Restriction on the Energy and Luminosity of e+e− Storage Rings due to Beamstrahlung

The role of beamstrahlung in high-energy ${e}^{+}{e}^{\ensuremath{-}}$ 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 $2{E}_{0}\ensuremath{\gtrsim}140\text{ }\text{ }\mathrm{GeV}$ for head-on collisions and $2{E}_{0}\ensuremath{\gtrsim}40\text{ }\text{ }\mathrm{GeV}$ for crab-waist collisions. With beamstrahlung taken into account, we explore the viability of SRCs in the $2{E}_{0}=240--500\text{ }\mathrm{GeV}$ range, which is of interest in the precision study of the Higgs boson. At $2{E}_{0}=240\text{ }\text{ }\mathrm{GeV}$, SRCs are found to be competitive with linear colliders; however, at $2{E}_{0}=400--500\text{ }\text{ }\mathrm{GeV}$, the attainable SRC luminosity would be a factor 15--25 smaller than desired.