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REVIEW 3 major objections 5 minor 20 references

Probing new physics in $B_s \to (K,K^*)\tau \nu$ and $B \to \pi \tau \nu$ decays

T0 review · 3 major / 5 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read The paper claims that under a common new-physics pattern for $b\to u$ and $b\to c$ transitions, the $\tau$ modes $B_s\to(K,K^*)\tau\nu$ and $B\to\pi\tau\nu$ deviate from the Standard Model, and measuring $P^\tau(q^2)$ can tell $V_L$ and…

desk verdict Useful extension of an existing EFT analysis with first predictions for new tau observables, but the headline discriminator claim is not supported by the paper's own tables. read the letter →

arxiv 1908.06244 v1 pith:DMZ6T35C submitted 2019-08-17 hep-ph

N Rajeev , Rupak Dutta This is my paper · ORCID
classification hep-ph PACS 14.40.Nd13.20.He13.20.-v
keywords Bmesondecayssemileptonictaupolarizationleptonflavoruniversalitytoutransitionsceffectivefieldtheorynewphysics
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper claims that known hints of lepton-flavor non-universality in $b\to c$ and $b\to u$ semileptonic $B$ decays, if they have a common origin, make concrete predictions for $\tau$ modes that have not yet been measured: $B_s\to K\tau\nu$, $B_s\to K^*\tau\nu$, and $B\to\pi\tau\nu$. Using an effective field theory with two vector-type new-physics couplings, $V_L$ and $\tilde{V}_L$, the authors fit the allowed parameter space from $R_D$, $R_{D^*}$, $R_{J/\psi}$, and $R_\pi^l$ at $2\sigma$ and propagate it to these decays. They find that $V_L$ shifts the branching ratios and ratios $R(q^2)$ upward, while $\tilde{V}_L$ also shifts the tau longitudinal polarization $P^\tau(q^2)$; they state that measuring $P^\tau(q^2)$ can easily differentiate the two couplings. The paper also reports averaged polarization and convexity values for the first time for these modes. A sympathetic reader would care because these are complementary observables that could confirm or reject the common new-physics explanation of the $B$ anomalies.

What carries the argument

The engine of the paper is the effective Lagrangian for $b\to u\,\ell\nu$ transitions with vector-type new-physics couplings, Eq. (1), which introduces the Wilson coefficients $V_L$, $V_R$, $\tilde{V}_L$, and $\tilde{V}_R$; only $V_L$ and $\tilde{V}_L$ are kept. The analysis combines this with the standard machinery of three-body semileptonic decay distributions for a pseudoscalar or vector meson final state, producing the $q^2$-dependent differential branching ratio, the ratio of branching ratios $R=B(B_q\to M\tau\nu)/B(B_q\to M\ell\nu)$, the forward-backward asymmetry $A_{FB}^\ell$, the charged-lepton polarization $P^\ell$, and the convexity $C_F^\ell$. A $2\sigma$ scan over the measured $R_D$, $R_{D^*}$, $R_{J/\psi}$, and $R_\pi^l$ maps out the allowed $V_L$ and $\tilde{V}_L$ regions, which are then propagated into the three $\tau$ modes. The discriminative step is that $V_L$ and $\tilde{V}_L$ produce nearly identical rate predictions but different $P^\tau(q^2)$, so polarization acts as the distinguishing observable.

What would settle it

Measure the $q^2$-dependent tau longitudinal polarization $P^\tau(q^2)$ in $B\to\pi\tau\nu$ or $B_s\to K\tau\nu$: $\tilde{V}_L$ pushes it outside the Standard-Model band, while $V_L$ leaves it inside. A high-statistics measurement matching the Standard Model would rule out $\tilde{V}_L$; one that misses both predicted bands would falsify the shared-pattern assumption.

