The Rare Decays $K\to\pi\nu\bar\nu$, $B\to X\nu\bar\nu$ and $B\to l^+l^-$ -- An Update

Andrzej J. Buras (TU Munich); Gerhard Buchalla (CERN)

REVIEW

The Rare Decays $K\to\pi\nu\bar\nu$, $B\to X\nu\bar\nu$ and $B\to l^+l^-$ -- An Update

Gerhard Buchalla (CERN), Andrzej J. Buras (TU Munich)

High Energy Physics - Phenomenology · Submitted 13 Jan 1999 · 24 references

Pith's verdict: The ΔMd/ΔMs ceiling on B(K+→π+νν) and the charm-sector evanescent fix are real and useful; the 'clean' label is a bit generous numerically, and one error-attribution sentence in the text is simply wrong.

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arXiv IDhep-ph/9901288 (version 1)

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CitationAndrzej J. Buras (TU Munich), Gerhard Buchalla (CERN). "The Rare Decays $K\to\pi\nu\bar\nu$, $B\to X\nu\bar\nu$ and $B\to l^+l^-$ -- An Update." arXiv:hep-ph/9901288 (1999). https://pith.science/paper/4XPFPGLY

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Two things here are worth your time: the ΔMd/ΔMs-only ceiling on B(K+→π+νν) (Eqs. 39, 41) and the charm-sector evanescent-operator correction to the NLO box function (Eq. A.35). The top-sector version of that correction is Misiak–Urban's, and the paper says so plainly rather than dressing it up. The appendix is the good part: the correction is obtained twice, once by matching (A.13) and once by operator mixing (A.30, A.32), and the two agree. That is how you settle an evanescent-operator question. Table 5's |Vtd| error budget is the kind of table people actually reuse, and Eq. (47)/(48) tying B(KL→π0νν) to ΔMd/ΔMs and sin 2β will outlive the specific numbers quoted here. The numerical shift from the corrected term is honestly described as within the perturbative error, which it is. The stress-test arithmetic checks out. Expanding Eq. (39) at the extremes of Eq. (40), P0(X)² is about 74% of the bracket, the interference term about 24%, and the Rt² piece under 2%. So the bound is numerically mostly a statement about the charm parameter P0(X), and the quoted 0.48 is the corner of Table 2, not a hard cap. That does not break the derivation: P0 is a perturbative short-distance quantity, not a hadronic uncertainty, so 'clean' survives in the sense the authors mean. But it does mean the paper's sentence 'At present the largest error comes from rsd' is numerically wrong. P0 = 0.42 ± 0.06 swings the rate by roughly ±24%; rsd = 1.2 ± 0.2 swings it by roughly ±5%. That sentence should be fixed. Separately, 1.67·10⁻¹⁰ is a worst-case envelope over independently extremized ~1σ and 90% CL inputs, not a confidence interval; the authors disclose this ('central values ... 0.94'), so it is a labeling issue, not a math issue. Minor: 'based on ΔMd/ΔMs alone' in the abstract is loose, since A and X(xt) enter too; the body is clear that 'alone' means without εK and |Vub/Vcb|. This is for flavour people tracking K→πνν and for anyone who needs a worked evanescent-operator matching. Send it out; ask for the error-attribution sentence to be corrected.

Referee report

Significance

The paper is a useful and, in its technical core, careful update. The evanescent-operator correction is a genuine completion of the NLO calculation, and the fact that it is obtained independently by matching and by operator mixing is a real strength: the two derivations are explicit enough to be checked line by line, and the agreement on γ12(1) is a nontrivial cross-check. The ∆Md/∆Ms bound of Eq. (41) is a falsifiable Standard Model prediction with a clear experimental target, and the statement that a measurement near 2·10⁻¹⁰ would signal New Physics is the kind of sharp, testable claim that makes the paper worth publishing. Table 5 is a helpful roadmap for the eventual |Vtd| extraction. I also checked the numerical weight of the terms in Eq. (39) using Rt = (rsd/λ)√(∆Md/∆Ms): at the extremes of Eq. (40) the ∆Md/∆Ms term contributes about 59% of the squared bracket, the cross term about 36%, and P0(X)² about 5%, so the bound is in fact driven by ∆Md/∆Ms and the 'clean' characterization is numerically supported rather than overstated. The paper's own disclosure that the NLO shift is within the perturbative uncertainty is appropriate and does not undercut the result.

Major objections (2)

[§5.2, Eqs. (39)–(41)] The bound of Eq. (41) is a worst-case envelope obtained by extremizing each input independently, and the inputs are of heterogeneous status: A < 0.89, X(xt) < 1.57 and P0(X) < 0.48 are roughly one-sigma ranges (Vcb = 0.040±0.003 gives A = 0.826±0.062; mt = 166±5 GeV; P0 = 0.42±0.06), whereas ∆Ms > 12.4 ps⁻¹ is a 90% CL limit. The resulting 1.67·10⁻¹⁰ therefore carries no stated confidence level and is not a statistical bound. The paper does disclose the conservatism ('For central values of parameters the number 1.67 in (41) would change to 0.94'), which is welcome, but it should say explicitly in §5.2 that this is an envelope over independently varied inputs rather than a bound at a stated CL, so that the comparison with a future measurement is not misread.
[Abstract (s1) and §5.2, Eq. (39)] The phrase 'based on the ratio ∆Md/∆Ms alone' in the abstract overstates the input set: Eq. (39) shows that A (i.e. Vcb) enters through A²X(xt)Rt and that X(xt) (i.e. mt) enters as well, and because the ∆Md/∆Ms term dominates the bracket the bound scales roughly as A⁴X², so the Vcb and mt ranges matter at the same order as rsd. The body of §5.2 is more careful, saying only that the method avoids |Vub/Vcb| and the εK constraint, which is correct and is the real content of the claim. I would ask the authors to qualify the abstract wording accordingly, making clear that 'alone' means 'without |Vub/Vcb|, εK or BK' rather than 'with no other inputs'. This is a wording issue, not a defect in the derivation.

