Final state interaction in the production of heavy unstable particles

TL;DR

This paper investigates final-state interactions in processes that produce unstable particles, focusing on non-factorizable radiative corrections arising from soft photons and gluons. It derives explicit O(α, αs) corrections for both single- and double-resonance production, revealing Coulomb-phase–like contributions that modify differential invariant-mass distributions while canceling in inclusive cross sections. The analysis employs soft-photon/gluon approximations, resummed unstable-particle propagators, and a hierarchy of three-, four-, and five-point functions to capture the infrared structure. The findings have practical implications for precision measurements of W+W− and t t̄ production in current and future colliders, where accurate modeling of resonance line shapes is essential for extracting fundamental parameters.

Abstract

We make an attempt to discuss in detail the effects originating from the final state interaction in the processes involving production of unstable elementary particles and their subsequent decay. Two complementary scenarios are considered: the single resonance production and the production of two resonances. We argue that part of the corrections due to the final state interaction can be connected with the Coulomb phases of the involved charge particles; the presence of the unstable particle in the problem makes the Coulomb phase ``visible''. It is shown how corrections due to the final state interaction disappear when one proceeds to the total cross-sections. We derive one-loop non-factorizable radiative corrections to the lowest order matrix element of both single and double resonance production. We discuss how the infrared limit of the theories with the unstable particles is modified. In conclusion we briefly discuss our results in the context of the forthcoming experiments on the $W^+W^-$ and the $t\bar t$ production at LEP $2$ and NLC.

Figures (6)

• Figure 1: Born graph and graphs responsible for the non-factorizable corrections for the simple model (see sect.2).
• Figure 2: The relative size of the non-factorizable radiative corrections in the simple model (see eq.(11) with $\eta$ from eq.(15)). Curves $A$, $B$, $C$ correspond to the total energies $\sqrt {s} = 180,~190,~200$ GeV respectively. We use $m_W =80$ GeV and $\alpha = 1/137$.
• Figure 3: Non-factorizable graphs for the process $\gamma ^* \to t\bar{t} \to bW^+\bar{b} W^-$.
• Figure 4: Geometry of the discussed reactions.
• Figure 5: Relative non-factorizable corrections to completely differential cross sectionon of the process $e^+e^-\to W^+W^-\to e^+\nu_e e^-\bar{\nu}_e$ as a function of invariant mass of the $e^+ \nu _e$ system $m_2$ in GeV for the fixed invariant mass of $e^- \bar{\nu} _e$$m_1=78$ GeV. We use $\sqrt{s} = 180$ GeV, $m_W = 80$ GeV, $\alpha =1/137$, $\theta _{W-e^-} = 30 ^{\circ},~ \theta _{W^-e^+} = 150 ^{\circ},~~ \varphi _{e^+e^-} =0$. Curves A, B, C correspond to the conrtibutions due to three--, four--, and five--point functions respectively.