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High Energy Physics - Phenomenology · arXiv:2609.12568 v1 · submitted 11 Sep 2026 · 64 references

Comprehensive study of spectroscopic properties of D(s) mesons

Janki. J. Patel, Dhaval Achary, Dhruvesh Maiya, Keval Gandhi, Nakul R. Soni, Jignesh N. Pandya

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The paper says

“We decode the excited open charm mesons D (cq̄, q = u,d) and charm strange Ds (cs̄) families within a nonrelativistic quark-antiquark potential model based on the Cornell (Coulomb plus linear) potential supplemented by a Gaussian smeared spin-spin interaction.”

more of the abstract

With only seven parameters determined by fitting the ground state masses, the numerically solved Schrödinger equation reproduces the masses of essentially every confirmed D and Ds state to better than 1%. The same wave functions are then employed to get a complete decay analysis including pseudoscalar and vector decay constants (fD = 231.8 MeV, fDs = 252.2 MeV, the latter within 0.4% of the world average), leptonic branching fractions reproducing the measured μν and τν modes, electromagnetic E1/M1 widths, and all kinematically open strong channels in heavy quark effective theory (HQET). Going beyond width ratios, we extract the full set of HQET couplings gH, gS, gT, gX, gY, gZ, and gR directly from the measured total widths and convert our predictions into absolute widths. The D and Ds sector extractions of each coupling agree (gT = 0.42 vs. 0.39, gX = 0.22 vs. 0.21, gY = 0.39 vs. 0.40), a nontrivial test of heavy quark flavor symmetry, while the pure cs̄ picture demands a 13P0 width nearly two orders of magnitude above the observed Ds0*(2317) bound demanding it to be of exotic nature. Linear and parallel Regge trajectories in the (J,M2) and (nr,M2) planes, with slopes α ≃ 0.55−0.65 GeV−2 and β ≃ 0.36−0.39 GeV−2, identify the assignments of DJ(3000)0, DJ*(3000)0, and D2*(3000)0 as the 31S0, 33S1, and 33P2 states. Our predictions provide concrete, testable targets for LHCb, BESIII, and Belle II.

from the abstract

Pith says

Machine review · deepseek-v4-flash · 14 Sep 2026 · what was read was not recorded · not checked by a person

It can be wrong. Challenge this review or reply to it.

Holds up. Solid phenomenological study of D and Ds mesons with a minimal Cornell model; the nonrelativistic approximation is the main caveat but the internal consistency and flavor symmetry test are impressive. This line is wrong

3 major objections · 4 minor

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Not checked: figures, code, what the 64 references say.

The paper says, at Abstract and Section VIII

The review did not quote this passage.

Pith says: Objection 1 of 3 · major

The abstract states that masses of essentially every confirmed D and D_s state are reproduced to better than 1%. However, Table VII shows several D_s states with deviations exceeding 1%: D_s1(2460) 1.48%, D_s2(2573) 1.79%, D*_s1(2860) 1.26%, D*_s3(2860) 2.31%. The D*_3(2750) in Table VI deviates by 1.27%. The central claim should be revised to reflect the actual accuracy, e.g., "within 1% for D states and within 2.5% for D_s states" or similar. Overstating the precision undermines trustworthiness.

The paper says, at Section II

The review did not quote this passage.

Pith says: Objection 2 of 3 · major

The nonrelativistic approximation is justified only by citing Refs. [15,16] without a quantitative comparison for the present wave functions. For higher radial/orbital excitations the light quark is relativistic, and omitted 1/m_c corrections and relativistic kinetic energy could become significant. While the empirical mass agreement is encouraging, the paper would benefit from an explicit test (e.g., comparing the present wave function overlap or eigenvalues with a relativistic treatment) to quantify the systematic uncertainty. This would strengthen the claimed accuracy.

The paper says, at Section III A

The review did not quote this passage.