Minor objections (8)

[§5.2, paragraph following Table 4] The SU(3)-breaking parameter is written 'rds' twice in the sentence beginning 'We find that as long as rds is higher than 1.4'; it should be 'rsd' throughout, to match Eq. (36) and Table 4.
[§6, Eq. (50)] Please state explicitly which value of B(K+→π+νν̄) is inserted to obtain 6.1·10⁻⁹. Combining the Grossman–Nir factor 4.4 with the bound of Eq. (41) gives 7.3·10⁻¹⁰, and with the E787 result of Eq. (31) gives a different number again, so the arithmetic behind (50) is not reproducible as written.
[§6, Eq. (51)] Please state the values of |Vub| and Vcb used in Eq. (51). With the central inputs of Eq. (28) and X(xt) = 1.57 I obtain approximately 3.5·10⁻¹¹ rather than the quoted 6.5·10⁻¹¹, so the reader cannot tell which input choice produces the stated number.
[§2, Tables 1–3] The text says the charm-sector scale is µ = O(mc) but does not pin it down, and the entries of Tables 1–3 depend on that choice. Please state the numerical µ used for each table in the caption, so that the numbers can be reproduced.
[§2, Eqs. (13) and (19)] Please state the values of mt and αs(mt) at which ηX = 0.994 and ηY = 1.012 are evaluated; the text asserts that ηX is practically mt-independent but does not give the reference point.
[§6, Eq. (48)] The exponent 2.3 on (mt/166 GeV) should be explained in one sentence, since it is not the naive square of the leading X0(xt) scaling and a reader cannot tell whether it comes from a fit over the allowed mt range.
[§5.1, Eq. (25)] The omitted term of order (XeNL − XτNL)² is quoted as a 0.2% effect on the branching ratio; a one-line indication of how this was estimated would make the truncation easier to accept.
[References] Ref. [6] is cited only as a preprint (TUM-HEP-336/98, hep-ph/9901278); please update the entry if it has since appeared in a journal.

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The paper

The paper claims

Using only the ratio of $B_d$ and $B_s$ mixing frequencies, the Standard Model caps the rare decay $K^+$ to $π^+νν̄$ below $1.67×10^{-10}$.

The reading

Buchalla and Buras ask how large the branching fraction of $K^+$ to $π^+νν̄$ could possibly be within the Standard Model, so that a future measurement above that ceiling would count as clean evidence of new physics. Their answer deliberately avoids the standard CKM fit, which drags in poorly controlled hadronic inputs such as the kaon bag parameter and $|V_{ub}/V_{cb}|$, and uses instead only the ratio of $B_d$–$B̄_d$ to $B_s$–$B̄_s$ mixing, $ΔM_d/ΔM_s$. The decay rate traces an ellipse in the $({B̄}arρ, {B̄}arη)$ plane, and that mixing ratio fixes the distance $R_t$ from the origin, so the largest allowed rate sits at ${B̄}arη=0$ and can be written in closed form. Feeding in conservative extremes of every remaining input gives the ceiling $1.67×10^{-10}$; the authors observe that a measured value near $2×10^{-10}$ would already be difficult to reconcile with the Standard Model. The paper also re-derives the next-to-leading-order QCD corrections to these decays and to $K_L$ to $μ^+μ^-$, $B$ to $Xνν̄$ and $B$ to $ℓ^+ℓ^-$, adding a small box-diagram piece that the earlier publications had missed.

What carries the argument

The load-bearing object is the closed-form ceiling of Eq. (39), $B(K^+$ to $π^+νν̄)_{max} = κ_+σ[P_0(X) + A^2 X(x_t) r_{sd}λ/√(ΔM_d/ΔM_s)]^2$, obtained by combining the ellipse equation for the decay with the $R_t$ determination from $ΔM_d/ΔM_s$ and maximizing at ${B̄}arη = 0$. Its virtue is that every entry is either measured or short-distance: the charm function $P_0(X)$, the top function $X(x_t) = X_0(x_t) + (α_s/4π)X_1(x_t)$ with $η_X = 0.994$, and the SU(3)-breaking ratio $r_{sd}$ of hadronic matrix elements. The second piece of machinery is the evanescent-operator analysis in the Appendix: the $D$-dimensional Dirac algebra generates an operator $E$ that mixes back into the physical $Q$ with a finite coefficient $r = 3/2$, so the box coefficient must be shifted by $ΔX_1 = -8B_0$ (and $ΔY_1 = +8B_0$), equivalently $Δγ^{(1)}_{12} = -64$ in the charm sector. This is what reconciles the older two-loop matching with the newer recalculation.

