Modeling of van-der-Meer scan at NICA

TL;DR

This paper revises the van-der-Meer method for luminosity calibration in hadron colliders, accounting for the hour-glass effect, especially relevant for the Nuclotron-based Ion Collider fAcility, and proposes a bias estimation approach for non-factorizable beams.

Contribution

It introduces a modified van-der-Meer formalism considering the hour-glass effect and proposes a general bias estimation method for non-factorizable beams.

Findings

Hour-glass effect significantly impacts luminosity measurements.

Revised formalism improves accuracy of van-der-Meer method under specific conditions.

Bias estimation approach aids in correcting non-factorizable beam measurements.

Abstract

Van-der-Meer method is used in hadron colliders for absolute luminosity calibration. In the letter the applicability of the method is discussed when particles desnsity is distorted by hour-glass effect next to interaction point. The study is motivated by close commisioning of Nuclotron based Ion Collider fAcility where hour-glass effected is significant by design. The theoretical van-der-Meer formalism is revised for this case. Importance of hour-glass effect for luminosity measurements and calibration is demonstrated. Also, the general approach to the estimation of van-der-Meer method bias when it is used for non-factorizable beams is proposed.