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\(^2\).