The CKM matrix sits at the heart of the Standard Model’s description of quark flavour mixing. Its element |Vcb| quantifies the charged-current transition strength between the charm and bottom quarks, and it plays a double role in particle physics: it is used to verify the unitarity of the CKM matrix, and it serves as a benchmark against which possible new physics beyond the Standard Model can be tested. A precise determination of |Vcb| has therefore long been one of the central goals of B-physics phenomenology. What makes the problem genuinely difficult is a long-standing discrepancy between exclusive extractions, which rely on specific decays such as B → D(*)ℓν, and inclusive extractions, which sum over many final states. That tension has motivated extensive theoretical and experimental work for years, and it remains unresolved.

The experimental side of the analysis draws on a decade of increasingly sophisticated measurements. The Belle collaboration measured the semileptonic decay B → Dℓν using fully reconstructed B meson tag events, obtained the isospin-averaged branching fraction, and extracted |Vcb| with two different form-factor parameterization frameworks, presenting binned differential decay rates in bins of the recoil variable w. Belle II then performed an analogous measurement adopting the BCL parameterization. For the vector-vector channel B⁰ → D*⁻ℓ⁺ν, independent fits using the CLN and BGL parameterizations have been carried out alongside full binned differential distributions, response matrices, and statistical and systematic correlation matrices, all designed to alleviate the inclusive–exclusive |Vcb| puzzle. Belle II has also provided separate partial decay rates for electron and muon final states as functions of the recoil parameter ω and three decay angular observables.

These experimental fits require form factors evaluated near zero recoil as external theoretical inputs, and lattice QCD has undergone steady methodological and precision improvements over the past decade. The first unquenched lattice gauge simulation of the B → Dℓν form factors came from the Fermilab-MILC collaborations. HPQCD then produced full-q² unquenched calculations of the scalar and vector form factors f₊(q²) and f₀(q²). For the exclusive mode B → Dℓν, unquenched lattice-QCD form factors at nonzero recoil were computed by Fermilab-MILC with 2+1 flavours, and HPQCD later delivered complete vector, axial-vector, and tensor form factors covering the entire q² range. JLQCD introduced Möbius domain-wall fermion discretization for the B → Dℓν transition, offering an independent cross-check against the widely used clover heavy-quark schemes. Collectively, these efforts trace a trajectory from narrow zero-recoil single-channel studies toward full-q², multi-flavour, multi-operator form factor sets with multiple independent discretization frameworks, drastically reducing lattice systematic uncertainties in the |Vcb| extraction.

The theoretical backbone of the new analysis is the BGL dispersive parameterization, a model-independent z-expansion scheme in which the form factors are written as series in a conformal variable z(q²) that maps the physical kinematic region into the unit disk. Blaschke factors remove poles associated with Bc resonances below the pair-production threshold, and outer functions φᵢ, built from perturbative QCD dispersion relations, control the series convergence. The authors impose strong unitarity bounds derived from four heavy-to-heavy transition channels — B → D, B → D*, B* → D and B* → D* — covering twenty form factors in total, with heavy-quark effective theory power corrections retained through O(αs), O(εb), O(εc) and O(εc²) terms. These bounds act as hard constraints in the fit, effectively restricting the space of BGL expansion coefficients and suppressing uncontrolled systematic uncertainties from z-series extrapolation. Sensitivity tests varying the HQET inputs over their quoted ranges shift the extracted |Vcb| by at most about 0.16σ of the nominal uncertainty.

A key innovation is the treatment of the light-cone sum-rule (LCSR) inputs at large hadronic recoil. The team used correlated SCET sum-rule predictions including next-to-leading-order QCD corrections and four sources of next-to-leading-power contributions, evaluated at six representative kinematic points q² ∈ {−3, −2, −1, 0, 1, 2} GeV². Rather than treating these predictions as independent numbers, the authors generated 1000 complete input-parameter sets by sampling the underlying LCSR parameters simultaneously according to their specified distributions, so that each replica is a full correlated prediction vector. This preserves parameter variations that alter the q² dependence, including those associated with the parameter λB. The empirical mean, standard deviations and correlation matrix of the replica ensemble then define the LCSR input to a correlated Gaussian χ². Because the predictions at different q² values are extremely strongly correlated, the raw correlation matrix is nearly singular; the authors regularize it mildly while retaining all correlation directions, and they verified that the regularization choice does not materially control the extracted |Vcb| or its uncertainty.

