Abstract
We determine the NNLO electroweak correction to the {e}^{+}{e}^{-}to boverline{b}{W}^{+}{W}^{-}X production cross section near the top-pair production threshold. The calculation includes non-resonant production of the final state as well as electroweak effects in resonant top anti-top pair production with non-relativistic resummation, and elevates the theoretical prediction to NNNLO QCD plus NNLO electroweak accuracy. We then study the impact of the new contributions on the top-pair threshold scan at a future lepton collider.
Highlights
The precision study of the top pair production threshold is among the main motivations for the construction of a high-energy e+e− collider [1]
Precision calculations of top pair production near threshold are most conveniently done in potential non-relativistic effective field theory (PNREFT) [33, 34], which describes the dynamics of slowly moving particles with three-momentum mtv coupled to ultrasoft radiation/massless particles with energy mtv2 after hard and soft effects have been integrated out
While Higgs/top-Yukawa coupling effects up to the third order were already obtained in [25], the present work completed the calculation of NNLO electroweak corrections and in particular the NNLO non-resonant contribution to the e+e− → bbW +W −X process near the top-pair production threshold
Summary
The precision study of the top pair production threshold is among the main motivations for the construction of a high-energy e+e− collider [1]. As will be discussed below, they are required to obtain a well-defined result, since the pure QCD cross section by itself contains divergences proportional to the top-quark decay width [15], which are cancelled only once the non-resonant production is included [26, 27]. The (αem/v)k terms arise from the QED Coulomb potential.2 These as well as all Yukawa coupling effects have already been included up to NNNLO in [25]. This result together with the NLO non-resonant and the NNNLO QCD calculation has been made available in the QQbar threshold code [32]. The NNLO non-resonant and the remaining NNLO electroweak contributions are computed in this work, elevating the precision at the top-pair threshold to complete NNNLO QCD+Yukawa and NNLO EW+non-resonant. Several appendices collect technical results, in particular the implementation of the new results into the QQbar threshold code
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