Nonleptonic weak decays of charmed mesons

A. Pugliese; F. Buccella; G. Miele; M. Lusignoli; P. Santorelli

REVIEW

Nonleptonic weak decays of charmed mesons

F. Buccella, M. Lusignoli, G. Miele, A. Pugliese, P. Santorelli

High Energy Physics - Phenomenology · Submitted 14 Nov 1994 · 25 references

Pith's verdict: A careful, self-aware update of a long-running charm-decay fit; the new piece is modest but real, and the reader's headline complaint about the chi-squared does not survive contact with the text.

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arXiv IDhep-ph/9411286 (version 1)

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CitationA. Pugliese, F. Buccella, G. Miele, M. Lusignoli, P. Santorelli. "Nonleptonic weak decays of charmed mesons." arXiv:hep-ph/9411286 (1994). https://pith.science/paper/2A4QXOAZ

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Editor's note

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This is the third installment of a program the same group has been running since 1992, and it reads like it: the machinery is settled, the new content is the extension to Cabibbo-forbidden D0 channels plus a refresh against the 1994 PDG. What is genuinely new is Section 3's three-parameter description of isoscalar rescattering — a mixing angle, a mass splitting, and a coupling constrained by unitarity — plus the observation that the eta-eta' mixing angle can now be fixed at -10 degrees from the axial anomaly rather than fitted. That last bit is a real improvement over their earlier papers and deserves credit. The treatment of K_S as an interference between Cabibbo-allowed and doubly-suppressed amplitudes is also handled properly, which is more than most analyses of this era bother to do. The physics logic holds together: factorization demonstrably fails on Cabibbo-allowed D0 decays, and the structural argument that A(D0 -> K0 K0) vanishes in factorization and can only be filled in by rescattering is analytic, not a fit artifact. That part of the 'crucial' claim in abstract:s1 is earned. First, a correction in the authors' favour. The reader flags chi-squared 80.6 in Section 4 against 90 in Section 6 as an internal inconsistency. It is not. Section 4's 80.6 covers the 25 allowed plus 12 charged first-forbidden points; the two D0-forbidden fits add 1.7 and 7.7, and 80.6 + 1.7 + 7.7 = 90. The stress-test note already caught this and it is right. The ablation critique does land, though more softly than stated. No fit is shown with W-exchange switched off, so 'crucial' for the W-exchange terms is asserted rather than demonstrated; the two mechanisms are tuned against the same anomalous channels and can trade off. The real soft spots are elsewhere. R'+ is predicted at 0.76e-2 against an experimental 5.8e-2 — a factor of seven, reported and then left alone. K*0 eta, D+ -> K*0 pi+, and Ds -> rho eta' are each off by factors of two to four with no theoretical error bars anywhere in the tables, so a reader cannot tell whether these are within parameter spread or not. And the CP asymmetries in Table 5 inherit strong phases from fitted resonance parameters and weak phases from an unpublished Roma preprint [25]; the quoted errors reflect only the (rho, eta) variation. The authors concede the parameter-count problem themselves, so I will not belabor it. Who should read it: charm phenomenologists, and anyone setting targets for charm CP searches at an e+e- factory. It is a legitimate paper from a group that knows what it is doing, and it would get refereed.

Referee report

Significance

If the model holds, this is a useful and substantive contribution: it offers a unified description of a large body of exclusive charm data, it makes two genuine out-of-fit predictions (R_Kπ0 = 0.89×10⁻² and R'_+ = 0.76×10⁻², Section 4) that were subsequently testable, and it produces a falsifiable table of CP asymmetries. The paper is also commendably candid about what it does not know: it states plainly that the isoscalar resonances are unobserved, that the number of new parameters must be reduced by phenomenological analogy with the tensor mesons f2(1270) and f'2(1525), and that the CP asymmetries 'may vary appreciably for parameter variations that still give reasonable fits' (Section 5). The reduction of the isoscalar sector to three parameters via the relation a = 1/(√2 tan φ) and a unitarity condition on c is a genuine attempt to avoid an unconstrained fit. These are real strengths and should be weighed alongside the concerns below.

