  We study constraints from perturbativity and vacuum stability as well as the EWPD in the type II seesaw model. As a result, we can put stringent limits on the Higgs triplet couplings depending on the cut-off scale. The EWPD tightly constrain the Higgs triplet mass splitting to be smaller than about 40 GeV. Analyzing the Higgs-to-diphoton rate in the allowed parameter region, we show how much it can deviate from the Standard Model prediction for specific parameter points. 
Vacuum Stability, Perturbativity, EWPD and Higgs-to-diphoton in Type II   Seesaw