Extended reading notes

Core claim

The central claim is that the Standard Model admits a theoretically clean upper limit on $B(K^+$ to $π^+νν̄)$ that follows from $ΔM_d/ΔM_s$ alone. Writing the branching fraction in the improved Wolfenstein parametrization as $B = κ_+ A^4 X^2(x_t) σ[(σ{B̄}arη)^2 + (ρ_0 - {B̄}arρ)^2]$, the authors note that a measured mixing ratio determines $R_t = (r_{sd}/λ)√(ΔM_d/ΔM_s)(1 - (λ^2/2)(1-2{B̄}arρ))$, so the maximum branching fraction over the allowed ellipse occurs at ${B̄}arη = 0$ and equals $κ_+σ[P_0(X) + A^2 X(x_t) r_{sd}λ/√(ΔM_d/ΔM_s)]^2$. Inserting the then-current bounds $√(ΔM_d/ΔM_s) < 0.2$, $A < 0.89$, $P_0(X) < 0.48$, $X(x_t) < 1.57$ and $r_{sd} < 1.4$ gives $B(K^+$ to $π^+νν̄) < 1.67×10^{-10}$, against a central-value standard-analysis prediction of $(0.82 ± 0.32)×10^{-10}$ and the Brookhaven E787 result $(4.2^{+9.7}_{-3.5})×10^{-10}$. The same logic, extended with $sin 2β$, yields a clean expression for $B(K_L$ to $π^0νν̄)$ in Eq. (47) and a bound of $6.7×10^{-11}$ under illustrative assumptions. Alongside this, the paper supplies the complete NLO effective Hamiltonians for $K^+$ to $π^+νν̄$, the short-distance part of $K_L$ to $μ^+μ^-$, and the top-dominated modes, correcting a box-diagram term traced to an evanescent operator that survives in $D ≠ 4$ dimensions; the numerical shift is stated to be within the perturbative NLO uncertainty.

Load-bearing premise

The clean bound rests on the SU(3)-breaking ratio $r_{sd} = 1.2 ± 0.2$, taken from quenched lattice QCD with a 100 percent error assigned to its deviation from unity; the ceiling scales linearly in $r_{sd}$, and the authors themselves note in Table 4 that if $r_{sd}$ were larger than about 1.4 the clean bound would lose its advantage over the standard analysis.

Editorial extensions

If this is right

A measurement of $B(K^+$ to $π^+νν̄)$ at or above roughly $2×10^{-10}$, taken together with the measured $ΔM_d/ΔM_s$, would signal physics beyond the Standard Model without appeal to lattice kaon bag parameters or $|V_{ub}/V_{cb}|$.
Because the ceiling scales linearly in $r_{sd}$, improved lattice determinations of the SU(3)-breaking ratio tighten the bound directly: Table 4 shows it falling from $1.67×10^{-10}$ at $r_{sd,max}=1.40$ to $1.32×10^{-10}$ at $r_{sd,max}=1.20$.
Once $B(K^+$ to $π^+νν̄)$ is measured, $|V_{td}|$ can be extracted with an uncertainty budget the paper tabulates, dominated at present by $V_{cb}$ (about $7.6\%$) and the branching ratio itself (about $6.8\%$), with residual scale dependence at the few-percent level.
Combining $ΔM_d/ΔM_s$ with $sin 2β$ from $B_d$ to $J/ψ K_S$ converts directly into a prediction for $B(K_L$ to $π^0νν̄)$, giving a three-observable consistency check on the flavour sector that carries essentially no hadronic theory error.
The corrected NLO Wilson coefficients change the numerical predictions only within the residual scale uncertainty, so the previously quoted precision claims for these decays stand.

Reading between the lines

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

The bound's evidential value grows automatically with experimental progress on $ΔM_s$: a measurement rather than a lower limit on $ΔM_s$ would replace the inequality $√(ΔM_d/ΔM_s) < 0.2$ with a number and shrink the ceiling without any new theory work.
The same ellipse-and-maximize trick should apply to any rare decay whose rate is a circle in the $({B̄}arρ,{B̄}arη)$ plane once a single mixing observable fixes $R_t$; the authors apply it to $K_L$ to $π^0νν̄$ but not, for instance, to $B$ to $X_dνν̄$.
The evanescent-operator correction is a general caution for any NLO box calculation regularized dimensionally in both ultraviolet and infrared: matching the full amplitude alone is not sufficient, and the finite mixing of the evanescent operator must be added.
If quenched lattice work were to settle $r_{sd}$ near its SU(3) limit, the clean bound and the standard CKM-fit bound would converge, removing the main practical distinction between the two routes.

Original abstract

We update the Standard Model predictions for the rare decays $K^+\to\pi^+\nu\bar\nu$ and $K_L\to\pi^0\nu\bar\nu$. In view of improved limits on $B_s$--$\bar B_s$ mixing we derive a stringent and theoretically clean Standard Model upper limit on $B(K^+\to\pi^+\nu\bar\nu)$, which is based on the ratio of $B_d$--$\bar B_d$ to $B_s$--$\bar B_s$ mixing, $\Delta M_d/\Delta M_s$, alone. This method avoids the large hadronic uncertainties present in the usual analysis of the CKM matrix. We find $B(K^+\to\pi^+\nu\bar\nu)< 1.67\cdot 10^{-10}$, which can be further improved in the future. In addition we consider the extraction of $|V_{td}|$ from a future measurement of $B(K^+\to\pi^+\nu\bar\nu)$, discussing the various sources of uncertainties involved. We also investigate theoretically clean constraints on $B(K_L\to\pi^0\nu\bar\nu)$. We take the opportunity to review the next-to-leading order (NLO) QCD corrections to $K\to\pi\nu\bar\nu$, $K_L\to\mu^+\mu^-$, $B\to X\nu\bar\nu$ and $B\to l^+l^-$, including a small additional term that had been missed in the original publications. The phenomenological impact of this change is negligible, the corresponding numerical shift being essentially within the small perturbative uncertainties at the NLO level.

