REVIEW
Channel coupling in e+ e- annihilation into heavy meson pairs at the D* {\bar D}* threshold
High Energy Physics - Phenomenology · Submitted 26 Feb 2006 · 23 references
Pith's verdict: A correct and honest threshold-parametrization note whose practical significance rests on an unmeasured scale w; worth sending to a serious referee.
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Referee report
The paper
The paper claims
A $D^*\bar D^*$ threshold resonance would put its visible imprint in lighter $e^+e^-$ channels at an energy set by one coupling parameter, not by the resonance position.
The reading
What carries the argument
The load-bearing object is the analytically continued P-wave resonance denominator, specifically the term $\frac{1}{2}\Delta\sqrt{\Delta/w}$ in Eq. (4). It arises from continuing $g_H^2 k^3 = W\sqrt{W/w}$ to negative $W=-\Delta$, and its non-monotonic real part — minimum $-16w/27$ at $\Delta_m=16w/9$ — is what moves cross-section features away from the nominal resonance energy. The parameter $w=g^{-4}M^{-3}$ encodes the coupling of the resonance to the vector-meson pair; the paper assumes $w\simeq 1$–10 MeV for the $D^*\bar D^*$ system, much smaller than the pseudoscalar values extracted from $\psi(3770)$ and $\Upsilon(4S)$. The same denominator, with two thresholds split by the isospin mass difference $\delta\approx 6.6$ MeV, governs all three energy regions in Eqs. (5)–(10).
Extended reading notes
Core claim
The paper's central claim is that the production amplitude in a light channel has the resonant form $A_L = a_L + b_L/(W-W_0 + (i/2)(\Gamma_0 + g_H^2 k^3))$ above the $D^*\bar D^*$ threshold, and that analytic continuation below threshold ($W=-\Delta$) gives $A_L = a_L + b_L/[(1/2)\Delta\sqrt{\Delta/w} - \Delta - W_0 + (i/2)\Gamma_0]$. The new term $(1/2)\Delta\sqrt{\Delta/w}$ is the continuation of the P-wave width $g_H^2 k^3 = W\sqrt{W/w}$; it is bounded below by $-16w/27$ at $\Delta_m=16w/9$. Since the real part of the denominator therefore cannot go arbitrarily negative, the magnitude of the resonant amplitude is non-monotonic in $\Delta$, and the position of the maximum effect is set by $w$ rather than by the nominal resonance position $W_0$ whenever $W_0$ is sufficiently far below threshold. Hence the observed features in the light channels generally do not coincide with the resonance energy.
Load-bearing premise
The predicted visible distortions in the lighter channels depend on the parameter $w$ being as small as 1–10 MeV for the $D^*\bar D^*$ resonance; if the resonance's coupling to vector mesons is not much stronger than the known $\psi(3770)$ and $\Upsilon(4S)$ couplings, $w$ would be much larger and the effect would shrink below visibility.
Editorial extensions
If this is right
- Above the $D^*\bar D^*$ threshold, the heavy-channel cross section is dominated by the P-wave $k^3$ rise and is only weakly sensitive to the resonance parameters, so the observed peak in the total cross section does not locate the resonance.
- The light-channel cross sections can show local maxima or minima whose positions depend on $w$ and on the relative phase of the coefficients $a_L$ and $b_L$, so different light channels can exhibit visibly different shapes across the same narrow energy range.
- Extracting the width parameter $\Gamma_0$ from data requires including the channel-coupling distortion, so the width quoted for the $D^*\bar D^*$ threshold peak may differ substantially from the nominal $\Gamma_0$.
- The isotopic splitting of the $D^*$ thresholds, about 6.6 MeV, creates three energy regions with distinct analytic forms in Eqs. (5)–(10), so a scan must treat the neutral and charged thresholds separately.
- The same reflected singularity should appear at other heavy-meson pair thresholds, such as $D^*\bar D$ near 3875 MeV, where analogous distortions may be observable.
Reading between the lines
- The offset formula gives a parameter-free diagnostic: if a subthreshold resonance sits far enough below threshold, the extremum in the light channels sits at $\Delta_m=16w/9$, so measuring that offset determines $w$ directly from data before any global fit.
- Because the effect for $w=1$ MeV lives within a few MeV of the threshold, Coulomb attraction between charged $D^*$ mesons — deliberately omitted here — overlaps exactly with the most interesting energy region, so including it is a natural next step for precision scans.
- The same logic would apply to any new heavy-meson threshold, including $B$-meson thresholds: an apparent peak sitting a few MeV away from the corresponding pole position could be the signature of exactly this reflection rather than of a second state.
Original abstract
A threshold singularity in a heavier meson channel, e.g. $D^* {\bar D}^*$, generally reflects in the amplitudes of $e^+e^-$ annihilation into lighter meson pairs, such as $D^* {\bar D}$, $D {\bar D}$, and $D_s {\bar D}_s$, due to the channel coupling. The behavior of the cross section of the $e^+e^-$ annihilation into each channel in this situation is considered using general properties of the amplitudes near the new threshold. It is argued that the effects of the channel coupling can be quite significant in the observable cross section, in particular near the $D^* {\bar D}^*$ threshold.
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
A threshold singularity in a heavier meson channel, e.g. $D^* {\bar D}^*$, generally reflects in the amplitudes of $e^+e^-$ annihilation into lighter meson pairs, such as $D^* {\bar D}$, $D {\bar D}$, and $D_s {\bar D}_s$, due to the channel coupling. The behavior of the cross section of the $e^+e^-$ annihilation into each channel in this situation is considered using general properties of the amplitudes near the new threshold. It is argued that the effects of the channel coupling can be quite significant in the observable cross section, in particular near the $D^* {\bar D}^*$ threshold.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | A threshold singularity in a heavier meson channel, e.g. $D^* {\bar D}^*$, generally reflects in the amplitudes of $e^+e^-$ annihilation into lighter meson pairs, such as $D^* {\bar D}$, $D {\bar D}$, and $D_s {\bar D}_s$, due to the channel coupling. | background 0.95 | 0.12 | 0.36 | asserted 0.69 |
| s1 | The behavior of the cross section of the $e^+e^-$ annihilation into each channel in this situation is considered using general properties of the amplitudes near the new threshold. | method 0.61 | 0.62 | 0.07 | asserted 0.63 |
| s2 | It is argued that the effects of the channel coupling can be quite significant in the observable cross section, in particular near the $D^* {\bar D}^*$ threshold. | interpretation 0.57 | 0.56 | 0.77 | hedged possibility 0.86 |
What was examined, and what was not
- arXiv listing abstract v2
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Figures
Figures reproduced from arXiv:hep-ph/0602233 by the authors.
References
How the literature uses it
18 arXiv papers cite this in 19 sentences
Papers citing it · 11 sentences without a confident label
Cites it as background 8 papers
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Dubynskiy and Voloshin suggested the possibility of the existence of a new resonance at the $D^*D̅^*$ threshold [ref] .
X(3872) and Other Possible Heavy Molecular States · Introduction · 0.84
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Dubynskiy and Voloshin indicated that there exists a possible new resonance at the $D^*D̅^*$ threshold [ref] .
Is X(3872) {\sl Really} a Molecular State? · Review of Molecular Picture · 0.96
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To explain the observed peaks, some models assign the $3^3D_1(4350)$, $5^3S_1(4660)$ with shifted masses [ref] , other explore coupled-channel effects and rescattering of charm mesons [ref] .
Measurement of the e+e- --> D0D*-pi+ cross section using initial-state radiation · Introduction · 0.87
Discussion
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