Four-fermion production near the W pair-production threshold

Abstract

We perform a dedicated study of the four-fermion production process e − e + → µ −ν µ ud X near the W pair-production threshold in view of the importance of this process for a precise measurement of the W boson mass. Accurate theoretical predictions for this process require a systematic treatment of finite-width effects. We use unstable-particle effective field theory (EFT) to perform an expansion in the coupling constants, Γ W /M W , and the non-relativistic velocity v of the W boson up to next-to-leading order in Γ W /M W ∼ α ew ∼ v 2 . We find that the dominant theoretical uncertainty in M W is currently due to an incomplete treatment of initial-state radiation. The remaining uncertainty of the NLO EFT calculation translates into δM W ≈ 10 -15 MeV, and to about 5 MeV with additional input from the NLO four-fermion calculation in the full theory.

Electroweak non-resonant NLO corrections to in the resonance region

“…The leading contribution to the forward-scattering amplitude arises from the one-loop diagrams with two top propagators. Just as in the case of W -boson pair production [34] the imaginary part of these diagrams vanishes in dimensional regularization to all orders in the expansion in E = √ s − 2m t in the hard region. Thus the leading imaginary parts of C (k) 4e arise from two-loop diagrams of order α 3 EW shown in Figure 1 below.…”

“…Accordingly the calculation of the coefficients C (k) 4e is performed in fixed-order perturbation theory in the full electroweak theory with no resummation of self-energy insertions in the top-quark propagator [34] and supplemented with an expansion of the amplitudes in δ = s/(4m 2 t ) − 1 ∼ v 2 . The corresponding contributions to the imaginary part of the forward-scattering amplitude are then reproduced by those imaginary parts of the short-distance coefficients C (k) 4e which can be identified with the W + W − bb final state.…”

“…The calculation is performed with unstable-particle effective field theory [32,33], which provides the framework for consistently including resonant and non-resonant effects while maintaining an expansion in the small parameters of the problem. There are many similarities with W -pair production considered in [34,35], though the top-quark case is technically more complicated due to the presence of a massive particle (the W boson) in top decay. We note that an alternative approach has been developed in parallel [36,37] that includes the effects of invariant-mass cuts on the W b pairs entirely through calculations in non-relativistic effective theory.…”

“…In the subsequent discussion of top-quark pair production near threshold we follow closely the formalism described in [34] for four-fermion production in e + e − collisions in the energy region of the W -pair production threshold, and refer to that paper for further details on the method. The matrix elements in (2) are evaluated in the "low-energy" effective theory, which includes elements of soft-collinear and non-relativistic effective theory.…”

“…The second term accounts for the remaining non-resonant contributions. Note that there is no separate term for the production of one resonant and one off-shell top [34,37], since such configurations are not sensitive to the particular low-energy dynamics that develops at the pair-production threshold. They are effectively short-distance and included in the coefficient functions C (k) 4e of non-resonant production-decay operators O (k) 4e (0).…”