- Alexander: eRHIC detector simulation
- All: discussion of eRHIC luminosity and energy requirements
Statistical estimate for TMDs with low luminosity
PYTHIA simulation for 5 x 250 with Q2 > 1 GeV2. I took this to be the most "efficient" configuration from a $ perspective, having the lowest electron energy coupled with the highest proton luminosity. π+ counts are binned in a couple of bins each of (Q2, x) and pT (w.r.t. virtual photon) and plotted as a function of z. Events are required to have 0.01 < y < 0.95 and pions are required to have abs(η) < 3. Statistical uncertainties are calculated by sqrt(2 / N) in each bin, with N scaled to represent 1 fb-1 integrated luminosity. PYTHIA reported a total sampled cross section of 0.48 microbarn, so 1 fb-1 would take approximately 30 weeks assuming 50% running efficiency and 1032 cm-2s-1 mean luminosity. I didn't scale for beam polarisation, but it's only intended as a rough estimate anyway.
Uncertainties still seems small enough to produce useful measurements. Uncertainties for kaons would be larger (potentially several percent for large pT and z). Measurements with D mesons (to access gluon Sivers) would be entirely unfeasible at this luminosity (they were already challenging at 1034).