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DOE OSTI2026

FLAG review 2024

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 → 𝜋 transition at zero momentum transfer, as well as the decay-constant ratio 𝑓 𝐾 ⁡/𝑓 𝜋 and its consequences for the Cabibbo–Kobayashi–Maskawa (CKM) matrix elements 𝑉 𝑢⁢𝑠 and 𝑉 𝑢⁢𝑑 . 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 𝛼 𝑠 . We review the determinations of nucleon charges from the matrix elements of both isovector and flavor-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.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Search for Nuclear Modifications of 𝐵 + Meson Production in 𝑝-Pb Collisions at $\sqrt{𝑠_{NN}}$ = 8.16 TeV

Nuclear medium effects on 𝐵 + meson production are studied using the binary-collision scaled cross section ratio between events of different charged-particle multiplicities from proton-lead collisions. Data, collected by the CMS experiment in 2016 at a nucleon-nucleon center-of-mass energy of $\sqrt{𝑠_{NN}}$ = 8.16 TeV, corresponding to an integrated luminosity of 175 nb −1 , were used. The scaling factors in the ratio are determined using a novel approach based on the 𝑍 → 𝜇 − ⁢𝜇 + cross sections measured in the same events. The scaled ratio for 𝐵 + is consistent with unity for all event multiplicities, putting stringent constraints on nuclear modification for heavy flavor.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Search for Lepton-Flavor-Violating Decay Modes 𝐵 0 →𝐾$^0_𝑆$⁢𝜏 ± ⁢ℓ ∓ with Hadronic 𝐵 Tagging at Belle and Belle II

We present the first search for the lepton-flavor-violating decay modes 𝐵 0 →𝐾$^0_𝑆$⁢𝜏 ± ⁢ℓ ∓ (ℓ=𝜇,𝑒) using the 711 and 365 fb −1 data samples recorded by the Belle and Belle II detectors, respectively. We use a hadronic 𝐵-tagging technique to fully reconstruct a 𝐵 meson and search for signal decays in the system recoiling against the tagged meson, considering 𝜏 decays to either light leptons, one charged hadron, or one charged hadron and a neutral pion. We find no evidence for 𝐵 0 →𝐾$^0_𝑆$⁢𝜏 ± ⁢ℓ ∓ decays and set 90% confidence level upper limits on the branching fractions in the range of [0.8,3.6] ×10 −5 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Measurement of 𝐵 meson production fraction ratios in proton-proton collisions at √𝑠 = 13 TeV using open-charm and charmonium decays

Production fraction ratios of 𝐵 + , 𝐵 0 , and 𝐵$^{0}_{𝑠}$ mesons are measured in proton-proton collisions at √𝑠 = 13 TeV using a special dataset recorded in 2018 with high-rate triggers designed to collect an unbiased sample of 1⁢010 𝑏 hadrons with the CMS experiment at the LHC. These data allow the study of the open-charm decays of 𝐵 mesons (𝐵 (𝑠) → 𝜋⁢𝐷 (𝑠) ) where the 𝐷 meson decays into fully hadronic final states. By utilizing known branching fractions and precise theoretical calculations, production fraction ratios as functions of 𝐵 meson transverse momentum (𝑝 T ) and rapidity (𝑦) are measured using open-charm decays in the kinematic range of 8 < 𝑝 T < 60 GeV and |𝑦| <2.25. In addition, the same dataset is used to measure the relative production fraction ratios with the charmonium decay channels [𝐵 (𝑠) →𝑋⁢𝐽/𝜓 with 𝑋 indicating a 𝐾 + , 𝐾*(892) 0 , or 𝜙⁡(1020) meson] where the 𝐽/𝜓 meson decays into a pair of muons. The open-charm results are used to normalize the relative production fraction ratios obtained from the charmonium samples. Measurements of the ratios of branching fractions of 𝐵 meson decays to charmonium and open-charm final states are also reported, which will improve the world-average values of these ratios. Finally, we test isospin invariance in 𝐵 meson production in proton-proton collisions and observe that it holds within the experimental precision.

