BESIII reports the first measurement of B(Ds+ → K0 μ+ νμ) = (2.89 ± 0.27stat ± 0.12syst) × 10^{-3} and extracts f^{K0}_+(0) = 0.623 ± 0.036stat ± 0.009syst and |Vcd| = 0.220 ± 0.013stat ± 0.003syst ± 0.001LQCD from 7.33 fb^{-1} of data.
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FLAG Review 2024
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abstract
We review lattice results related to pion, kaon, $D$-meson, $B$-meson, and nucleon physics with the aim of making them easily accessible to the nuclear and particle physics communities. More specifically, we report on the determination of the light-quark masses, the form factor $f_+(0)$ arising in the semileptonic $K \to \pi$ transition at zero momentum transfer, as well as the decay-constant ratio $f_K/f_\pi$ and its consequences for the CKM matrix elements $V_{us}$ and $V_{ud}$. We review the determination of the $B_K$ parameter of neutral kaon mixing as well as the additional four $B$ parameters that arise in theories of physics beyond the Standard Model. For the heavy-quark sector, we provide results for $m_c$ and $m_b$ as well as those for the decay constants, form factors, and mixing parameters of charmed and bottom mesons and baryons. These are the heavy-quark quantities most relevant for the determination of CKM matrix elements and the global CKM unitarity-triangle fit. We review the status of lattice determinations of the strong coupling constant $\alpha_s$. We review the determinations of nucleon charges from the matrix elements of both isovector and flavour-diagonal axial, scalar and tensor local quark bilinears, and momentum fraction, helicity moment and the transversity moment from one-link quark bilinears. We also review determinations of scale-setting quantities. Finally, in this review we have added a new section on the general definition of the low-energy limit of the Standard Model.
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representative citing papers
The anomalous dimension of |ΔS|=1 current-current operators is calculated analytically at NNNLO in QCD, with basis transformation rules provided.
Lattice QCD strategy interpolates sub-physical mass data with OPE to obtain the inclusive anti-B_s to X_sc l nu decay rate, yielding 7% precision on limited ETMC ensembles via a new four-point correlator method.
Earth screening of quadratically coupled ultralight dark matter produces a multi-band frequency structure in the induced force whose sideband amplitudes vary annually, enabling improved constraints from MICROSCOPE and future EP missions.
A hierarchy of semidefinite programs provides rigorous bounds on spectral density functionals from Monte Carlo data subject to reflection positivity, converging to statistical error limits.
Lattice QCD supplies Standard Model branching-fraction predictions for all four K to l nu l' l' channels with controlled uncertainties of 2-7 percent, consistent with published data and preliminary NA62 results.
The causal bootstrap computes rigorous bounds on smeared spectral functions from non-perturbative Euclidean data by optimizing over the convex set of compatible positive spectral densities and reducing dual problems to semidefinite programs for certain kernels.
First lattice QCD calculation at the physical pion mass of the isovector third moments of nucleon unpolarized, polarized, and transversity PDFs via forward matrix elements of local operators.
A hierarchical generative model for critical lattice scalar field theories achieves orders-of-magnitude lower autocorrelation times than HMC while enabling exact multilevel Monte Carlo.
First measurement of form factors r_A ≈ -0.112 and r_V ≈ -0.043 in D semileptonic decays to K1(1270) via amplitude analysis, plus improved branching fractions and upper limits on K1(1400) modes.
First non-asymptotic-scaling determination of the large-N Yang-Mills Λ-parameter yields √(8t₀)Λ_MS(N=∞) = 0.639(36).
NNLO-QCD corrections to the free b-quark decay and NLO corrections to dimension-five operators reduce uncertainties in HQE predictions for b-baryon lifetimes, yielding excellent agreement with experiment.
New A and V gradient flow schemes enable nonperturbative renormalization of composite fermion operators via conserved currents and ratios of correlation functions, demonstrated on domain-wall ensembles for Z_V/Z_A and strange quark mass.