Major objections (5)

[Abstract (abstract:s1) and Section 4] The abstract asserts that annihilation/W-exchange and rescattering effects are 'in fact crucial' to the agreement with the data, but no ablation is reported anywhere in the paper. The only cross-check described in Section 4 is a refit to the Cabibbo-allowed subset alone, which varies the data set, not the model. Because W_PP, W_PV and the rescattering phases are all tuned against the same small set of anomalous channels (K⁺K⁻/π⁺π⁻, D0→K⁰K̄⁰, R⁺), the two mechanisms can trade off against one another, and the reader cannot tell whether FSI alone, W-exchange alone, or neither is doing the work. Please report the χ² for at least three variants: W_PP = W_PV = 0 with FSI retained, rescattering phases switched off with W-exchange retained, and both switched off. Without this, 'crucial' is a sufficiency statement dressed as a necessity statement.
[Section 4 and Tables 1–3] The characterization of the fit as a 'reasonable agreement' is generous relative to what the tables show. A total χ² of about 90 for 45 data points and eleven parameters corresponds to roughly 2.6 per degree of freedom, and several individual channels are missed by three to four standard deviations: Table 2, D⁺→K*⁰π⁺ is 2.2±0.4 experimentally against 0.64 predicted; Table 1, D0→K*⁰η is 1.9±0.5 against 0.51; Table 3, D_s⁺→ρ⁺η′ is 12.0±3.0 against 2.61. In addition, Table 4 quotes the 90% c.l. upper limit B.R.(D0→K*⁰K⁰) < 0.08 while the model predicts 0.099, i.e. the prediction lies outside the bound it is being compared with. Please state the number of degrees of freedom explicitly, identify the channels that dominate the χ², and either soften the 'reasonable agreement' language or explain why these particular channels are expected to be poorly described.
[Section 2 (a_cd) and Section 6] Two fitted parameters sit uncomfortably relative to the expectations invoked in the conclusion. The axial charge a_cd = a_cu is reported as exactly 1.0, which is the upper edge of the range [0.5, 1] imposed in Section 2, and the text itself notes that 'an even better fit would be obtained allowing larger values for a_cd'; a parameter at a boundary is not at an interior minimum, so the quoted χ² is not a true best fit and the fit is effectively constrained by hand. Separately, ξ = −0.027 is far from the QCD expectation of 1/3. The concluding claim in Section 6 that the eleven parameters 'assume values close to the expected ones' is therefore not supported for at least these two. Please widen the a_cd range, report the χ² profile in ξ and a_cd, and revise the concluding sentence accordingly.
[Section 4, Section 5 and Table 5] No uncertainties are quoted for any fitted parameter anywhere in the paper, and the errors in Table 5 reflect only the variation of the CKM parameters (ρ,η) within the region of Ref. [25]. Since the strong phases that generate the asymmetries are computed from the same resonance masses, widths and couplings that were fitted to the branching ratios, the dominant uncertainty on Table 5 is the model uncertainty, which Section 5 itself acknowledges is large ('the actual numbers may vary appreciably for parameter variations that still give reasonable fits'). As presented, the quoted errors are lower bounds presented as if they were total errors. Please either propagate the spread over acceptable fits into Table 5 or state explicitly in the caption that the quoted errors omit the dominant model uncertainty. The same request applies to the fitted parameters of Section 4: with eleven parameters and 45 points, the reader needs errors and correlations at least for ξ, W_PP, W_PV, a_cs, M_K*0 and Γ_K*0 to judge which are actually determined.
[Section 3] The rescattering sector contains two discrete choices that are resolved without a stated criterion, and both affect the fit. First, Eq. (3.4) determines δ8 only up to a 180° ambiguity; the paper resolves it by a resonance-counting argument and then notes that 'in our recent preprint a different choice was made for the PV channels', which means the fit result depends on a convention that has already changed between versions. Second, for the isoscalar sector the parameter c is 'chosen between the two solutions of a quadratic consistency condition' with no stated rule for the choice. Please give the explicit criterion for each branch, and report how much the χ² and the entries of Table 5 change when the alternative branch is taken.

