I don’t know what you consider to be “strong research”. But, there are several sports psychology papers that take up the concept of “mental toughness”. In the Journal Of Applied Sport Psychology (2002), Jones, Hanton and Connaughton from the University of Wales studied ten international elite athletes to determine what mental toughness is, and, what the attributes are of someone who is mentally tough. Although it’s a relatively small study, it does define mental toughness:
Mental toughness is having the natural or developed psychological edge
that enables you to:
Generally, cope better than your opponents with the many demands (competition, training, lifestyle) that sport places on a performer.
Specifically, be more consistent and better than your opponents in remaining determined, focused, confident, and in control under pressure.
The definition came about after a three stage study that consisted of focus groups, individual interviews, and an “individual rating of the definition and ranking of mental toughness attributes”. They identified 12 attributes of mental toughness and applied an "importance ranking". The researchers claim the results of the study have helped teams and individual performers in archery, field hockey, athletics, gymnastics, ice skating, weightlifting, squash, swimming, speed skating, cycling, association football, judo, rowing, and modern pentathlon. They did not differentiate outcomes based on different sports or athletes.