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Discusses the development of the theory of the existence of neutrinos, and examines the struggle to detect and understand the tiny particles.

The second-order equation in the (1/2, 0) [direct sum] (0, 1/2) representation of the Lorentz group has been proposed by A. Barut in the 70s [1]. It permits to explain the mass splitting of leptons (e, [mu], [tau]). The interest is growing in this model (see, for instance, the papers by S. Kruglov [2] and J. P. Vigier et al. [3,4]). We note some additional points of this model.

Status of the Bc meson excitatons search is presented in our work. We discuss the 2S Bc states first discovered by ATLAS and newly confirmed by CMS and LHCb collaborations. We review the observation prospects for the rest predicted states (B∗c, 2P wave, 3P wave and D wave) at LHC experiments. Cascade decays to the ground state as well as direct decays to the lepton pair are regarded for these states.

In the paper, we study the \\[\\Upsilon (1S)\\] leptonic decay width \\[\\Gamma (\\Upsilon (1S)\\rightarrow \\ell ^+\\ell ^-)\\] by using the principle of maximum conformality (PMC) scale-setting approach. The PMC adopts the renormalization group equation to set the correct momentum flow of the process, whose value is independent to the choice of the renormalization scale and its prediction thus avoids the conventional renormalization scale ambiguities. Using the known next-to-next-to-next-to-leading order perturbative series together with the PMC single scale-setting approach, we do obtain a renormalization scale independent decay width, \\[\\Gamma _{\\Upsilon (1S) \\rightarrow e^+ e^-} = 1.262^{+0.195}_{-0.175}\\] keV, where the error is squared average of those from \\[\\alpha _s(M_{Z})=0.1181\\pm 0.0011\\], \\[m_b=4.93\\pm 0.03\\] GeV and the choices of factorization scales within \\[\\pm 10\\%\\] of their central values. To compare with the result under conventional scale-setting approach, this decay width agrees with the experimental value within errors, indicating the importance of a proper scale-setting approach.

A bstract Charged lepton flavor violation is forbidden in the Standard Model but possible in several new physics scenarios. In many of these models, the radiative decays τ ± → ℓ ± γ ( ℓ = e, μ ) are predicted to have a sizeable probability, making them particularly interesting channels to search at various experiments. An updated search via τ ± → ℓ ± γ using full data of the Belle experiment, corresponding to an integrated luminosity of 988 fb − 1 , is reported for charged lepton flavor violation. No significant excess over background predictions from the Standard Model is observed, and the upper limits on the branching fractions, B ( τ ± → μ ± γ ) ≤ 4 . 2 × 10 − 8 and B ( τ ± → e ± γ ) ≤ 5 . 6 × 10 − 8 , are set at 90% confidence level.

One-loop on-shell and off-shell decays H → VV with VV = γγ, Zγ, ZZ are presented in this paper. The effects of one-loop on-shell and off-shell Higgs decays via Higgs productions at future lepton colliders are also then examined. We find that the impacts of one-loop Higgs decays are significant and they are should be taken into account at future lepton colliders.

We present a comprehensive analysis of neutrino mass and lepton mixing in theories with A4 modular symmetry, where the only flavon field is the single modulus field τ, and all masses and Yukawa couplings are modular forms. Similar to previous analyses, we discuss all the simplest neutrino sectors arising from both the Weinberg operator and the type I seesaw mechanism, with lepton doublets and right-handed neutrinos assumed to be triplets of A4. Unlike previous analyses, we allow right-handed charged leptons to transform as all combinations of 1, 1′ and 1′′ representations of A4, using the simplest different modular weights to break the degeneracy, leading to ten different charged lepton Yukawa matrices, instead of the usual one. This implies ten different Weinberg models and thirty different type I seesaw models, which we analyse in detail. We find that fourteen models for both NO and IO neutrino mass ordering can accommodate the data, as compared to one in previous analyses, providing many new possibilities.