Minor objections (7)

[Abstract (abstract:s0, abstract:s2) and Section 6] The abstract says the previous analysis 'has been adjourned', which appears to be a mistranslation of 'aggiornata' and should read 'updated'; 'informations' in abstract:s2 should be 'information'; and 'successfull' in Section 6 should be 'successful'. The author list also renders 'Napoli' as 'Na poli', and Ref. [17] contains the typo '91983)'.
[Eq. (2.12)] The experimental rate is converted with Γ(D→K_S+X) ≡ ½ Γ_exp(D→K⁰+X), which is the no-interference limit, yet the text immediately states that interference with the doubly Cabibbo-suppressed amplitude is included and is 'not negligible'. Please clarify whether the ½ rule is used only to define the experimental number being fitted or also in the theory side, since the two cannot both be exact.
[Eq. (2.16) and Table 5] The penguin contributions in Eq. (2.16) scale as 1/(m_u+m_c) and 1/(m_u+m_d), so the Cabibbo-forbidden amplitudes and hence the CP asymmetries inherit a strong sensitivity to the light quark mass m_u = 4.5 MeV. This sensitivity is not discussed, and it is not obviously small compared with the CKM variation that dominates the quoted errors in Table 5. A sentence quantifying it would help.
[Table 5] The rows for D0→K*⁰K⁰ and D0→K*⁰K̄⁰ are numerically identical to all quoted digits (+0.67 ± 0.39). A common sign flip of the amplitude leaves a_CP invariant, so equality is not by itself wrong, but please confirm that this is not a transcription duplication.
[Section 2] The weak charges are set to v_cs = v_cd = v_cu = 0.79 by SU(3) assumption, while the rest of the paper argues at length that SU(3) is badly broken in these decays. A sentence justifying why SU(3) is trusted here but not elsewhere would preempt the obvious objection.
[References [14] and [25]] Ref. [14] is cited as 'to appear in Phys. Rev. D' in support of the statement that the fitted axial charges disagree with the QCD sum rule calculation, and Ref. [25], a Roma preprint, supplies the (ρ,η) values that feed the central values of Table 5. Please update the publication status of both, or note that the comparison rests on unpublished work.
[Section 3, Eq. (3.2) and following text] The phrase 'with δ8 close to 12π' appears to be a garbled '½π'; please correct and state the assumed phase convention explicitly, since the whole FSI sector depends on it.

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The paper

The paper claims

Two-body charmed-meson decays only come out right when W-exchange, annihilation, and rescattering through nearby resonances are added to the factorized weak Hamiltonian.

The reading

The paper asks whether the mess of two-body nonleptonic $D$ branching ratios — including the ones that badly violate flavour SU(3) — can be reproduced by one coherent calculational scheme. Its answer is that factorization alone cannot do it, but factorization plus two things the standard treatment drops can: W-exchange and annihilation terms taken as free parameters, and final-state rescattering assumed to proceed through nearby resonances whose masses and widths are taken from experiment where they exist and fitted where they do not. The payoff is a fit to 45 measured branching ratios with eleven parameters and a total $χ^2$ of about 90, with the striking SU(3) violations — the large $K^+K^-$ to $π^+π^-$ ratio, the non-zero $D^0 → K^0 K^0$ rate, the enhanced $D^+ → π^+π^0$ rate — emerging as consequences rather than inputs. If the scheme holds, the strong phases that make those rates come out are the same phases that generate CP asymmetries, and the paper uses them to predict asymmetries around $10^{-3}$ in Cabibbo-forbidden channels, larger than earlier estimates. The reader should care because this is a claim that a handful of poorly measured resonances, not short-distance QCD, control the size and pattern of charm decay rates.

