high permittivity on radiation pattern

The use of high dielectric constant for increasing the bandwidth of patch antennas is well know. what are its effects on efficiency and radiation pattern.

Thanks

Efficiency should go down however, radiation pattern remains almost the same if you change the physical dimension of the patch to get same electrical dimension as in previous substrate.

Actually, a higher dielectric constant increase
the Q which in turn lower the bandwidth.

@Jallem
Yes you are true but higher permittivity also helps to lower the resonance frequency.