Left: L1-$\gamma$ trigger efficiency for inclusive clusters and isolated-narrow clusters with $R=$ 0.2 (similar for $R=$ 0.4) obtained with PYTHIA 8 simulations combining $\gamma-$jet and jet$-$jet processes, embedded in data in the considered centrality class for Pb$-$Pb collisions and considering the corresponding trigger thresholds ($E_{\rm trig}$) in each system. Right: L1-$\gamma$ trigger rejection factor calculated by applying the trigger efficiency for pp collisions and for each of the Pb$-$Pb centrality classes considered. Solid lines over points result from a constant fit, values given in Table 2, dashed lines indicate the fit uncertainty obtained with the procedure explained in Sect. 4. For clusters above 12 GeV/$c$ and peripheral Pb$-$Pb collisions, the rejection factor and trigger efficiency are calculated for the sum of the two triggered samples with thresholds at 5 and 10 GeV.