[Paper Review] Remarks on the decays chi_{bJ}^\prime -> omega Upsilon

M.B. Voloshin|arXiv (Cornell University)|Apr 16, 2003

Particle physics theoretical and experimental studies5 references3 citations

TL;DR

This paper analyzes CLEO-observed cascade decays Upsilon(3S) → γχ′_bJ → γωΥ within nonrelativistic bottomonium theory. It predicts that the branching ratio ratio for χ′_b2 → ωΥ versus χ′_b1 → ωΥ should equal the ratio of their S-wave phase space factors, implying nearly equal decay rates. The study further suggests testing this prediction via angular correlation measurements of the final-state ω and Υ particles.

ABSTRACT

The recently observed by CLEO cascade decays Upsilon(3S) -> gamma chi_{bJ}^\prime -> gamma omega Upsilon are discussed. It is shown that within the nonrelativistic description of bottomonium in the heavy b quark limit, the ratio of the rates of the transitions chi_{bJ}^\prime -> omega Upsilon with J=1 and J=2 should be given by the ratio of the corresponding S wave phase space factors. As a result, the rate of the observed cascade transitions through the chi_{b2}^\prime resonance should be close to that through the chi_{b1}^\prime. It is suggested that the ratio of the discussed cascade rates can also be tested by measuring a simple angular correlation.

Motivation & Objective

• To interpret the observed CLEO cascade decays Upsilon(3S) → γχ′_bJ → γωΥ within the nonrelativistic QCD framework.
• To determine the expected ratio of decay rates for χ′_b2 → ωΥ and χ′_b1 → ωΥ in the heavy b quark limit.
• To propose a measurable observable—angular correlation between ω and Υ—that can test the predicted rate ratio experimentally.
• To provide a theoretical benchmark for comparing the inclusive decay rates of different chi_bJ′ resonances into the same final state.

Proposed method

• Apply the nonrelativistic description of bottomonium states in the heavy b quark limit to model the decay amplitudes of χ′_bJ → ωΥ.
• Use the S-wave phase space factor as the dominant contribution to the decay width ratio for J=1 and J=2 states.
• Derive the theoretical prediction that the rate ratio should be determined solely by the phase space factor ratio.
• Suggest measuring the angular distribution of the ω and Υ in the rest frame of the χ′_bJ resonance to extract the relative branching fractions.
• Utilize the angular correlation between the ω and Υ to probe the spin structure of the decaying χ′_bJ state.

Experimental results

Research questions

• RQ1 What is the expected ratio of the decay rates χ′_b2 → ωΥ and χ′_b1 → ωΥ in the heavy b quark limit?
• RQ2 How does the nonrelativistic bottomonium model predict the relative strength of these transitions?
• RQ3 Can the angular correlation between the ω and Υ mesons be used to test the predicted rate ratio experimentally?
• RQ4 Does the phase space factor alone determine the branching ratio ratio for these transitions?

Key findings

• The ratio of the decay rates χ′_b2 → ωΥ and χ′_b1 → ωΥ is predicted to be equal to the ratio of their respective S-wave phase space factors.
• Given the small mass difference between the χ′_b2 and χ′_b1 states, the phase space factor ratio is close to unity, implying nearly equal decay rates.
• The predicted rate ratio is independent of dynamics and depends only on kinematics in the nonrelativistic limit.
• The angular correlation between the ω and Υ mesons can be used to experimentally verify the predicted rate ratio.