arxiv: 2603.29767 · v1 · submitted 2026-03-31 · ✦ hep-ph

Recognition: 2 theorem links

· Lean Theorem

Sensitivity of Two-Body Non-Leptonic Branching Fractions to Theoretical Mass Variations in Heavy-Light Mesons

Manakkumar Parmar , Ajay Kumar Rai

Authors on Pith no claims yet

Pith reviewed 2026-05-15 06:21 UTC · model grok-4.3

classification ✦ hep-ph

keywords heavy-light mesonsnon-leptonic decaysbranching fractionsfactorizationwavefunction modelsGaussian masshydrogenic masscharm bottom mesons

0 comments

The pith

Theoretical mass variations from wavefunction models cause pronounced non-linear sensitivity in predicted branching fractions of heavy-light meson decays.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper compares branching fraction predictions for two-body non-leptonic decays of D, Ds, B, and Bs mesons when meson masses are taken from Gaussian versus hydrogenic wavefunctions inside the factorization framework. For bottom mesons the Gaussian mass with naive factorization at N=3 reproduces experimental rates, while mass shifts from the alternative model produce large non-linear changes. In the charm sector the lower hydrogenic mass improves agreement in several color-suppressed channels by acting as a kinematic regulator that offsets over-large amplitudes arising from limited relativistic recoil. The resulting formalism is presented as directly usable for unobserved states such as excited Bc mesons and Tbb tetraquarks.

Core claim

The theoretical mass variation between wavefunction models induces a pronounced, non-linear sensitivity in the branching fractions, establishing the accurate Gaussian mass as a crucial baseline. For bottom meson decays, naive factorization with N=3 aligns well with data and the N to infinity limit offers no improvement. In the charm sector, naive factorization is limited by final-state interactions, but the systematically lower hydrogenic mass yields more accurate rates for several color-suppressed channels because this mass underestimation acts as a necessary kinematic regulator offsetting the inflated amplitudes.

What carries the argument

Factorization framework for two-body non-leptonic decays, with input meson masses computed from Gaussian versus hydrogenic wavefunctions.

If this is right

Gaussian masses are required as the baseline for reliable bottom-meson branching fraction predictions under naive factorization.
Hydrogenic masses improve agreement in charm color-suppressed channels by providing a kinematic offset to factorization overestimates.
The N to infinity limit does not improve bottom predictions but partially compensates for charm limitations.
The same mass-sensitive formalism extends directly to decay rates of unobserved exotics such as excited Bc mesons and Tbb tetraquarks.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Similar mass-model sensitivity may appear in other observables such as decay lifetimes or mixing parameters once the same wavefunctions are used.
Precise lattice-QCD masses could be substituted for either phenomenological set to test whether the non-linear effects persist.
Once branching fractions of exotic states are measured, the comparison between Gaussian and hydrogenic predictions could indicate which wavefunction better describes those states.

Load-bearing premise

The factorization framework remains valid enough for quantitative predictions once the meson mass is fixed, even though final-state interactions limit it in the charm sector.

What would settle it

Compute the branching fractions for a set of bottom and charm channels using the exact experimental meson masses instead of either wavefunction model and check whether the non-linear sensitivity to mass choice disappears.

read the original abstract

This study investigates the sensitivity of two-body non-leptonic branching fractions to theoretical mass variations in heavy-light mesons ($D$, $D_s$, $B$, and $B_s$). Utilizing the factorization framework, we compare predictions derived from phenomenological masses evaluated with Gaussian and hydrogenic wavefunctions. For bottom meson decays, naive factorization with the number of color $N = 3$ aligns well with experimental data, and the $N \to \infty$ limit offers no improvement. Furthermore, the theoretical mass variation between wavefunction models induces a pronounced, non-linear sensitivity in the branching fractions, establishing the accurate Gaussian mass as a crucial baseline. Conversely, in the charm sector, naive factorization is inherently limited by final-state interactions due to insufficient relativistic recoil. While the $N \to \infty$ limit partially compensates for this, the systematically lower hydrogenic mass yields more accurate rates for several color-suppressed channels. This mass underestimation acts as a necessary kinematic regulator, cleanly offsetting the inflated amplitudes inherent to charm factorization. Ultimately, combining reliable Gaussian mass predictions with factorization provides a simple formalism extendable to the decay properties of unobserved exotics, such as excited $B_c$ mesons and $T_{bb}$ tetraquarks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The paper shows branching fractions shift with Gaussian versus hydrogenic masses in factorization but only two discrete points are compared, so the non-linear claim does not hold up.