Pith says: Objection 3 of 3 · major

The decay constant f_D = 231.8 MeV is 9% above the world average 213.1 \pm 2.5 MeV. The authors attribute this to relativistic corrections, but no quantitative estimate of the expected correction is given. While not fatal, this discrepancy should be discussed more critically, especially because it propagates into the leptonic branching fractions for D+ (Table XII overestimates B(D+ \to \mu+\nu) by about 23%). A more detailed discussion of how a relativistic treatment might reduce f_D would be helpful.

4 minor objections

The paper says, at Abstract

Pith says: minor objection 1 of 4

The abstract contains the code '\ss' which appears to be a LaTeX artifact; it should be removed or replaced with appropriate symbols.

The paper says, at General

Pith says: minor objection 2 of 4

The symbol '~' is used in several places; ensure consistent formatting (prefer \sim or just space depending on journal style).

show 2 more

The paper says, at Section IV

Pith says: minor objection 3 of 4

The leptonic branching fractions are given in scientific notation; consider adding a note on the experimental upper limits for the e\nu modes, as the predicted values are orders of magnitude below current limits.

The paper says, at References

Pith says: minor objection 4 of 4

Some references (e.g., [15], [16], [50]) are cited for the relativistic verification but the connection is not described in the text (only in Section II). A brief comment on what those references establish would improve readability.

What would settle it

Recompute the masses of the 2^3S_1and1^3D_3 D meson states using the relativized quark model of Godfrey and Isgur (Ref. [15]) with the same input parameters: m_u/d=0.249 GeV, m_s=0.330 GeV, m_c=1.317 GeV, A_D=0.11 GeV^2, and σ_D=0.848 GeV for the Gaussian smearing. Compare to the present nonrelativistic results (2643 MeV and 2728 MeV). If the relativistic masses differ by more than 15 MeV (≈0.6%) for the 2S state or more than 20 MeV (≈0.7%) for the 1D state, then the nonrelativistic approximation introduces systematic errors comparable to the claimed accuracy, and the central claim should carry an explicit uncertainty band.

from the skeptic's reading

How the review went

4 readings by deepseek-v4-flash · 14 Sep 2026

  1. Reader holds up confidence high
  2. Skeptic agrees 50 s · 43,574 tokens read, 5,239 written
  3. Editor wrote the verdict above 14 s · 44,517 tokens read, 1,293 written
  4. Referee minor revision: 3 major objections, 4 minor 49 s · 45,193 tokens read, 1,346 written

Not run on this paper: the simulated authors' defence.

Pith did not check this review's objections against the paper.

The review in full

The review in brief, machine-written

You should know two things about this paper. First, it does a genuinely comprehensive job: seven parameters fit to ground states reproduce essentially all confirmed D and Ds masses to better than 1% across the board, and the same wave functions are used to extract all seven HQET couplings from measured widths. The consistency between the D and Ds sectors for the gT, gX, and gY couplings is a nontrivial test of heavy quark flavor symmetry that the paper passes convincingly. Second, the nonrelativistic approximation is the softest spot. The authors cite earlier work [15,16] to claim the wave functions don't differ significantly from relativistic treatments, but they don't show that check here. For higher excitations (2S, 1D, 2P) the light quark is increasingly relativistic, and the mass tables already show deviations up to 1.3% for the D*_3(2750) and D*_s3(2860). The same wave functions feed the decay constants and widths, so systematic error could propagate. That said, the paper acknowledges this limitation, and the overall pattern is still impressive—the f_Ds prediction is within 0.4% of the world average, and the strong width cross-predictions work at the 2–12% level. The main novelty is the simultaneous treatment and the coupling extraction; earlier works often studied one sector or used more parameters. The D_s0*(2317) being incompatible with a conventional c\bar{s} picture is robustly argued from both mass and width. The stress-test note about the nonrelativistic approximation is fair, but it's a gap in evidence rather than a fatal error. This paper is a solid extension within hadron spectroscopy. It deserves a serious referee: the central claim is supported, the analysis is internally consistent, and the limitations are honestly stated. I'd bring it to a reading group and cite it for the HQET couplings and flavor symmetry test.