Bottom mesons↗

DOE OSTI2025

Test of lepton flavor universality in semileptonic 𝐵$^+_𝑐$ meson decays in proton-proton collisions at $\sqrt{𝑠}$ = 13 TeV

A measurement of the ratio of branching fractions 𝑅⁢(𝐽/𝜓) =ℬ⁡(𝐵$^+_𝑐$ →𝐽/𝜓⁢𝜏 + ⁢𝜈 𝜏 )/ℬ⁡(𝐵$^+_𝑐$ →𝐽/𝜓⁢𝜇 + ⁢𝜈 𝜇 ) in the 𝐽/𝜓 →𝜇 + ⁢𝜇 − , 𝜏 + →𝜇 + ⁢𝜈 𝜇 ⁢$\bar{𝜈}$ 𝜏 decay channel is presented. This measurement uses a sample of proton-proton collision data collected at a center-of-mass energy of 13 TeV by the CMS experiment in 2018, corresponding to an integrated luminosity of 59.7 fb −1 . The measured ratio, 𝑅⁢(𝐽/𝜓) = 0.1⁢7$^{+0.18}_{−0.17}⁢$(stat)$^{+0.21}_{−0.22⁢}$(syst)$^{+0.19}_{−0.18}$⁢(theo) =0.17 ± 0.33, agrees with the value of 0.2582 ± 0.0038 predicted by the standard model, which assumes lepton flavor universality. By testing lepton flavor universality, this measurement is a probe of new physics using 𝐵$^+_𝑐$ mesons, which are currently only produced at the LHC.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

First Exclusive Reconstruction of the 𝐵* + , 𝐵* 0 , and 𝐵$^{*0}_{𝑠}$ Mesons and Precise Measurement of Their Masses

Using proton-proton collision data collected by the CMS experiment at √𝑠 = 13 TeV in 2016–2018, corresponding to an integrated luminosity of 140 fb −1 , the first full reconstruction of the three vector 𝐵 meson states, 𝐵* + , 𝐵* 0 , and 𝐵$^{*0}_{𝑠}$, is performed. The mass differences between the excited mesons and their corresponding ground states are measured to be 𝑚⁡(𝐵* + )−𝑚⁡(𝐵 + ) = 45.277 ± 0.039 ± 0.027 MeV, 𝑚⁡(𝐵 *0 )−𝑚⁡(𝐵 0 ) = 45.471 ± 0.056 ± 0.028 MeV, and 𝑚⁡(𝐵$^{*0}_{𝑠}$)−𝑚⁡(𝐵$^{0}_{𝑠}$) = 49.407 ± 0.132 ± 0.041 MeV, where the first uncertainties are statistical and the second are systematic. These results improve on the precision of previous measurements by an order of magnitude.

Bottom mesons↗

DOE OSTI2026

Axionlike particles and sterile neutrinos solve the 𝐵 → 𝐾⁢$𝜈⁢\bar{𝜈}$ and 𝐵 → 𝜋⁢𝐾 puzzles

The recent measurement of the branching ratio of 𝐵 + → 𝐾 + +inv (where “inv” denotes invisible states) by the Belle II Collaboration is enhanced relative to the standard model expectation by 2.7⁢𝜎. An older puzzle persists in measurements of the branching ratios and 𝐶⁢𝑃 asymmetries of 𝐵 → 𝜋⁢𝐾 decays. We address these two anomalies in flavor-changing neutral current 𝐵 decays, with a short-lived axionlike particle (ALP) with mass close to that of the 𝜋 0 . In the model with the minimum number of new couplings, the ALP has couplings to the photon, top quark and a heavy sterile neutrino. The ALP contributes to the 𝐵 → 𝜋 0 ⁢𝐾 decays by mixing with the 𝜋 0 . It contributes to 𝐵 + → 𝐾 + + inv by its off-shell coupling to sterile neutrino pairs. The model can explain the excess in the total rate, but not the observed distribution of signal events. We make predictions for all 𝐵 → 𝐾 (*) + inv modes and for the rare kaon decays, 𝐾 + → 𝜋 + + inv and 𝐾 𝐿 → 𝜋 0 + inv. We find an appreciable contribution to the magnetic moment of the muon, and negligible contributions to the magnetic moment of the electron and 𝑏 → 𝑠⁢𝑒 + ⁢𝑒 − .