The numerical analysis proceeds through three nested fit scenarios with progressively enlarged constraint sets. The first relies purely on lattice-QCD form-factor simulations; the second adds the correlated SCET sum-rule predictions; the third supplements both with binned differential decay spectra and angular observables from Belle and Belle II, which is the only scenario in which |Vcb| can be determined. Comparing across the scenarios shows that incorporating the correlated large-recoil LCSR predictions dramatically shrinks the uncertainties of high-order BGL coefficients, while the inclusion of precise Belle II decay observables yields further moderate tightening of the parameter space. The complete global fit yields χ²min = 218.505 for 229 degrees of freedom, corresponding to a healthy p-value of 0.680, with the lattice-QCD, LCSR and experimental contributions to the χ² being 42.91, 14.44 and 161.16 respectively.

From the full global fit the team extracts |Vcb| = (39.18 ± 0.47) × 10⁻³. Individual channel fits give |Vcb| = (40.3 ± 0.8) × 10⁻³ from B → Dℓν and |Vcb| = (38.6 ± 0.6) × 10⁻³ from B → D*ℓν, and the authors document in detail how methodological choices — the exclusion of the Belle 2017 dataset, the retention of only the muonic mode of the Belle 2018 measurement to mitigate well-documented electron–muon tension, and the use of constrained frequentist χ² minimization rather than Bayesian MCMC or nested sampling — shift the central value relative to previous analyses. Robustness checks are thorough: a constrained profile-likelihood scan gives |Vcb| = (39.1801 +0.4611/−0.4577) × 10⁻³, consistent with the Hessian uncertainty, and increasing the BGL truncation from O(z²) to O(z³) shifts the central value by only 0.032 × 10⁻³ while the four strong unitarity bounds become essentially saturated, showing that the extra cubic coefficients are only weakly constrained by the present data.

Using the fitted form-factor coefficients from the combined lattice-QCD and LCSR fit, the team derives updated Standard Model predictions for the lepton-flavour-universality ratios R(D) = 𝓑𝓡(B → Dτντ)/𝓑𝓡(B → Dμνμ) = 0.3069 ± 0.0080 and R(D*) = 0.2548 ± 0.0043, alongside full differential decay distributions in the momentum transfer and angular variables for both the muon and tau channels. The muonic spectrum rises sharply near q² → 0 and decreases monotonically, while the tau channel has a nonvanishing kinematic threshold at finite q² owing to the tauon’s larger mass. Belle II measurements broadly follow the theoretical trend for the muonic channel, though mild local deviations appear in certain angular regions. At present precision, the authors emphasize, these discrepancies do not provide compelling evidence for physics beyond the Standard Model.

The persistent tension, however, remains vivid. Experimental world averages for both R(D) and R(D) lie systematically above the aggregate Standard Model theoretical band, and the team’s two-dimensional correlated 68% confidence contour in the (R(D), R(D)) plane shows little overlap with the experimental average. Their R(D*) central value aligns well with the global theory average, while their R(D) prediction sits slightly above pure lattice averages such as the FLAG 2024 result. The discrepancy may originate from underestimated lattice or LCSR systematic uncertainties, residual shape biases in the BGL z-expansion, missing higher-order or higher-power corrections, or unvalidated experimental reconstruction efficiencies. Improved lattice-QCD calculations, refined sum-rule predictions, and high-statistics Belle II measurements will be essential for determining whether the remaining gaps are theoretical artefacts or genuine signals of new physics in charged-current b → cℓν transitions — and this complete set of correlated Standard Model predictions now provides a robust, up-to-date reference for that decisive comparison.

