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Register a new userFermionic NNLO contributions to Bhabha scattering
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We derive the two-loop corrections to Bhabha scattering from heavy fermions using dispersion relations. The double-box contributions are expressed by three kernel functions. Convoluting the perturbative kernels with fermionic threshold functions or with hadronic data allows to determine numerical results for small electron mass m_e, combined with arbitrary values of the fermion mass m_f in the loop, $m_e^2<<s,t,m_f^2$, or with hadronic insertions. We present numerical results for m_f = m_{mu}, m_{tau}, m_{top} at typical small- and large-angle kinematics ranging from 1 GeV to 500 GeV.
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We evaluate the two-loop corrections to Bhabha scattering from fermion loops in the context of pure Quantum Electrodynamics. The differential cross section is expressed by a small number of Master Integrals with exact dependence on the fermion masses me, mf and the Mandelstam invariants s,t,u. We determine the limit of fixed scattering angle and high energy, assuming the hierarchy of scales me^2 << mf^2 << s,t,u. The numerical result is combined with the available non-fermionic contributions. As a by-product, we provide an independent check of the known electron-loop contributions.
Using dispersion relations, we derive the complete virtual QED contributions to Bhabha scattering due to vacuum polarization effects in photon propagation. We apply our result to hadronic corrections and to heavy lepton and top quark loop insertions. We give the first complete estimate of their net numerical effects for both small and large angle scattering at typical beam energies of meson factories, LEP, and the ILC. The effects turn out to be smaller, in most cases, than those corresponding to electron loop insertions, but stay, with amounts of typically one per mille, of relevance for precision experiments. Hadronic corrections themselves are typically about 2-3 times larger than those of intermediate muon pairs (the largest heavy leptonic terms).
We provide an exact calculation of next-to-next-to-leading order (NNLO) massive corrections to Bhabha scattering in QED, relevant for precision luminosity monitoring at meson factories. Using realistic reference event selections, exact numerical results for leptonic and hadronic corrections are given and compared with the corresponding approximate predictions of the event generator BabaYaga@NLO. It is shown that the NNLO massive corrections are necessary for luminosity measurements with per mille precision. At the same time they are found to be well accounted for in the generator at an accuracy level below the one per mille. An update of the total theoretical precision of BabaYaga@NLO is presented and possible directions for a further error reduction are sketched.
Virtual hadronic contributions to the Bhabha process at the NNLO level are discussed. They are substantial for predictions with per mil accuracy. The studies of heavy fermion and hadron corrections complete the calculation of Bhabha virtual effects at the NNLO level.
We present the calculation of the elastic and inelastic high--energy small--angle electron--positron scattering with a {it per mille} accuracy. PACS numbers 12.15.Lk, 12.20.--m, 12.20.Ds, 13.40.--f
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