axion-like particles↗

DOE OSTI2025

𝐵 → 𝜌⁢ℓ⁢$\bar{v}$ Resonance Form Factors from 𝐵→ 𝜋⁢𝜋⁢ℓ⁢$\bar{v}$ in Lattice QCD

The decay 𝐵 → 𝜌⁢ℓ⁢$\bar{v}$ is an attractive process for determining the magnitude of the smallest Cabibbo-Kobayashi-Maskawa matrix element, |𝑉 𝑢⁢𝑏 |, and can provide new insights into the origin of the long-standing exclusive-inclusive discrepancy in determinations of this standard-model parameter. This requires a nonperturbative QCD calculation of the 𝐵 → 𝜌 form factors 𝑉, 𝐴 0 , 𝐴 1 , and 𝐴 12 . The unstable nature of the 𝜌 resonance has prevented precise lattice QCD calculations of these form factors to date. Here, we present the first lattice QCD calculation of the 𝐵 → 𝜌 form factors in which the 𝜌 is treated properly as a resonance in 𝑃-wave 𝜋⁢𝜋 scattering. To this end, we use the Lellouch-Lüscher finite-volume formalism to compute the 𝐵 → 𝜋⁢𝜋 form factors as a function of both momentum transfer and 𝜋⁢𝜋 invariant mass, and then analytically continue to the 𝜌 resonance pole. This calculation is performed with 2 + 1 dynamical quark flavors at a pion mass of approximately 320 MeV, and demonstrates a clear path toward results at the physical point.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2026

Binding energy of the 𝑇 𝑏⁢𝑏 tetraquark from lattice QCD with relativistic and nonrelativistic heavy-quark actions

We present a new determination of the $b\bar{b}$𝑢⁢𝑑 (𝐽 𝑃 = 1 + , 𝐼 = 0) tetraquark binding energy using lattice quantum chromodynamics (QCD) with domain-wall light quarks and a nonperturbatively tuned three-parameter anisotropic-clover “relativistic” action for the 𝑏 quarks. We also perform a direct comparison with a reanalysis of data generated in prior work using a lattice-nonrelativistic QCD (NRQCD) action for the 𝑏 quarks and otherwise identical parameters. Using the new data with relativistic 𝑏 quarks from seven different ensembles with multiple lattice spacings and pion masses, we perform combined chiral and continuum extrapolations and obtain (𝑚 𝑇 𝑏⁢𝑏 −𝑚 𝐵 −𝑚 𝐵* ) RHQ =(−76 ±23) MeV. For the NRQCD data from five ensembles, we perform chiral-only extrapolations and obtain (𝑚 𝑇 𝑏⁢𝑏 −𝑚 𝐵 −𝑚 𝐵* ) NRQCD = (−74 ±17 ±10) MeV. The lower magnitude of the results obtained here, compared to the original analysis in [Phys. Rev. D 100, 014503 (2019)], is due to the use of the symmetric parts of the correlation matrices with local four-quark operators only.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Charm and bottom hadrons in hot hadronic matter

Heavy quarks, and the hadrons containing them, are excellent probes of the QCD medium formed in high-energy heavy-ion collisions, as they provide essential information on the transport properties of the medium and how quarks color-neutralize into hadrons. Large theoretical and phenomenological efforts have been dedicated thus far to assess the diffusion of charm and bottom quarks in the quark–gluon plasma and their subsequent hadronization into heavy-flavor (HF) hadrons. However, the fireball formed in heavy-ion collisions also features an extended hadronic phase, and therefore any quantitative analysis of experimental observables needs to account for the rescattering of charm and bottom hadrons. This is further reinforced by the presence of a QCD cross-over transition and the notion that the interaction strength is maximal in the vicinity of the pseudo-critical temperature. We review existing approaches for evaluating the interactions of open HF hadrons in a hadronic heat bath and the pertinent results for scattering amplitudes, spectral functions and transport coefficients. While most of the work to date has focused on D -mesons, we also discuss excited states as well as HF baryons and the bottom sector. Both the HF hadro-chemistry and bottom observables will play a key role in future experimental measurements. We also conduct a survey of transport calculations in heavy-ion collisions that have included effects of hadronic HF diffusion and assess its impact on various observables.

effective field theories↗

DOE OSTI2025

Bottom quark energy loss and hadronization with B + and ${\textrm{B}}_{\textrm{s}}^0$ nuclear modification factors using pp and PbPb collisions at $\sqrt{s_{\textrm{NN}}}$ = 5.02 TeV

