Complex sentence: The minus sign here is due to the minus sign in Eq.4, which is in turn due to the Minkowski signature, had we used Euclidean signature, (+, +, +, +), instead there would have been a positive sign.
Split into simpler sentences: The minus sign here is due to the minus sign in Eq.4, which is in turn due to the Minkowski signature. Had we used Euclidean signature, i.e. (+, +, +, +), instead there would have been a positive sign.