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Two-lepton tales: Dalitz decays of heavy quarkonia

Pietro Colangelo, Fulvia De Fazio, Riccardo Pinto

TL;DR

This work formulates heavy-quarkonium Dalitz decays by relating the dilepton distributions to radiative decays through a transition form factor, using heavy-quark spin symmetry to connect charmonium and bottomonium states. By fitting simple pole forms of the form factor to existing radiative and Dalitz data, the authors extract mass-scale parameters and predict numerous unobserved channels, including testable cases involving the debated $\chi_{c1}(3872)$. They also explore bottomonium modes with LHCb data and assess sensitivity to a light dark vector mediator, finding only modest effects within current experimental constraints. The results provide a comprehensive HQ-consistent prediction set for upcoming measurements and establish a methodology for constraining new light mediators with heavy-quarkonium Dalitz decays.

Abstract

We study the Dalitz decays of heavy quarkonia, which result from the internal virtual photon conversion into an $\ell^+ \ell^-$ lepton pair. Heavy-quark symmetries allow us to establish systematic relations between transitions of different quarkonium states, and to precisely determine the branching fractions for several charmonium and bottomonium decay modes. For charmonium, existing data on $χ_{cJ}(1P)\to J/ψ\ell^+ \ell^-$ and $ψ(2S)\to χ_{cJ}(1P) \ell^+ \ell^-$ enable us to determine the parameters of the transition form factors and to predict the rates of yet-unobserved modes. The Dalitz transitions of $χ_{c1}(3872)$ are important, as they can help assessing the structure of this meson. For bottomonium, recent LHCb measurements allow us to predict the branching fractions of $χ_{bJ}(nP)\to Υ(1S)\ell^+ \ell^-$ and $h_b(nP)\to η_b(1S) \ell^+ \ell^-$ ($n=1,\,2)$. We also investigate the sensitivity of heavy quarkonia Dalitz modes to the contribution of a new light vector mediator, such as the putative $X(17)$.

Two-lepton tales: Dalitz decays of heavy quarkonia

TL;DR

This work formulates heavy-quarkonium Dalitz decays by relating the dilepton distributions to radiative decays through a transition form factor, using heavy-quark spin symmetry to connect charmonium and bottomonium states. By fitting simple pole forms of the form factor to existing radiative and Dalitz data, the authors extract mass-scale parameters and predict numerous unobserved channels, including testable cases involving the debated . They also explore bottomonium modes with LHCb data and assess sensitivity to a light dark vector mediator, finding only modest effects within current experimental constraints. The results provide a comprehensive HQ-consistent prediction set for upcoming measurements and establish a methodology for constraining new light mediators with heavy-quarkonium Dalitz decays.

Abstract

We study the Dalitz decays of heavy quarkonia, which result from the internal virtual photon conversion into an lepton pair. Heavy-quark symmetries allow us to establish systematic relations between transitions of different quarkonium states, and to precisely determine the branching fractions for several charmonium and bottomonium decay modes. For charmonium, existing data on and enable us to determine the parameters of the transition form factors and to predict the rates of yet-unobserved modes. The Dalitz transitions of are important, as they can help assessing the structure of this meson. For bottomonium, recent LHCb measurements allow us to predict the branching fractions of and (. We also investigate the sensitivity of heavy quarkonia Dalitz modes to the contribution of a new light vector mediator, such as the putative .

Paper Structure

This paper contains 12 sections, 30 equations, 6 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Dalitz decays of heavy quarkonia
  3. Dilepton mass distribution in Dalitz decays
  4. Heavy quark symmetries and radiative decays of quarkonia
  5. Heavy quarkonium Dalitz modes
  6. Charmonium $1P \to 1S$ Dalitz decays
  7. Charmonium $2S \to 1P$ Dalitz decays
  8. Charmonium $2P \to 1S$ Dalitz decays
  9. Bottomonium $1P \to 1S$ and $2P \to 1S$ Dalitz modes
  10. Sensitivity of heavy quarkonium Dalitz modes to a dark photon
  11. Conclusions
  12. Radiative decay widths of heavy quarkonium

Figures (6)

  • Figure 1: Transition form factor $f(q^2)$ for $\chi_{c1}(1P) \to J/\psi \mu^+ \mu^-$ (left panel) and $\chi_{c2}(1P) \to J/\psi \mu^+ \mu^-$ (right panel). The binned cyan regions are the BESIII results BESIII:2019yeu. The magenta regions are obtained using Eq. \ref{['fpole']} with the values $a_{c1}$ and $a_{c2}$ determined independently for the two modes, the blue regions are obtained for the common value $a_c$ in \ref{['ac']}.
  • Figure 2: $M_{e^+ e^-}$ distributions for $\chi_{cJ}(1P) \to J/\psi \, e^+ e^-$ ($J=1,2$) in the full kinematical range, computed using the TFF in \ref{['fpole']} and the pole mass parameter in \ref{['ac']} (continuous line), compared to the BESIII data BESIII:2017ung.
  • Figure 3: $M_{e^+ e^-}$ distributions for $\chi_{cJ}(1P) \to J/\psi \, e^+ e^-$ ($J=0,1,2$) in the low range of dilepton mass, computed using the TFF in \ref{['fpole']} and the pole mass parameter in \ref{['ac']} (continuous line). The dots are the BESIII measurement BESIII:2025otp.
  • Figure 4: $M_{e^+ e^-}$ distributions of $\psi(2S) \to \chi_{cJ}(1P) \, e^+ e^-$ (for $J=1,2$) in the full kinematical range, computed using the TFF in \ref{['fpole']} with the parameter in \ref{['ac2S']} (continuous line), compared to the BESIII data BESIII:2017ung.
  • Figure 5: Correlation between ${\cal B}(\chi_{b2}(1P) \to \Upsilon(1S) \,\mu^+ \mu^-)$ and ${\cal B}(\chi_{b1}(1P) \to \Upsilon(1S) \,\mu^+ \mu^-)$ (left panel) and between ${\cal B}(\chi_{b2}(2P) \to \Upsilon(1S) \,\mu^+ \mu^-)$ and ${\cal B}(\chi_{b1}(2P) \to \Upsilon(1S) \,\mu^+ \mu^-)$ (right panel), obtained varying the TFF parameters $a_{b,1P}$ and $a_{b,2P}$ in the ranges in Eq. \ref{['ab']}.
  • ...and 1 more figures