The path to 0.01% theoretical luminosity precision for the FCC-ee

Abstract

The current status of the theoretical precision for the Bhabha luminometry is critically reviewed and pathways are outlined to the requirement targeted by the FCC-ee precision studies. Various components of the pertinent error budget are discussed in detail -starting from the context of the LEP experiments, through their current updates, up to prospects of their improvements for the sake of the FCC-ee. It is argued that with an appropriate upgrade of the Monte Carlo event generator BHLUMI and/or other similar MC programs calculating QED effects in the low angle Bhabha process, the total theoretical error of 0.01% for the FCC-ee luminometry can be reached. A new study of the Z and s-channel γ exchanges within the angular range of the FCC-ee luminometer using the BHWIDE Monte Carlo was instrumental in obtaining the above result. Possible ways of BHLUMI upgrade are also discussed.

Electroweak corrections to e+e− → γγ as a luminosity process at FCC-ee

“…The factorized approach as in Eq. (6) gives rise to corrections dominated by O(α 2 L 2 ) contributions and was proved in Ref. [39] to be an excellent approximation of the perturbative result based on an exact NNLO calculation.…”

“…Note that the parametric uncertainty induced by the hadronic contribution to ∆α is much smaller than the target accuracy and therefore is not a limiting factor for the theoretical predictions for e + e − → γγ. This is a strength of two photon production and is in contrast to small-angle Bhabha scattering, where the same uncertainty presently contributes at the 10 −4 level [6]. It must be also noticed that a sound assessment of this class of corrections requires an explicit two-loop computation, as well as the combination of loop effects with the same-order contribution of real pair emission, which partially cancels the fermion-loop correction, as shown in past precision calculations for Bhabha scattering [39][40][41][42].…”

QED challenges at FCC-ee precision measurements

“…In ref. [55]) (Table 3) it was pointed out that due to twice wider angle of the FCC-ee Bhabha luminometer (64-86 mrads) than at LEP, the actual theoretical error according to the present state of the art (inherited from LEP) would be in fact 0.090% due to the bigger Z-exchange contribution. However, this error can be reduced to the negligible level already now using the BHWIDE Monte Carlo [27], see ref.…”

“…However, this error can be reduced to the negligible level already now using the BHWIDE Monte Carlo [27], see ref. [55]) for the details.…”

“…As pointed out in ref. [55], due to the angular range of the FCC-ee luminosity detector being factor two wider, the contribution from the Z exchange near the Z peak will rise by factor of four. If one estimates its uncertainty the same way as at LEP, then the total luminosity error would jump to 0.097%, see Table 3 in ref.…”