REVIEW
Radiative transitions from Upsilon(5S) to molecular bottomonium
High Energy Physics - Phenomenology · Submitted 29 May 2011 · 9 references
Pith's verdict: A short, clean HQSS note: the new content is the radiative rate pattern of Eq. (12), and it holds up conditional on the Υ(5S) spin assignment the author states openly.
T0 · AI review
Why Pith says this
Highlight any text to comment on it.
Referee report
The paper
The paper claims
Heavy-quark spin symmetry predicts four new bottomonium molecules and a fixed pattern for finding them.
The reading
What carries the argument
The load-bearing device is the $H times SLB$ decomposition: the $b$ and $bar b$ spins combine to a total heavy spin $S_H$, while all the light degrees of freedom (the light quark spins, the orbital motion, the pion or photon) are bundled into an effective $S_{SLB}$ that behaves as if the $b$ quark had no spin. The phenomenological Hamiltonian $H_s = mu (s_b . s_{bar q}) + mu (s_{bar b} . s_q)$, rewritten as $(mu/2)(S_H . S_{SLB}) - (mu/2)(Delta_H . Delta_{SLB})$, both reproduces the $B$-$B^*$ mass splitting with $mu = M(B^*) - M(B)$ about 46 MeV and organises the six physical molecular states into definite $S_H times S_{SLB}$ combinations with fixed energy shifts. That same decomposition then supplies the coefficients multiplying the $1^-_H times 1^-_{SLB}$ piece in each $W_{bJ}$, which is exactly what the radiative-rate ratio needs.
Extended reading notes
Core claim
The paper argues that heavy quark spin symmetry, applied consistently to both the initial $Upsilon(5S)$ and the final molecular states, fixes the relative rates of the radiative transitions $Upsilon(5S) -> W_{bJ} gamma$. Treating the $Upsilon(5S)$ as dominantly a $1^-_H$ (ortho-$b bar b$) times $0^+_{SLB}$ state in a decomposition into heavy-quark spin and 'spinless-$b$' light degrees of freedom, and treating the photon as emitted by the light-quark current so that the heavy spin passes through unchanged, the amplitude reduces to a single term $C omega (psi . a)$ with one unknown constant $C$. Combining that with the amplitudes of the $1^-_H$ times $1^-_{SLB}$ component inside each $W_{bJ}$ gives $f(W_{b0} gamma) : f(W'_{b0} gamma) : f(W_{b1} gamma) : f(W_{b2} gamma) = (3/4) omega_0^3 : (1/4) omega_2^3 : 3 omega_1^3 : 5 omega_2^3$ for photon energies of about 305, 260 and 215 MeV. Numerically that is about 8.5 : 1 : 21 : 20 with the phase-space factors, or 3 : 1 : 12 : 20 without them, so the $W_{b1}$ and $W_{b2}$ states are the most promising targets.
Load-bearing premise
The whole rate pattern rests on the $Upsilon(5S)$ being dominantly a $1^-_H$ times $0^+_{SLB}$ state, a claim supported here only by the rough agreement of predicted 7:3:1 and 4.2:2.4:1 meson-pair yields with Belle's measured fractions.
Editorial extensions
If this is right
- Radiative decays of the $Upsilon(5S)$ become a realistic search channel for the $G$-odd molecular states, which cannot be produced in the single-pion transitions that revealed the $Z_b$'s.
- The predicted pattern singles out $W_{b1}$ and $W_{b2}$ as the most accessible: their transitions are an order of magnitude stronger than the two $J^P = 0^+$ states.
- The total widths of the family are tied together by $Gamma(W_{b2}) = Gamma(W_{b1}) = (3/2) Gamma(W_{b0}) - (1/2) Gamma(W'_{b0})$, giving a second consistency check once any two are measured.
- Exclusive decay ratios such as $Gamma(W_{b0} -> Upsilon rho) : Gamma(W'_{b0} -> Upsilon rho) : Gamma(W_{b1} -> Upsilon rho) : Gamma(W_{b2} -> Upsilon rho) = 3/4 : 1/4 : 1 : 1$ offer a separate handle for identifying which state is which.
- The isoscalar counterparts of these molecules are expected to be suppressed by roughly a factor of nine in radiative production, but may be reachable in high-energy $p bar p$ and $p p$ collisions.