Watch

Extended reading notes

Core claim

The central claim is that the $b\to u$ transitions $B_s\to (K,K^*)\tau\nu$ and $B\to\pi\tau\nu$ are not just bystanders in the flavor anomalies: under the assumption that $b\to u$ and $b\to c$ decays share the same new-physics pattern, the existing $R_D$, $R_{D^*}$, $R_{J/\psi}$, and $R_\pi^l$ constraints force the Wilson coefficients $V_L$ and $\tilde{V}_L$ into ranges that produce visible deviations from the Standard Model in the $\tau$ modes. In the $V_L$ scenario, the differential branching ratio and $R(q^2)$ deviate while angular observables $A_{FB}^\tau$, $P^\tau$, and $C_F^\tau$ stay SM-like; in the $\tilde{V}_L$ scenario the same rate observables deviate and, additionally, $P^\tau(q^2)$ shifts. The paper's explicit conclusion is that a measurement of $P^\tau(q^2)$ can easily differentiate $V_L$ and $\tilde{V}_L$ new-physics contributions.

Load-bearing premise

The load-bearing premise is that the $b\to u$ and $b\to c$ decay sectors share the same new-physics pattern; if the two sectors are not aligned, the predicted $V_L$ and $\tilde{V}_L$ bands for $B_s\to(K,K^*)\tau\nu$ and $B\to\pi\tau\nu$ do not follow from the fitted anomalies.

Editorial extensions

If this is right

  • With $V_L$ constrained by the anomalies, the $q^2$-dependent branching ratios and $R(q^2)$ for $B_s\to K\tau\nu$, $B_s\to K^*\tau\nu$, and $B\to\pi\tau\nu$ rise above their Standard-Model bands.
  • With $\tilde{V}_L$, the same rate observables deviate and the averaged tau polarization changes, for example $\langle P^\tau\rangle=[-0.026,0.217]$ for $B_s\to K\tau\nu$ within the allowed $2\sigma$ range.
  • A measurement of $P^\tau(q^2)$ can distinguish $V_L$ from $\tilde{V}_L$, since only the right-handed-neutrino coupling shifts the polarization.
  • These three modes complement $R_D$, $R_{D^*}$, and $R_{J/\psi}$ as independent tests of the same new physics.

Reading between the lines

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

  • If measurements later show $P^\tau(q^2)$ tracking the Standard Model while rates deviate, that would single out $V_L$ and effectively exclude the right-handed-neutrino vector coupling in this setup.
  • The same scan could be extended to other $b\to u$ tau modes, such as baryonic or excited-meson final states, where the $V_L$/$\tilde{V}_L$ rate degeneracy may be broken differently.
  • If independent fits of the $b\to u$ and $b\to c$ sectors disagree, that would signal that the common-pattern assumption is too strong and that new physics distinguishes the two transitions.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 5 minor

Summary. This paper studies the semileptonic decays B_s -> (K,K*) tau nu and B -> pi tau nu in an effective field theory with vector new physics (NP) couplings V_L and tilde V_L. The authors impose 2 sigma constraints from RD, RD*, RJ/psi, and R_l^pi to obtain allowed ranges for these couplings, using an explicitly stated assumption that b -> u and b -> c transitions share a common NP pattern. They then compute branching fractions, ratios R, forward-backward asymmetries, tau polarization, and convexity parameters for the target modes in the SM and in the presence of V_L and tilde V_L. The central claim is that these modes can probe the NP implied by the B anomalies, and that the tau polarization P_tau(q^2) can distinguish the V_L and tilde V_L scenarios.