Trie-based algorithms evaluate HPE coefficients through κ^12 on SU(Nc) configurations at roughly 20, 460, and 8900 staple costs, verified against a reference implementation.
A global NNLO chiral-perturbation-theory fit with explicit Delta to lattice-QCD axial form factors gives g_A = 1.257 ± 0.011 and r_A² = 0.312 ± 0.037 fm².
A mapping of the Jaynes-Cummings-Hubbard model onto the spin-1/2 Quantum Link Model via tuned polaritonic resonances in cavity arrays enables analog simulation of U(1) LGT dynamics with matter, verified by exact diagonalization.
Normalizing flows enable all-order QED corrections in lattice scalar QED in 2-4 dimensions with reduced variance and transferability from small to large lattices.
A symmetry-guided phenomenological model organizes leading current-current operators for charged-current decays of heavy-light mesons and reproduces heavy-quark scaling relations for decay constants and form factors.
Isospin-corrected inclusive τ spectral functions yield light-quark-connected HVP and window quantities consistent with lattice QCD, but the 2π⁻π⁺π⁰ mode differs significantly from e⁺e⁻-based Pais expectations.
A symmetry-protected mirror extension predicts fifth-force strength α ≈ 10^{-4} at meter scales for scalaron mass m_σ ≈ 10^{-7} eV without relying on environmental screening.
Orbifold lattices incur m^4 Trotter overhead, m^2 contamination, and mandatory mass extrapolation, rendering them 10^4 to 10^10 times costlier than alternatives for a 10^3 calculation.
Derives α_S(μ) ≃ Λ_S²/μ² from a scale-invariant gluon condensate via gradient flow, reaching an infrared fixed point consistent with confinement.
Virtual electromagnetic corrections largely cancel radiative-channel contributions in data-driven HVP evaluations for muon g-2, reconciling timelike and spacelike methods via a VMD model.
Twisted mass fermions in the Hamiltonian two-flavor Schwinger model yield O(a) improvement and milder finite-volume effects once mass renormalization tunes the system to maximal twist.
citing papers explorer
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First Measurement of the $D_s^+\rightarrow K^0\mu^+\nu_{\mu}$ Decay
BESIII reports the first measurement of B(Ds+ → K0 μ+ νμ) = (2.89 ± 0.27stat ± 0.12syst) × 10^{-3} and extracts f^{K0}_+(0) = 0.623 ± 0.036stat ± 0.009syst and |Vcd| = 0.220 ± 0.013stat ± 0.003syst ± 0.001LQCD from 7.33 fb^{-1} of data.
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Four-loop QCD mixing of current-current operators
The anomalous dimension of |ΔS|=1 current-current operators is calculated analytically at NNNLO in QCD, with basis transformation rules provided.
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Inclusive $\bar B_s\mapsto X_{\bar sc} \ell \bar \nu$ decays from lattice QCD: computational strategy and a first physical result
Lattice QCD strategy interpolates sub-physical mass data with OPE to obtain the inclusive anti-B_s to X_sc l nu decay rate, yielding 7% precision on limited ETMC ensembles via a new four-point correlator method.
-
Background-Induced Forces from Quadratically Coupled Ultralight Dark Matter
Earth screening of quadratically coupled ultralight dark matter produces a multi-band frequency structure in the induced force whose sideband amplitudes vary annually, enabling improved constraints from MICROSCOPE and future EP missions.
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Certified spectral functions from lattice Monte Carlo data
A hierarchy of semidefinite programs provides rigorous bounds on spectral density functionals from Monte Carlo data subject to reflection positivity, converging to statistical error limits.
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Rare kaon decays $K^- \to \ell^- \bar{\nu}_\ell \ell'^{+} \ell'^{-}$: Standard Model predictions from lattice QCD
Lattice QCD supplies Standard Model branching-fraction predictions for all four K to l nu l' l' channels with controlled uncertainties of 2-7 percent, consistent with published data and preliminary NA62 results.
