TLDR: this is a handful of references from my superficial familiarity with the subject, but modern historians seem to be pretty much in agreement that ahadith are sources of very little historical veracity and largely forgeries.
Two assumptions made in hadith studies that are unscientific are:
- the acceptance of the tenets of Islam; ahadith contain many anti-scientific claims that are not considered a reason to dismiss them based on content. Take for example the splitting of the moon, Adam and Hawa (Eve) having been 60 cubits tall, a common ancestor of mankind in Noah some 30000-40000 years ago going by ahadith, stones talking to Muhammad, water springing forth from between his fingers to quench the thirst his followers, the coccyx not decaying, etc. Generally, hard-science findings are irrelevant to hadith studies.
- the sahaba (minus known hypocrites) are considered to be trustworthy
From the outset, hadith studies do not incorporate the scientific method due to the first item, and start from a position of credulity due to the second.
A scientific field that is comparable in purpose to the study of hadith would be history, the relevant method the historical method. The study of hadith among Muslim scholars has - to my knowledge, and by modern standards - dimly documented roots with poor archeological evidence in the form of relics, i.e. original manuscripts, other textual sources mentioning ahadith, etc. Just one example of how poor the documentation is: Christopher Melchert in "Bukhari and early hadith criticism" writes:
Actually, the Sahih of Bukhari seems not to have been widely published
until well into the tenth century, for virtually all known
transmissions were through a single man, Muhammad ibn Yusuf ibn Matar
al-Firabri (d. 320/ 932). Somehow, no one else of the many illustrious
traditionists who related hadith of Bukhari (al-Mizzi lists over
eighty) recognized the value of his collection of sound hadith and
transmitted it. Its organization, in particular its chapter headings,
seem not to have stabilized until the mid-tenth century. It first
attracted commentaries in the later tenth century. The earliest hadith
collection based on the Sahih of Muslim is said to have been that of
Abu Bakr ibn Raja' al-Sindi al-Isfarayini (d. 286/ 899-900); however,
the earliest that might have been based on the Sahih of Bukhari is
that of Abu Ali Said ibn 'Uthman ibn al-Sakan (d. 353/964).
Thus the earliest collections we can find are roughly three centuries after the death of Muhammad, and go back to decades or more than a century after the death of their suggested author through a very small number of transmitters. The paper goes on to talk about the formation of the current text.
Another source of distrust in hadith ignored by Islamic discourse (at least to my knowledge) about hadith criticism is their relation to politics. Goldziher in "Muhammadan Studies" vol.2 p.44 writes:
it is not surprising that, among the hotly debated controversial
issues of Islam, whether political or doctrinal, there is not one in
which the champions of the various views are unable to cite a number
of traditions, all equipped with imposing isnads
Wiki has a couple links pointing to works by modern historians about the authenticity of hadith, its origins, the available evidence, etc. They seem to be in agreement that the corpus of hadith is largely fabrications and evidence for it even existing can't be traced any earlier than almost a century after the death of Muhammad.
The work of Jonathan Brown, a sunni Muslim professor of Islamic studies at Georgetown university, in particular the book "The canonization of al-Bukhari and Muslim", may be of interest. Overall the field is vast, but there's very little trust, if any, accorded to hadith as having historical veracity among modern historians.