Yes there is quite a lot of research on mood, perception, and bias related to color.
The terms you are looking for are color theory and color psychology. Doing a search on these terms will yield the body of research.
The research paper Effects of Color on Emotions should provide a decent overview as well as a good set of references if you need to dig deeper.
It's probably outside the scope of this answer to discuss at length how emotions are affected by color, but a lot of the mood and emotional qualities ascribed to color are actually the results of visual perception and color biases rather than a direct psychological link between color and emotion.
You're right to be skeptical of articles which claim a direct link between color and emotions (e.g. "red is sexy"). This article from Psychology Today points out that the relationship between color and emotion is complex, and depends on the object being evaluated, convention, context, culture, and other variables. So a simplistic
color X = emotion Y relationship is misleading.