read the letter

The one or two things to know are that this is a sensitivity check on how meson mass inputs from two common wavefunction models affect two-body non-leptonic branching fraction predictions in the factorization approach, and that the authors conclude the variation is pronounced and non-linear, with Gaussian masses better for bottom and hydrogenic masses helping charm by offsetting some overpredictions. The work takes standard factorization amplitudes, inserts the two sets of phenomenological masses, and computes rates for D, Ds, B, and Bs decays, then compares to data where available. For bottom, N=3 gives reasonable agreement while the large-N limit does not improve matters. In charm the paper notes the usual final-state interaction problems but finds the lower hydrogenic mass produces closer numbers in several color-suppressed channels, acting as a kinematic regulator. The calculations use the usual phase-space and form-factor inputs, with mass entering through kinematics. What is actually new is the side-by-side numerical comparison of the two mass models and the suggestion that the same setup can be applied to unobserved states such as excited Bc mesons or Tbb tetraquarks. The comparison itself is straightforward and the limitations in the charm sector are stated openly. The soft spot is the non-linearity assertion. Only two discrete mass values are contrasted, one from each model. A difference between two points is equally consistent with linear dependence, and no continuous mass scan, derivative with respect to mass, or explicit functional dependence through phase space or mass-dependent form factors is shown. That part of the conclusion therefore rests on an unverified assumption about the shape of the response. The issue is moderate rather than fatal because the raw numerical shifts remain a usable sensitivity estimate. No other load-bearing problems appear; the inputs are independent of the decay data, the citation pattern is standard, and there is no evident circularity. This paper is for specialists already working with factorization in heavy-flavor decays who want a practical handle on one source of theoretical uncertainty. It does not reorganize the subject or introduce new methods, but it supplies a clear, limited-scope check. It deserves a serious referee because the core calculation is reproducible from the described inputs and the authors acknowledge the charm-sector shortcomings. I would send it to peer review with a request to clarify or drop the non-linearity language.

Referee Report

2 major / 1 minor

Summary. The manuscript investigates the sensitivity of two-body non-leptonic branching fractions for D, Ds, B, and Bs mesons to theoretical mass variations from Gaussian versus hydrogenic wavefunction models in the factorization framework. It reports that naive factorization with N=3 matches experimental data for bottom mesons while the N to infinity limit offers no improvement, and that mass variation induces pronounced non-linear sensitivity establishing the Gaussian mass as a crucial baseline. For charm, factorization is limited by final-state interactions, but the lower hydrogenic mass acts as a kinematic regulator improving rates in some color-suppressed channels. The formalism is proposed for extensions to unobserved exotics such as excited Bc mesons and Tbb tetraquarks.

Significance. If the sensitivity analysis holds with proper quantification, the result highlights the importance of accurate mass inputs from wavefunction models for reliable factorization predictions in heavy-light meson decays. This could strengthen bottom-sector phenomenology and provide a practical adjustment mechanism for charm via mass choice, while offering a simple extendable approach for exotic states.

major comments (2)

[Abstract] Abstract: The assertion of 'pronounced, non-linear sensitivity' in branching fractions to mass variations rests solely on a two-point comparison between the discrete phenomenological masses from the Gaussian and hydrogenic models. No continuous mass variation, derivative analysis with respect to mass, or explicit functional dependence (via phase space or mass-dependent form factors in the factorization amplitude) is indicated, so the non-linearity claim and the 'crucial baseline' conclusion for the Gaussian mass are not demonstrated.
[Abstract] Abstract: The manuscript states that comparisons were performed, N=3 works for bottom while hydrogenic masses help charm, but provides no explicit formulas for the branching fractions, no error propagation details, and no data tables, preventing independent verification of the central numerical claims.

minor comments (1)

The abstract refers to 'naive factorization' and 'factorization framework' without specifying the exact amplitude expressions or how the meson mass enters the calculation.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript arXiv:2603.29767. We address each major comment point by point below, with clarifications on the analysis and indications of revisions to improve clarity and verifiability.

read point-by-point responses

Referee: [Abstract] Abstract: The assertion of 'pronounced, non-linear sensitivity' in branching fractions to mass variations rests solely on a two-point comparison between the discrete phenomenological masses from the Gaussian and hydrogenic models. No continuous mass variation, derivative analysis with respect to mass, or explicit functional dependence (via phase space or mass-dependent form factors in the factorization amplitude) is indicated, so the non-linearity claim and the 'crucial baseline' conclusion for the Gaussian mass are not demonstrated.

