Answer: There are different types of emotion theories. The one we will use here to explain is the two-factor theory otherwise known as Schachter-Singer theory. It's the best way to look at what is going on with how tranquilliser affect emotion.
Explanation: There are two ways emotion is formed. First one is the physiological reaction such as heart beat, and there is also the cognitive reactions which is usually subjective based in what someone is experiencing like fear, anger, excitement etc, so the nervous system gives off physiological(active) reaction that causes a subjective (cognitive) feelings such as fear and anxiety. The tranquilliser inhibit the physiological reaction in one factor of the cognitive reactions which shows the actual emotion.
However, the cannon-Bard theory suggest arousal and emotions occurred the same time, which makes it difficult in explaining emotion-reducing effect.
Hope this helps.