Recently, the Belle Collaboration has updated the analysis of the cross sections for the processes + − → Υ() + − (= 1, 2, 3) in the + − center-of-mass energy range from 10.52 to 11.02 GeV. A new structure, called (10750), with the mass () = (10752.7 ± 5.9 +0.7 −1.1) MeV and the Breit-Wigner width Γ() = (35.5 +17.6+3.9 −11.3−3.3) MeV was observed. We interpret (10750) as a compact = 1 −− state with a dominant tetraquark component. The mass eigenstate (10750) is treated as a linear combination of the diquark-antidiquark and ¯ components due to the mixing via gluonic exchanges shown recently to arise in the limit of large number of quark colors. The mixing angle between and Υ(5) can be estimated from the electronic width, recently determined to be Γ () = (13.7 ± 1.8) eV. The mixing provides a plausible mechanism for (10750) production in high energy collisions from its ¯ component and we work out the Drell-Yan and prompt production cross sections for → (10750) → Υ() + − at the LHC. The resonant part of the dipion invariant mass spectrum in (10750) → Υ(1) + − and the corresponding angular distribution of +-meson in the dipion rest frame are presented.

Heavy-quark symmetry (HQS), despite being approximate, allows to relate dynamically many hadron systems. In the HQS-limit, heavy mesons and doubly-heavy baryons are very similar as their dynamics is determined by a light quark moving in a color field of a static source. As in the meson case, matrix elements of non-local interpolation currents between the baryon state and vacuum are determined by light-cone distribution amplitudes (LCDAs). The first inverse moment of the leading twist -meson distribution amplitude is a hadronic parameter needed for an accurate theoretical description of B-meson exclusive decays. It is quite natural that a similar moment of doubly-heavy baryon is of importance in exclusive doubly-heavy baryons' decays. We obtain HQET sum rules for the first inverse moment based on the correlation functions containing nonlocal heavy-light operator of the doubly-heavy baryon and its local interpolating current.

In the Standard Model (SM), the 𝑏 → 𝑠 (𝑑) flavor-changing neutral currents, being loop-induced, are standard experimental channels for testing the SM precisely and searching for possible physics beyond the SM. Pure annihilation 𝐵-meson decays originating by these currents are of significant interest as they are extremely suppressed in the SM and New Physics effects can increase substantially their decay widths. Typical examples of these annihilation processes are radiative and semileptonic decays with 𝜌 0 -, 𝜔-, and 𝜙-production like 𝐵 0 𝑠 → 𝜌 0 (𝜔) 𝛾, 𝐵 0 𝑠 → 𝜌 0 (𝜔) ℓ + ℓ − , 𝐵 0 → 𝜙 𝛾, and 𝐵 0 → 𝜙 ℓ + ℓ − , where ℓ = 𝑒, 𝜇 is the charged lepton. At the beginning of 2022, the LHCb Collaboration presented the upper limit on the 𝐵 0 → 𝜙𝜇 + 𝜇 − decay branching fraction B exp (𝐵 0 → 𝜙𝜇 + 𝜇 − ) < 3.2 × 10 −9 , and it is important to have a precise SM prediction for this decay. Here, we present theoretical predictions for 𝐵 0 → 𝜙 ℓ + ℓ − branching fraction in the lepton-pair invariant mass range 1 GeV 2 < 𝑞 2 < 8 GeV 2 , so far without taking into account 𝜔 − 𝜙 mixing effect. The main goal is to study a dependence of the branching fraction on the choice of the 𝐵-meson distribution amplitude model. Theoretical prediction for the total branching fraction B th (𝐵 0 → 𝜙ℓ + ℓ − ) ∼ 10 −12 , being an order of magnitude estimate, is far below the LHCb experimental limit.

The non-diagonal correlator of vector and tensor fermionic currents is considered as the concrete example of the two-point one-loop amplitudes modified by a constant homogeneous magnetic field. The crossed-field limit of this correlator is found. The tensor current is a fermionic part of the Pauli Lagrangian relevant for the electromagnetic interaction of fermions through the anomalous magnetic moment. Under assumption that this interaction enters the effective QED Lagrangian, the contribution to the photon polarization operator linear in AMM is calculated.

In the Standard Model, the → and → flavor-changing neutral currents (FCNC) are induced by loop effects. Rare semileptonic -meson decays originated by these currents are standard channels for testing the Standard Model precisely and in searching for possible physics beyond it. Here, we consider the rare + → + ℓ + ℓ − decay, where ℓ = , is a charged lepton, and present its dilepton invariant-mass spectrum and decay rate based on the effective electroweak Hamiltonian approach for the → ℓ + ℓ − transitions in the Standard Model, taking into account weak annihilation and long-distance contributions, of which the later is from the light vector mesons. Our prediction for the total branching fraction of + → + + − agrees with the latest LHCb result within the experimental and theoretical uncertainties. Moreover, including the annihilation diagrams and contributions from the 0 -and -resonances together gives better agreement with the experimental data in the low 2 -part of the dimuon mass spectrum. We also present theoretical predictions for the total and partial branching fractions for + → + + − in the Standard Model. These results are potentially useful in testing the lepton flavor universality in the FCNC → ℓ + ℓ − decays.