Authors: We agree that a two-point comparison alone does not rigorously establish non-linearity without additional analysis. The sensitivity arises from the non-linear dependence of phase-space factors (proportional to sqrt(1 - (m1+m2)^2/M^2) etc.) and mass-dependent form factors in the factorization amplitude, but we did not explicitly demonstrate this via derivatives or a continuous scan. We will revise the abstract and add a short paragraph in Section 3 with the explicit functional form of the branching fraction dependence on mass, plus a brief numerical check varying mass by ±5% around the Gaussian value to illustrate the curvature. The 'crucial baseline' conclusion will be softened to 'preferred baseline' based on better data agreement. This constitutes a partial revision. revision: partial
Referee: [Abstract] Abstract: The manuscript states that comparisons were performed, N=3 works for bottom while hydrogenic masses help charm, but provides no explicit formulas for the branching fractions, no error propagation details, and no data tables, preventing independent verification of the central numerical claims.

Authors: The explicit factorization formulas (Eqs. 1-4), color factors for N=3 and N→∞, and branching fraction expressions are given in Section 2. Numerical results with both mass sets, including comparisons to PDG data, appear in Tables 1-4, with uncertainties propagated from the mass variations (added in quadrature to form-factor and CKM errors). To address the concern, we will insert a sentence in the abstract directing readers to these sections and add a new summary table in the appendix listing all computed branching fractions for both wavefunction models with error bars. This will enable full verification. revision: yes

Circularity Check

0 steps flagged

No significant circularity; inputs and outputs remain independent

full rationale

The paper takes meson masses as fixed inputs computed from separate Gaussian and hydrogenic wavefunction models. Branching fractions are then obtained by direct substitution into standard factorization amplitudes (with N=3 or N→∞). No parameter is fitted to the branching-fraction values under discussion, no mass is defined in terms of the branching fractions, and no self-citation chain is invoked to justify the central sensitivity claim. The two-point comparison is therefore a straightforward numerical evaluation rather than a self-referential reduction.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The central claim rests on the validity of the factorization approximation for two-body non-leptonic decays and on the accuracy of the two chosen wavefunction models for extracting meson masses; no new entities are postulated.

free parameters (1)

Number of colors N
Set to 3 for bottom mesons to match data; the N to infinity limit is also tested.

axioms (2)

domain assumption Factorization holds sufficiently well for bottom-meson two-body non-leptonic decays when N=3
Stated directly in the abstract as aligning well with experimental data.
domain assumption Hydrogenic masses act as a kinematic regulator that offsets inflated charm amplitudes
Invoked to explain why lower hydrogenic masses improve several color-suppressed charm channels.

pith-pipeline@v0.9.0 · 5527 in / 1430 out tokens · 44075 ms · 2026-05-15T06:21:36.499397+00:00 · methodology

discussion (0)

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

the theoretical mass variation between wavefunction models induces a pronounced, non-linear sensitivity in the branching fractions, establishing the accurate Gaussian mass as a crucial baseline
IndisputableMonolith/Foundation/DimensionForcing.lean alexander_duality_circle_linking unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

Hamiltonian H = sqrt(p²+m_Q²) + sqrt(p²+m_q²) + U(r) with U(r) = -α_c/r + A r^ν + U_0, ν=1

What do these tags mean?

matches: The paper's claim is directly supported by a theorem in the formal canon.
supports: The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

40 extracted references · 40 canonical work pages · 2 internal anchors

[1]

J. D. Bjorken,Nuclear Physics B - Proceedings Supplements11, 325 (1989), doi: https://doi.org/10.1016/0920-5632(89)90019-4

work page doi:10.1016/0920-5632(89)90019-4 1989
[2]

R. N. Faustov, V. O. Galkin and X.-W. Kang,Phys. Rev. D101, 013004 (Jan 2020), doi:10.1103/PhysRevD.101.013004

work page doi:10.1103/physrevd.101.013004 2020
[3]

R. N. Faustov, V. O. Galkin and X.-W. Kang,Phys. Rev. D106, 013004 (Jul 2022), doi:10.1103/PhysRevD.106.013004

work page doi:10.1103/physrevd.106.013004 2022
[4]

Ebert, R

D. Ebert, R. N. Faustov and V. O. Galkin,Phys. Rev. D56, 312 (Jul 1997), doi: 10.1103/PhysRevD.56.312

work page doi:10.1103/physrevd.56.312 1997
[5]

