Controversy about Crescent Moon's Sighting

Q: If controversy happens between two reliable, big groups about the sighting of the crescent moon (of the month of Ramadan or Shawwal), what can we do?

A: If they differ in sighting is proved or not and if among those who claim sighting there are just persons who testify that they saw it, one should accept theirs. But, if one group say it is proved that the moon is sighted and the second group say it is proved that the moon is not sighted, the two claims contradict each other and neither of them is reliable.