Bottomonium mesons and strategies for their observation
Bibliographic record
Abstract
The $B$-factories and Large Hadron Collider experiments have demonstrated the ability to observe and measure the properties of bottomonium mesons. In order to discover missing states it is useful to know their properties to develop a successful search strategy. To this end we calculate the masses and decay properties of excited bottomonium states. We use the relativized quark model to calculate the masses and wave functions and the ${^{3}P}_{0}$ quark-pair creation model to calculate decay widths to open bottom. We also summarize results for radiative transitions, annihilation decays, hadronic transitions and production cross sections which are used to develop strategies to find these states. We find that the $b\overline{b}$ system has a rich spectroscopy that we expect to be substantially extended by the LHC and ${e}^{+}{e}^{\ensuremath{-}}$ experiments in the near future. Some of the most promising possibilities at the LHC are observing the ${\ensuremath{\chi}}_{b(1,2)}(3P)$, ${\ensuremath{\chi}}_{b(1,2)}(4P)$ and ${\ensuremath{\eta}}_{b}(3S)$ states in $\ensuremath{\gamma}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ final states that proceed via radiative transitions through $\mathrm{\ensuremath{\Upsilon}}(nS)$ intermediate states and $1{^{3}D}_{J}$ and $2{^{3}D}_{J}$ into $\ensuremath{\gamma}\ensuremath{\gamma}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ final states proceeding via $1{^{3}P}_{J}\ensuremath{\rightarrow}1{^{3}S}_{1}$ and $2{^{3}P}_{J}\ensuremath{\rightarrow}2{^{3}S}_{1}$ intermediate states respectively. Some of the most interesting possibilities in ${e}^{+}{e}^{\ensuremath{-}}$ collisions are studying the $1{^{3}D}_{J}$ states via $4\ensuremath{\gamma}$ cascades starting with the $\mathrm{\ensuremath{\Upsilon}}(3S)$ and the $3{^{3}P}_{J}$ states in $\ensuremath{\gamma}\ensuremath{\gamma}{\ensuremath{\mu}}^{+}{\ensuremath{\mu}}^{\ensuremath{-}}$ final states starting with the $\mathrm{\ensuremath{\Upsilon}}(4S)$ and proceeding via $\mathrm{\ensuremath{\Upsilon}}(nS)$ intermediate states. Completing the bottomonium spectrum is an important validation of lattice QCD calculations and a test of our understanding of bottomonium states in the context of the quark model.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.002 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".