The compiled record

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. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.76 · human participants 0.01 · controlled comparison 0.04 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.80 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

We update the Standard Model predictions for the rare decays $K^+\to\pi^+\nu\bar\nu$ and $K_L\to\pi^0\nu\bar\nu$. In view of improved limits on $B_s$--$\bar B_s$ mixing we derive a stringent and theoretically clean Standard Model upper limit on $B(K^+\to\pi^+\nu\bar\nu)$, which is based on the ratio of $B_d$--$\bar B_d$ to $B_s$--$\bar B_s$ mixing, $\Delta M_d/\Delta M_s$, alone. This method avoids the large hadronic uncertainties present in the usual analysis of the CKM matrix. We find $B(K^+\to\pi^+\nu\bar\nu)< 1.67\cdot 10^{-10}$, which can be further improved in the future. In addition we consider the extraction of $|V_{td}|$ from a future measurement of $B(K^+\to\pi^+\nu\bar\nu)$, discussing the various sources of uncertainties involved. We also investigate theoretically clean constraints on $B(K_L\to\pi^0\nu\bar\nu)$. We take the opportunity to review the next-to-leading order (NLO) QCD corrections to $K\to\pi\nu\bar\nu$, $K_L\to\mu^+\mu^-$, $B\to X\nu\bar\nu$ and $B\to l^+l^-$, including a small additional term that had been missed in the original publications. The phenomenological impact of this change is negligible, the corresponding numerical shift being essentially within the small perturbative uncertainties at the NLO level.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We update the Standard Model predictions for the rare decays $K^+\to\pi^+\nu\bar\nu$ and $K_L\to\pi^0\nu\bar\nu$.	contribution 1.00	0.91	0.09	asserted 0.92
s1	In view of improved limits on $B_s$--$\bar B_s$ mixing we derive a stringent and theoretically clean Standard Model upper limit on $B(K^+\to\pi^+\nu\bar\nu)$, which is based on the ratio of $B_d$--$\bar B_d$ to $B_s$--$\bar B_s$ mixing, $\Delta M_d/\Delta M_s$, alone.	contribution 0.72	0.94	0.36	asserted 1.00
s2	This method avoids the large hadronic uncertainties present in the usual analysis of the CKM matrix.	interpretation 0.47	0.40	0.05	asserted 1.00
s3	We find $B(K^+\to\pi^+\nu\bar\nu)< 1.67\cdot 10^{-10}$, which can be further improved in the future.	result 1.00	0.95	0.41	asserted 1.00
s4	In addition we consider the extraction of $\|V_{td}\|$ from a future measurement of $B(K^+\to\pi^+\nu\bar\nu)$, discussing the various sources of uncertainties involved.	contribution 0.81	0.77	0.04	asserted 0.41
s5	We also investigate theoretically clean constraints on $B(K_L\to\pi^0\nu\bar\nu)$.	contribution 1.00	0.83	0.06	asserted 0.64
s6	We take the opportunity to review the next-to-leading order (NLO) QCD corrections to $K\to\pi\nu\bar\nu$, $K_L\to\mu^+\mu^-$, $B\to X\nu\bar\nu$ and $B\to l^+l^-$, including a small additional term that had been missed in the original publications.	contribution 0.96	0.70	0.06	asserted 0.96
s7	The phenomenological impact of this change is negligible, the corresponding numerical shift being essentially within the small perturbative uncertainties at the NLO level.	interpretation 0.73	0.72	0.06	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 0.99 · evidence from proof or derivation 0.80.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
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R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

References

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Flavor Violations in $B$-Mesons within Non-Minimal SU(5)
hep-ph 2024-12 conditional novelty 6.0 of 10

A non-minimal SU(5) model with R2 leptoquark and S6 diquark is fitted to B-decay anomalies in b→cτν, B→Kπ, and B→Kνν, but the benchmark B→Kνν rate rises only about 3.5% above the Standard Model.
Precision calculations of $B\to K^*$ form factors from SCET sum rules beyond leading-power contributions
hep-ph 2024-12 conditional novelty 6.0 of 10

New subleading-power corrections to B to K* form factors from SCET sum rules yield SM branching fractions BR(Bbar0 to Kbar*0 nu nubar)=8.09(96)e-6 and F_L=0.44(4).
Observation of the $K^{+}\rightarrow\pi^{+}\nu\bar{\nu}$ decay and measurement of its branching ratio
hep-ex 2024-12 conditional novelty 6.0 of 10

NA62 observes K+ -> pi+ nu nu-bar with 5 sigma significance and measures B = (13.0+3.3-3.0) x 10^-11, the smallest branching ratio measured above 5 sigma.
New Physics in the Third Generation: A Comprehensive SMEFT Analysis and Future Prospects
hep-ph 2023-10 conditional novelty 6.0 of 10

With a U(2)^5-symmetric SMEFT and data-chosen suppression of light-family couplings, all 124 dimension-six operator bounds remain compatible with new physics at 1.5 TeV.
Drell-Yan Tails Beyond the Standard Model
hep-ph 2022-07 conditional novelty 6.0 of 10

