[Paper Review] Scalar mesons and glueball in B-decays and gluon jets

Peter Minkowski, Wolfgang Ochs|ArXiv.org|Apr 15, 2003

Particle physics theoretical and experimental studies6 references3 citations

TL;DR

This paper proposes that the $f_0(980)$ scalar meson and a broad $0^{++}$ glueball state exhibit significant gluonic content, analogous to the $η'$ meson, based on its enhanced production in charmless $B$ decays and gluon jets. The authors argue that the observed $f_0(980)$ and $K\bar{K}$ S-wave enhancements in $B$ decays and gluon jets point to a flavor-singlet nature due to gluonic coupling, with the $0^{++}$ glueball contributing up to $132 \times 10^{-6}$ to the $B^+ \to K^+ \text{glueball}$ rate, suggesting gluonic mesons may saturate the $b \to sg$ decay rate.

ABSTRACT

We discuss the recent observation of f_0(980) in charmless B-decays and in gluon jets which hints toward a gluonic coupling of this meson similar to eta'. Further predictions on B-decays into scalar particles are presented. Charmless B decays also show a broad K Kbar (and possibly pi pi) S-wave enhancement which we relate to the 0^{++} glueball. These gluonic mesons represent a sizable fraction of the theoretically derived decay rate for b -> sg.

Motivation & Objective

• To clarify the nature of the $f_0(980)$ scalar meson and the $0^{++}$ glueball in light of new experimental data from $B$ decays and gluon jets.
• To test whether $f_0(980)$ and the broad $K\bar{K}$ S-wave enhancement are consistent with a gluonic or glueball component.
• To estimate the contribution of scalar glueballs and gluonic mesons to the $b \to sg$ decay rate, comparing with perturbative QCD predictions.
• To assess the role of flavor-singlet mixing and gluonic couplings in $B$ decays involving scalar and pseudoscalar mesons.
• To provide a phenomenological framework linking $B$ decay rates and gluon jet data to the low-mass scalar spectroscopy and glueball content.

Proposed method

• Analyzes experimental data from BELLE and BaBar on charmless $B \to Khh$ decays, focusing on $f_0(980)$ and $K\bar{K}$ S-wave enhancements.
• Uses a phenomenological model of scalar nonet spectroscopy with large flavor mixing, identifying $f_0(980)$ as a near-flavor-singlet state due to gluonic coupling.
• Applies $U(3)$ flavor symmetry to relate $B \to K\eta^\prime$, $B \to K^*\eta^\prime$, and $B \to K\bar{K}$ decay amplitudes, extending to scalar final states.
• Estimates the $0^{++}$ glueball branching fraction from $B^+ \to K^+ \text{glueball}$ by extrapolating $K\bar{K}$ and $\pi\pi$ S-wave rates in mass windows.
• Compares the inclusive $b \to sg$ decay rate in leading and next-to-leading order QCD with the sum of observed gluonic meson rates.
• Uses chromoelectric-magnetic duality symmetry to estimate $B \to gb(0^{-+})$ rate as comparable to $B \to gb(0^{++})$, assuming similar gluonic couplings.

Experimental results

Research questions

• RQ1 Is the $f_0(980)$ meson primarily a $q\bar{q}$ state or a gluonic state with significant $K\bar{K}$ molecule or 4-quark components?
• RQ2 Does the observed $K\bar{K}$ S-wave enhancement in $B$ decays and gluon jets indicate the presence of a $0^{++}$ glueball?
• RQ3 To what extent do the observed $B$ decay rates into scalar mesons saturate the theoretical $b \to sg$ decay rate?
• RQ4 What is the mixing angle between the $f_0(980)$ and the $0^{++}$ glueball, given the observed production rates?
• RQ5 Can the $b \to sg$ decay rate be explained by the production of scalar and pseudoscalar glueballs, assuming symmetric couplings?

Key findings

• The $f_0(980)$ meson shows enhanced production in $B \to Khh$ decays and in the leading system of gluon jets, suggesting a gluonic component similar to $\eta^\prime$.
• A broad $K\bar{K}$ S-wave enhancement in the 1.0–1.7 GeV range is observed, interpreted as a $0^{++}$ glueball with a branching fraction of $132 \times 10^{-6}$ for $B^+ \to K^+ \text{glueball}$.
• The estimated total rate for $B^+ \to gb(0^{++}) + X_s$ is $1.2 \times 10^{-3}$, consistent with the leading-order $b \to sg$ rate of $(2-5) \times 10^{-3}$.
• The combined rate for $B \to gb(0^{++}) + f_0(980) + \eta^\prime + X_s$ is estimated at $(1.5 \pm 0.5) \times 10^{-3}$, comparable to the NLO $b \to sg$ rate of $(5 \pm 1) \times 10^{-3}$.
• The mixing angle between $f_0(980)$ and the $0^{++}$ glueball is constrained to $\sin^2\varphi_g \lesssim 14/132$, implying $\varphi_g \lesssim 20^\circ$.
• The $B \to gb(0^{-+})$ rate is estimated to be comparable to $B \to gb(0^{++})$, suggesting that scalar and pseudoscalar glueballs may collectively saturate the $b \to sg$ decay rate.