Measurement of the diffractive structure function $F_2^{D(3)}$

Measurements of the diffractive structure function $F_2^{D(3)}(x_{\PO}, \beta, Q^2)$, describing the process $ep \to eXY$, are presented in the two kinematic regions $0.4 \leq Q^2 \leq 5$, ${\rm GeV}^2$, $0.001 \leq \beta \leq 0.65$, and $200 \leq \beta \leq 800 {\rm GeV^2}$, $0.4 \leq \beta \leq 0.9$, both with $\xpom < 0.05$, $M_{_Y} < 1.6 {\rm GeV}$ and $|t| < 1.0 {\rm GeV^2}$. Together with published measurements at intermediate $Q^2$, the data are compared with models based on QCD and Regge phenomenology. The diffractive trajectory is found to have an intercept larger than that describing soft hadronic data and consistent with that determined using previously published H1 measurements at intermediate $Q^2$ alone. The data are also parameterised using a QCD motivated model based on the exchange of two gluons from the proton. In this model, the higher twist contribution to $F_2^{D(3)}$ at large $\beta$ is found to be important at low $Q^2$. The data are also compared with models based on BFKL dynamics.