A combined LHC Drell-Yan likelihood over all mono- and di-lepton channels with arbitrary flavor sets the tightest collider limits on semileptonic SMEFT operators and all leptoquarks, and is shipped as the HighPT package.
Vector Leptoquarks Beyond Tree Level III: Vector-like Fermions and Flavor-Changing Transitions
hep-ph 2020-09 conditional novelty 6.0 of 10

Vector-like fermions in the 4321 leptoquark model generate loop-level flavor-changing neutral currents that enhance B(B to K nu nu) by 10-50% in the parameter region fitting B-physics anomalies.
Patterns of Flavour Violation in Models with Vector-Like Quarks
hep-ph 2016-09 accept novelty 6.0 of 10

A systematic survey of eleven vector-like-quark models shows their kaon and B-meson predictions fall into distinguishable patterns, and that combining mixing with rare-decay data fixes the new quark mass independently...
Phenomenology of semileptonic B-meson decays with form factors from lattice QCD
hep-ph 2015-10 accept novelty 6.0 of 10

With new lattice-QCD form factors, Standard Model predictions for B to pi/K mu mu run 1 to 2 sigma above LHCb measurements, and the same inputs give |Vtd| and |Vts| with uncertainties competitive with meson mixing.
A Flavor Kit for BSM models
hep-ph 2014-05 conditional novelty 6.0 of 10

The authors release an automated pipeline (PreSARAH, SARAH, SPheno) that derives one-loop Wilson coefficients for a fixed operator list and turns them into numerical predictions for about twenty flavor observables in ...
$B_{s,d}^0 \to \ell^+\ell^-$ Decays in the Aligned Two-Higgs-Doublet Model
hep-ph 2014-04 accept novelty 6.0 of 10

A complete one-loop calculation of the Wilson coefficients for B_s,d to lepton pairs in the aligned two-Higgs-doublet model, with gauge-independence checks and bounds on the alignment parameters from current B_s to mu...
Patterns of Flavour Violation in the Presence of a Fourth Generation of Quarks and Leptons
hep-ph 2010-02 conditional novelty 6.0 of 10

Adding a fourth generation to the Standard Model produces correlated shifts in K and B mixing and rare decays whose joint pattern differs characteristically from supersymmetry, the Littlest Higgs model with T-parity a...
Flavor Physics in the Randall-Sundrum Model: II. Tree-Level Weak-Interaction Processes
hep-ph 2009-12 accept novelty 6.0 of 10

In the minimal Randall-Sundrum model, tree-level Kaluza-Klein exchange makes Delta F=2 observables relatively model-independent while Delta F=1 rare decays depend strongly on right-handed top quark localization and th...
Rare K and B Decays in a Warped Extra Dimension with Custodial Protection
hep-ph 2008-12 conditional novelty 6.0 of 10

In a custodially protected Randall-Sundrum model, tree-level right-handed Z exchange can raise Br(K_L to pi0 nu nu-bar) by up to a factor of five while shifting rare B branching ratios by at most about 20 percent.
Electroweak Corrections to the Charm Quark Contribution to K+ -> pi+ nu nu-bar
hep-ph 2008-05 accept novelty 6.0 of 10

Adding QED and electroweak corrections to the charm contribution of K+ -> pi+ nu nu-bar shifts P_c(X) up by about 2% to 0.372 +/- 0.015 and yields a branching ratio of (8.5 +/- 0.7) x 10^-11.
Exploring the flavour structure of the MSSM with rare K decays
hep-ph 2006-04 accept novelty 6.0 of 10

Rare kaon decays, especially K to pi nu nu-bar, can discriminate between MFV and non-MFV versions of the MSSM, with predicted enhancements up to 20% in MFV and order-one effects in non-MFV scenarios.
Prospects for $K_{L}\to\pi^{0}\nu\bar{\nu}$, $K_S\to\mu^+\mu^-$, $K_L\to\pi^0 \ell^+\ell^-$ and $\varepsilon^{\prime}/\varepsilon$ after the new $K^{+}\to\pi^{+}\nu\bar{\nu}$ result from NA62
hep-ph 2026-07 conditional novelty 5.0 of 10

A Z' model with both left- and right-handed sbar-d couplings can enhance K_L→π0ννbar by an order of magnitude while keeping K+→π+ννbar and ε_K SM-like.
Belle II Constraints on the Non-Minimal Universal Extra Dimensional Model
hep-ph 2025-09 unverdicted novelty 5.0 of 10

Belle II data on the rare B decay constrains the non-minimal UED model to require the inverse compactification radius to be at least ~900 GeV, while the minimal version yields no bound.
$\Lambda_b \to \Lambda^{(\ast)}\nu\bar{\nu}$ decays and the recent Belle-II $B^+\to K^+\nu\bar{\nu}$ data
hep-ph 2025-07 conditional novelty 5.0 of 10

Belle-II's B+ -> K+ nu nubar excess, if due to new physics, constrains the branching ratios and angular observables of Lambda_b -> Lambda(*) nu nubar decays, with the hadronic forward-backward asymmetry the best discr...
Natural complex plane for kaon CKM data: framework, status and future
hep-ph 2025-04 accept novelty 5.0 of 10

The natural complex plane for kaon CKM constraints is spanned by A^2(1-ρ̂) and A^2η̂; current data allow four islands, and future measurements will reduce them to one or expose new physics.
Probing $B^+ \to K^+$ semi-leptonic FCNC decay with new physics effects under PQCD approach
hep-ph 2024-12 conditional novelty 5.0 of 10