Subject of Research: Exclusive determination of the CKM matrix element |Vcb| from semileptonic B meson decays

Article Title: Exclusive determination of (|V_{cb}|) from semileptonic decays (B\rightarrow D^{(*)}\ell \nu _{\ell })

Article References: Chen, X.-W., Cui, B.-Y., Zhang, J.-W., Zhao, X.-C., & Chen, Y.-H. (2026). Exclusive determination of $$|V_{cb}|$$ from semileptonic decays $$B\rightarrow D^{(*)}\ell \nu _{\ell }$$. The European Physical Journal C, 86(10), Article 1174. https://doi.org/10.1140/epjc/s10052-026-16486-2

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16486-2

Keywords: CKM matrix, Vcb, semileptonic decays, B mesons, lattice QCD, BGL parameterization, Belle II, R(D), R(D*), lepton flavour universality, Standard Model, flavour physics

The framework builds on the classic Sakharov conditions, formulated in 1967, which identify three requirements for dynamically generating a matter–antimatter asymmetry: baryon number violation, violation of the charge conjugation and charge–parity symmetries (C and CP), and departure from thermal equilibrium. Kilic and Mathai relax the first condition in an elegant way. Rather than violating baryon number outright, they consider a hidden sector containing baryon-number-carrying particles that is effectively decoupled from ordinary matter at late times. If baryon number is transferred between the two sectors in the early universe, equal and opposite baryon abundances can be sequestered, one in the visible sector and one in the hidden sector, while the net baryon number of the universe remains exactly zero.

The two sectors communicate through a so-called baryon portal, a dimension-six operator coupling right-handed up- and down-type quarks to a new fermionic mediator. In the benchmark model, this portal arises from integrating out a heavy colored scalar, a fundamental of the strong-interaction gauge group with hypercharge −2/3, which couples to pairs of down-type quarks through one set of couplings and to up-type quarks and the portal fermions through another. The hidden sector itself is deliberately minimal: a Majorana fermion and a scalar that carries baryon number, both stable and neutral under the Standard Model, making them plausible dark matter candidates. Crucially, the model contains order-one CP-violating phases in its couplings, satisfying the second Sakharov condition far more generously than the tiny CP violation observed in the Standard Model.

Timing is everything in this scenario. The baryon number transfer must occur below the electroweak scale, at temperatures of roughly 100 GeV or less, so that sphaleron processes cannot wash out the generated asymmetry, yet above the temperatures probed by primordial nucleosynthesis so that the latter’s successful predictions remain intact. That leaves only a narrow energy window in which the entire observed asymmetry must be manufactured. The authors first analyzed the case in which the asymmetry is generated through the decays of top quarks. Setting up a Boltzmann equation for the top quark population as the universe cools from 100 GeV down to 10 GeV, they found that even a loop-suppressed CP asymmetry suffices, with the required branching ratio of the top quark into the hidden sector being a minuscule 10⁻¹⁹, far beyond the reach of any collider constraint. The catch is that the couplings involved are so small that this version of the scenario would be nearly impossible to test experimentally.

The more interesting and more testable case involves bottom quarks, and here the mathematics becomes dramatically tighter. Rare decays of bottom quarks have been searched for at the BaBar and Belle experiments, which bound non-Standard-Model branching ratios at roughly the 10⁻⁵ level. In the mesogenesis variant of the scenario, the universe reheats after inflation to a temperature below the QCD scale, and a reheaton field with a mass of tens of GeV produces a non-thermal population of bottom quarks that hadronize and then decay, seeding the visible plasma and generating the asymmetry through rare CP-violating decays. Combining the existing branching-ratio limits with the required yield shows that a generic loop-level efficiency, of order 10⁻³, is simply not enough. The efficiency of baryon number transfer must be pushed close to unity, and that is where the new paper makes its central contribution.

