Update

The introduced improvements are essentially applied to the energy measurement and the positron position measurement. Two mistakes are also found and corrected. The applied adjustments can be summerized in this way:

• Calorimeter Energy correction : Due to the miscalibration of the calorimeter a correction of 6$\%$ in BCAL and 2.5$\%$ in RCAL is applied to the measured energy.
• Positron Energy correction: The new energy correction function for the scattered positron is now applied. No calorimeter correction is applied to the uncorrected positron energy.
• Positron position: The misalignment of the SRTD is taken into consideration. The calorimeter position informations are used when the SRTD is not avaible. In this way is possible to extend the measurement towards higher values of $Q^2$.
• Noise suppression: The noise suppression routine NOISE95m is applied both to the data and to the MC events. In this way a better agreement between data and MC in the low $y_{JB}$ and $E-P_z$ region is achieved.
• Timing: A bug was corrected in the old analysis: before the events without timing information were excluded from the analysis while now they are included (thanks to Mike Wodarczyk).
• Photoproduction background : This source of background was estimated using the PYTHIA Monte Carlo generator. For this analysis a sample corresponding to 253 nb$^{-1}$ was used with a cut of $Q^2 < 2$ GeV$^2$. With this cut not all the positrons are lost in the beam pipe, due to the new geometry of the detector, and so there was an overestimation of the PHP background. This problem has been fixed using only the events with a $Q^2_{app} < 0.3$ GeV$^2$.
• New bins : In order to have a real comparison with the other analysis, a new binning in $y$ and $Q^2$ was chosen. Figure 1 shows the bins used in this analysis. There are now 12 bins in $Q^2$ and 5 in $x$ except for the low $Q^2$ bins, where there are only 1 and 3 bins for $Q^2 = 0.6$ GeV$^2$ and $Q^2 = 0.9$ GeV$^2$, respectively.
• F$_L$: The value of F$_L$ is quoted using now the BKS model [5], instead of the ZEUS NLO fit to the '94 data.
• smoothing function: Different checks were made to see if the smoothing function used during the unfolding procedure biases the data.