REVIEW 3 major objections 6 minor 1 cited by
New physics effects in $R(K^{(*)})$, $B_s\to\mu^+\mu^-$, and $B^+\to K^+\nu{\bar\nu}$
T0 review · 3 major / 6 minor · reviewed 2026-08-08 · deepseek-v4-flash
Pith's one-line read This paper claims that the Belle II excess in $B^+\to K^+\nu\bar\nu$ and the SM-like values of $R(K^{(*)})$ and $\mathrm{Br}(B_s\to\mu^+\mu^-)$ together select a finite mass window, $3.17\,\mathrm{TeV}\le M_{\rm NP}\le…
desk verdict A genuinely generic NP-scale fit with an honest caveat, but the lower edge of the headline window looks like a scan artifact. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is the one-scale parametrization $C_{9,10}^{\rm NP}=\lvert\alpha_{\rm em}V_{tb}V_{ts}^*\rvert^{-1}A_{9,10}(v/M_{\rm NP})^\alpha$, together with the analogous linear-plus-quadratic expansion of $\mathrm{Br}(B^+\to K^+\nu\bar\nu)$ in powers of $(v/M_{\rm NP})^\alpha$. The power $\alpha$ encodes the type of new physics: $\alpha=2$ corresponds to a tree-level exchange of a heavy mediator, while non-integer $\alpha$ mimics unparticle-like or other exotic scaling. This single scale carries the argument because the observables constrain it from opposite sides: the SM-like $R(K^{(*)})$ and $\mathrm{Br}(B_s\to\mu^+\mu^-)$ push $M_{\rm NP}$ upward, while the $B^+\to K^+\nu\bar\nu$ excess pushes it downward, producing the window.
What would settle it
A future measurement that brings $\mathrm{Br}(B^+\to K^+\nu\bar\nu)$ back into agreement with the SM would erase the upper bound and collapse the claimed window, while a direct search that excludes a $b\to s\mu\mu$ mediator with couplings inside the scanned ranges across the whole $3.17\text{–}14.9\,\mathrm{TeV}$ interval would rule the window out.
Extended reading notes
Core claim
On the paper's own terms, the central claim is that combining these observables selects a narrow window for the new-physics scale rather than only a lower bound. The muonic $b\to s\ell\ell$ Wilson coefficients are written as $C_{9,10}^{\rm NP}=\lvert\alpha_{\rm em}V_{tb}V_{ts}^*\rvert^{-1}A_{9,10}(v/M_{\rm NP})^\alpha$, and the $B^+\to K^+\nu\bar\nu$ branching ratio is expanded through linear and quadratic terms $L$ and $Q$ of the same form. A $\chi^2$ fit over $\alpha\in[0,5]$, $M_{\rm NP}\in[1,50]\,\mathrm{TeV}$, $\lvert A_{9,10}\rvert\le 1$, $\lvert A_L\rvert\le 10$, and $\lvert A_Q\rvert\le 100$ gives a best fit at $\alpha\approx 1.53$ and $M_{\rm NP}\approx 26.4\,\mathrm{TeV}$. Fixing $\alpha=2$, the ordinary tree-level case, the $2\sigma$ allowed region is $3.17\,\mathrm{TeV}\le M_{\rm NP}\le 14.9\,\mathrm{TeV}$; adding $\mathrm{Br}(B^+\to K^+\mu^+\mu^-)$ and the angular observable $P'_5$ widens this to $4.66\,\mathrm{TeV}\le M_{\rm NP}\le 83.7\,\mathrm{TeV}$ and raises the best-fit scale to $47.9\,\mathrm{TeV}$.
Load-bearing premise
The $B^+\to K^+\nu\bar\nu$ excess is assumed to come from the same heavy, tree-level new physics whose scale the scan varies, and the chosen coupling ranges ($\lvert A_{9,10}\rvert\le 1$, $\lvert A_L\rvert\le 10$, $\lvert A_Q\rvert\le 100$) are set by hand; if light new states or an underestimated SM prediction produce the excess, the upper bound on $M_{\rm NP}$ disappears.
Editorial extensions
If this is right
- Any tree-level mediator of $b\to s$ transitions—leptoquark, $Z'$, new scalar—that is to explain the $B^+\to K^+\nu\bar\nu$ excess while keeping $R(K^{(*)})$ and $\mathrm{Br}(B_s\to\mu^+\mu^-)$ SM-like must have mass inside the $3.17\text{–}14.9\,\mathrm{TeV}$ window for the scanned coupling ranges.
- The HL-LHC is expected to exclude leptoquark masses only up to about $1.7\text{–}2.8\,\mathrm{TeV}$, below the window's lower edge, so leptoquarks in this scenario could remain invisible at the HL-LHC, while $Z'$ searches reaching about $6.5\,\mathrm{TeV}$ would probe the window's interior.
- The best-fit $\alpha\approx 1.5$ differs from $\alpha=2$, leaving room for non-ordinary scaling of the new-physics effects; the paper notes that larger $\alpha$ would prefer smaller $M_{\rm NP}$.