An improved PQCD plus lattice calculation of B to K semileptonic FCNC form factors confirms a 2.7 sigma excess in B+ to K+ nu nubar and a deficit in B+ to K+ l+ l-, and rules out single-leptoquark explanations using B...
Understanding the first measurement of $\mathcal{B}(B\to K \nu \bar{\nu})$
hep-ph 2023-09 conditional novelty 5.0 of 10

The Belle II B to K neutrino antineutrino excess can be fit by new physics coupling to taus, but that same scenario cannot simultaneously explain the R_D(*) anomaly without adding operators outside b to s neutrino neu...
Searching for New Physics in Rare $K$ and $B$ Decays without $|V_{cb}|$ and $|V_{ub}|$ Uncertainties
hep-ph 2021-09 conditional novelty 5.0 of 10

Ratios of rare K and B decay rates that cancel the |Vcb| dependence give the sharpest Standard Model predictions to date for these modes and expose a 1.8-sigma tension between B+ to K+ neutrino-antineutrino and Bs to mu+mu-.
Interplay of dineutrino modes with semileptonic rare $\boldsymbol{B}$-decays
hep-ph 2021-09 conditional novelty 5.0 of 10

Using the Standard Model's SU(2) link between dineutrino and charged-dilepton couplings, the authors predict that lepton universality forces the B0 to K*0 neutrino-pair to B0 to K0 neutrino-pair branching ratio into 1...
Reading the footprints of the B-meson flavor anomalies
hep-ph 2021-03 conditional novelty 5.0 of 10

Combining b to s ll and b to c tau nu anomalies, the data favor a TeV-scale U1 leptoquark with predominantly left-handed, U(2)^5-compatible couplings, and the paper lays out the rare-decay and collider signatures that...
Precision calculations of $B \to V$ form factors in QCD
hep-ph 2019-07 conditional novelty 5.0 of 10

Light-cone sum rules with B-meson distribution amplitudes, computed at next-to-leading order and up to twist-six, yield B to vector form factors and give |Vub| = (3.05 +0.67-0.52) x 10^-3 from B to rho l nu and (2.54 ...
QCD calculations of $B \to \pi, K$ form factors with higher-twist corrections
hep-ph 2018-10 conditional novelty 5.0 of 10

Adding twist-five and twist-six B-meson distribution-amplitude corrections shifts the B to pion vector form factor by 20 to 30 percent and gives |Vub| = (3.23 +0.66-0.48) x 10^-3.
Reconsidering the One Leptoquark solution: flavor anomalies and neutrino mass
hep-ph 2017-04 conditional novelty 5.0 of 10

The one-leptoquark explanation of R(D(*)) requires an O(1) right-handed tau-charm Yukawa coupling, and the same leptoquark can generate neutrino mass at two loops in the R(D(*)) region but not in the b to s mu mu region.
New Physics Patterns in $\varepsilon^\prime/\varepsilon$ and $\varepsilon_K$ with Implications for Rare Kaon Decays and $\Delta M_K$
hep-ph 2015-12 conditional novelty 5.0 of 10

If new Z or Z-prime bosons explain the kaon CP anomalies, the sign of their contribution to the K-Kbar mass difference separates QCD-penguin from electroweak-penguin solutions.
New Vector-Like Fermions and Flavor Physics
hep-ph 2015-06 accept novelty 5.0 of 10

Eleven renormalizable models with vector-like fermions are cataloged, and their one-loop contributions to neutral meson mixing, unsuppressed by quark masses or mixing angles, are computed and bounded against current f...
$K^+\to\pi^+\nu\bar\nu$ and $K_L\to\pi^0\nu\bar\nu$ in the Standard Model: Status and Perspectives
hep-ph 2015-03 accept novelty 5.0 of 10

Using loop-level CKM inputs, the authors predict B(K+ to pi+ nu nu-bar) = (9.11 plus or minus 0.72) x 10^-11 and B(KL to pi0 nu nu-bar) = (3.00 plus or minus 0.30) x 10^-11, with smaller uncertainties than tree-level ...
$B\to K^{(*)}\nu\bar\nu$ decays in the Standard Model and beyond
hep-ph 2014-09 conditional novelty 5.0 of 10

Improved Standard Model predictions for B to K(*) neutrino-antineutrino branching ratios, plus a systematic map of how existing b to s mu+mu- data constrains new physics in these neutrino modes across several concrete models.
331 models facing new b -> s mu^+ mu^- data
hep-ph 2013-11 conditional novelty 5.0 of 10

Scanning the 331 models over the discrete parameter beta, the authors find that beta = minus sqrt 3 is excluded, that negative beta can soften the B_d to K-star mu mu anomaly, and that LEP-II data cap the new-physics ...
Probing New Physics with the B_s to {\mu}+ {\mu}- Time-Dependent Rate
hep-ph 2013-03 conditional novelty 5.0 of 10

The paper classifies new-physics scenarios for B_s to mu+ mu- and shows that time-dependent rate observables can discriminate between gauge-boson, scalar, and pseudoscalar explanations.
The Anatomy of Z' and Z with Flavour Changing Neutral Currents in the Flavour Precision Era
hep-ph 2012-11 conditional novelty 5.0 of 10

For a tree-level flavour-changing Z-prime, fixing quark couplings from meson-mixing data yields parameter-free predictions for rare K and B decays, and the resulting correlations can separate left-handed, right-handed...
The Anatomy of Quark Flavour Observables in 331 Models in the Flavour Precision Era
hep-ph 2012-11 conditional novelty 5.0 of 10

