Restriction on the Energy and Luminosity of $e^{\mathbf{+}}{e}^{\mathbf{-}}$ Storage Rings due to Beamstrahlung

The role of beamstrahlung in high-energy $e^{+}{e}^{-}$ storage-ring colliders (SRCs) is examined. Particle loss due to the emission of single energetic beamstrahlung photons is shown to impose a fundamental limit on SRC luminosities at energies $2E_0\gtrsim 140\mathrm{GeV}$ for head-on collisions and $2E_0\gtrsim 40\mathrm{GeV}$ for crab-waist collisions. With beamstrahlung taken into account, we explore the viability of SRCs in the $2E_0=240–500\mathrm{GeV}$ range, which is of interest in the precision study of the Higgs boson. At $2E_0=240\mathrm{GeV}$, SRCs are found to be competitive with linear colliders; however, at $2E_0=400–500\mathrm{GeV}$, the attainable SRC luminosity would be a factor 15–25 smaller than desired.