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REVIEW 3 minor 124 references

Constraints on New Physics from $B$ mesons

T0 review · 0 major / 3 minor · reviewed 2026-08-14 · deepseek-v4-flash

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Pith's one-line read Persistent anomalies in B-meson decays and mixing may be the first indirect signs of new physics.

desk verdict A solid, honest proceedings review that makes no new claims but accurately maps the 2019 B-decay anomaly landscape; worth a referee's time only to check accuracy. read the letter →

arxiv 1908.09713 v2 pith:5OTKK6AH submitted 2019-08-26 hep-ph

Monika Blanke This is my paper · ORCID
classification hep-ph
keywords BmesondecaysleptonflavouruniversalitychangingneutralcurrentsnewphysicsmixingCKManglegammaepsilon'/epsilonrarekaon
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 proceedings paper argues that several outstanding deviations in flavour physics — the lepton-flavour-universality ratios $R(D^{(*)})$ and $R_{K^{(*)}}$, a nearly $2\sigma$ tension between the directly measured CKM angle $\gamma$ and the value inferred from $\Delta M_d/\Delta M_s$, and a $2.9\sigma$ shortfall of the Standard Model prediction for $\varepsilon'/\varepsilon$ — may be the first indirect signs of new physics beyond the LHC's reach. The author's case rests on flavour-changing neutral currents being loop-, CKM-, and GIM-suppressed in the Standard Model, so even small new-physics contributions would show up in these clean observables. The paper does not claim any single model explains everything; it surveys which simplified new-physics scenarios fit which anomaly and which measurements would discriminate between them. A sympathetic reader would care because these anomalies, if confirmed, would locate new physics in flavour transitions even though no new particle has been discovered directly.

What carries the argument

The central objects are flavour-changing neutral current (FCNC) transitions, which are loop-, CKM-, and GIM-suppressed in the Standard Model and therefore intrinsically sensitive to small new-physics effects. The argument is carried by a set of normalised observables: the lepton-flavour-universality ratios $R(D^{(*)})$ and $R_{K^{(*)}}$, the ratio $\Delta M_d/\Delta M_s$ of neutral $B$-meson mass differences, and the direct-CP-violation parameter $\varepsilon'/\varepsilon$ in $K\to\pi\pi$. Model-independently, new physics is parametrised by effective Hamiltonians with Wilson coefficients such as $C_9^{bs\mu\mu}$, $C_{10}^{bs\mu\mu}$, and the $b\to c\tau\nu$ coefficients $C_V^L$, $C_S^L$, $C_S^R$, $C_T$. For the mixing tension, the load-bearing comparison is between the tree-level measurement of $\gamma$ from $B\to DK$ and the indirect value obtained from $\Delta M_d/\Delta M_s$ together with the lattice QCD ratio $\xi$ of hadronic matrix elements; the author uses this machinery to argue that the resulting pattern would require flavour-non-universal new physics in $\Delta F=2$ transitions, with larger effects in $b\to d$ than in $b\to s$.

What would settle it

A more precise measurement of $\gamma$ from $B\to DK$ at LHCb and Belle II, combined with an independent lattice-QCD determination of $\xi$, would settle the mixing question: if $\gamma$ moves down toward $(63.0\pm2.1)^\circ$ with reduced uncertainty, the new-physics interpretation is supported, whereas if $\gamma$ stays near $74^\circ$ while the lattice average shifts to the HPQCD value, the anomaly vanishes. For $\varepsilon'/\varepsilon$, an improved lattice calculation of the $K\to\pi\pi$ hadronic matrix elements that brings the Standard Model prediction up to $(16.6\pm2.3)\times10^{-4}$ would remove that anomaly; a NA62 or KOTO measurement of $K\to\pi\nu\bar\nu$ at the Standard Model rate would likewise disfavour the new-physics interpretation.

