After an engine failure the aircraft will try to roll and yaw towards the failed engine side. As per lateral Normal Law if there is no input on the sidestick the roll rate is 0. So to counter the roll rate caused by engine failure, the ailerons and spoilers will deflect. Net effect will be approx 5 deg bank angle, constant sideslip and a slow diverging heading rate.
Deflected ailerons and spoilers will increase the Drag. This increase in drag reduces Climb performance {Climb gradient = (T - D)/W}. So from a performance standpoint it will be better to fly a constant heading with roll surfaces retracted. Beta target indicates the amount of rudder required to fly a computed residual sideslip which when centered will allow the aircraft to fly a constant heading will roll surfaces close to neutral position.
Climb performance is critical during Take off and Go around and so Blue Beta target replaces the yellow sideslip index in Take off and Go around configs i.e. Config 1,2 or 3 {along with any ENG N1 > 80 % / EPR > 1.25 or one Thrust Lever > MCT (≥ FLX if FLX or DERATED TO)and the difference between the ENG N1’s / EPR's exceeds 35 % / 0.25}