What carries the argument

The load-bearing device is the rescattering replacement $A(D → V_h P_k) = A_w(D → V_h P_k) + c_{hk}[e^{iδ_8} - 1] Σ_{h'k'} c_{h'k'} A_w(D → V_{h'}P_{k'})$, where the $c_{hk}$ are normalized couplings of the resonance to the two-body channel and $sin δ_8 e^{iδ_8} = Γ_R / (2(M_R - M_D) - iΓ_R)$ fixes the strong phase from the resonance mass and width. This is what turns a set of real factorized amplitudes into amplitudes with large relative strong phases, and it is what produces the SU(3) violations, since the $K$ and $π$ resonances sit at different masses and therefore give different phases in different isospin channels. For the Cabibbo-forbidden $D^0$ channels the same logic requires isoscalar scalar resonances; the authors compress their freedom to three parameters by analogy with the tensor mesons $f_2(1270)$ and $f'_2(1525)$, imposing $a = 1/(√2 tan φ)$ so that the lighter isoscalar does not decay to $ππ$.

Extended reading notes

Core claim

The central claim is that a factorized weak amplitude is the wrong starting point unless it is immediately dressed by two effects the authors treat as physics rather than as corrections: W-exchange/annihilation matrix elements, written via current divergences and parametrized by two numbers $W_{PP}$ and $W_{PV}$ that turn out considerably larger than naive pole estimates, and final-state interactions modelled as rescattering through the nearest $0^-$ and $0^+$ resonances. With these, the authors refit the Cabibbo-allowed $D^0$ and $D^+$ rates, the Cabibbo-allowed and first-forbidden $D^+$ and $D_s^+$ rates, and extend the analysis to the Cabibbo-forbidden $D^0$ channels, adding only three parameters for the unmeasured isoscalar scalars. The fit reproduces the observed SU(3) violations: the $K^+K^-$-to-$π^+π^-$ ratio far above the symmetric prediction, a non-zero $D^0 → K^0 K^0$ rate that vanishes in factorization, and the ratio $R_+ ≃ 3.55$ in the exotic $D^+$ channels, which arises here from several small SU(3)-breaking effects adding coherently. The authors also note where the model strains: the predicted $R'_+ = B.R.(D^+ → φK^+)/B.R.(D^+ → φπ^+)$ is much smaller than the quoted measurement, which itself is only 2.5 standard deviations from zero.

Load-bearing premise

The strong phases that make the whole scheme work are generated by resonances whose masses, widths, and couplings are either unmeasured or themselves fitted, so the agreement with data rests on objects the paper has to postulate.

Editorial extensions

If this is right

The $K^+K^-$ to $π^+π^-$ ratio and the non-zero $D^0 → K^0K^0$ rate are consequences of rescattering phases rather than of short-distance SU(3) breaking, so any model that gets them from quark-mass or decay-constant differences alone is aiming at the wrong mechanism.
The large value $R_+ ≃ 3.55$ of $D^+ → π^+π^0$ relative to $D^+ → K_S π^+$ follows from several small SU(3)-breaking effects contributing with the same sign.
CP-violating asymmetries of order $10^{-3}$ are expected in Cabibbo-forbidden $D$ channels, with the strong phases supplied by the same resonance model used for the rates.
The doubly Cabibbo-suppressed ratio $R_{Kπ}^0$ is predicted at $0.89 × 10^{-2}$, about 3.4 times the SU(3) expectation of $tan^4θ_C$, driven mainly by W-exchange contributions of opposite sign in the two amplitudes.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

If the scalar isoscalar states invoked here are later found near the fitted masses of about 1778 and 2148 MeV with roughly the fitted widths, the same resonance-rescattering bookkeeping becomes a template for $B$ decays, where strong phases are otherwise almost unconstrained.
The three-parameter compression rests on an analogy with the tensor mesons rather than on data; measuring the $f_0 → K\bar K$ versus $f'_0 → ππ$ branching pattern would either fix the mixing angle independently or break the analogy outright.
Because every predicted asymmetry traces back to fitted strong phases, a measured asymmetry at the $10^{-3}$ level would not by itself confirm this particular phase assignment; the rates and the asymmetries would have to be checked jointly.