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The Causal Bootstrap: Bounding Smeared Spectral Functions from Non-Perturbative Euclidean Data
The causal bootstrap computes rigorous bounds on smeared spectral functions from non-perturbative Euclidean data by optimizing over the convex set of compatible positive spectral densities and reducing dual problems to semidefinite programs for certain kernels.
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Third moments of nucleon unpolarized, polarized, and transversity parton distribution functions from physical-point lattice QCD
First lattice QCD calculation at the physical pion mass of the isovector third moments of nucleon unpolarized, polarized, and transversity PDFs via forward matrix elements of local operators.
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Scalable Generative Sampling and Multilevel Estimation for Lattice Field Theories Near Criticality
A hierarchical generative model for critical lattice scalar field theories achieves orders-of-magnitude lower autocorrelation times than HMC while enabling exact multilevel Monte Carlo.
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First Measurement of the Decay Dynamics in the Semileptonic Transition of the $D^{+(0)}$ into the Axial-vector Meson $\bar K_1(1270)$
First measurement of form factors r_A ≈ -0.112 and r_V ≈ -0.043 in D semileptonic decays to K1(1270) via amplitude analysis, plus improved branching fractions and upper limits on K1(1400) modes.
-
The large-$N$ Yang--Mills $\Lambda$-parameter from step scaling
First non-asymptotic-scaling determination of the large-N Yang-Mills Λ-parameter yields √(8t₀)Λ_MS(N=∞) = 0.639(36).
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Predictions for $b$-baryon lifetimes at NNLO-QCD
NNLO-QCD corrections to the free b-quark decay and NLO corrections to dimension-five operators reduce uncertainties in HQE predictions for b-baryon lifetimes, yielding excellent agreement with experiment.
-
Gradient Flow Renormalization Schemes for Composite Fermion Operators
New A and V gradient flow schemes enable nonperturbative renormalization of composite fermion operators via conserved currents and ratios of correlation functions, demonstrated on domain-wall ensembles for Z_V/Z_A and strange quark mass.
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Higher-order hopping-parameter expansion by human-AI collaboration
Trie-based algorithms evaluate HPE coefficients through κ^12 on SU(Nc) configurations at roughly 20, 460, and 8900 staple costs, verified against a reference implementation.
-
Extraction of the nucleon axial form factor from Lattice QCD using NNLO chiral perturbation theory
A global NNLO chiral-perturbation-theory fit with explicit Delta to lattice-QCD axial form factors gives g_A = 1.257 ± 0.011 and r_A² = 0.312 ± 0.037 fm².
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Photonic Analog Quantum Simulation of (1+1)-Dimensional $U(1)$ Lattice Gauge Theory with Dynamical Matter
A mapping of the Jaynes-Cummings-Hubbard model onto the spin-1/2 Quantum Link Model via tuned polaritonic resonances in cavity arrays enables analog simulation of U(1) LGT dynamics with matter, verified by exact diagonalization.
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Normalizing flows for all-orders QED corrections in lattice field theory
Normalizing flows enable all-order QED corrections in lattice scalar QED in 2-4 dimensions with reduced variance and transferability from small to large lattices.
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A Phenomenological Model of Mesons for Charged Current Weak Decays
A symmetry-guided phenomenological model organizes leading current-current operators for charged-current decays of heavy-light mesons and reproduces heavy-quark scaling relations for decay constants and form factors.
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Comparison of the hadronic vacuum polarization between hadronic $\tau$-decay data and lattice QCD
Isospin-corrected inclusive τ spectral functions yield light-quark-connected HVP and window quantities consistent with lattice QCD, but the 2π⁻π⁺π⁰ mode differs significantly from e⁺e⁻-based Pais expectations.
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Technically Natural Suppression of Fifth Force
A symmetry-protected mirror extension predicts fifth-force strength α ≈ 10^{-4} at meter scales for scalaron mass m_σ ≈ 10^{-7} eV without relying on environmental screening.
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Ether of Orbifolds
Orbifold lattices incur m^4 Trotter overhead, m^2 contamination, and mandatory mass extrapolation, rendering them 10^4 to 10^10 times costlier than alternatives for a 10^3 calculation.