Reading between the lines
- Because the ratio depends on the photon energy cubed, a measurement of the four rates at fixed energy would test the spin algebra alone, while the observed energies test the mass assignments; the two can be separated experimentally.
- The same bookkeeping predicts that the $Upsilon(5S)$ should show no strong $D$-wave ($1^-_H times 2^+_{SLB}$) component, so a precise angular analysis of $Upsilon(5S) -> B^* bar B^* pi$ would independently constrain the input that fixes the radiative pattern.
- If the $1^-_{SLB}$ channel has no near-threshold singularity, only the two $J^P = 0^+$ states exist, and the radiative pattern collapses to the two weakest lines; the absence of $W_{b1}$ and $W_{b2}$ signals would therefore itself be informative about which light-quark channel binds.
- The paper's own note that the $W_{b1}$ is the bottomonium analogue of $X(3872)$ suggests a cross-check: the corresponding charmonium radiative transitions from an excited vector state could be searched for with the same ratio logic.
Original abstract
The heavy quark spin symmetry implies that in addition to the recently observed Z(10610) and Z(10650) molecular resonances with $I^G=1^+$ there should exist two or four molecular bottomonium-like states with $I^G=1^-$. Properties of these G-odd states are considered, including their production in the radiative transitions from Upsilon(5S), by applying the same symmetry to the Upsilon(5S) resonance and the transition amplitudes. The considered radiative processes can provide a realistic option for observing the yet hypothetical states.
The compiled record
The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.
The abstract, sentence by sentence
The heavy quark spin symmetry implies that in addition to the recently observed Z(10610) and Z(10650) molecular resonances with $I^G=1^+$ there should exist two or four molecular bottomonium-like states with $I^G=1^-$. Properties of these G-odd states are considered, including their production in the radiative transitions from Upsilon(5S), by applying the same symmetry to the Upsilon(5S) resonance and the transition amplitudes. The considered radiative processes can provide a realistic option for observing the yet hypothetical states.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | The heavy quark spin symmetry implies that in addition to the recently observed Z(10610) and Z(10650) molecular resonances with $I^G=1^+$ there should exist two or four molecular bottomonium-like states with $I^G=1^-$. | background 0.80 | 0.14 | 0.49 | asserted 0.77 |
| s1 | Properties of these G-odd states are considered, including their production in the radiative transitions from Upsilon(5S), by applying the same symmetry to the Upsilon(5S) resonance and the transition amplitudes. | contribution 0.75 | 0.74 | 0.11 | asserted 0.85 |
| s2 | The considered radiative processes can provide a realistic option for observing the yet hypothetical states. | interpretation 0.93 | 0.22 | 0.48 | hedged possibility 0.96 |
What was examined, and what was not
- arXiv listing abstract v1
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
- S sections
- T body sentences
- C citations
- R cross-paper relations
Figures
Figures reproduced from arXiv:1105.5829 by the authors.
References
How the literature uses it
71 arXiv papers cite this in 120 sentences
Papers citing it · 94 sentences without a confident label
Builds on it 2 papers
-
This expansion can be essentially read off the known formulas [ref] for the hidden-bottom meson-antimeson pairs, with the only difference being that the $B^* D$ and $B D^*$ are analogs of the sum and the difference of the definite charge parity states $B^* B̅ ±B B̅^*$.
Quark spin structures of bottom-charmed threshold molecular states · Introduction · 0.96
-
The idea put forward in [ref] that the $Z_b$ and $Z_b'$ states can be explained as molecule-type structures residing at the corresponding $B^(*)B^*$ thresholds was extended further in [ref] and a possible existence of a few sibling states, denoted as $W_bJ^(')$ with $J=0,1,2$ and defined by four orthogonal combinations, 1^-(2^+) W_b2: 1_bb̅ ⊗1_qq̅|_J = 2, 1^-(1^+) W_b1: 1_bb̅ ⊗1_qq̅|_J = 1, 1^-(0^+) W_b0': √(3)/2 0_bb̅ ⊗0_qq̅ + 1/2 1_bb̅ ⊗1_qq̅|_J = 0, 1^-(0^+) W_b0: √(3)/2 1_bb̅ ⊗1_qq̅|_J = 0 - 1/2 0_bb̅ ⊗0_qq̅,was predicted and their properties were outlined.
