Subleading logarithmic QED initial state corrections to e+e−→γ⁎/Z0⁎ to O(α6L5)

• Main Authors: J. Ablinger, J. Blümlein, A. De Freitas, K. Schönwald
• Format: Article
• Language: English
• Published: Elsevier 2020-06-01
• Series: Nuclear Physics B
• Online Access: http://www.sciencedirect.com/science/article/pii/S0550321320301310

Using the method of massive operator matrix elements, we calculate the subleading QED initial state radiative corrections to the process e+e−→γ⁎/Z⁎ for the first three logarithmic contributions from O(α3L3),O(α3L2),O(α3L) to O(α5L5),O(α5L4),O(α5L3) and compare their effects to the leading contribution O(α6L6) and one more subleading term O(α6L5). The calculation is performed in the limit of large center of mass energies squared s≫me2. These terms supplement the known corrections to O(α2), which were completed recently. Given the high precision at future colliders operating at very large luminosity, these corrections are important for concise theoretical predictions. The present calculation needs the calculation of one more two–loop massive operator matrix element in QED. The radiators are obtained as solutions of the associated Callen–Symanzik equations in the massive case. The radiators can be expressed in terms of harmonic polylogarithms to weight w = 6 of argument z and (1−z) and in Mellin N space by generalized harmonic sums. Numerical results are presented on the position of the Z peak and corrections to the Z width, ΓZ. The corrections calculated result into a final theoretical accuracy for δMZ and δΓZ which is estimated to be of O(30keV) at an anticipated systematic accuracy at the FCC_ee of ∼100keV. This precision cannot be reached, however, by including only the corrections up to O(α3).