A bstract A search is presented for physics beyond the standard model (SM) using electron or muon pairs with high invariant mass. A data set of proton-proton collisions collected by the CMS experiment at the LHC at s = 13 TeV from 2016 to 2018 corresponding to a total integrated luminosity of up to 140 fb − 1 is analyzed. No significant deviation is observed with respect to the SM background expectations. Upper limits are presented on the ratio of the product of the production cross section and the branching fraction to dileptons of a new narrow resonance to that of the Z boson. These provide the most stringent lower limits to date on the masses for various spin-1 particles, spin-2 gravitons in the Randall-Sundrum model, as well as spin-1 mediators between the SM and dark matter particles. Lower limits on the ultraviolet cutoff parameter are set both for four-fermion contact interactions and for the Arkani-Hamed, Dimopoulos, and Dvali model with large extra dimensions. Lepton flavor universality is tested at the TeV scale for the first time by comparing the dimuon and dielectron mass spectra. No significant deviation from the SM expectation of unity is observed.

Following the updated measurement of the lepton flavour universality (LFU) ratio R K in B → K ℓ ℓ decays by LHCb, as well as a number of further measurements, e.g. R K ∗ by Belle and B s → μ μ by ATLAS, we analyse the global status of new physics in b → s transitions in the weak effective theory at the b -quark scale, in the Standard Model effective theory above the electroweak scale, and in simplified models of new physics. We find that the data continues to strongly prefer a solution with new physics in semi-leptonic Wilson coefficients. A purely muonic contribution to the combination C 9 = - C 10 , well suited to UV-complete interpretations, is now favoured with respect to a muonic contribution to C 9 only. An even better fit is obtained by allowing an additional LFU shift in C 9 . Such a shift can be renormalization-group induced from four-fermion operators above the electroweak scale, in particular from semi-tauonic operators, able to account for the potential discrepancies in b → c transitions. This scenario is naturally realized in the simplified U 1 leptoquark model. We also analyse simplified models where a LFU effect in b → s ℓ ℓ is induced radiatively from four-quark operators and show that such a setup is on the brink of exclusion by LHC di-jet resonance searches.

The charge-conjugation and parity-reversal (CP) symmetry of fundamental particles is a symmetry between matter and antimatter. Violation of this CP symmetry was first observed in 1964 1 , and CP violation in the weak interactions of quarks was soon established 2 . Sakharov proposed 3 that CP violation is necessary to explain the observed imbalance of matter and antimatter abundance in the Universe. However, CP violation in quarks is too small to support this explanation. So far, CP violation has not been observed in non-quark elementary particle systems. It has been shown that CP violation in leptons could generate the matter–antimatter disparity through a process called leptogenesis 4 . Leptonic mixing, which appears in the standard model’s charged current interactions 5 , 6 , provides a potential source of CP violation through a complex phase δ CP , which is required by some theoretical models of leptogenesis 7 – 9 . This CP violation can be measured in muon neutrino to electron neutrino oscillations and the corresponding antineutrino oscillations, which are experimentally accessible using accelerator-produced beams as established by the Tokai-to-Kamioka (T2K) and NOvA experiments 10 , 11 . Until now, the value of δ CP has not been substantially constrained by neutrino oscillation experiments. Here we report a measurement using long-baseline neutrino and antineutrino oscillations observed by the T2K experiment that shows a large increase in the neutrino oscillation probability, excluding values of δ CP that result in a large increase in the observed antineutrino oscillation probability at three standard deviations (3 σ ). The 3 σ confidence interval for δ CP , which is cyclic and repeats every 2π, is [−3.41, −0.03] for the so-called normal mass ordering and [−2.54, −0.32] for the inverted mass ordering. Our results indicate CP violation in leptons and our method enables sensitive searches for matter–antimatter asymmetry in neutrino oscillations using accelerator-produced neutrino beams. Future measurements with larger datasets will test whether leptonic CP violation is larger than the CP violation in quarks. The T2K experiment constrains CP symmetry in neutrino oscillations, excluding 46% of possible values of the CP violating parameter at a significance of three standard deviations; this is an important milestone to test CP symmetry conservation in leptons and whether the Universe’s matter–antimatter imbalance originates from leptons.