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Production of dileptonic bound states in the Higgs boson decay

F. A. Martynenko, A. P. Martynenko, A. V. Eskin

TL;DR

This work investigates rare Higgs decays into dilepton bound states (positronium, dimuonium, ditauonium) using a relativistic quasipotential framework based on the Bethe–Salpeter formalism to incorporate relativistic corrections in both production amplitudes and bound-state wave functions. It develops a comprehensive set of production mechanisms for single and paired bound states, including photon and Z-boson channels, ZZ processes, and heavy W-quark loops, with amplitudes expressed in a unified tensor structure through functions g1 and g2 and the key bound-state normalization psi(0). The paper provides explicit analytic forms and numerical results for decay widths, highlighting that loop contributions (notably W-loops) often dominate single-bound-state production, while pair production is strongly suppressed, yielding branching fractions that are small but potentially measurable at future high-luminosity colliders. These results test bound-state QFT methods in Higgs decays, and outline the practical prospects for observing dilepton bound states in rare Higgs decay channels, thereby offering a benchmark for bound-state dynamics in electroweak processes.

Abstract

The production of single and paired lepton bound states in the decay of the Higgs boson has been studied. We explore different decay mechanisms that contribute significantly to the decay width. The decay widths are calculated taking into account relativistic corrections in the decay amplitude and in the wave function of the bound state of leptons.

Production of dileptonic bound states in the Higgs boson decay

TL;DR

This work investigates rare Higgs decays into dilepton bound states (positronium, dimuonium, ditauonium) using a relativistic quasipotential framework based on the Bethe–Salpeter formalism to incorporate relativistic corrections in both production amplitudes and bound-state wave functions. It develops a comprehensive set of production mechanisms for single and paired bound states, including photon and Z-boson channels, ZZ processes, and heavy W-quark loops, with amplitudes expressed in a unified tensor structure through functions g1 and g2 and the key bound-state normalization psi(0). The paper provides explicit analytic forms and numerical results for decay widths, highlighting that loop contributions (notably W-loops) often dominate single-bound-state production, while pair production is strongly suppressed, yielding branching fractions that are small but potentially measurable at future high-luminosity colliders. These results test bound-state QFT methods in Higgs decays, and outline the practical prospects for observing dilepton bound states in rare Higgs decay channels, thereby offering a benchmark for bound-state dynamics in electroweak processes.

Abstract

The production of single and paired lepton bound states in the decay of the Higgs boson has been studied. We explore different decay mechanisms that contribute significantly to the decay width. The decay widths are calculated taking into account relativistic corrections in the decay amplitude and in the wave function of the bound state of leptons.
Paper Structure (13 sections, 87 equations, 8 figures, 1 table)

This paper contains 13 sections, 87 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Production of single leptonic bound states
  3. Pair production of leptonic bound states
  4. Lepton - photon production mechanism A
  5. Lepton - Z-boson production mechanism B
  6. Lepton - photon production mechanism C
  7. Lepton - Z-boson production mechanism D
  8. ZZ-boson production mechanism E
  9. Quark loop and W-boson loop production mechanism
  10. Relativistic corrections
  11. Relativistic parameters in production amplitude
  12. Relativistic corrections to the wave function
  13. Numerical results and Conclusions

Figures (8)

  • Figure 1: Different mechanisms of single leptonium production in the Higgs boson decay.
  • Figure 2: Quark loop and $W$-boson loop mechanisms of single leptonium production in the Higgs boson decay.
  • Figure 3: Lepton - photon mechanism A of pair leptonium production in Higgs boson decay.
  • Figure 4: Lepton - $Z$-boson mechanism B of pair leptonium production in the Higgs boson decay.
  • Figure 5: Lepton - photon mechanism C of pair leptonium production in the Higgs boson decay.
  • ...and 3 more figures