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Renormalization Group Approach to Confinement
Derives α_S(μ) ≃ Λ_S²/μ² from a scale-invariant gluon condensate via gradient flow, reaching an infrared fixed point consistent with confinement.
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Field-theoretic versus data-driven evaluations of electromagnetic corrections to hadronic vacuum polarization in $(g-2)_\mu$
Virtual electromagnetic corrections largely cancel radiative-channel contributions in data-driven HVP evaluations for muon g-2, reconciling timelike and spacelike methods via a VMD model.
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Fermion Discretization Effects in the Two-Flavor Lattice Schwinger Model: A Study with Matrix Product States
Twisted mass fermions in the Hamiltonian two-flavor Schwinger model yield O(a) improvement and milder finite-volume effects once mass renormalization tunes the system to maximal twist.
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Lattice Calculation of Short-Range Contributions to Neutrinoless Double-Beta Decay $\pi^-\to\pi^+ ee$ at Physical Pion Mass
Lattice QCD evaluation of π⁻→π⁺ee matrix elements at physical pion mass with a new around-the-world subtraction technique and RI/SMOM renormalization that reduces uncertainties and cross-checks prior results.
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Highly improved staggered quarks on anisotropic lattices
Tuning study of aHISQ action on anisotropic lattices from 1 to 8, with comparison of fermion anisotropy tuning and an empirical model for pion taste splittings showing qualitatively different behavior versus naive staggered quarks.
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Machine learning unveils the quark mass dependence of the pseudoscalar meson decay constants in three-flavour N$^2$LO ChPT
LASSO regression on LQCD data determines quark-mass dependence of f_π, f_K, f_η in N²LO three-flavor ChPT and supplies LECs for SU(3)-limit baryon mass predictions.
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$F_K/F_\pi$ as a precision test of a new four flavor Domain Wall Fermion action
New four-flavor smeared Möbius Domain Wall Fermion ensembles yield F_K/F_pi = 1.1962(34) as a precision test for inexpensive chiral fermion calculations in lattice QCD.
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The strange and flavor-singlet axial form factors of the nucleon from lattice QCD
Lattice QCD yields the singlet axial form factor G_A^{u+d+s}(Q^2) and strange G_A^s(Q^2) with full error budget after chiral, continuum, and infinite-volume extrapolations.
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Tightening energy-based boson truncation bound using Monte Carlo-assisted methods
New analytic and Monte Carlo-assisted method tightens energy-based boson truncation bounds, reducing volume dependence in (1+1)D scalar and (2+1)D U(1) gauge theories.
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Inclusive semileptonic $D_s\to X_s\ell\bar\nu$ decays from lattice QCD: continuum and chiral extrapolation
Lattice QCD yields the Ds to Xs l nu inclusive decay rate in agreement with experiment after full chiral and continuum extrapolations, with few-percent total uncertainty.
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Hadronic tau decays at higher orders in QCD
Sequence transformations applied to the fixed-order QCD series for hadronic tau decays produce estimates c5,1 = 298 ± 15, c6,1 = 3431 ± 256, c7,1 = 2.29 ± 0.29 × 10^4 and a predicted δ^(0)_FOPT = 0.2119 ± 0.0040.
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Determination of $B$-meson distribution amplitudes from $B\to \pi,K,D$ transition form factors
A global fit to B→π,K,D lattice form factors and B→πℓν data yields λ_B=217(19)+82−17 MeV and |V_ub|=3.68(13)+0−1×10−3.
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Angular Analysis of $B \to D^{*}\ell \bar{\nu}_{\ell}$ from Lattice and Experiment: $|V_{cb}|$ and New Physics Constraints
Joint Bayesian fit of lattice form factors and Belle angular data gives |V_cb| = 0.03997(71) in the SM with no resolution of the exclusive-inclusive puzzle and excludes scalar leptoquark NP at 1.0 TeV and vector leptoquark at 2.5 TeV at 68% CL.
