Michael Zacharias for the CTAO Consortium, Elina Lindfors for the CTAO Consortium, Patrizia Romano for the CTAO Consortium, Daniela Dorner for the CTAO Consortium, Stefano Vercellone for the CTAO Consortium, Matteo Cerruti for the CTAO Consortium, Jonathan Biteau for the CTAO Consortium

Correlations between various multiwavelength (MWL) bands are an intermittent feature in blazar light curves; that is, they are observed in some instances but not in others. With the CTAO we will obtain detailed very-high-energy (VHE) gamma-ray light curves for many sources also during their low states, enabling detailed MWL correlation studies. For two blazars, the HBL Mrk\,421 and the FSRQ PKS\,1510-089, the long-term X-ray and optical light curves are used to induce variations in input parameters of the lepto-hadronic one-zone code OneHaLe. We show light curves in the CTA energy range for three different energy thresholds. The results are: 1) the presence of relativistic protons has a significant effect on the correlation of the light curves as the emerging pair cascade prolongs flaring states at the highest energies; and 2) comparison of the theoretical light curves with existing VHE gamma-ray data shows that both leptonic and hadronic models can only partially reproduce the data.