Luminosity and beam-beam tune shifts with crossing angle and hourglass effects in e$^+$-e$^-$ colliders

TL;DR

This paper develops theoretical models to accurately calculate luminosity and beam-beam tune shifts in electron-positron colliders considering crossing angle and hourglass effects, aiding collider design.

Contribution

It provides new theoretical expressions for luminosity and tune shifts that incorporate crossing angle and hourglass effects for current and future colliders.

Findings

Derived formulas applicable to Fermilab Higgs factory design

Applied theory to FCC-ee collider parameters

Enhanced understanding of collider performance limitations

Abstract

We develop theoretical expressions for the luminosity and beam-beam tune shifts in the presence of both a crossing angle and hourglass effects for the present and next generation of symmetric e$^+$-e$^-$ colliders. The theory is applied to the design of the Fermilab site filler Higgs factory and to the FCC-ee collider.