In the mind-body realms such as yoga and meditation, it is often held that our breath is a go-between our physical body and mind. Any disturbance in the breath (its flows, depth, length and speed) would have measurable impact on the nature of mind and its states. E.g. anger will have different signature of breath than calm and repose. Worry and anxiety will have different rhythms than equanimity.
In fact, large part of yogic and meditative benefits draw from proper use of breath during movements and rest. E.g. some studies have shown that out-breath tends to calm down neurons firing in the amygdala, the threat-perception center of our brain. In-breath tended to intensify the activity in amygdala. Initially these findings were observed in cats but similar findings were also noted in human amygdala to some degree later. Even in pranayama practice, we see that specific lengths of in-breath and out-breath are mandated to elicit different states of mind and alter physiological ambience in the body.
From yogic and meditative perspective, it is not an overstatement to say that breathing can have significant impact on the nature of emotions and fear. One recent study also suggests that our breathing rhythm can have measurable impact on fear and emotions. A recent paper published in the Journal of Neuroscience indicates that breath is very much tied to mental states of fear and other emotions. One notable aspect of this study was these impacts were only noticeable during nasal breathing and were largely reduced during mouth breathing.