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Extended reading notes

Core claim

The paper's central assessment is that the observed anomalies in charged and neutral current $B$ decays, together with tensions in $\Delta M_d/\Delta M_s$ and $\varepsilon'/\varepsilon$, may be first signs of new physics. For neutral $B$ mixing, using the Fermilab/MILC lattice value of the hadronic ratio $\xi$ to convert $\Delta M_d/\Delta M_s$ into an indirect determination of $\gamma$ yields $\gamma=(63.0\pm 2.1)^\circ$, nearly $2\sigma$ below the LHCb measurement $\gamma=(74.0^{+5.0}_{-5.8})^\circ$; the author states that if future measurements confirm this, it 'would unambiguously imply the presence of NP in $\Delta M_d$ and/or $\Delta M_s$.' She also stresses that this anomaly is not unambiguous, because the HPQCD lattice results show no deviation. In the $b\to c\tau\nu$ sector, $R(D^{(*)})$ sits $3.1\sigma$ above the Standard Model, and in $b\to s\ell^+\ell^-$ global fits a non-zero $C_9^{bs\mu\mu}\simeq -0.97$ or $C_9^{bs\mu\mu}=-C_{10}^{bs\mu\mu}\simeq -0.53$ is preferred at about $6\sigma$. The paper further records a $2.9\sigma$ gap between the measured $\varepsilon'/\varepsilon$ and the recent lattice-based Standard Model prediction.

Load-bearing premise

The load-bearing premise is that the Fermilab/MILC lattice calculation of $\xi$, the ratio of hadronic matrix elements entering $B_d$ and $B_s$ mixing, is the correct input for converting $\Delta M_d/\Delta M_s$ into $\gamma$; if the competing HPQCD value is right instead, the tension disappears and the case for new physics in $B$ mixing collapses.

Editorial extensions

If this is right

  • If the $\Delta M_d/\Delta M_s$ tension is confirmed by more accurate determinations of $\gamma$, new physics must modify $\Delta F=2$ transitions with larger effects in $b\to d$ than in $b\to s$, which cannot be accommodated by constrained minimal flavour violation or minimally broken $U(2)^3$ symmetry.
  • The $R(D^{(*)})$ and $R_{K^{(*)}}$ anomalies can be jointly explained by an $SU(2)_L$-singlet vector leptoquark, which arises naturally from Pati-Salam unification and is least constrained by complementary observables such as $B_s-\bar B_s$ mixing and $B\to K^{(*)}\nu\bar\nu$.
  • Global fits to $b\to s\ell^+\ell^-$ data single out $C_9^{bs\mu\mu}\simeq -0.97$ (or $C_9^{bs\mu\mu}=-C_{10}^{bs\mu\mu}\simeq -0.53$) with about $6\sigma$ pull relative to the Standard Model, and a non-zero $C_{10}^{bs\mu\mu}$ is needed to accommodate the suppression of $B_s\to\mu^+\mu^-$.
  • Rare kaon decays $K\to\pi\nu\bar\nu$ can probe new physics at scales beyond $100$ TeV, and a new-physics contribution to $\varepsilon'/\varepsilon$ is generally correlated with a deviation in $\mathrm{BR}(K_L\to\pi^0\nu\bar\nu)$ from its Standard Model prediction.
  • None of the currently considered simplified models fully resolves all anomalies: the charged Higgs scalar gives the best fit to $b\to c\tau\nu$ data but predicts $\mathrm{BR}(B_c\to\tau\nu)>50\%$ and sits in tension with mono-$\tau$ searches.

Reading between the lines

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

  • One testable extension the review leaves implicit: if the $\Delta M_d$ anomaly reflects a new CP-violating phase of about $\pi/2$ in the $b\to d$ transition, the same phase should generate enhanced CP asymmetries in $b\to d$ penguin-influenced decays such as $B_d\to\pi\pi$; Belle II and LHCb data on these decays could corroborate the mixing signal.
  • Because the $SU(2)_L$-singlet vector leptoquark that fits $R(D^{(*)})$ and $R_{K^{(*)}}$ has TeV-scale mass and flavour non-universal couplings, it also predicts lepton-flavour-violating decays such as $B\to K\tau\mu$; the review notes the related constraints from $K_L\to\mu e$ but does not list $B\to K\tau\mu$ as a headline signature worth searching for.
  • The CKM-hierarchy argument that makes kaon FCNCs the most sensitive probes implies an experimental prioritisation the author does not state: if new physics is to be discovered through flavour, the highest-yield searches may be $K_L\to\pi^0\nu\bar\nu$ and $K^+\to\pi^+\nu\bar\nu$ at KOTO and NA62, rather than further $B$-decay asymmetry measurements.
  • If the $\varepsilon'/\varepsilon$ anomaly and the $K\to\pi\nu\bar\nu$ rates both stay at their Standard Model values while lattice QCD improves, the logical conclusion would be that the current $2.9\sigma$ gap is a hadronic-matrix-element artefact; this is a possible outcome of the review's own logic but not one it emphasises.
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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