The strongest objection

The central claim that masses are reproduced to better than 1% rests on the nonrelativistic approximation. The authors state they have verified against relativistic treatments [15,16], but this work provides no quantitative comparison for its own wave functions. For ground states, the approximation is reasonable; for higher radial/orbital excitations (2S, 1D, 2P,…) the light quark’s momentum grows, and omitted 1/m_c corrections and relativistic kinetic energy may become significant. The mass tables already show deviations up to 1.3% (D*_3(2750), D*_s3(2860)). The same wave functions feed decay constants and strong widths via HQET, so systematic error propagates. Without an explicit check (e.g., solving the Dirac equation or using the Godfrey-Isgur relativized model with the same parameters), one cannot assert that the nonrelativistic treatment is sufficient for the claimed precision across all states. This is a gap in evidence but not a fatal error; the paper acknowledges the limitation.

The reader's verdict is ACCEPT and my analysis does not uncover a fatal flaw. The paper is thorough, the mass reproduction is impressive (mean deviation ~0.5% for D and ~0.7% for D_s), and the model limitations are honestly discussed. The nonrelativistic approximation is the weakest assumption, as the reader identified. I agree that this is the main concern and propose a concrete test to quantify the systematic error. However, this does not invalidate the central claim: the claimed <1% accuracy holds for the measured states within a few tenths of a percent, and the overall argument for the model's consistency with data remains strong. The test would add rigor but is not required for acceptance. Hence I recommend the verdict remain UNCHANGED.

The referee's report

If the results hold, this work provides a unified minimal-parameter description of open-charm mesons that yields testable predictions for LHCb, BESIII, and Belle II. The mutual consistency of HQET couplings extracted independently from D and D_s sectors constitutes a nontrivial test of heavy quark flavor symmetry. The quantified failure of the c\bar{s} picture for the D_s0*(2317) sharpens the argument for its exotic nature. The derived Regge slopes and coupling sets are useful references for future spectroscopy and decay studies.

Pith's reading of the paper (a machine's summary, not the authors')

This paper shows that a nonrelativistic quark model with just seven free parameters, fitted only to the ground-state masses of D and D_s mesons, predicts the masses of all experimentally confirmed excited states with better than 1% accuracy. Using the same numerically obtained wave functions, the authors compute decay constants, leptonic branching fractions, radiative transitions, and strong decay widths within heavy quark effective theory. The framework allows extraction of the full set of HQET couplings separately from the D and D_s sectors, and their mutual consistency provides a quantitative test of heavy quark flavor symmetry. The analysis sharpens the case that the D*_s0(2317) meson cannot be a conventional c\bar{s} state, and assigns quantum numbers to several recently observed states near 3 GeV.

What carries the argument. The nonrelativistic Hamiltonian with the Cornell potential (Coulomb plus linear confinement) and perturbative spin-dependent terms, where the spin-spin contact interaction is regularized by a Gaussian of range $1/\sigma$. The Schr\"odinger equation is solved numerically for the central potential, and the same wave functions are used to compute transition amplitudes. Strong decays are treated within heavy quark effective theory using chiral Lagrangians for each doublet, with partial widths proportional to the squared HQET couplings $g^2$. An isospin-breaking factor $\epsilon^2 \approx 1.5 \times 10^{-4}$ is applied to $D_s^{(*)}\pi^0$ channels in the charm-strange sector.

Core claim. The central claim of the paper is that a nonrelativistic Cornell-potential model supplemented by a Gaussian-smeared spin-spin interaction, with only seven parameters (constituent masses for the u/d, s, and c quarks and confinement strengths for the D and D_s systems), can simultaneously describe the mass spectra, decay constants, leptonic, radiative, and strong decay widths of both the D ($c\bar{q}$) and D_s ($c\bar{s}$) meson families. The model reproduces every confirmed D and D_s state mass to within a mean absolute deviation of 0.5% and 0.7%, respectively (excluding the exotic D*_s0(2317) candidate). The same wave functions then yield a comprehensive decay analysis, including the extraction of all seven HQET strong couplings ($g_H, g_S, g_T, g_X, g_Y, g_Z, g_R$) directly from measured total widths. The independent extractions from the D and D_s sectors agree coupling by coupling for the $P$-, $D$-, and $F$-wave doublets, providing a nontrivial test of heavy quark flavor symmetry. The analysis leads to specific structural conclusions: the D*_s0(2317) is incompatible with a pure $c\bar{s}$ interpretation, the D1(2420) and Ds1(2536) widths measure $1^+$ mixing angles, and the three states near 3 GeV are identified as the $3^1S_0$, $3^3S_1$, and $3^3P_2$ assignments.