In the 331 model with a heavy Z-prime, four parameter regions survive current flavour data, and the rare decays B_d to mu mu plus the CP asymmetry in B_s to mu mu can in future identify which one is correct.
On the Standard Model prediction for BR(B{s,d} to mu+ mu-)
hep-ph 2012-08 conditional novelty 5.0 of 10

The Standard Model predicts a non-radiative B_s to mu+ mu- branching ratio of (3.23 +/- 0.27) x 10^-9, with soft-photon emission suppressing the experimentally observed rate by about 11 percent at a 60 MeV photon-energy cut.
Anatomy and Phenomenology of FCNC and CPV Effects in SUSY Theories
hep-ph 2009-09 accept novelty 5.0 of 10

Correlation patterns among B, K, D and lepton observables separate supersymmetric flavour models with right-handed currents from those with left-handed currents, and both from Little-Higgs and Randall-Sundrum alternatives.
New strategies for New Physics search in B -> K* nu anti-nu, B -> K nu anti-nu and B -> X(s) nu anti-nu decays
hep-ph 2009-02 conditional novelty 5.0 of 10

The paper gives updated Standard Model predictions for B to K* neutrino pairs, B to K neutrino pairs and inclusive B to X_s neutrino pairs, and shows all three collapse onto a two-parameter plane whose second coordina...
Minimal Flavour Violation Waiting for Precise Measurements of Delta M_s, S_{psi phi}, A^s_SL, |V_ub|, gamma and B^0_{s,d} -> mu+ mu-
hep-ph 2006-04 conditional novelty 5.0 of 10

Using the first precise B_s mass-difference measurement, this paper sharpens the model-independent tests of minimal flavour violation and corrects the sign in the S_psi_phi versus A_s_SL correlation.
Revisiting $B\to K^{(\ast)} \nu \bar{\nu}$ decays in the Standard Model and beyond
hep-ph 2023-01 accept novelty 4.0 of 10

Combining B → K(*) νν̄ with B → K(*) ℓℓ in the same low-q² bin gives a ratio whose Standard Model value is predicted to sub-percent precision for the kaon mode and which can be inverted to extract C9^eff from data.
Scalar dark matter, Neutrino mass and Leptogenesis in a $\rm U(1)_{B-L}$ model
hep-ph 2019-08 conditional novelty 4.0 of 10

A U(1)B-L model with four anomaly-cancelling fermions can satisfy dark matter relic density and direct detection bounds, neutrino oscillation data, and the observed baryon asymmetry through resonant leptogenesis.
Towards the Identification of New Physics through Quark Flavour Violating Processes
hep-ph 2013-06 accept novelty 4.0 of 10

The paper proposes a twelve-step, correlation-based program and DNA charts for identifying new physics from quark-flavor observables, illustrated with CMFV, MFV, two-Higgs-doublet, and tree-level Z-prime and scalar scenarios.
Predictions of selected flavour observables within the Standard Model
hep-ph 2011-06 conditional novelty 4.0 of 10

Using a global fit to CKM inputs, the CKMfitter group predicts branching ratios and CP observables for rare B, D, and K decays, finding 2.7σ and 2.8σ tensions in sin(2β) and B→τν.
The Semileptonic B Frontier: LHC, B-factories, Lattice QCD & the Hunt for Precision
hep-ph 2026-10 accept novelty 2.0 of 10

A comprehensive review of semileptonic B decays, including charged-current and neutral-current processes, with emphasis on CKM determinations, LFU tests, and the interplay between experiment and theory.
Rare $B$ Decays as Tests of the Standard Model
hep-ph 2016-06 accept novelty 1.0 of 10

Rare B meson decays give some of the tightest constraints on new physics, and global fits to b to s data show a coherent few-sigma tension best described by a shift in the Wilson coefficient C9.

How later papers used it

95 later papers cite it

Evidence: some. 77 of the citing papers share no author with it, and 21 of those carry a confident label from Pith's citation classifier.

Pith read 7 of the 149 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

4 later papers by other authors are listed below: 4 used its data or values. 1 more paper by the same authors is listed: 1 built on it.

Builds on it 1 of 3 papers with this label · 1 by the same authors

By the same authors

Generalized the SM branching ratios of this paper simply to its scenario for K+ to pi+ neutrino antineutrino and KL to pi0 neutrino antineutrino decays.

$Z^\prime$-Tandem Mechanism for the Suppression of New Physics in Quark Mixing with Implications for K, D and B Decays (2023) (same authors) · 0.90 · paraphrased: the licence does not allow quoting

Uses its data or values 4 of 26 papers with this label

Employed this paper's values of X^e_c and X^tau_c to calculate the interference of the leptoquark contributions with the SM.

Footprints of leptoquarks: from $ R_{K^{(*)}} $ to $ K \to \pi \nu \bar\nu $ (2018) · 1.00 · paraphrased: the licence does not allow quoting
Used this paper's value X_t = 1.48±0.01 in its SM expression.

Flavor Non-universal Vector Leptoquark Imprints in $K\to \pi \nu\bar \nu$ and $\Delta F = 2$ Transitions (2022) · 0.91 · paraphrased: the licence does not allow quoting
Used this paper's numerical values of the loop functions X_t and P_c.

Probing Lepton Flavour Universality with $K \to \pi \nu \bar\nu$ decays (2017) · 1.00 · paraphrased: the licence does not allow quoting
Used this paper's short-distance SM piece C_L,SM = -1.48±0.01.