The mechanism for this boost is resonant enhancement, a phenomenon familiar from studies of leptogenesis involving nearly degenerate heavy neutrinos. In the benchmark model there are two portal fermions, and when their masses are nearly degenerate, the internal propagator in the loop diagram that supplies the CP-odd phase goes on shell. The CP asymmetry then takes a Breit–Wigner shape, peaking when the mass splitting between the two fermions is comparable to their decay widths. In precisely this regime the two portal fermions do not propagate as independent resonances but as a single coherent, mixing pair, and the authors employ a closed-time-path, density-matrix treatment in which the resonant pole is regulated by the coherent sum of the two widths rather than their difference. Their analytical result shows the asymmetry can reach approximately 0.7 at the peak of the resonance, compared with the generic loop-suppressed value of a thousandth.

Importantly, this enhancement does not require any special tuning of flavor structures. The authors performed a Monte Carlo scan over the model parameters, fixing the portal fermion mass at 4 GeV with bottom decays in mind, sampling coupling magnitudes from Gaussian distributions centered on perturbative values, and drawing all CP phases uniformly. They found that roughly ten percent of the sampled parameter points yield an average CP asymmetry of at least 0.5, and that the asymmetry falls to the generic non-resonant value only a vanishing fraction of the time, of order 10⁻⁴ to 10⁻⁵. The two CP asymmetries associated with the two portal flavors are guaranteed to have the same sign, so there is no cancellation of the transferred baryon number. Resonant enhancement, in other words, is generic.

The stakes for experiment are unusually sharp. Even with a maximally efficient CP asymmetry near unity, generating the observed baryon asymmetry through bottom meson decays requires a branching fraction into the hidden sector of at least order 10⁻⁸. Current limits sit at 10⁻⁵, and Belle-II is expected to push them to 10⁻⁷. That means the entire viable parameter space of the mesogenesis scenario lies within a factor of a hundred of existing bounds, and improvements of just two to three orders of magnitude in sensitivity would either discover the rare decay channels or rule the framework out completely. The authors describe this as a final stand for mesogenesis: if the limits drop below about 1.3 × 10⁻⁸, even perfect efficiency cannot save the mechanism, and non-thermal bottom meson decays can be excluded in full as the source of the cosmic matter surplus.

Complementary probes come from other directions. The colored scalar mediator can be produced at the Large Hadron Collider, either resonantly through its couplings to quark pairs or through ordinary strong pair production, with current direct searches requiring its mass to exceed about 1.2 TeV. At that mass the scalar decays promptly on collider timescales, so R-hadron searches do not add further constraints, but future colliders could reach deeper. The authors also examined electric dipole moment constraints, since coupling a maximally CP-violating hidden sector to the visible world risks observable low-energy signatures. Three-loop contributions generate the CP-violating Weinberg operator and shift the neutron electric dipole moment, but the suppression by the fourth power of the mediator mass pushes the effect well below even the Standard Model’s own tiny prediction of 10⁻³² e·cm, making neutron EDM measurements unlikely to probe this scenario.

The broader significance of the work lies in its fusion of two ideas that have largely developed on parallel tracks: resonant enhancement, imported wholesale from the leptogenesis literature with a single substitution in the CP-odd invariant, and mesogenesis, which ties the origin of matter to rare decays of heavy mesons at temperatures far below those usually associated with baryogenesis. By proving that order-one efficiency emerges generically rather than by construction, Kilic and Mathai have transformed a speculative scenario into a sharply falsifiable one. Within the coming decade, as Belle-II and successor experiments grind down the limits on rare bottom decays, the question of whether our matter came from a hidden, CP-violating mirror world may be answered not by better theory but by a simple null result, or by the discovery of a decay that should not exist.

