[Paper Review] Study of the ${\Upsilon}(1S)$ ${ o}$ $DP$ decays

Yueling Yang, Mingfei Duan+3 more|arXiv (Cornell University)|Jan 2, 2021

Particle physics theoretical and experimental studiesPhysics and Astronomy42 references1 citations

TL;DR

This study investigates the rare weak decays Υ(1S) → D⁻π⁺, D⁰π⁰, and Dₛ⁻K⁺ using the perturbative QCD (pQCD) approach within the Standard Model. It finds branching ratios on the order of 10⁻¹⁸, far below current experimental sensitivity, suggesting that any observation would require significant new physics contributions due to the extreme suppression by the OZI rule and small CKM matrix elements.

ABSTRACT

Inspired by the potential prospects of high-luminosity dedicated colliders and the high enthusiasms in searching for new physics in the flavor sector at the intensity frontier, the ${\Upsilon}(1S)$ ${ o}$ $D^{-}{\pi}^{+}$, $\overline{D}^{0}{\pi}^{0}$ and $D_{s}^{-}K^{+}$ weak decays are studied with the perturbative QCD approach. It is found within the standard model that the branching ratios for the concerned processes are tiny, about ${\cal O}(10^{-18})$, and far beyond the detective ability of current experiments unless there exists some significant enhancements from a noval interaction.

Motivation & Objective

• To evaluate the branching ratios of Υ(1S) → DP decays (P = π, K) within the Standard Model using the perturbative QCD approach.
• To provide a theoretical reference for future high-luminosity experiments like Belle-II and upgraded LHCb, which will collect vast datasets of b¯b pairs.
• To assess the feasibility of detecting these rare decays and to identify potential signatures of new physics beyond the Standard Model.
• To compute hadronic matrix elements and Wilson coefficients for weak decays involving bottomonium states.
• To examine the role of QCD corrections and factorization in the decay amplitude calculation.

Proposed method

• Employing the perturbative QCD approach to calculate decay amplitudes for Υ(1S) → DP decays, including both tree-level and penguin contributions.
• Using the effective Hamiltonian formalism with Wilson coefficients evolved from the mW scale down to the µ scale via renormalization group equations.
• Calculating the hadronic matrix elements ⟨DP|Oi|Υ⟩ using light-cone wave functions for the Υ(1S), D, and P mesons.
• Applying the Sudakov resummation to suppress large logarithms in the soft and collinear regions of the phase space.
• Incorporating QCD radiative corrections through the anomalous dimension γq = −αs/π in the evolution of the soft functions.
• Using the Bessel function-based hard functions Hab and Hcd to model the transverse momentum dependence of the quark distributions.

Experimental results

Research questions

• RQ1 What are the predicted branching ratios for Υ(1S) → D⁻π⁺, D⁰π⁰, and Dₛ⁻K⁺ decays within the Standard Model?
• RQ2 Can these decays be observed in current or near-future experiments like Belle-II or LHCb?
• RQ3 What is the dominant contribution to the decay amplitude—tree-level or penguin operators?
• RQ4 How do QCD corrections and factorization effects influence the final branching ratio?
• RQ5 Could any deviation from the predicted branching ratio signal new physics beyond the Standard Model?

Key findings

• The branching ratios for Υ(1S) → D⁻π⁺, D⁰π⁰, and Dₛ⁻K⁺ decays are predicted to be approximately 10⁻¹⁸ within the Standard Model.
• The extremely small branching ratios are primarily due to the small CKM matrix element |Vub V*cb| and suppression by the OZI rule.
• The dominant contributions come from tree-level operators O1 and O2, with penguin operators O3–O10 providing subdominant but non-negligible corrections.
• QCD radiative corrections are included via the anomalous dimension and Sudakov factors, which suppress large logarithms and stabilize the perturbative series.
• The hadronic matrix elements are calculated using light-cone wave functions for the D and P mesons, with transverse momentum dependence modeled through Bessel functions.
• The results indicate that these decays are currently unobservable with existing experimental luminosities, and any signal would require significant new physics enhancements.