Modern Physics Letters A

The LHCb experiment is one of four major experiments at the large hadron collider (LHC). Despite being designed for the study of beauty and charm particles, it has made important contributions in other areas, such as the production and decay of W and Z bosons. Such measurements can be used to study and constrain parton distribution functions (PDFs), as well as to test perturbative quantum chromodynamics (QCD) in hard scattering processes. The angular structure of Z boson decays to leptons can also be studied and used to measure the weak mixing angle. The phase–space probed by LHCb is particularly sensitive to this quantity, and the LHCb measurement using the dimuon final state is currently the most precise determination of ${sin}^2{𝜃}_{\mathrm{\text{eff}}.}^{\mathrm{\text{lept}}.}$ at the LHC. LHCb measurements made using data collected during the first period of LHC operations (LHC Run 1) are discussed in this review. The paper also considers the potential impact of related future measurements.

To accommodate the recently observed nonzero reactor mixing angle ${𝜃}_{13}$, we consider the lepton mixing matrix as tri-bimaximal mixing (TBM) form in the leading order along with a perturbation in neutrino sector. The perturbation is taken to be a rotation in 23 plane followed by a rotation in 13 plane, i.e. $R_{23}({𝜃}_{23}^{\prime })R_{13}({𝜃}_{13}^{\prime },\varphi )$. We obtain the allowed values of the parameters ${𝜃}_{23}^{\prime }$, ${𝜃}_{13}^{\prime }$ and $\varphi$, which can accommodate all the observed mixing angles consistently and calculate the phenomenological observables such as the Dirac CP violating phase $({\delta }_{\mathrm{\text{CP}}})$, Jarlskog invariant $(J_{\mathrm{\text{CP}}})$, effective Majorana mass $M_{ee}^{\nu }$ and $m_{{\nu }_e}$, the electron neutrino mass. We find that ${\delta }_{\mathrm{\text{CP}}}$ can take any values between $0$ and $-\pi /2$ and $M_{ee}^{\nu }$ always comes below its experimental upper limit.

Motivated by the heavy-flavor experiments at running Large Hadron Collider (LHC) and upgrading SuperKEKB, which provide abundant $\mathrm{{\rm Y}}$ data samples, the tree-dominated $\mathrm{{\rm Y}}(nS)\to B_c\rho$ and $B_c{K}^{\ast }$ (n =1, 2, 3) weak decays are studied within the framework of quantum chromodynamics (QCD) factorization. The QCD corrections to the longitudinal and transverse amplitudes are evaluated at next-to-leading order, and the branching fractions and polarization fractions are predicted. Numerically, the $\mathrm{{\rm Y}}(nS)\to B_c\rho$ decays have relatively large branching fractions at the order of ${𝒪}(10^{-10})$ and are in the scope of the LHC and SuperKEKB/Belle-II experiments.

Fermion bilinear operators of mass dimension 3, such as the axial-vector and vector currents, the pseudo-scalar and scalar densities, whose normalizations are fixed by Ward–Takahashi (WT) relations, are related to small flow-time behavior of composite operators of fermion fields evolved by Lüscher’s flow equation. The representations can be useful in lattice numerical simulations, as recently demonstrated by the WHOT QCD collaboration for the chiral condensation of the $N_f=2+1$ quantum chromodynamics (QCD) at finite temperature.

We report on a measurement of the constancy and anisotropy of the speed of light relative to the electrons in photon–electron scattering. We used the Compton scattering asymmetry measured by the new Compton polarimeter in Hall C at Jefferson Lab (JLab) to test for deviations from unity of the vacuum refractive index (n). For photon energies in the range of 9–46 MeV, we obtain a new limit of 1 − n < 1.4 × 10${}^{-8}$. In addition, the absence of sidereal variation over the six-month period of the measurement constrains any anisotropies in the speed of light. These constitute the first study of Lorentz invariance (LI) using Compton asymmetry. Within the minimal Standard Model extension (MSME) framework, our result yield limits on the photon and electron coefficients ${\tilde{\kappa }}_{0^{+}}^{YZ}$, $c_{TX}$, ${\tilde{\kappa }}_{0^{+}}^{ZX}$ and $c_{TY}$. Although these limits are several orders of magnitude larger than the current best limits, they demonstrate the feasibility of using Compton asymmetry for tests of LI. Future parity-violating electron-scattering experiments at JLab will use higher energy electrons enabling better constraints.

Inspired by some recent works of Lovelock Brans–Dicke (BD) gravity and mimetic gravity, cosmology solutions in extensions of these two modified gravities are investigated. A nonlocal term is added to the Lovelock BD action and Gauss–Bonnet (GB) terms to the mimetic action, correspondingly. de Sitter and power scale factor solutions are then obtained in both theories. They can provide natural new approaches to a more accurate description of the unverse evolution.

As a new step in the study of rectangularly-colored knot polynomials, we reformulate the prescription [A. Morozov, arXiv:1606.06015v8] for twist knots in the double-column representations $R=[rr]$ in terms of skew Schur polynomials. These, however, are mysteriously shifted from the standard topological locus, which makes further generalization to arbitrary $R=[r^s]$ not quite straightforward.