Measurement of inclusive \varvec{ep} cross sections at high {\varvec{Q}^{2}} at \varvec{\sqrt{s}}=225 and 252 GeV and of the longitudinal proton structure function {\varvec{F}_{\varvec{L}}} at HERA

Inclusive $$ep$$ double differential cross sections for neutral current deep inelastic scattering are measured with the H1 detector at HERA. The data were taken with a lepton beam energy of $$27.6$$ GeV and two proton beam energies of $$E_p=460$$ and 575 GeV corresponding to centre-of-mass energies of 225 and 252 GeV, respectively. The measurements cover the region of $$6.5\times 10^{-4} \le x \le 0.65$$ for $$35\le Q^2 \le 800$$ GeV $$^2$$ up to $$y=0.85$$ . The measurements are used together with previously published H1 data at $$E_p=920$$ GeV and lower $$Q^2$$ data at $$E_p=460$$ , $$575$$ and $$920$$ GeV to extract the longitudinal proton structure function $$F_L$$ in the region $$1.5\le Q^2 \le 800$$ GeV $$^2$$ .