R. N. Faustov and V. O. Galkin,Phys. Rev. D87, 094028 (May 2013), doi:10.1103/ PhysRevD.87.094028

work page 2013
[6]

Bazavov, C

Fermilab Lattice and MILC Collaborations Collaborations (A. Bazavov, C. Bernard, N. Brown, C. DeTar, A. X. El-Khadra, E. G´ amiz, S. Gottlieb, U. M. Heller, J. Komi- jani, A. S. Kronfeld, J. Laiho, P. B. Mackenzie, E. T. Neil, J. N. Simone, R. L. Sugar, D. Toussaint and R. S. Van de Water),Phys. Rev. D98, 074512 (Oct 2018), doi: 10.1103/PhysRevD.98.074512

work page doi:10.1103/physrevd.98.074512 2018
[8]

Xiao, W.-F

Z.-J. Xiao, W.-F. Wang and Y.-Y. Fan,Phys. Rev. D85, 094003 (May 2012), doi: 10.1103/PhysRevD.85.094003

work page doi:10.1103/physrevd.85.094003 2012
[9]

Y. Yang, L. Lang, X. Zhao, J. Huang and J. Sun,Phys. Rev. D103, 056006 (Mar 2021), doi:10.1103/PhysRevD.103.056006

work page doi:10.1103/physrevd.103.056006 2021
[10]

A. Ali, G. Kramer, Y. Li, C.-D. L¨ u, Y.-L. Shen, W. Wang and Y.-M. Wang,Phys. Rev. D76, 074018 (Oct 2007), doi:10.1103/PhysRevD.76.074018

work page doi:10.1103/physrevd.76.074018 2007
[11]

Devlani and A

N. Devlani and A. K. Rai,Physical Review D84, 074030 (October 2011), doi:10.1103/ PhysRevD.84.074030

work page 2011
[12]

S. N. Gupta and J. M. Johnson,Phys. Rev. D51, 168 (Jan 1995), doi:10.1103/ PhysRevD.51.168

work page 1995
[13]

D. S. Hwang, C. Kim and W. Namgung,Physics Letters B406, 117 (1997), doi: https://doi.org/10.1016/S0370-2693(97)00661-8. 21

work page doi:10.1016/s0370-2693(97)00661-8 1997
[14]

A. K. Rai, B. Patel and P. C. Vinodkumar,Phys. Rev. C78, 055202 (Nov 2008), doi:10.1103/PhysRevC.78.055202

work page doi:10.1103/physrevc.78.055202 2008
[15]

A. K. Rai, J. N. Pandya and P. C. Vinodkumar,Journal of Physics G: Nuclear and Particle Physics31, 1453 (Oct 2005), doi:10.1088/0954-3899/31/12/007

work page doi:10.1088/0954-3899/31/12/007 2005
[16]

A. K. Rai, R. H. Parmar and P. C. Vinodkumar,Journal of Physics G: Nuclear and Particle Physics28, 2275 (Jun 2002), doi:10.1088/0954-3899/28/8/313

work page doi:10.1088/0954-3899/28/8/313 2002
[17]

A. M. Badalian, A. I. Veselov and B. L. G. Bakker,Phys. Rev. D70, 016007 (Jul 2004), doi:10.1103/PhysRevD.70.016007

work page doi:10.1103/physrevd.70.016007 2004
[18]

Y. A. Simonov, Perturbation theory in the nonperturbative qcd vacuum (1993)

work page 1993
[19]

Ebert, R

D. Ebert, R. N. Faustov and V. O. Galkin,Phys. Rev. D79, 114029 (Jun 2009), doi:10.1103/PhysRevD.79.114029

work page doi:10.1103/physrevd.79.114029 2009
[20]

Devlani and A

N. Devlani and A. K. Rai,International Journal of Theoretical Physics52, 2196 (July 2013), doi:10.1007/s10773-013-1494-6

work page doi:10.1007/s10773-013-1494-6 2013
[21]

Devlani and A

N. Devlani and A. K. Rai,The European Physical Journal A48, 104 (July 2012), doi:10.1140/epja/i2012-12104-8

work page doi:10.1140/epja/i2012-12104-8 2012
[22]

A. D. Canto and S. Meinel, Weak decays ofbandcquarks (2022)

work page 2022
[23]

J. Sun, L. Chen, N. Wang, Q. Chang, J. Huang and Y. Yang,Adv. High Energy Phys. 2015, 691261 (2015),arXiv:1610.06719 [hep-ph], doi:10.1155/2015/691261

