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Let $X$ be a smooth complex projective algebraic variety. Given a line bundle$\mathcal{L}$ over $X$ and an integer $r>1$ one defines the stack$\sqrt[r]{\mathcal{L}/X}$ of $r$-th roots of $\mathcal{L}$. Motivated byGromov-Witten theoretic questions, in this paper we analyze the structure ofmoduli stacks of genus $0$ twisted stable maps to $\sqrt[r]{\mathcal{L}/X}$.Our main results are explicit constructions of moduli stacks of genus $0$twisted stable maps to $\sqrt[r]{\mathcal{L}/X}$ starting from moduli stack ofgenus $0$ stable maps to $X$. As a consequence, we prove an exact formulaexpressing genus $0$ Gromov-Witten invariants of $\sqrt[r]{\mathcal{L}/X}$ interms of those of $X$.

Gromov-Witten theory of root gerbes I: structure of genus $0$ moduli spaces