Hadron physics potential of future high-luminosity B-factories at the Upsilon(5S) and above · $W_bJ$ states · 0.98
Uses its method or tool 2 papers
-
The short-ranged contact potentials can be derived either from the effective Lagrangians or from the decomposition of the spin structures of the charm-anticharm and light degrees of freedom in the heavy-quark limit following, e.g., Ref. [ref] .
Revisiting the nature of the $P_c$ pentaquarks · Contact potentials · 0.91
-
To proceed, it is convenient to adopt the classification scheme suggested in [ref] exploiting the heaviness of the $b$ quark, that implies that its spin is decoupled from the remaining degrees of freedom, so that a convenient basis can be built in terms of the states $H⊗SLB$, where $H$ stands for the heavy pair spin ($S_H=0,1$), while $SLB$ denotes all remaining degrees of freedom, like angular momentum, light quark spins, etc.
Hadron physics potential of future high-luminosity B-factories at the Upsilon(5S) and above · $W_bJ$ states · 0.93
Uses its data or values 1 paper
-
The masses and decay widths averaged over the five different final states are [ref] : [equation] Due to the proximity of the $Z_b$ and $Z_b^'$ masses with the $BB̅^*$ and $B^*B̅^*$ thresholds [ref] , it has been proposed that the former could be realized as $S$-wave $BB̅^*$ and $B^*B̅^*$ molecular states, respectively [ref] .
Exotic Heavy Quark Spectroscopy - Theory Interpretation vs Data · $Z_b(10610)$ and $Z_b(10650)$ · 0.94
Compares with it 1 paper
-
Some relationships among the widths of the $W^(')_bJ$ and $Z^(')$ states derived in this paper appear in Ref. [ref] , while the prediction in Eq. [ref] is new.
Heavy Quark Symmetry Predictions for Weakly Bound B-Meson Molecules · Introduction · 0.97
Cites it as support 1 paper
-
These facts strongly suggest that $Z_b$'s have a molecular type structures as noted in Ref. [ref]
Exotic mesons with hidden charm and bottom near thresholds · Introduction · 0.99
Cites it as background 18 papers
-
A complete classification of $S$-wave threshold states of heavy meson pairs in terms of their $S_H ⊗S_SLB$ structure is described in Refs. [ref] .
Heavy quark spin symmetry breaking in near-threshold $J^{PC}=1^{--}$ quarkonium-like resonances · Introduction · 0.90
-
Considering $Z_b^+$ and $Z_b^'+$ to be $B B̅^*$ and $B^* B̅^*$ molecular states, Voloshin estimates their production in the radiative decay of $Υ(5S)$ [ref] , and the pion-emission transitions from $Z_b^+$ and $Z_b^'+$ to lighter bottomonia are investigated by Refs. [ref] .
$Z_b/Z_b^\prime \to \Upsilon\pi$ and $h_b \pi$ decays in intermediate meson loops model · Introduction · 0.94
-
Under the frameworks of $BB̅^*$ and $B^*B̅^*$ molecular states, the radiative decay of $Υ(5S)$ into molecular bottomonium was calculated [ref] , and the processes of $Z_b(10610)$ and $Z_b(10650)$ decaying into bottomonium and pion were also investigated very recently [ref] .
Interpretation of $Z_b(10610)$ and $Z_b(10650)$ in the ISPE mechanism and the Charmonium Counterpart · Introduction · 0.96
What it cites · 7 sentences without a confident label
Uses data or values from 1 paper
-
The fraction for the yield in each of the three meson-antimeson channels at the $Υ(5S)$ resonance as measured by Belle [ref] corresponds to $f(B^* B̅^*)=(37.5^+2.1_-1.9±3.0)%, f(B^* B̅ + B B̅^*)=(13.7 ±1.3 ±1.1)%, f(B B̅) = (5.5^+1.0_-0.9±0.4)%$, which reasonably agrees with the 7:3:1 ratio, and given the errors, with the kinematically modified ratio.
Measurement of Y(5S) decays to B^0 and B^+ mesons · Introduction · 0.93
Cites as background 1 paper
-
Such C-even molecular resonances $X_bJ$ were considered in Ref. [ref] .
Heavy quark spin structure in Z_b resonances · Introduction · 0.80
Discussion
Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.