Comparisons of exact results for the virtual photon contribution to single hard bremsstrahlung in radiative return fore+e−annihilation

Abstract

We compare fully differential exact results for the virtual photon correction to single hard photon bremsstrahlung obtained using independent calculations, both for e e ÿ annihilation at high-energy colliders and for radiative return applications. The results are compared using Monte Carlo evaluations of the matrix elements as well as by direct analytical evaluation of certain critical limits. Special attention is given to the issues of numerical stability and the treatment of finite-mass corrections. It is found that agreement on the order of 10 ÿ5 or better is obtained over most of the range of hard photon energies, at CMS energies relevant to both high-energy collisions and radiative return experiments.

Quest for precision in hadronic cross sections at low energy: Monte Carlo tools vs. experimental data

“…The conservative estimate of the accuracy of PHOKHARA from ISR is 0.5%. This has been confirmed by comparisons with KKMC [264,265], where the biggest observed difference is about 0.3% in the invariant mass regions which are not close to the nominal energies of the experiments. Improving the accuracy of PHOKHARA below 0.5%, however, will be required to meet the growing experimental requirements in the near future.…”

“…The second term in (84) is the cross section containing the one-loop corrections to single hard-photon emission, and its uncertainty can be estimated by relying on partial results existing in the literature. Actually the exact perturbative expression of σ α 2 SV,H is not yet available for full s + t Bhabha scattering, but using the results valid for smallangle Bhabha scattering [47,263] and large-angle annihilation processes [264,265] the relative uncertainty of the theoretical tools in the calculation of σ α 2 SV,H can be conservatively estimated to be at the level of 0.05%. Indeed the papers [47,[263][264][265] show that a YFS matching of NLO and HO corrections gives SV one-loop results for the tchannel process e + e − → e + e − γ and s-channel annihilation e + e − → ff γ (f = fermion) differing from the exact perturbative calculations by a few units in 10 −4 at most.…”

“…the exact NLO SV QED corrections to the single hard bremsstrahlung process e + e − → e + e − γ , is still missing for the full s + t Bhabha process 10. However, partial results obtained for t-channel small-angle Bhabha scattering[47,263] and large-angle annihilation processes are available[264,265]. 3.…”

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

“…Let us note in passing that we know from the s-channel analog in [38] that the pure O(L e α 2 ) correction of this class (neglecting the O(L 0 e α 2 ) term) is amazingly compact -it consists of merely a 3-line formula at the amplitude level. Let us add for completeness that the above 3 At 350 GeV, the FCC-ee luminometer will have |t| = 12.5 GeV.…”

The radiative return method - a short theory review

“…It means that one can tests the initial state emission and in fact detailed tests were performed [22] leading to an excellent agreement of the non exponentiated matrix elements of the virtual corrections to single photon emission (a relative difference of a few times 10 −5 was found). The higher order effects, that can be seen as a difference between the exponentiated and the non exponentiated matrix elements reach at most 2 per mile with the exception of the region of the invariant mass of the hadronic system very close to the nominal energy of the experiment.…”