  We present a universal form of the $T$-matrices renormalized in
nonperturbative regime and the ensuing notions and properties that fail
conventional wisdoms. A universal scale is identified and shown to be
renormalization group invariant. The effective range parameters are derived in
a nonperturbative scenario with some new predictions within the realm of
contact potentials. Some controversies are shown to be due to the failure of
conventional wisdoms.