The production cross sections of $ {\textrm{B}}_{\textrm{s}}^0 $ and B$^{+}$ mesons are reported in proton-proton (pp) collisions recorded by the CMS experiment at the CERN LHC with a center-of-mass energy of 5.02 TeV. The data sample corresponds to an integrated luminosity of 302 pb$^{−1}$. The cross sections are based on measurements of the $ {\textrm{B}}_{\textrm{s}}^0 $→ J/ψ(μ$^{+}$μ$^{−}$)ϕ(1020)(K$^{+}$K$^{−}$) and B$^{+}$→ J/ψ(μ$^{+}$μ$^{−}$)K$^{+}$ decay channels. Results are presented in the transverse momentum (p$_{T}$) range 7–50 GeV/c and the rapidity interval |y| < 2.4 for the B mesons. The measured p$_{T}$-differential cross sections of B$^{+}$ and $ {\textrm{B}}_{\textrm{s}}^0 $ in pp collisions are well described by fixed-order plus next-to-leading logarithm perturbative quantum chromodynamics calculations. Using previous PbPb collision measurements at the same nucleon-nucleon center-of-mass energy, the nuclear modification factors, R$_{AA}$, of the B mesons are determined. For p$_{T}$> 10 GeV/c, both mesons are found to be suppressed in PbPb collisions (with R$_{AA}$ values significantly below unity), with less suppression observed for the $ {\textrm{B}}_{\textrm{s}}^0 $ mesons. In this p$_{T}$ range, the R$_{AA}$ values for the B$^{+}$ mesons are consistent with those for inclusive charged hadrons and D$^{0}$ mesons. Below 10 GeV/c, both B$^{+}$ and $ {\textrm{B}}_{\textrm{s}}^0 $ are found to be less suppressed than either inclusive charged hadrons or D$^{0}$ mesons, with the $ {\textrm{B}}_{\textrm{s}}^0 $R$_{AA}$ value consistent with unity. The R$_{AA}$ values found for the B$^{+}$ and $ {\textrm{B}}_{\textrm{s}}^0 $ are compared to theoretical calculations, providing constraints on the mechanism of bottom quark energy loss and hadronization in the quark-gluon plasma, the hot and dense matter created in ultrarelativistic heavy ion collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2024

Charmonium Transport in Heavy-Ion Collisions at the LHC

We provide an update on our semi-classical transport approach for quarkonium production in high-energy heavy-ion collisions, focusing on 𝐽/𝜓 and 𝜓(2𝑆) mesons in 5.02 TeV Pb-Pb collisions at the Large Hadron Collider (LHC) at both forward and mid-rapidity. In particular, we employ the most recent charm-production cross sections reported in pp collisions, which are pivotal for the magnitude of the regeneration contribution, and their modifications due to cold-nuclear-matter (CNM) effects. Multi-differential observables are calculated in terms of nuclear modification factors as a function of centrality, transverse momentum, and rapidity, including the contributions from feeddown from bottom hadron decays. For our predictions for 𝜓(2𝑆) production, the mechanism of sequential regeneration relative to the more strongly bound 𝐽/𝜓 meson plays an important role in interpreting recent ALICE data.

Astronomy & Astrophysics↗

DOE OSTI2025

Exotic hidden-heavy hadrons and where to find them

The Born-Oppenheimer potentials for QCD with light quarks include adjoint-hadron potentials that are repulsive at short distances and heavy-hadron-pair potentials that approach thresholds at large distances. The adjoint-hadron potentials must connect smoothly to the heavy-hadron-pair potentials at intermediate distances. We identify exotic hidden-heavy hadrons as bound states and resonances in adjoint-hadron potentials that cross below a heavy-hadron-pair threshold before approaching it. This explains why many exotic hidden-charm and hidden-bottom hadrons have energies near heavy-hadron-pair thresholds. The remarkable properties of some exotic hidden-heavy mesons can be explained by fine tunings of adjoint-meson energies in QCD.

Born-Oppenheimer approximation↗

DOE OSTI2025

Hidden-strangeness tetraquarks in the dynamical diquark model

The dynamical diquark model describes multiquark exotic hadrons in terms of diquark components nucleated by heavy quarks and successfully explains multiple features of hidden-charm and hidden-bottom exotics. Here, we apply the model to the marginally heavy case of hidden-strange states to probe whether mesons near 2 GeV with peculiar properties, such as 𝜙⁡(2170), 𝑓 2 ⁡(2340), and 𝑋⁡(2370), are possible tetraquark candidates. We calculate spin-multiplet average masses using potentials obtained through lattice simulations and quark models, and we also describe the detailed spectra of the expected multiplets as a diagnostic to discern the nature of future hadrons likely to be discovered in this mass region by experiments at facilities such as BESIII, JLab, and the EIC.