Significance. If the underlying model-dependent assumption is accepted, the paper provides a straightforward extension of the standard EFT analysis to a set of decay modes that are experimentally accessible at LHCb and Belle II. The numerical results for integrated and q^2-dependent observables, especially the tau polarization and convexity parameter, are potentially useful predictions. The authors correctly propagate existing constraints and clearly separate SM and NP expectations. However, the significance is limited by the explicitly acknowledged b -> u / b -> c equality, which is not derived or tested, and by the absence of any quantitative sensitivity estimate for the claimed discriminating power of P_tau. The paper does not ship code or machine-checked proofs, but the calculation follows standard, reproducible EFT machinery.

major comments (3)
  1. [Section II.A, Eq. (1)] The effective Lagrangian is labeled as the b -> u transition but contains c-quark fields in every operator (e.g., \bar c_L \gamma^\mu b_L). This is a formal inconsistency in the central definition of the theory. If it is a typographical error, the fields should be u quarks; if not, the relation of this Lagrangian to the b -> u decays studied in the paper and to the b -> c constraints used for the fit is unclear. The authors must correct this and confirm that all subsequent expressions use the intended quark fields.
  2. [Section III.B, first bullet; Table III; Fig. 4] The claim that "the measurement of P^tau(q^2) can easily differentiate V_L and tilde V_L NP contributions" is not supported by the paper's own integrated results. Since V_L does not alter tau polarization, the V_L prediction for P_tau is the SM band. Table III shows that the tilde V_L integrated range for B_s -> K tau nu is [-0.026, 0.217], while the SM 1 sigma range is [-0.035, 0.279]; the tilde V_L band is a strict subset of the SM band. For B_s -> K* tau nu and B -> pi tau nu the overlap is also large. The q^2-dependent plots in Fig. 4 show some separation in certain bins, but no quantitative separation test or experimental sensitivity estimate is provided. The authors should either soften the "easily differentiate" claim or add a quantitative discrimination study, such as chi^2 or expected exclusion power with realistic uncertainties.
  3. [Section I and abstract; Section III.B] The entire NP parameter space for the target modes relies on the "strict model dependent assumption" that b -> u and b -> c transitions have the same NP Wilson coefficients V_L and tilde V_L. This assumption is explicitly admitted, but it is load-bearing: without it, the RD, RD*, and RJ/psi constraints cannot be transferred to B_s -> (K,K*) tau nu and B -> pi tau nu. The paper should state more prominently in the conclusions that all predictions are conditional on this equality, and ideally investigate how the allowed ranges change under modest violations of the assumption (for example, allowing separate b -> u and b -> c coefficients). Without such a stability check, the central prediction is only as strong as the untested assumption.
minor comments (5)
  1. [Table I] The experimental value for B(B -> tau nu) is quoted as (1.09 ± 2.4) × 10^-4; the uncertainty likely should be 0.24 rather than 2.4, and the notation should be fixed.
  2. [Section II.A] The word "psudoscalar" appears to be a typo for "pseudoscalar".
  3. [Section III, figures] The figures contain duplicated panels in Fig. 2 and some labels are not legible in the printed version; the authors should ensure each panel is uniquely labeled and referenced in the text.
  4. [Section II.A, Eq. (2)] The ratio R is defined generically, but the normalization mode is later specified as l = mu. It would be clearer to define R with the muon mode explicitly in Eq. (2).
  5. [Section I, Table I] The text states a "combined deviation of 3.78 sigma" for RD and RD* but the table lists RD and RD* separately without showing the combined uncertainty; a reference to the source of the combined significance would be helpful.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: the Wilson coefficients are constrained by external RD/RD*/RJ/psi/R_l^pi data and then used to compute different B_s->K(*) tau nu and B->pi tau nu observables; the b->u/b->c equality is an explicit assumption, not a reduction.