- Including $\mathrm{Br}(B^+\to K^+\mu^+\mu^-)$ and $P'_5$ worsens the fit and widens the mass window to $4.66\text{–}83.7\,\mathrm{TeV}$, pushing the preferred scale beyond the direct reach of the HL-LHC.
Reading between the lines
- Read as a mass selector, the $B^+\to K^+\nu\bar\nu$ excess does nearly all the work of bounding $M_{\rm NP}$ from above; if future Belle II data pull the excess toward the SM prediction, the window will widen or disappear, making the $14.9\,\mathrm{TeV}$ ceiling the most fragile number in the analysis.
- The numerical window is set by the chosen coupling ranges as much as by the data: scaling the allowed $\lvert A_L\rvert$ and $\lvert A_Q\rvert$ ranges up would roughly scale the upper bound up, so the window is best read as an order-of-magnitude target rather than a sharp physical threshold.
- The same parametrization could be applied immediately to $B^0\to K^{*0}\nu\bar\nu$ and other $b\to s\nu\bar\nu$ modes with only upper bounds today; these would give independent cross-checks of whether the required neutrino couplings are flavor-universal.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. This paper constructs a generic effective parametrization for new physics in b→s transitions, writing the NP Wilson coefficients as C_NP = N A (v/M_NP)^α for the charged-lepton operators C9, C10 and for the neutrino-sector contributions L and Q. It fits R(K), R(K*), Br(Bs→μ+μ−), and Br(B+→K+νν), and finds that for α=2 the allowed region implies 3.17 TeV ≤ M_NP ≤ 14.9 TeV. Including Br(B+→K+μ+μ−) and P5'(B+→K*+μ+μ−) widens this to 4.66 TeV ≤ M_NP ≤ 83.7 TeV. The paper also compares the window with specific Z′ and leptoquark models and with HL-LHC reach.
Significance. If the claimed mass window were robust, it would provide a useful phenomenological bridge between b→s flavor anomalies and direct LHC searches. The explicit M_NP dependence in Eq. (35) is a practical feature, and the simultaneous treatment of the charged-lepton and neutrino b→s modes is a sensible strategy. The paper is also honest in several places about its limitations, notably the statement in Sec. II that light NP states contributing to B+→K+νν are outside the framework. However, the central quantitative claim is not established: the lower bound in Eq. (40) is not supported by the data once the decoupling limit A9=A10=0 is admitted, and the numerical window as a whole is set by ad hoc coupling ranges. The framework is useful, but the headline window requires substantial revision.
major comments (3)
- [Sec. III, Eq. (40), Fig. 3] The lower bound M_NP ≥ 3.17 TeV is not implied by the fitted observables. Consider α=2, M_NP=1 TeV, A9=A10=0, AL=−0.08, and AQ=0.0015. Equations (35)–(39) then give C9,10^NP=0, L≈+2.4, Q≈+1.4, so Br(B+→K+νν)≈2.1×10−5 while all four R(K^(*)) values and Br(Bs→μ+μ−) sit at their SM predictions. These predictions are within about 1.1σ of the experimental values quoted in Eqs. (2), (3), (6), and (8). This point satisfies every stated scan bound (1 TeV ≤ M_NP ≤ 50 TeV, |A9,10| ≤ 1, |AL| ≤ 10, |AQ| ≤ 100) and should therefore appear in the 2σ allowed region of Fig. 3. Its absence indicates that the lower bound is generated by the numerical grid or by an undocumented Δχ² cut rather than by the data or the physics of the parametrization.
- [Sec. III, chi-square definition] The fit that produces Eq. (40) is not fully specified. The text says only that a χ² fit is implemented, without giving the covariance matrix, the treatment of asymmetric experimental errors, the inclusion of theoretical uncertainties from form factors or CKM parameters, or the Δχ² threshold used to define the 2σ contours. This matters directly for the central claim, because the point described above must be tested against the same criterion. Please provide the explicit χ² function, the error model, and the contour definition used in Figs. 1–5.
- [Sec. III, Eqs. (35), (39), scan ranges] The quantitative window in Eq. (40) is fixed by the ad hoc scan ranges |A9,10| ≤ 1, |AL| ≤ 10, and |AQ| ≤ 100. No perturbativity, naturalness, or model-based argument is given for these ranges, and the paper itself notes that the window varies with the coupling ranges. As a result, the numerical window is a conditional artifact of the scan prior rather than a model-independent prediction. The claim should be reframed, or the analysis should show explicitly how Eq. (40) changes under physically motivated alternatives, for example all couplings bounded by 1 or by 4π.
minor comments (6)
- [Sec. II, Eq. (38)] The expansion Br(B+→K+νν)=Br_SM |1+L+Q| should define more precisely how L and Q are related to the complex neutrino Wilson coefficients in Eq. (37), including whether real coefficients are assumed and how the phase conventions are fixed.
- [Sec. III, text near Fig. 3] There is a typo in the text, “for those vales of α ≳ 1.6”, which should read “values”.
- [Sec. II, text near Eq. (35)] The sentence referring to “the B+ → K ++ missing energy” contains a typographical artifact and should read “B+ → K+ missing energy”.
