Picard group of moduli of parabolic Higgs bundles

Let $X$ be a compact Riemann surface of genus $g\ge 3$ and let ${\mathcal{M}}_{\mathrm{p}\mathrm{a}\mathrm{r}}$ be the moduli space of semistable parabolic bundles over $X$. Let ${\mathcal{M}}_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{H}}$ denote the moduli space of semistable parabolic Higgs bundles over $X$. In this article, we study the Picard group of ${\mathcal{M}}_{\mathrm{p}\mathrm{a}\mathrm{r}}$ and ${\mathcal{M}}_{\mathrm{p}\mathrm{a}\mathrm{r}\mathrm{H}}$.