full rationale

The paper's derivation chain is not circular. In Section III.B, the allowed ranges of V_L and \tilde V_L are obtained by imposing 2-sigma constraints from the measured values of R_D, R_{D*}, R_{J/\psi}, and R_l^\pi, which are external inputs. These fitted couplings are then used to compute branching ratios, ratios of branching ratios, forward-backward asymmetries, tau polarization, and convexity parameters for B_s -> K tau nu, B_s -> K* tau nu, and B -> pi tau nu. The target observables are different from the quantities that entered the fit: they involve different mesons, different form factors, and different kinematic regions, so the predictions are not forced by construction. The 'strict model dependent assumption' that b->u and b->c transitions exhibit a similar new physics pattern is a substantive physical hypothesis explicitly stated in the abstract and Section I, not a tautology or a renaming of inputs. The citation to [20] for the differential decay-rate expressions is a reference to a prior derivation of standard EFT formulas; it does not import the target prediction itself and is independently checkable. Concerns that the P^tau discrimination claim is not quantitatively supported by Table III, and that Eq. (1) contains c-quark fields in a b->u Lagrangian, are correctness or typographical issues rather than circularity. No step reduces a predicted observable to its own fitted input.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The central predictions rest on two scanned Wilson coefficients, the unproven equality of b to u and b to c new physics, the restriction to vector operators, and the reliability of external form factor inputs. No new particles, forces, or conserved quantities are introduced.

free parameters (2)
  • V_L = 2 sigma range from RD, RD*, RJ/psi, R_l^pi constraints; allowed region shown in Fig. 2 left panels
    Left-handed vector Wilson coefficient for b to u / b to c tau nu transitions. It is constrained by existing measured ratios and then scanned to generate the new physics predictions. The numerical range is not tabulated in the text.
  • V_tilde_L = 2 sigma range from the same constraints; allowed region shown in Fig. 2 left panels
    Tilde (right-handed neutrino) vector Wilson coefficient. It is likewise constrained by the b to c and b to u ratio data, and its effect on tau polarization is the advertised discriminator.
assumptions (4)
  • ad hoc to paper b to u and b to c transitions share identical vector new physics Wilson coefficients V_L and V_tilde_L.
    The abstract and Section I call this a strict model dependent assumption. It is what lets RD, RD*, RJ/psi and R_l^pi constraints be transferred to the b to u modes. No symmetry or mechanism is offered.
  • domain assumption Only vector type new physics operators contribute; scalar, tensor and other Lorentz structures are neglected.
    Eq. (1) defines the operator basis, and Section III B scans only V_L and V_tilde_L. If scalar or tensor operators are present, the observable shifts will differ.
  • domain assumption The hadronic form factors for B_s to K, B_s to K* and B to pi from the cited lattice and QCD calculations are reliable across the q^2 range after a 1 sigma random scan.
    Section III A states that a random scan over CKM and form factor inputs is performed, but the form factor parametrizations themselves are not shown in this paper and are taken from the cited literature.
  • domain assumption Standard Model CKM and input parameters are correctly taken from the PDG and cited averages in Table I.
    The central values and uncertainties used for the Standard Model predictions and for the new physics constraints come from external averages, assumed to be accurate.

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Cite this review

Pith. "Pith review of Probing new physics in $B_s \to (K,K^*)\tau \nu$ and $B \to \pi \tau \nu$ decays." pith.science (2026). https://pith.science/paper/DMZ6T35C

@misc{pith2026190806244,
  author       = {Pith},
  title        = {Pith review of: Probing new physics in $B_s \to (K,K^*)\tau \nu$ and $B \to \pi \tau \nu$ decays},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DMZ6T35C}},
  note         = {Machine review of arXiv:1908.06244}
}
abstract

Motivated by the anomalies present in $b \to u$ and $b \to c$ semileptonic decays, we study the corresponding $B_s \to (K,K^*) \tau \nu$ and $B \to \pi \tau \nu$ decays within an effective field theory formalism. Our analysis is based on a strict model dependent assumption, i.e., we assume that $b \to u$ and $b \to c$ transition decays exhibit similar new physics pattern. We give prediction of various observables such as the branching fraction, ratio of branching ratio, lepton side forward-backward asymmetry, longitudinal polarization fraction of the charged lepton and convexity parameter in the standard model and in the presence of vector type new physics couplings.

Figures

Figures reproduced from arXiv: 1908.06244 by the authors.

Figure 1
Figure 1. FIG. 1 [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: In the left panel we show the allowed ranges in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3 [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png]

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Reference graph

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