Subject of Research: Resonantly enhanced baryon number transfer from a CP-violating hidden sector as a mechanism for the cosmic matter–antimatter asymmetry

Article Title: Resonant Enhancement for the transfer of baryon number from a CP-violating hidden sector

Article References: Kilic, C., & Mathai, S. (2026). Resonant Enhancement for the transfer of baryon number from a CP-violating hidden sector. The European Physical Journal C, 86(9), Article 1124. https://doi.org/10.1140/epjc/s10052-026-16384-7

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16384-7

Keywords: baryogenesis, hidden sector, CP violation, mesogenesis, baryon portal, resonant enhancement, bottom quark decays, Belle-II, dark matter, sphalerons, neutron electric dipole moment, Standard Model

The appeal of K+ → π+ ν ν̄ lies in its extraordinary cleanliness. Within the Standard Model the decay proceeds only through highly suppressed flavour-changing neutral-current processes, in which a strange quark converts into a down quark without altering its electric charge. The GIM mechanism, an interference effect among virtual quarks, suppresses the rate to roughly one part in ten billion. Unlike many other rare decays, the theoretical uncertainty is remarkably small, well under control thanks to decades of work on the electroweak corrections that dominate the amplitude. That combination of rarity and theoretical purity makes the branching ratio a precision probe of flavour violation among the first two quark generations, a sector where new heavy particles could otherwise leave faint but detectable fingerprints.

Allwicher and Bordone frame their analysis within the Standard Model Effective Field Theory, asking what the NA62 result implies under different assumptions about how new physics might couple to quarks and leptons. The first scenario they examine posits that new physics modifies the couplings of the Z boson to pairs of down-type quarks. A flavour-changing Z coupling of this kind would feed directly into rare decays at tree level, affecting both dineutrino channels such as K → π ν ν̄ and B → K ν ν̄ and the charged-lepton channel Bs → μ+ μ−. The relative impact on each process is governed by the flavour structure of the modified couplings, while the lepton couplings retain their Standard Model universality, making the correlation between observables especially transparent.

The authors test two competing flavour hypotheses within this scenario. Under Minimal Flavour Violation, new physics respects the CKM pattern of the Standard Model, and right-handed couplings are further suppressed by light-quark masses. In that case Bs → μ+ μ−, measured by ATLAS, CMS and LHCb with a combined uncertainty of roughly eight percent, remains the most constraining observable, and the kaon decay adds comparatively little. Partial Compositeness, inspired by composite Higgs and warped extra-dimension models, behaves very differently. There, the usual mass suppression of right-handed couplings is partially offset by inverse CKM factors, and kaon decays become strikingly sensitive. The analysis reveals a double solution in this case: one compatible with the Standard Model, and a second in which a new-physics contribution twice the size but opposite in sign cancels the Standard Model amplitude, leaving the decay rate unchanged. The newly measured B+ → K+ ν ν̄ branching fraction, recently observed by Belle II at a rate mildly above the Standard Model, can help discriminate between the two solutions.

The second scenario extends the analysis beyond neutral-current processes into semileptonic interactions. Here the authors work within a U(2)^5 flavour symmetry, a framework in which new physics couples predominantly to third-generation fermions, with small breaking terms connecting to the lighter families through CKM-suppressed spurions. This choice is motivated by the current experimental landscape, in which several tensions involving third-generation particles, including the R D(*) ratios of B decays into tau leptons, persist and are naturally accommodated in such a setup. The framework is governed by only four independent parameters, whose Wilson coefficients are constrained by a global fit spanning high-momentum Drell–Yan searches at the LHC, electroweak precision observables, lepton-flavour universality tests in tau decays, the semileptonic B anomalies, B → K ν ν̄ data, and the new kaon measurement itself.

The global fit produces a striking picture of correlated predictions. The scalar operator considered in the framework is tightly bounded by high-momentum searches and found consistent with zero, but the vector operators remain viable. Notably, the new NA62 measurement, with its substantially reduced uncertainty, dramatically narrows the region in which the kaon and B-meson dineutrino observables can be simultaneously satisfied. A particularly interesting branch of the fit corresponds to a large new-physics contribution that nearly cancels the Standard Model amplitude in K+ → π+ ν ν̄, producing an apparently SM-like branching ratio while permitting sizeable effects elsewhere. Upcoming NA62 precision at the fifteen percent level would severely test this cancellation, and the analysis shows how the remaining allowed region would shrink correspondingly.