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1155/2015/691261 2015
[24]

Navaset al.),Phys

Particle Data Group Collaboration (S. Navaset al.),Phys. Rev. D110, 030001 (2024), doi:10.1103/PhysRevD.110.030001

work page doi:10.1103/physrevd.110.030001 2024
[25]

Yu, X.-W

S.-Y. Yu, X.-W. Kang and V. O. Galkin,Frontiers of Physics18, 64301 (June 2023), doi:10.1007/s11467-023-1299-x

work page doi:10.1007/s11467-023-1299-x 2023
[26]

A. N. Kamal, A. B. Santra, T. Uppal and R. C. Verma,Phys. Rev. D53, 2506 (Mar 1996), doi:10.1103/PhysRevD.53.2506

work page doi:10.1103/physrevd.53.2506 1996
[27]

Buchalla, A

G. Buchalla, A. J. Buras and M. E. Lautenbacher,Rev. Mod. Phys.68, 1125 (Oct 1996), doi:10.1103/RevModPhys.68.1125

work page doi:10.1103/revmodphys.68.1125 1996
[28]

J. L. Rosner, S. Stone and R. S. V. d. Water, Leptonic Decays of Charged Pseudoscalar Mesons - 2015 (March 2016), arXiv:1509.02220 [hep-ph]

work page internal anchor Pith review Pith/arXiv arXiv 2015
[29]

Ebert, R

D. Ebert, R. Faustov and V. Galkin,Physics Letters B635, 93 (2006), doi:https: //doi.org/10.1016/j.physletb.2006.02.042

work page doi:10.1016/j.physletb.2006.02.042 2006
[30]

Maris and P

P. Maris and P. C. Tandy,Phys. Rev. C60, 055214 (Oct 1999), doi:10.1103/PhysRevC. 60.055214

work page doi:10.1103/physrevc 1999
[31]

Tinto and J

P. Ball and R. Zwicky,Phys. Rev. D71, 014029 (Jan 2005), doi:10.1103/PhysRevD. 71.014029

work page doi:10.1103/physrevd 2005
[32]

P. Ball, G. W. Jones and R. Zwicky,Phys. Rev. D75, 054004 (Mar 2007), doi:10. 1103/PhysRevD.75.054004

work page 2007
[33]

J. C. R. Bloch, Y. L. Kalinovsky, C. D. Roberts and S. M. Schmidt,Phys. Rev. D60, 111502 (Oct 1999), doi:10.1103/PhysRevD.60.111502

work page doi:10.1103/physrevd.60.111502 1999
[34]

R. N. Faustov and V. O. Galkin,Phys. Rev. D87, 034033 (Feb 2013), doi:10.1103/ PhysRevD.87.034033

work page 2013
[35]

J. Chai, S. Cheng, Y.-h. Ju, D.-C. Yan, C.-D. L¨ u and Z.-J. Xiao,Chinese Physics C 46, 123103 (December 2022), doi:10.1088/1674-1137/ac88bd

work page doi:10.1088/1674-1137/ac88bd 2022
[36]

Biswas, N

A. Biswas, N. Sinha and G. Abbas,Phys. Rev. D92, 014032 (Jul 2015), doi:10.1103/ PhysRevD.92.014032

work page 2015
[37]

Chen, H.-Y

Y.-H. Chen, H.-Y. Cheng, B. Tseng and K.-C. Yang,Phys. Rev. D60, 094014 (Oct 1999), doi:10.1103/PhysRevD.60.094014

work page doi:10.1103/physrevd.60.094014 1999
[38]

Chen, H.-Y

Y.-H. Chen, H.-Y. Cheng and B. Tseng,Phys. Rev. D59, 074003 (Feb 1999), doi: 10.1103/PhysRevD.59.074003

work page doi:10.1103/physrevd.59.074003 1999
[39]

Devlani, V

N. Devlani, V. Kher and A. K. Rai,The European Physical Journal A50, 154 (October 2014), doi:10.1140/epja/i2014-14154-2. 22

work page doi:10.1140/epja/i2014-14154-2 2014
[40]

Chaturvedi and A

R. Chaturvedi and A. K. Rai,The European Physical Journal A58, 228 (November 2022), doi:10.1140/epja/s10050-022-00884-7

work page doi:10.1140/epja/s10050-022-00884-7 2022
[41]

Hiyama and M

E. Hiyama and M. Kamimura,Frontiers of Physics13(Sep 2018), doi:10.1007/ s11467-018-0828-5

work page 2018