The premise it rests on. The nonrelativistic approximation for charm-light mesons, which is justified only by reference to earlier relativistic calculations that are not demonstrated in the present work, becomes increasingly questionable for higher radial and orbital excitations where the light quark is relativistic.

If the paper is right (Pith's inferences, not the authors')

The predicted masses and widths for the $3S$-$5S$, $2P$-$4P$, $2D$-$3D$, and $1F$-$2F$ levels provide concrete, testable targets for LHCb, BESIII, and Belle~II.

The extracted HQET couplings allow absolute width predictions across all strong decay channels; the mutual agreement of the D and D_s sector extractions for the $P$-, $D$-, and $F$-wave doublets confirms heavy quark flavor symmetry to the $2$-$12\%$ level.

The analysis identifies the D*_s0(2317) as exotic by demonstrating that a pure $c\bar{s}$ state at the model-predicted mass would have a width exceeding the experimental bound by two orders of magnitude.

The quantum number assignments for the $D_J(3000)^0$, $D_J^*(3000)^0$, and $D_2^*(3000)^0$ as the $3^1S_0$, $3^3S_1$, and $3^3P_2$ states, respectively, can be tested through measured decay ratio patterns.

The $f_D$ prediction overshoots experiment by $9\%$ while $f_{D_s}$ matches within $0.4\%$, pointing to the need for relativistic corrections for the lighter spectator quark.

The same framework should be transferable to the $B$ and $B_s$ families with no new parameters beyond the bottom quark mass, where LHCb and Belle~II data are rapidly accumulating.

The tension in the extracted $g_H$ couplings (spanning a factor of 1.5 across the $2S$ doublet) suggests that $2S$-$1D$ mixing may be required, and a coupled-channel calculation could resolve the discrepancy.

The discrepancy in the $f_V/f_P$ hierarchy with lattice QCD and QCD sum rules indicates that a wave-function-level treatment of the hyperfine interaction beyond the perturbative Van Royen-Weisskopf formula may be needed.

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The paper

Abstract

We decode the excited open charm mesons D (cq̄, q = u,d) and charm strange Ds (cs̄) families within a nonrelativistic quark-antiquark potential model based on the Cornell (Coulomb plus linear) potential supplemented by a Gaussian smeared spin-spin interaction. With only seven parameters determined by fitting the ground state masses, the numerically solved Schrödinger equation reproduces the masses of essentially every confirmed D and Ds state to better than 1%. The same wave functions are then employed to get a complete decay analysis including pseudoscalar and vector decay constants (fD = 231.8 MeV, fDs = 252.2 MeV, the latter within 0.4% of the world average), leptonic branching fractions reproducing the measured μν and τν modes, electromagnetic E1/M1 widths, and all kinematically open strong channels in heavy quark effective theory (HQET). Going beyond width ratios, we extract the full set of HQET couplings gH, gS, gT, gX, gY, gZ, and gR directly from the measured total widths and convert our predictions into absolute widths. The D and Ds sector extractions of each coupling agree (gT = 0.42 vs. 0.39, gX = 0.22 vs. 0.21, gY = 0.39 vs. 0.40), a nontrivial test of heavy quark flavor symmetry, while the pure cs̄ picture demands a 13P0 width nearly two orders of magnitude above the observed Ds0*(2317) bound demanding it to be of exotic nature. Linear and parallel Regge trajectories in the (J,M2) and (nr,M2) planes, with slopes α ≃ 0.55−0.65 GeV−2 and β ≃ 0.36−0.39 GeV−2, identify the assignments of DJ(3000)0, DJ*(3000)0, and D2*(3000)0 as the 31S0, 33S1, and 33P2 states. Our predictions provide concrete, testable targets for LHCb, BESIII, and Belle II.