The most tantalizing prediction concerns K_L → π^0 ν ν̄, the neutral partner mode that has never been observed. In the semileptonic third-generation scenario, the charged and neutral kaon modes respond differently to the underlying new-physics coefficient, and the fit predicts a characteristic hierarchy. Within the preferred region, the branching ratio of the neutral mode is expected to be enhanced relative to the Standard Model more strongly than the charged mode, with a ratio of roughly 1.5 between the two normalized enhancements. All predictions remain safely within the Grossman–Nir bound, the model-independent ceiling derived from the charged mode. The projected sensitivities of NA62 and the KOTO-II experiment at J-PARC, the latter targeting twenty-five percent precision, would put this correlation to a direct test, and together with Belle II’s projected eight percent precision on B+ → K+ ν ν̄ would provide a tripartite check of the entire framework.

The two scenarios also translate into very different statements about the energy scale of whatever new physics might be responsible. For modified Z couplings, the effective scale of the new interaction must exceed roughly eight teraelectronvolts, a value common to both flavour hypotheses because the dominant constraint acts on left-handed couplings. Although this scale sounds dauntingly high, the tree-level nature of the couplings means the high-luminosity LHC programme can still access the relevant phenomena directly. In the semileptonic third-generation scenario, by contrast, the effective scale sits near 1.8 teraelectronvolts, far closer to energies the LHC already explores, and the authors show that adding further operators would not qualitatively alter this conclusion because the new parameters enter largely independently of the fitted sector.

What emerges from the study is a vision of precision flavour physics as a connected network rather than a collection of isolated measurements. In the modified-Z scenario under Minimal Flavour Violation, an enhancement in the charged kaon mode is directly tied to an enhancement in B+ → K+ ν ν̄, and the authors further show that B → K* ν ν̄ responds differently to right-handed couplings than its charged counterpart, so measuring both B modes separately sharpens the constraints. Under Partial Compositeness the kaon measurement itself becomes the decisive observable, capable of resolving ambiguities that B_s → μ+ μ− alone cannot. In the semileptonic scenario, the kaon and B dineutrino branching ratios become coupled predictions of a single four-parameter framework, meaning that future measurements of any one of them will stress-test the whole edifice.

The timing of this convergence is no accident. The NA62 result, with a relative uncertainty below twenty percent, brings kaon decays into an era where they can genuinely compete with and complement B-factory and LHC measurements. Even though the current central values agree with the Standard Model, the study demonstrates that agreement is not the same as closure: under motivated flavour hypotheses, sizeable new physics can masquerade as a null result in one channel while manifesting openly in another. The coming generation of measurements, from NA62’s final precision through KOTO-II’s assault on the neutral kaon mode to Belle II’s dineutrino programme, will convert these theoretical correlations into concrete verdicts. If the patterns predicted by either scenario hold, particle physicists may finally glimpse the flavour structure of physics beyond the Standard Model; if they fail, entire classes of models will be swept away by the quietest decays in nature.

Subject of Research: Theoretical implications of the rare kaon decay K+ → π+ ν ν̄ for constraining new physics in B meson decays

Article Title: Implications of (K\rightarrow \pi \nu \bar{\nu }) for new physics in B decays

Article References: Allwicher, L., & Bordone, M. (2026). Implications of $$K\rightarrow \pi \nu \bar{\nu }$$ for new physics in B decays. The European Physical Journal C, 86(9), Article 1063. https://doi.org/10.1140/epjc/s10052-026-16313-8

Image Credits: AI Generated

DOI: 10.1140/epjc/s10052-026-16313-8

Keywords: kaon decay, NA62, flavour physics, new physics, B meson decays, Standard Model, effective field theory, Belle II, KOTO-II, rare decays, Z couplings, U(2) flavour symmetry