Original abstract

A previous analysis of two-body Cabibbo allowed nonleptonic decays of $D^0$ mesons and of Cabibbo allowed and first-forbidden decays of $D^+$ and $D_s^+$ has been adjourned using more recent experimental data and extended to the Cabibbo forbidden decays of $D^0$. Annihilation and W-exchange contributions as well as final state interaction effects (assumed to be dominated by nearby resonances) have been included and are in fact crucial to obtain a reasonable agreement with the experimental data, which show large flavour SU(3) violations. New fitting parameters are necessary to describe rescattering effects for Cabibbo forbidden $D^0$ decays, given the lack of experimental informations on isoscalar resonances. We keep their number to a minimum - three - using phenomenologically based considerations. We also discuss CP violating asymmetries.

The compiled record

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What the abstract itself states, as probabilities: claims first 0.06 · states limitation 0.88 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.60 · compares with prior results 0.70 · mentions code or data availability 0.02.

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arXiv listing abstract v1. Results and the main claim are underlined; show every role.

A previous analysis of two-body Cabibbo allowed nonleptonic decays of $D^0$ mesons and of Cabibbo allowed and first-forbidden decays of $D^+$ and $D_s^+$ has been adjourned using more recent experimental data and extended to the Cabibbo forbidden decays of $D^0$. Annihilation and W-exchange contributions as well as final state interaction effects (assumed to be dominated by nearby resonances) have been included and are in fact crucial to obtain a reasonable agreement with the experimental data, which show large flavour SU(3) violations. New fitting parameters are necessary to describe rescattering effects for Cabibbo forbidden $D^0$ decays, given the lack of experimental informations on isoscalar resonances. We keep their number to a minimum - three - using phenomenologically based considerations. We also discuss CP violating asymmetries.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
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s0	A previous analysis of two-body Cabibbo allowed nonleptonic decays of $D^0$ mesons and of Cabibbo allowed and first-forbidden decays of $D^+$ and $D_s^+$ has been adjourned using more recent experimental data and extended to the Cabibbo forbidden decays of $D^0$.	contribution 0.86	0.65	0.10	asserted 1.00
s1	Annihilation and W-exchange contributions as well as final state interaction effects (assumed to be dominated by nearby resonances) have been included and are in fact crucial to obtain a reasonable agreement with the experimental data, which show large flavour SU(3) violations.	method 0.53	0.69	0.36	asserted 1.00
s2	New fitting parameters are necessary to describe rescattering effects for Cabibbo forbidden $D^0$ decays, given the lack of experimental informations on isoscalar resonances.	method 0.59	0.62	0.09	asserted 0.99
s3	We keep their number to a minimum - three - using phenomenologically based considerations.	method 0.95	0.88	0.06	asserted 0.97
s4	We also discuss CP violating asymmetries.	contribution 0.99	0.81	0.06	asserted 0.61

What kind of paper the classifier reports this is: theoretical result 0.98 · evidence from analysis of existing data 1.00.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

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Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

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How the literature uses it

36 arXiv papers cite this in 42 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 29 sentences without a confident label

Uses its data or values 1 paper

Some time ago, $ΔΓ_D$ was determined in this manner and the result $y_D ≃10^-3$ was found [ref] .

Charm Mixing - Theory · Hadron-level Analysis · 0.83

Cites it as background 12 papers

The discovery of charm CP violation [ref] in singly-Cabibbo suppressed (SCS) two-body $D→PP$ decays, where $P$ is a pseudoscalar meson [ref] , was the result of a multi-year effort [ref] and triggered immediate theoretical interpretations [ref] .

Probing the $\Delta U=0$ Rule in Three Body Charm Decays · Introduction · 0.93
Measurements in the charm sector have only recently achieved a sufficient level of precision to be sensitive to violation in charm transitions, which is suppressed due to the Glashow-Iliopoulos-Maiani mechanism [ref] and the small size of the Cabibbo-Kobayashi-Maskawa matrix element $|V_cb|$ [ref] .

Measurement of the CP asymmetry in $D^+ \to \pi^+ \pi^0$ decays at Belle II · Introduction · 0.81
Small CPV was subsequently predicted in [ref] using a model for final-state interactions.

A consistent picture for large penguins in D -> pi+ pi-, K+ K- · Introduction · 0.80

Discussion

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