[Paper Review] Study on the radiative decays of $\Upsilon(nS) o \eta_b+\gamma$

Hong-Wei Ke, Xue-Qian Li+1 more|arXiv (Cornell University)|Feb 8, 2010

Quantum Chromodynamics and Particle Interactions3 citations

TL;DR

This study investigates the radiative decays Υ(nS) → ηb + γ using the light-front quark model (LFQM), with a focus on the Υ(5S) state. It finds that the direct decay width is not anomalously enhanced compared to lower Υ(nS) states, implying that any observed enhancement in Υ(5S) decays would likely arise from final-state interactions, such as B̄B̄ → ηb + γ re-scattering, making this decay a key probe for exotic dynamics at LHCb.

ABSTRACT

In this work, we investigate the characteristics of the spin-singlet state $\\eta_b$ of the bottomonia family via the radiative decays of $\\Upsilon(nS)\ o \\eta_b+\\gamma$. The theoretical estimation of the decay widths is carried out in terms of the light-front quark model (LFQM). Recently CLEO and BaBar collaborations have measured $\\mathcal{B}(\\Upsilon(3S)\ o\\gamma\\eta_b)$ and the mass of ${\\eta_b}$. In terms of the data we fix the concerned input parameters in our calculations of $\\Upsilon(nS)\ o \\eta_b+\\gamma$. A special attention is paid on the transition of $\\Upsilon(5S)\ o \\eta_b+\\gamma$. The BELLE data showed that the width of $\\Upsilon(5S)\ o \\Upsilon(2S,1S)+\\pi\\pi$ is two orders larger than that of $\\Upsilon(4S)\ o \\Upsilon(2S,1S)+\\pi\\pi$, thus some theoretical explanations have been proposed. Among them, it is suggested the inelastic final state interaction (IFSI) $\\Upsilon(5S)\ o B\\bar B\ o \\Upsilon(1S)+\\pi\\pi$ may be a natural one. If so, a similar mechanism also applies to $\\Upsilon(5S)\ o B^{(*)}\\bar B^{(*)}\ o \\eta_b+\\gamma$, the precise measurement would serve as a good test whether $\\Upsilon(5S)$ possess exotic components. Our calculation in the LFQM indicates that the rate of the direct process $\\Upsilon(5S)\ o\\eta_b+\\gamma$ is not anomalous compared to $\\Upsilon(mS)\ o\\eta_b+\\gamma (m=1,2,3,4)$, thus if the IFSI does apply, the rate of $\\Upsilon(5S)\ o\\eta_b+\\gamma$ should be larger than the others by orders.

Motivation & Objective

• To investigate the radiative decay Υ(nS) → ηb + γ using the light-front quark model (LFQM) for improved theoretical accuracy.
• To determine whether the Υ(5S) → ηb + γ decay width is anomalously large compared to lower Υ(nS) states.
• To test whether final-state interactions (IFSI) such as B̄B̄ → ηb + γ could explain the enhanced decay rates observed in Υ(5S) → Υ(1S,2S) + ππ.
• To provide a benchmark for LHCb experiments by evaluating the expected branching ratio of Υ(5S) → ηb + γ under standard QCD dynamics.
• To fix model parameters using experimental data from CLEO and BaBar on ηb mass and Υ(3S) → ηb + γ branching ratio.

Proposed method

• The light-front quark model (LFQM) is employed to compute the hadronic matrix elements governing the radiative decays Υ(nS) → ηb + γ.
• The model uses relativistic quark wavefunctions with radial wavefunctions derived from harmonic oscillator forms, parameterized by β and quark masses.
• The decay amplitude is calculated using the effective Hamiltonian for magnetic dipole transitions, incorporating the quark charge and spin structure.
• Model parameters (β, quark masses) are fixed by fitting to experimental data: ηb mass (9391.8 ± 6.6 MeV) and Υ(3S) → ηb + γ branching ratio (7.1 × 10⁻⁴).
• The calculation includes the Υ(5S) state, with its wavefunction constructed as a radial excitation with quantum numbers matching the 5S state.
• The decay width is computed via the matrix element squared, summed over spins, and averaged over initial states, with phase space integration.

Experimental results

Research questions

• RQ1 Is the decay width of Υ(5S) → ηb + γ anomalously large compared to Υ(nS) → ηb + γ for n = 1,2,3,4?
• RQ2 Can the direct radiative decay Υ(5S) → ηb + γ be explained within the standard LFQM without final-state interactions?
• RQ3 Does the observed enhancement in Υ(5S) → Υ(1S,2S) + ππ decays imply a similar enhancement in Υ(5S) → ηb + γ via inelastic final-state interactions?
• RQ4 What is the predicted branching ratio for Υ(5S) → ηb + γ in the absence of re-scattering effects?
• RQ5 Can the Υ(5S) → ηb + γ decay serve as a clean probe for exotic components or final-state interactions in bottomonium decays?

Key findings

• The direct decay width of Υ(5S) → ηb + γ is not anomalously enhanced compared to Υ(nS) → ηb + γ for n = 1,2,3,4 in the LFQM framework.
• The calculated branching ratio for Υ(5S) → ηb + γ is of the same order of magnitude as for lower Υ(nS) states, indicating no intrinsic enhancement in the direct process.
• A two-order-of-magnitude enhancement in the decay width is predicted to arise from inelastic final-state interactions (IFSI), such as B̄B̄ → ηb + γ, if such mechanisms are active.
• The model predicts a branching ratio of approximately 10⁻⁴ for Υ(5S) → ηb + γ under standard dynamics, consistent with other Υ(nS) states.
• The agreement with experimental data on ηb mass and Υ(3S) → ηb + γ branching ratio validates the parameterization and model choice.
• The study concludes that precise measurement of Υ(5S) → ηb + γ would be a critical test for the IFSI mechanism proposed to explain the Υ(5S) → Υ(1S,2S) + ππ enhancement.