[Paper Review] Mass and width of the Upsilon(4S)

Eef van Beveren, George Rupp|ArXiv.org|Oct 6, 2009

Quantum Chromodynamics and Particle Interactions32 references3 citations

TL;DR

This paper reanalyzes BABAR data on $e^+e^-$ annihilation into open-bottom states using a multichannel formalism that separates resonant and nonresonant contributions, incorporating the universal confinement frequency $\omega = 0.190$ GeV. It identifies the $\Upsilon(4S)$ resonance at 10.735 GeV with a width of 38 MeV, attributing open-bottom production primarily to intermediate light-quark ($u/d$) states rather than direct $b\bar{b}$ production.

ABSTRACT

Recent data on e(-)+e(+)-->b+anti-b by the BABAR Collaboration [B. Aubert et al, Phys. Rev. Lett. 102, 012001 (2009), arXiv:0809.4120] in the energy range delimited by the B+anti-B and Lambda(b)(+)+Lambda(b)(-) thresholds are analyzed in a multichannel formalism that incorporates the usual Breit-Wigner resonances, but interfering with a background signal due to the opening of open-bottom thresholds. In particular, the Upsilon(4S) resonance is determined to have a mass of 10.735 GeV and a width of 38 MeV. Also two higher Upsilon resonances are identified, parametrized, and classified. Moreover, it is found that near the B+anti-B threshold open-bottom production in electron-positron annihilation is dominated by the reaction chain e(-)+e(+)-->n+anti-n-->B+anti-B (n=u/d) rather than e(-)+e(+)-->b+anti-b-->B+anti-B whereas near the B(s)+anti-B(s) threshold the reaction chain e(-)+e(+)-->s+anti-s-->B+anti-B dominates the production amplitude. The vital role played in this analysis by the universal confinement frequency, defined in 1980 [E. van Beveren, C. Dullemond, and G. Rupp, Phys. Rev. D21, 772 (1980)] and accurately determined in 1983 [E. van Beveren, G. Rupp, T.A. Rijken, and C. Dullemond, Phys. Rev. D27, 1527 (1983)], is further confirmed.

Motivation & Objective

• To resolve discrepancies in $\Upsilon(4S)$ mass and width measurements from BABAR, CUSB, and CLEO by applying a refined multichannel formalism.
• To clarify the mechanism of open-bottom meson pair production in $e^+e^-$ annihilation near thresholds, particularly the role of intermediate quark states.
• To validate the role of the universal confinement frequency $\omega = 0.190$ GeV in modeling hadronic production amplitudes and phase relations.
• To spectroscopically identify and parametrize higher $\Upsilon$ resonances ($\Upsilon(3D)$, $\Upsilon(5S)$) in the $b\bar{b}$ spectrum using amplitude relations.
• To test whether observed enhancements near thresholds arise from resonances or threshold effects, using a formalism that separates resonant and nonresonant contributions.

Proposed method

• Applies a Breit-Wigner approximation to a formalism derived from meson-meson scattering amplitudes to model $e^+e^-$ annihilation into hadronic final states.
• Uses Watson’s theorem to relate production and scattering amplitudes, ensuring unitarity and phase consistency in the multichannel framework.
• Incorporates the universal confinement frequency $\omega = 0.190$ GeV to relate interaction radii and phase shifts between nonresonant and resonant contributions.
• Constructs form factors for open-bottom meson-pair production using $^3P_0$ quark-pair creation model distributions.
• Fits the $R_b$ data from BABAR (10.5–11.24 GeV) to extract resonance parameters, distinguishing between $B\bar{B}$, $B^*\bar{B}^*$, and $B_s\bar{B}_s$ final states.
• Analyzes reaction chains $e^+e^- \to n\bar{n} \to B\bar{B}$ ($n = u/d$) and $e^+e^- \to s\bar{s} \to B\bar{B}$ to determine dominance of light vs. strange quark intermediate states.

Experimental results

Research questions

• RQ1 What is the true mass and width of the $\Upsilon(4S)$ resonance, given conflicting measurements from BABAR, CUSB, and CLEO?
• RQ2 Why do observed enhancements near the $B\bar{B}$ threshold not correspond to a $b\bar{b}$ resonance, and what mechanism dominates open-bottom production?
• RQ3 How do intermediate light-quark ($u/d$) and strange-quark ($s$) states contribute to $B\bar{B}$ production in $e^+e^-$ annihilation?
• RQ4 To what extent does the universal confinement frequency $\omega$ govern phase relations and interaction radii in hadronic production amplitudes?
• RQ5 Can the $\Upsilon(4S)$, $\Upsilon(3D)$, and $\Upsilon(5S)$ resonances be consistently parametrized and spectroscopically identified via amplitude relations?

Key findings

• The $\Upsilon(4S)$ resonance is determined to have a mass of 10.735 GeV and a width of 38 MeV, significantly lower than previous world averages.
• Open-bottom production near the $B\bar{B}$ threshold is dominated by the reaction chain $e^{-}e^{+} \to n\bar{n} \to B\bar{B}$ ($n = u/d$), not direct $b\bar{b}$ production.
• Near the $B_s\bar{B}_s$ threshold, the chain $e^{-}e^{+} \to s\bar{s} \to B\bar{B}$ dominates the production amplitude.
• The universal confinement frequency $\omega = 0.190$ GeV plays a critical role in linking nonresonant and resonant contributions and in determining interaction radii.
• The formalism successfully separates resonant and nonresonant contributions, revealing that the observed enhancement just above $B\bar{B}$ threshold is not due to a $b\bar{b}$ resonance.
• Higher resonances $\Upsilon(3D)$ and $\Upsilon(5S)$ are identified and parametrized, with their couplings to the $b\bar{b}$ propagator related via a consistent amplitude relation.