down, far and wide, for valid, legitimate studies and research papers, but ultimately your best bet will be to study and get to know the method itself. It is absolutely possible to find unbiased, detailed information about Montessori herself, the pedagogy, and the current implementations in schools today in the US.
I will say, that after my studies, I hired a nanny when my son was born who was a former Montessori infant/toddler teacher. I promise I am not one of those parents who just thinks their child is some magical, gifted prodigy, but I believe Montessori principles have been very good for him. He is two and a half now, and while I obviously can't state any true long term effects of Montessori on him directly, I can say he is more capable in practical life than any other 2 year old I have encountered personally. That's not to say there aren't kids out there that are more capable than he, but the beauty of Montessori is it very much emphasizes teaching children to do things themselves based on their capabilities. That said, he can only barely count, and doesn't yet know his alphabet. But he throws away his own trash, puts his dishes in the sink, wipes up spills, prepares his own snacks, helps cook, dresses himself, was potty trained at 18 months without any types of rewards/bribes, etc. I consider those things life skills that are every bit as valuable as knowing your ABCs (and I've never met an adult who didn't know his colors, but I have met an 8 year old who had never been shown how to crack an egg into a bowl).
Instead of baby proofing, for instance, we create a "yes" environment. It is technically child proof, in the sense that it is safe, but nothing is off-limits. In other words, chemicals and things that could harm them are moved far out of reach (like way up high in a closet or cabinet), and things that are fine for them to access (like pots and pans) are left in lower cabinets, where they are free to explore. Children under the Montessori philosophy are treated as an equal member of the household. They are respected in the same way an adult wishes to be respected. That doesn't mean they get to do everything an adult gets to do, of course, there are limits and boundaries, but they are logical instead of arbitrary and defined by society.
Contrary to popular belief, academia as we tend to think of it is not the focus of Montessori's principles. In fact, if you look at her "10 commandments" (for lack of a better term), not a single one of them refer to academics. Now, granted her teachings involve formal academics - math, science, language, etc. - but the Montessori philosophy is so much more than that, so it can't be compared directly with, say, a normal public elementary school.
Which is another thing that makes it very difficult to create a scientific study. What would you be looking for? Grades? Academic assessments? Overall achievements? The point of Montessori isn't to make sure a child excels at math or reading. The point is that you follow the child's lead. You don't treat every child equally, because their personalities, their temperaments, their interests, are vastly different from one another. You don't sit 20 of them in a classroom and teach them all the exact same thing, give them the exact same tests, and expect them to score the exact same grade at the exact same time. Some children learn faster than others, some are more skilled at reading than math, some are more interested in science than language. Montessori knew that all children would eventually learn these things (and others), if shown via repetition and with respect, via their absorbent mind. But her goal was to empower children to learn them in their own time, and to not attempt to compare their progress in one area with other children of the same age.
Finally, I think the most important thing is to know that Montessori is not all or nothing. Plenty of kids who go to Montessori schools don't live Montessori-inspired lives at home, and plenty of kids who have a Montessori home life don't go to Montessori schools. You would have to get to know the method to find out which principles are right for you and your family. For my family, my son now goes to a daycare which isn't anywhere near Montessori, and that's okay. We are still a Montessori household, as I am a very big fan of the fundamental principles of respecting our children to the utmost degree, and teaching them to be independent in their thinking, to lead by example, and to be gracious towards others.
** Just adding one more thing, in Montessori, there is no such thing as punishment for "bad" behavior, nor reward for "good" behavior. This is something that trips up a lot of parents, and it did me at first, but the more I researched child development / child psychology alongside, the more her views on this aligned with many major life-span psychologists. That there is truly no benefit to punishing children; that it doesn't teach them anything and that time and energy are better spent on preparing their environment and teaching them about their surroundings, and redirecting unwanted behavior. Again, I bring it up, because it's something a LOT of parents hone in on and decide they can't function as parents if they can't put their child in time-out.
I see that this question has generated interest without an actual answer provided. The required sample size to do a study like this is quite large and the length of time needed to truly evaluate the benefits of a school is a lifetime. Also, there are so many contributing factors that will determine the success of a person from schooling until death. Many factors even outweigh the impact of schooling on a person.
With that being said, I believe that it is not feasible to conduct a scientific study. But that will not stop people from doing so and producing results to the general public, like the fluff pieces you mention. I think that by being concerned about what school to send your children, you are demonstrating that you will try to give your child a successful future. That is great. I would suggest that you take any studies or research with a grain of salt on this matter.
If there was an equation to determine the future level of success of a child, almost every parent would be doing it, thereby nullifying the equation.
Also, define 'benefits'. What may seem like a benefit in the short term can be a detriment over the long term.
As a parent, you already know what is best for your child. Your gut tells you. I would suggest going with your gut and leave the research papers on "How to educate/raise/discipline your child" out of your parental decisions.