Soft Photons in W + W − Production at LEP 200

The pattern of soft photon radiation in e+e− → W+W− has a rich structure, with contributions from photon emission off the initial state and off the final state particles both before and after decay. In particular, the interference between the contributions involving the decaying W ’s depends on the decay width. We review the theoretical result for the radiation pattern, and present predictions for LEP200, i.e. in e+e− annihilation just above W+W− threshold. Address after September 1, 1993: Department of Physics and Astronomy, University of Rochester, Rochester, NY 14627, USA 1 Radiation Pattern Near Threshold Heavy unstable charged particles such as the W boson can emit photons before and after they decay. The relative size of the two contributions, and consequently the overall radiation pattern, depends sensitively on the timescale of the emission compared to the lifetime of the unstable particle [1]. A particularly important process which exhibits these effects is soft photon production in ee → WW → f f̄f f̄ ′ at energies just above threshold, which will be studied at LEP200 [2]. The radiation pattern of a soft photon of energy ω is sensitive to the W decay width for ω ∼ ΓW . In a previous study we have derived some general results for the radiation pattern for this process [3], and in this Letter we present specific numerical predictions for LEP200. The general formalism for calculating the distribution of soft radiation in a process involving the production and decay of unstable particles can be found in references [3–5]. The differential distribution for the production of a soft photon with momentum (k) in the process e−(k1) + e (k2) →W(q1) +W(q2) → f(p1) + f̄(r1) + f̄ ′(p2) + f ′(r2) , (1) is given by 1 N dN dω d cos θ dφ = α 4π2 ω F , (2) where ω (the photon energy), θ and φ are measured in the ee centre-of-mass frame. The radiation pattern is described by the function F . The result for this is calculated in two steps. First, for the case of soft photon radiation in stable WW production, we have the well-known result [6] F0 = 2k̂1k2 − k̂1k1 − k̂2k2 + 2k̂1q1 − 2k̂1q2 − 2k̂2q1 + 2k̂2q2 + 2q̂1q2 − q̂1q1 − q̂2q2 , (3) where the ‘antennae’ are defined by [7] p̂q ≡ p · q p · k q · k . (4) Note contributions from initial state radiation, final state radiation, and the interference between them. For unstable W ’s, decaying to fermions as in (1), we have F0 → F with F given by (3) with the replacements: k̂1k2, k̂1k1, k̂2k2 → k̂1k2, k̂1k1, k̂2k2 k̂1q1 → k̂1q1 + χ1 [Qk̂1p1 + (1−Q)k̂1r1 − k̂1q1] k̂1q2 → k̂1q2 + χ2 [Q′k̂1p2 + (1−Q)k̂1r2 − k̂1q2] k̂2q1 → k̂2q1 + χ1 [Qk̂2p1 + (1−Q)k̂2r1 − k̂2q1]