Luminosity determination at HERA-B

Abstract

A detailed description of an original method used to measure the luminosity accumulated by the HERA-B experiment for a data sample taken during the 2002–2003 HERA running period is reported. We show that, with this method, a total luminosity measurement can be achieved with a typical precision, including overall systematic uncertainties, at a level of 5% or better. We also report evidence for the detection of $\mathrm{\delta }$-rays generated in the target and comment on the possible use of such delta rays to measure luminosity.

Introduction

A precise determination of the luminosity is required for the measurement of absolute cross-sections. The integrated luminosity ($\mathcal{L}$) is defined by

$$\mathcal{L}=\frac{N_{\mathrm{P}}}{{\sigma }_{\mathrm{P}}}$$

where $N_{\mathrm{P}}$ is the number of events of a given process and ${\sigma }_{\mathrm{P}}$ is the corresponding cross-section. In the case of HERA-B, which is a forward spectrometer [1], [2] experiment, operated at the 920 GeV proton beam of the HERA accelerator at the DESY Laboratory in Hamburg, the proton beam is bunched and interacts with a nuclear target placed on the halo of the beam. The number of proton–nucleus (pA) interactions per bunch crossing is subject to statistical fluctuations. For HERA-B, as for all other experiments having a bunched beam, the luminosity can be expressed as

$$\mathcal{L}=\frac{N_{\mathit{BX}}·\lambda }{\sigma }$$

where $\lambda$ is the average number of interactions per bunch crossing BX, $N_{\mathit{BX}}$ is the number of beam bunches crossing the apparatus and $\sigma$ is the interaction cross-section (for a more detailed discussion, see 4 The cross-sections, 5 General remarks on the luminosity determination). As a consequence, given the cross-section of proton–nucleus interactions, the luminosity can be measured by determining $\lambda$ and $N_{\mathit{BX}}$. The average number of interactions per BX can be obtained from a fully unbiased sample of events in various ways: by looking at inclusive quantities which are proportional to the number of interactions in one event (such as the number of tracks or the energy released in a calorimeter), by counting the number of primary vertices or by counting the number of empty events. The first method has the advantage of entailing only a rather straightforward analysis of the data, but the signal corresponding to a single interaction must be evaluated precisely and detector stability becomes a relatively critical issue. In the second method, the vertex reconstruction efficiencies must be known precisely as well as the probability of erroneously merging or splitting primary vertices during reconstruction. In the third method, the distribution of the number of interactions per bunch crossing must be either known or assumed and the efficiency for detecting non-empty events and the impact of noise events must be evaluated.

After careful studies the HERA-B Collaboration has decided to exploit the method based on counting events with evidence of at least one interaction (which is equivalent to the third method listed above), since this method minimizes the systematic error on the luminosity determination allowing to achieve a final precision of about 5%.

The paper is organized in the following way. In 2 The HERA accelerator and the target, 3 The HERA-B detector and the data sample the main features of the HERA accelerator relevant for this analysis and the HERA-B detector are briefly described. Section 4 summarizes all of the published proton–nucleus cross-section measurements which are used for the luminosity determination. In 5 General remarks on the luminosity determination, 6 The determination of, the relevant relations for the determination of the luminosity are described. In Section 7 we discuss the systematic uncertainties and comment on delta ray production, while in Section 8 we report the results obtained for the interaction trigger (defined below) data sample.