- [Eq. (4)] The SM predictions used for R(K)L in the experimental bin [0.1,1.1] GeV² are not listed; only R(K)SM for [1.0,6.0] GeV² is given. Please specify the exact SM values used for all experimental bins.
- [Sec. III, Table I] Best-fit values in Tables I and II are quoted without uncertainties; reporting 1σ ranges for the fitted parameters would make the results more useful.
- [Sec. III, Fig. 3] The color coding in Fig. 3 (“free α” vs. “fixed α=2”) is hard to read in grayscale; using different markers or line styles would improve clarity.
Circularity Check
No significant circularity: the MNP window is a fit-derived allowed region, not an out-of-sample prediction, and self-citations are not load-bearing.
full rationale
The paper performs a chi-square fit of its NP parametrization, Eqs. (35) and (39), to the same observables it discusses, and the quoted window 3.17 TeV <= MNP <= 14.9 TeV is the resulting 2-sigma allowed region rather than a prediction from independent data. The derivation chain is self-contained: decay-rate formulas and SM inputs are taken from external literature, the Wilson coefficients are defined explicitly in Eqs. (35) and (39), and the allowed region follows from a numerical scan. The upper bound arises algebraically from needing an enhanced B+ -> K+ nu nubar rate, while the lower bound comes from keeping R(K(*)) and Br(Bs -> mu+ mu-) near their SM values; neither bound is an input that has been renamed as an output. The self-citations [41,42] introduce the same power-law ansatz, but the parametrization is restated and used directly in this paper, not invoked as an external uniqueness theorem or as the sole justification for the central claim. The claim that the allowed window can be used to test specific NP models is a legitimate use of a fit result, not circularity. A possible numerical fragility of the lower bound, e.g. the A9=A10=0 decoupling point at small MNP, would be a correctness or scan-resolution concern rather than a circularity of the derivation.
Assumptions & free parameters
free parameters (7)
- α =
1.53 (best fit); 1.36 with extra observables
- MNP =
26.4 TeV best fit; window 3.17-14.9 TeV for α=2; 4.66-83.7 TeV with extra observables
- A9 =
0.064 (Table I); -0.239 (Table II)
- A10 =
0.115 (Table I); 0.019 (Table II)
- AL =
0.0791 (AL×10=0.791 in Table I); 0.0107 (Table II)
- AQ =
-0.00722 (AQ×10^2=-0.722 in Table I); -0.00991 (Table II)
- coupling scan ranges =
|A9,10|≤1, |AL|≤10, |AQ|≤100
assumptions (5)
- domain assumption NP enters only in the muon sector for C9,C10; Ae_9,10=0
- domain assumption NP in C7 is negligible
- domain assumption The B+→K+νν excess is due to heavy NP described by Eq. (35)/(39), not light NP or SM theory error
- domain assumption SM predictions for R(K), R(K*), Br(Bs→μμ), and Br(B+→Kνν) are correct within quoted errors
- domain assumption Form factors from Ali et al. with exponential parametrization Eq. (17) are used without propagating their uncertainties
Cite this review
Pith. "Pith review of New physics effects in $R(K^{(*)})$, $B_s\to\mu^+\mu^-$, and $B^+\to K^+\nu{\bar\nu}$." pith.science (2026). https://pith.science/paper/5S74JLFL
@misc{pith2026250206370,
author = {Pith},
title = {Pith review of: New physics effects in $R(K^(*))$, $B_s\to\mu^+\mu^-$, and $B^+\to K^+\nu\bar\nu$},
year = {2026},
howpublished = {\url{https://pith.science/paper/5S74JLFL}},
note = {Machine review of arXiv:2502.06370}
}
abstract
We analyze possible new physics (NP) effects on $b\to s$ transition processes, $R(K^{(*)})$, $B_s\to\mu^+\mu^-$, and $B^+\to K^+\nu{\bar\nu}$ decays. Though recent data for $R(K^{(*)})$ and ${\rm Br}(B_s\to\mu^+\mu^-)$ are compatible with the standard model (SM), there are still rooms for NP beyond the SM. Especially ${\rm Br}(B^+\to K^+\nu{\bar\nu})$ is measured to exceed the theoretical predictions. We parameterize the NP effects in a generic way with explicit NP scale $M_{\rm NP}$ and some possible powers of it. For reasonable ranges of NP fermionic couplings we find a window of $3.17~{\rm TeV} \le M_{\rm NP}\le 14.9~{\rm TeV}$ for new particles. When including ${\rm Br}(B^+\to K^+\mu^+\mu^-)$ and the angular observable $P_5'(B^+\to K^{*+}\mu^+\mu^-)$ we have a wider range of the window. Implications of our analysis about specific NP models are discussed.
Figures
Forward citations
Cited by 1 Pith paper
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A Unified Dark Matter Explanation for $\boldsymbol{B^+ \!\to K^+\nu\bar{\nu}}$ and the Super-Kamiokande Antineutrino Excess
A UV-complete complex scalar DM model under gauged U(1)Lμ−Lτ accommodates the SK antineutrino excess, the Belle II B+→K+νν̄ excess, and the DM relic density with one light dark sector.
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