Hard-photon emission in with realistic cuts

Abstract

We derive compact analytical formulae of the Bonneau-Martin type for the reaction e + e − →f f γ with cuts on minimal energy and acollinearity of the fermions, where the photons may be emitted both from the initial or final states. Soft-photon exponentiation is also taken into account.One of the cleanest scattering processes at elementary particle accelerators is fermion-pair production in e + e − annihilation, potentially accompanied by one or few photons:( 1) Initial-state corrections may be written as an integral over the (normalized) invariant mass squared R = s ′ /s of the final-state fermion pair:where σ 0 (s ′ ) is an effective Born cross-section. The radiator function ρ ini T (R) for the initialstate first-order corrections to the total cross-section σ T , with soft-photon exponentiation, is [1]:where h.o. stands for higher orders, and [2]:Experiments at LEP1, SLC, LEP2, and those planned at a linear collider aim at precisions well below a per cent and need theoretical predictions with an accuracy of the order of 0.1 % a Supported by Bulgarian foundation for Scientific Research with grant Φ-620/1996.

QED challenges at FCC-ee precision measurements

“…Fortunately, in ref. [62] the source of these discrepancies between IFI implementation in ZFITTER and TOPAZ0 were identified and new precision estimates δA l F B (M Z ) = 0.0002 and δA l F B (M Z ± 3GeV ) = 0.0013 were provided. However, this estimate is not reliable for higher order effects in IFI, because both ZFITTER and TOPAZ0 implement essentially the same additive combination of the ISR and FSR collinear radiator functions with O(α 1 ) results, integrated analytically over a single real photon within some simple cut-offs.…”

“…was believed to be ∼ 1%, see ref. [62]. More systematic studies of the QED uncertainty, including IFI, at LEP2 energies were done in refs.…”

30 years, 750 integrals, and 1 desert

“…For the explicit expressions for ρ FB (s /s) and ρ T (s /s), as well for more involved contributions, see e.g. [20,21,22,23,24,25]. Because at the Z resonance the soft photon radiation dominates over hard photon emission, and the radiator kernels ρ FB (s /s) and ρ T (s /s) start to deviate from each other for hard emissions, one may use ρ T (s /s) in some approximation for the prediction of all the realistic observables: At the resonance, hard radiative emissions are kinematically suppressed.…”

Predictions for fermion pair production at e+e− colliders

“…or to scattering angle distributions like dσ/dcos θ, then with different effective Born terms and radiators. Kinematical cuts to the final-state phase space may also be applied [81,[23][24][25]95]. Also a more modelindependent description of cross section observables, e.g.…”

“…Earlier program descriptions are [19,20]. The core of ZFITTER relies on a complete electroweak oneloop calculation [21][22][23][24][25]. It is also based on many additional formulae; from [18] one may extract a list of papers that ZFITTER uses in addition, .…”