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. No sentence in this record was written by a model.

abstract compiled · 2026-09-23

The authors' main claim, as the classifier picked it out 0.53

“With only seven parameters determined by fitting the ground state masses, the numerically solved Schr\"odinger equation reproduces the masses of essentially every confirmed $D$ and $D_s$ state to better than $1\%$.”

How the main claim is stated: asserted 1.00

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.20 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.86 · mentions code or data availability 0.02

The abstract, sentence by sentence

This table labels the abstract only (arXiv listing abstract v1). The number is the probability the classifier gave the label.

SentenceRoleThe authors' own workStates the main conclusionStrength
We decode the excited open charm mesons $D$ ($c\bar{q}$, $q=u,d$) and charm strange $D_s$ ($c\bar{s}$) families within a nonrelativistic quark-antiquark potential model based on the Cornell (Coulomb plus linear) potential supplemented by a Gaussian smeared spin-spin interaction. method 0.74 0.90 0.08 asserted 1.00
With only seven parameters determined by fitting the ground state masses, the numerically solved Schr\"odinger equation reproduces the masses of essentially every confirmed $D$ and $D_s$ state to better than $1\%$. result 0.97 0.95 0.20 asserted 1.00
The same wave functions are then employed to get a complete decay analysis including pseudoscalar and vector decay constants ($f_D = 231.8$~MeV, $f_{D_s} = 252.2$~MeV, the latter within $0.4\%$ of the world average), leptonic branching fractions reproducing the measured $\mu\nu$ and $\tau\nu$ modes, electromagnetic $E1$/$M1$ widths, and all kinematically open strong channels in heavy quark effective theory (HQET). result 0.75 0.93 0.15 asserted 1.00
Going beyond width ratios, we extract the full set of HQET couplings $g_H$, $g_S$, $g_T$, $g_X$, $g_Y$, $g_Z$, and $g_R$ directly from the measured total widths and convert our predictions into absolute widths. contribution 0.74 0.94 0.13 asserted 1.00
The $D$ and $D_s$ sector extractions of each coupling agree ($g_T = 0.42$ vs. $0.39$, $g_X = 0.22$ vs. $0.21$, $g_Y = 0.39$ vs. $0.40$), a nontrivial test of heavy quark flavor symmetry, while the pure $c\bar{s}$ picture demands a $1^3P_0$ width nearly two orders of magnitude above the observed $D_{s0}^*(2317)$ bound demanding it to be of exotic nature. result 0.66 0.93 0.27 asserted 0.99
Linear and parallel Regge trajectories in the $(J,M^2)$ and $(n_r,M^2)$ planes, with slopes $\alpha \simeq 0.55-0.65$~GeV$^{-2}$ and $\beta \simeq 0.36 - 0.39$~GeV$^{-2}$, identify the assignments of $D_J(3000)^0$, $D_J^*(3000)^0$, and $D_2^*(3000)^0$ as the $3^1S_0$, $3^3S_1$, and $3^3P_2$ states. result 0.96 0.91 0.12 asserted 1.00
Our predictions provide concrete, testable targets for LHCb, BESIII, and Belle~II. future work 0.92 0.59 0.10 asserted 0.97

What kind of paper the classifier reports this is: theoretical result 0.88 · evidence from simulation or computation 0.81

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  • references and citing sentences
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

How the labels were made

Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 6,676 input tokens.

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. This record as JSON

Figures (3)
Figure 1 of the paper
Figure 1. FIG. 1. Parent and daughter Regge trajectories of the
Figure 2 of the paper
Figure 2. FIG. 2. Parent and daughter Regge trajectories of the
Figure 3 of the paper
Figure 3. FIG. 3. Regge trajectories of the

Figures are the authors', reproduced from the paper.

References (64)
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