Bound states↗

DOE OSTI2025

Structure of open-flavor four-quark states in the charm and bottom region

We present quantitative results for masses and the internal structure of four-quark states with two heavy quarks, i.e., Q Q ′ q ¯ q ¯ ′ with Q , Q ′ ∈ { c , b } and q , q ′ ∈ { u , d , s } , and J P ∈ 1 + . The composition of these states in terms of meson-meson and diquark-antidiquark pairs, extracted from a relativistic four-body Faddeev-Yakubowski equation, is dynamically determined from underlying QCD forces. We find states at energy levels in very good agreement with lattice QCD and, where available, with experimental states. Their internal structure, most notably between the T c c + , T b c and T b b − , show significant and sizeable variations. Published by the American Physical Society 2025

Hoffer, Joshua (ORCID:0009000871793956)↗

DOE OSTI2026

Averages of 𝑏-hadron, 𝑐-hadron, and 𝜏-lepton properties as of 2023

This paper reports world averages of measurements of 𝑏-hadron, 𝑐-hadron, and 𝜏-lepton properties obtained by the Heavy Flavor Averaging Group using results available before October 2023. In rare cases, significant results obtained several months later are also used. For the averaging, common input parameters used in the various analyses are adjusted (rescaled) to common values, and known correlations are taken into account. The averages include branching fractions, lifetimes, neutral meson mixing parameters, 𝐶⁢𝑃 violation parameters, parameters of semileptonic decays, and Cabibbo-Kobayashi-Maskawa matrix elements.

Bottom quark production↗

DOE OSTI2025

Measurement of 𝐵 + →𝜏 + ⁢𝜈 𝜏 branching fraction with a hadronic tagging method at Belle II

We present a measurement of the branching fraction of 𝐵 + →𝜏 + ⁢𝜈 𝜏 decays using 387±6×10 6 ϒ⁡(4⁢𝑆) collected between 2019 and 2022 with the Belle II detector at the SuperKEKB 𝑒 + ⁢𝑒 − collider. We reconstruct the accompanying 𝐵 − meson using the hadronic tagging method, while 𝐵 + →𝜏 + ⁢𝜈 𝜏 candidates are identified in the recoil. We find evidence for 𝐵 + →𝜏 + ⁢𝜈 𝜏 decays at 3.0 standard deviations, including systematic uncertainties. The measured branching fraction is ℬ⁡(𝐵 + →𝜏 + ⁢𝜈 𝜏 )=[1.24±0.41⁢(stat)±0.19⁢(syst)]×10 −4 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2025

Test of lepton flavor universality with measurements of 𝑅⁡(𝐷 + ) and 𝑅⁡(𝐷* + ) using semileptonic 𝐵 tagging at the Belle II experiment

We report measurements of the ratios of branching fractions ℛ⁡(𝐷 (*)+ ) = ℬ⁡($\bar{𝐵}$ 0 → 𝐷 (*)+ ⁢𝜏 −⁢ $\bar{𝜈}$ 𝜏 )/ℬ⁡($\bar{𝐵}$ 0 → 𝐷 (*)+ ⁢ℓ − $\bar{𝜈}$ ℓ ), where ℓ denotes either an electron or a muon. These ratios test the universality of the charged-current weak interaction. The results are based on a 365 fb −1 data sample collected with the Belle II detector at the SuperKEKB 𝑒 + ⁢𝑒 − collider, which operates at a center-of-mass energy corresponding to the ϒ⁡(4⁢𝑆) resonance, just above the threshold for $𝐵\bar{𝐵}$ production. Signal candidates are reconstructed by selecting events in which the companion 𝐵 meson from the ϒ⁡(4⁢𝑆) → $𝐵\bar{𝐵}$ decay is identified in semileptonic modes. The 𝜏 lepton is reconstructed via its leptonic decays. We obtain ℛ⁡(𝐷 + ) = 0.418$^{+0.075}_{−0.073}$⁢(stat)$^{+0.049}_{−0.056}$⁢(syst) and ℛ⁡(𝐷 *+ ) = 0.306$^{+0.035}_{−0.033}$⁢(stat)$^{+0.016}_{−0.018⁢}$(syst), which are consistent with world average values. Accounting for the correlation between them, these values differ from the Standard Model expectation by a collective significance of 1.7 standard deviations.

bottom quark↗