0 major / 3 minor

Summary. This is a conference proceedings review by Monika Blanke, based on a talk at LeptonPhoton 2019, summarizing the status of New Physics in flavour-violating B decays. The paper reviews three main areas: (i) neutral B meson mixing, where a roughly 2 sigma tension is reported between the tree-level CKM determination of gamma and the ratio Delta M_d/Delta M_s, a tension that is explicitly flagged as not unambiguous because it depends on the lattice value of xi and disappears with the HPQCD determination; (ii) the charged-current b to c tau nu anomalies in R(D^(*)) and related observables, with a survey of simplified NP models and their tensions; and (iii) the neutral-current b to s l+ l- anomalies, including global-fit pulls and popular leptoquark or Z' explanations. The final section advocates kaon physics, discussing epsilon'/epsilon and K to pi nu nu bar as probes of very high scales. The paper makes no new quantitative claim and its conclusions are explicitly conditional on future measurements and improved lattice inputs.

Significance. As a proceedings review, the paper's value lies in its compact, balanced, and well-referenced status report of active anomalies in flavour physics. It usefully collects the relevant global-fit results, lattice inputs, and simplified-model constraints, and it explicitly flags the fragility of the Delta M_d/Delta M_s tension and the epsilon'/epsilon tension. The central conditional claim, that confirmation of the gamma discrepancy together with the Fermilab/MILC lattice value of xi would unambiguously require NP in Delta M_d and/or Delta M_s, is internally sound given its stated assumptions. The review also credits and cross-checks the author's own work against independent lattice determinations by Fermilab/MILC, RBC/UKQCD, HPQCD, and QCD sum rules. The significance is moderate but appropriate for the venue: a useful, honest snapshot rather than a new quantitative result.

minor comments (3)
  1. [Section 2] The sentence 'Using instead the values of xi found by RBC/UKQCD [11], HPQCD [12], or QCD sum rules [13-17] yields similar results' is difficult to reconcile with the later statement in the same section that the HPQCD results [12] 'show no deviation from the data in either Delta M_d or Delta M_s.' Please rephrase to attribute the 'similar results' statement to RBC/UKQCD and the sum-rule determinations and to state explicitly that HPQCD is the outlier; as written, the two sentences are contradictory.
  2. [References] Reference [75] (Kowalska, Kumar, Sessolo) does not appear to be cited in the body text; either add a citation at the appropriate place in Section 4 or remove the entry from the bibliography.
  3. [Section 5] In the sentence 'Interestingly the presence of an anomaly is supported by dual QCD calculations [105, 112]; however it is not seen with the use of chiral perturbation theory methods [113]', the phrase 'it is not seen' is slightly ambiguous about whether the tension or the anomaly is not seen; consider rephrasing to state explicitly that the chiral perturbation theory analysis does not find a deviation from the Standard Model prediction.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the review is a survey of external data and independent fits; self-citations are traceable to published analyses with external inputs and are not load-bearing.

full rationale

This proceedings article makes no new quantitative claim; its content is a report on external experimental results (LHCb, Belle, BaBar, ATLAS, CMS) and on global fits and lattice calculations by independent groups. The strongest statements are conditional: Section 2 quotes a 2sigma tension between tree-level gamma and the indirect determination from DeltaM_d/DeltaM_s using the Fermilab/MILC value of xi, and states that 'This tension, if confirmed by future more accurate determinations of gamma, would unambiguously imply the presence of NP in DeltaM_d and/or DeltaM_s.' The input xi is external lattice data, and the review explicitly flags the anomaly as 'not unambiguous' because HPQCD [12] sees no deviation and QCD sum rules [17] are compatible with both. The R(D(*)) and b->s l+l- sections report fits by external groups [49] and model scenarios from published papers; the R(Lambda_c) sum-rule prediction in Eq. (3.3) is a model-independent relation applied to external measurements, not a parameter fitted from the predicted observable. The epsilon'/epsilon discussion cites independent lattice and dual-QCD calculations with the experimental value, and notes the chiral perturbation theory countervailing result. Self-citations to the author's own works [7,10,26,38,39,101] are present, but they point to published EPJC/PRD/PRL analyses whose inputs are external experimental and lattice data; none of these citations is used to define away an independent test or to import an unverified uniqueness claim. The review's own caveats identify the load-bearing uncertainties (notably xi and the lattice determination of K->pi pi matrix elements) rather than hiding them. The derivation chain therefore does not reduce to its inputs by construction.

