Gamma Factory and Precision Physics at the LHC

In this paper, we argue that the only way to improve systematic precision of W-boson mass and weak-mixing angle measurements at the LHC is to replace proton beams with isoscalar-ion beams. This results in a significant simplification of relations between W- and Z-boson production processes, with the latter serving as a precision "standard candle". However, with the presently operating LHC ion injectors, partonic luminosity for ion-ion collisions is significantly lower than the one for proton-proton collisions. Therefore, statistical precision of the above measurements is lower for the former case. The proposed way out to improve the partonic luminosity in the ion-ion mode is to transversely cool the beams. The Gamma Factory project can achieve this goal with the use of laser cooling. This will allow to improve the precision of experimental determination of the above parameters to delta MW < 5 MeV and delta sin(2) theta(W) < 10(-4). The proposed calcium beams are also optimal for exclusive Higgs-boson production in multiperipheral gamma gamma collisions and studies of H -> bb decays in a clean environment.