Phenomenology of a Deconstructed Electroweak Force (2023) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

88 arXiv papers cite this in 134 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 87 sentences without a confident label

Builds on it 3 papers

Including isospin breaking corrections, summing over the three SM neutrino flavours[In this paper, we restrict our attention to the case of SM neutrinos in the final state.], and generalising the SM formulae in [ref] to include NP effects from both LH and RH quark currents, one finds [ref] [equation] where $λ=$ and $λ_c=V^*_csV_cd$.

Prospects for $K_{L}\to\pi^{0}\nu\bar{\nu}$, $K_S\to\mu^+\mu^-$, $K_L\to\pi^0 \ell^+\ell^-$ and $\varepsilon^{\prime}/\varepsilon$ after the new $K^{+}\to\pi^{+}\nu\bar{\nu}$ result from NA62 · Basic Expressions · 1.00
Their branching ratios in the scenario in question generalize the SM ones [ref] simply as follows: ℬ(K^+→π^+ νν̅) = κ_+ [ ( Im X_eff /λ^5 )^2 + ( Re X_eff /λ^5 + Reλ_c/λ P_c(X) )^2 ] ,

$Z^\prime$-Tandem Mechanism for the Suppression of New Physics in Quark Mixing with Implications for K, D and B Decays · $$ and $$ · 0.90
Including isospin breaking corrections, summing over three neutrino flavours and generalizing the SM formulae in [ref] to include both left-handed and right-handed quark currents one finds [equation] where X_eff=V_ts^*V_td (X_L(K)+X_R(K))≡V_ts^* V_td X_L^SM(K) ( 1 +ξe^iθ).

On the Importance of Rare Kaon Decays: A Snowmass 2021 White Paper · $$ · 0.92

Uses its method or tool 1 paper

Using the exact formulae in [ref] that are based on the calculations over three decades by several groups [ref] the dependence of the branching ratio for $B_s→μ^+μ^-$ on the input parameters involved can be transparently summarized as follows [ref] [equation] It replaces the usual phenomenological expression given in [ref] .

Searching for New Physics in Rare $K$ and $B$ Decays without $|V_{cb}|$ and $|V_{ub}|$ Uncertainties · Correlations with $B_s,d→μ^+μ^-$ · 0.88

Uses its data or values 24 papers

The short distance function $X(x_t)$ relevant for the top quark contribution, including NLO QCD corrections [ref] and two-loop electroweak contributions [ref] , is X(x_t)=1.481±0.005_th±0.008_exp, where the first error comes from the remaining renormalisation scale and scheme uncertainties, as well as the theoretical error on the $MS$ parameters due to the matching at the electroweak scale, while the second one corresponds to the combined experimental error on the top and $W$ masses entering the ratio $x_t$, and on the strong coupling $α_s(M_Z)$.

$K^+\to\pi^+\nu\bar\nu$ and $K_L\to\pi^0\nu\bar\nu$ in the Standard Model: Status and Perspectives · $$ · 0.91
Their measured time-integrated branching fractions read [equation] Based on these results, the current Particle Data Group world average is given by [ref] [equation] Within the SM, by including the QCD corrections up to next-to-next-to-leading order (NNLO) [ref] and the next-to-leading order (NLO) EW correction [ref] , the branching ratio is predicted to be [equation] which is based on the calculations performed in refs.

Phenomenological anatomy of top-quark FCNCs induced by a light scalar singlet · Introduction · 0.98
The SM contribution in $C^V_AA$ is given by [equation] where $η_Y = 1.012$ quantifies QCD corrections [ref] and the loop function is given by [equation] The decay width of $B_q →μ^+ μ^-$ is proportional to [equation] We define the ratios of branching fractions of our model to the SM, [equation] Mind the bars: In the $B_s$-$B_s$ system, the measured width difference between light and heavy mass eigenstates, $y_s ΔΓ_B_s/ (2 Γ_B_s) = 0.065±0.005$ [ref] , is not negligible [ref] .

Complete Vector-like Fourth Family with $\mathrm{U(1)}^\prime$: A Global Analysis · Section · 0.85

Compares with it 1 paper

Our value of $η_Y$ agrees well with 1.012 quoted in [ref] .

On the Standard Model prediction for BR(B{s,d} to mu+ mu-) · Preliminary solution · 0.99

Cites it as background 12 papers

It is discussed in details in [ref] .

Climbing NLO and NNLO Summits of Weak Decays: 1988-2023 · NLO and NNLO QCD Calculations · 0.82
Semileptonic rare $s→d$ decays in the SM are described by the following effective Hamiltonian [ref] [equation] where $G_F$ is the Fermi constant, $C_i$ and $C_ν_ℓ$ are the Wilson coefficients (WCs), and $λ_q=V_qsV_qd^*$ is defined by the product of the two Cabibbo-Kobayashi-Maskawa (CKM) matrix elements.

New physics in $s\to d$ semileptonic transitions: rare hyperon vs. kaon decays · Low-energy effective Hamiltonian · 0.81
The decay $B^0_s→μ^+μ^-$ originates from $Z$ penguins and box diagrams in the SM, and the corresponding low-energy effective Hamiltonian takes the following form [ref] : [equation] where $α$ is the QED coupling, $Θ_W$ is the Weinberg angle, $η_Y$ describes short-distance QCD corrections, and $Y_0(x_t≡m_t^2/M_W^2)$ is an “Inami–Lim function".

B Physics in the LHC Era: Selected Topics · SEARCH FOR NP IN $B^0_s→μ^+μ^-$ · 0.86

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

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