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

This review introduces no new free parameters, axioms beyond those already in the cited literature, or invented entities. The assumptions it adopts from the literature include the SM effective theory and the reliability of lattice QCD matrix elements, the latter explicitly contested within the review itself.

assumptions (2)
  • domain assumption The Standard Model effective Hamiltonian describes the relevant b to s, b to c, and s to d transitions.
    The review interprets deviations from SM predictions as new physics signals; this requires the SM short-distance and long-distance (lattice) inputs to be trustworthy.
  • domain assumption The CKM matrix is described by four real parameters, and tree-level determinations of gamma, Vub, and Vcb are free of new physics contamination.
    Section 2 builds the Delta M_d tension on a tree-level determination of gamma from B to D K and tree-level Vcb, which the review acknowledges is still debated (inclusive versus exclusive).

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Cite this review

Pith. "Pith review of Constraints on New Physics from $B$ mesons." pith.science (2026). https://pith.science/paper/5OTKK6AH

@misc{pith2026190809713,
  author       = {Pith},
  title        = {Pith review of: Constraints on New Physics from $B$ mesons},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/5OTKK6AH}},
  note         = {Machine review of arXiv:1908.09713}
}
abstract

These proceedings review the status of New Physics contributions to flavour violating $B$ decays. The anomalies in charged and neutral current $B$ decays related to lepton flavour universality violation have received a substantial amount of attention over the past years, and we discuss the current status in light of the new data presented earlier this year. We also recall a tension in the neutral $B$ meson mixing observables $\Delta M_d$ and $\Delta M_s$ and in particular their ratio, when compared with their SM predictions obtained using tree-level determinations of the CKM matrix and the recent lattice QCD results for the relevant hadronic matrix elements. Last but not least, we advocate kaon physics as a unique probe of very high energy scales and briefly discuss the current status of $\varepsilon'/\varepsilon$ and $K\to\pi\nu\bar\nu$.

Figures

Figures reproduced from arXiv: 1908.09713 by the authors.

Figure 1
Figure 1. Left: Constraints on the Unitarity Triangle from the measurement of sin 2β (blue), the ratio ∆Md/∆Ms (green), and the tree-level determination of the angle γ (red). The future expected 1◦ sensitivity for γ by LHCb and Belle II is shown in black. Right: SM predictions for ∆Md (red) and ∆Ms (green), normalised to their experimental values, as a function of γ. The LHCb measurement of the latter angle is displayed by th… view at source ↗
Figure 2
Figure 2. Fit results for various two-dimensional scenarios of NP in b → cτν. The grey-shaded areas display the contribution to the branching ratio BR(Bc → τν), while the constraints from LHC mono-τ searches are shown in purple. Figures taken from [39]. data, with modest contributions to the Bc → τν branching ratio (displayed in grey) and in agreement with the high-pT constraints from mono-τ searches (purple region excluded) … view at source ↗
Figure 3
Figure 3. Result of a global fit (red) to b → s` +` − observables in the  C bsµµ 9 ,C bsµµ 10  plane, assuming all other Wilson coefficients to be SM-like. The constraint from the LFU ratios is shown in blue, while the fit to b → sµ +µ − data is displayed in orange. Figure taken from [49]. Turning our attention from the EFT picture to concrete NP models, the most popular ex￾planations include the tree-level exchange of a he… view at source ↗
Figures from the paper (1 more)
Figure 4
Figure 4. Figure 4: Left: Constraints on the scale of NP of the various operators contributing to neutral meson mixing. Figure taken from [103]. Right: The rare decay branching ratios BR(K + → π +νν¯) and BR(KL → π 0νν¯) in the presence of a heavy flavour-violating Z 0 gauge boson with ma…

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