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Semi-leptonic decays $B \to D^{(*)}(1S,2S)\ell \nu_{\ell}$ within the covariant light-front approach
Covariant light-front quark model calculations of B to D(1S,2S) and D*(1S,2S) semi-leptonic branching ratios match light-lepton data but underpredict tau modes, yielding R(D)=0.261 and R(D*)=0.228.
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Twist-3 contributions to $\gamma\gamma\to\pi^0\pi^0,\,K_S^0K_S^0$ in $k_T$ factorization
Twist-3 LCDA contributions in k_T factorization dominate twist-2 for neutral channels, bringing predictions closer to data while neutral-to-charged ratios remain flat unlike observations.
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Study of $\Lambda^0_b \to \Lambda D$ decays with the rescattering mechanism
Rescattering enhances the anti-D0 Lambda branching fraction by two orders of magnitude and produces large direct CP asymmetries (0.28 and -0.14) in Lambda_b to Lambda D channels.
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CP asymmetries in charged meson decay to two pions
CP asymmetries for B+ to pi+ pi0, D+ to pi+ pi0, and K+ to pi+ pi0 are estimated in the Standard Model at roughly 3 times 10 to the -3, 10 to the -5, and 10 to the -6 using a unified formalism for isospin violation.
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$CP$ violation in neutral kaon mixing in $D^0\rightarrow K_SK_S$
Neutral kaon mixing adds a CP-violating effect of order 10^{-6} to a_CP in D0 -> Ks Ks, arising only from second-order weak processes and thus negligible for experiments.
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Revisiting $\mu$-$e$ conversion in $R$-parity violating SUSY
RG running changes limits on certain RPV SUSY λ and λ' couplings by up to 80 percent, with upcoming μ-e conversion experiments expected to set stronger bounds than μ→eγ or μ→eee decays.
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$f_K/f_{\pi}$ in iso-symmetric QCD and the CKM matrix unitarity
Lattice QCD result for f_K/f_π in isoQCD gives |V_us|/|V_ud| consistent with CKM unitarity once isospin and QED effects are included.
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Combined effective field theory interpretation of Higgs boson, electroweak vector boson, top quark, and multi-jet measurements
CMS performs a combined SMEFT fit to multiple LHC measurements and precision data, yielding individual constraints on 64 Wilson coefficients and 43 linear combinations.
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$b\to c \bar u q$ decay and CP violating observables in the presence of new physics contributions
Phenomenological constraints on complex Wilson coefficients for b→cūq transitions from branching fraction tensions, yielding predictions for ΔΓd/Γd, ASL^d and ACP under color-singlet and color-rearranged scenarios.
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Review of experimental studies of charmed meson decays at BESIII
A review of BESIII charmed meson decay studies presents the most precise averages for |V_cs|, |V_cd|, D and D_s decay constants, and several hadronic form factors from combined experimental results.
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The theory of electric dipole moments: the view from below
A bottom-up review organizing the theory of EDMs from quark-gluon CP violation via chiral perturbation theory and structure calculations, with emphasis on paramagnetic system sensitivity to hadronic sources.
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Quantification of the Flavor Diagonal Hadronic CP Violation
A review of progress in quantifying flavor-diagonal hadronic CP violation effects on EDMs, neutron optics, beta decay, and an attempt to address the strong CP problem without new fields or interactions.
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An Update on the Isospin-Breaking Effects in the Pion Decay Constant with Staggered Quarks
Preliminary update on isospin-breaking corrections to the pion decay constant in staggered N_f=2+1+1 QCD with QED_L, including correlator data for scale setting.
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Isospin-symmetry violation -- kaons and beyond (ISO-BREAK 25: summary and outlook)
The ISO-BREAK 25 workshop report summarizes evidence and discussions on unexplained isospin symmetry breaking in nucleus-nucleus collisions and sets priorities for further work.
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Towards better nuclear charge radii
An effort is described to produce more precise and transparent recommended values for nuclear charge radii through integrated experimental and theoretical approaches.
- Scalar and Tensor Form Factors for $\Lambda \rightarrow p\ell \bar{\nu}_\ell$ from Lattice QCD