International Journal of Modern Physics A

The BESIII and the LHCb became the leading experiments in the study of the exotic states after the Belle and BaBar experiments finished their data taking in the first decade of this century. We review the progress in the study of the XYZ states at BESIII and LHCb experiments with their unique data samples in $e^{+}{e}^{-}$ annihilation at center-of-mass energies of 3.8–4.6 GeV and in $pp$ collision at center-of-mass energies 7, 8, and 13 TeV, respectively. With these data samples, we have deepened our understanding of the most famous charmonium-like states $X(3872)$, $Y(4260)$, $Z_c(3900)$, and $Z_c(4430)$, as well as other similar states like the $Y(4140)$ and $X(3823)$. We review the progress in the study of these states and also discuss perspectives at future experiments.

In a strong magnetic field utilizing a two-flavor NJL model, the isospin symmetry and asymmetry can be realized by altering the fraction parameter $\alpha$ of the two kinds of interactions, i.e. the scalar coupling and instanton-induced coupling. As $\alpha$ increases, the $u$ quark mass decreases while $d$ quark mass increases monotonously. The two mass lines cross at $\alpha =0.5$ with an isospin symmetry mass $M_u=M_d$. Even in the flavor-decoupled state, i.e. the strong isospin asymmetry, the $u$ and $d$ mass lines can have a common mass at a critical temperature $T_{\mathrm{\text{s}}}$. As the magnetic field becomes stronger, the $T_{\mathrm{\text{s}}}$ will move towards the chiral restoration phase. The strong isospin asymmetry will lead to a split of the pseudocritical temperatures for $u$ and $d$ quarks, which can be reflected by the two peaks of the specific heat and sound velocity.

We consider the production of the new gauge boson $Z_{\mu \tau }$ predicted by the $U{(1)}_{L_{\mu }-L_{\tau }}$ model via SM-like Higgs boson $h_1$ decaying in the $t\bar{t}{h}_1$ production at LHC. Considering the current constraints on the relevant free parameters, we calculate its production cross-section and further investigate the possibility of detecting $Z_{\mu \tau }$ through the process $pp\to t(\to bjj)\bar{t}(\to \bar{b}{l}^{-}{\bar{\nu }}_l)h_1(\to Z_{\mu \tau }{Z}_{\mu \tau })\to b\bar{b}jj{l}^{-}{\bar{\nu }}_l+{/E}_T$ at LHC. We find that $Z_{\mu \tau }$ might be detected via this process at LHC with high integrated luminosity.

The rare semileptonic $B\to K{\mu }^{+}{\mu }^{-}$ and $B\to \varphi {\mu }^{+}{\mu }^{-}$ decay modes mediated by the $b\to s{\mu }^{+}{\mu }^{-}$ transition are studied in this paper. We analyze observables such as the differential branching ratio, lepton polarization asymmetry and forward–backward asymmetry within the standard model in the low $q^2$ region. We then perform an analysis of the same modes within the 331 or $S{U}_C(3)\times S{U}_L(3)\times U_X(1)$ model in which a new heavy $Z^{\prime }$ boson contributes. The effects of the $Z^{\prime }$-mediated flavor-changing neutral current (FCNC) transitions on these modes are investigated by varying the mass $M_{Z^{\prime }}$ and the model parameter $\beta$. The new $Z^{\prime }$ couplings are constrained by flavor observables of $B_s-{\bar{B}}_s$ mixing and branching ratio of $B_s\to {\mu }^{+}{\mu }^{-}$. We find that for some values of these couplings, the observables are quite sensitive to $Z^{\prime }$ effects and deviations from Standard Model can be large.

We study the 2D massive fields in the presence of moving mirrors. We do that for standing mirror and mirror moving with constant velocity. We calculate the modes and commutation relations of the field operator with the corresponding conjugate momentum in each case. We find that in case of the ideal mirror, which reflects modes with all momenta equally well, the commutation relations do not have their canonical form. However, in the case of nonideal mirror, which is transparent for the modes with high enough momenta, the commutation relations of the field operator and its conjugate momentum have their canonical form. Then, we calculate the free Hamiltonian and the expectation value of the stress-energy tensor in all the listed situations. In the presence of moving mirrors the diagonal form in terms of the creation and annihilation operators has the operator that performs translations along the mirror’s worldline rather than the one which does translations along the time-line. For the massive fields in the presence of a mirror moving with constant velocity the expectation value of the stress-energy tensor has a nondiagonal contribution which decays with the distance from the mirror.

We show that MSSM with three right-handed neutrinos (RHNs) incorporating a renormalizable Type-I seesaw superpotential and no-scale SUGRA Kähler potential can lead to a Starobinsky kind of inflation potential along a flat direction associated with gauge invariant combination of Higgs, slepton and right-handed sneutrino superfields. The inflation conditions put constraints on the Dirac Yukawa coupling and the Majorana masses required for the neutrino masses and also demand the tuning among the parameters. The scale of inflation is set by the mass of the heaviest right-handed neutrino. We also fit the neutrino data from oscillation experiments at low scale using the effective RGEs of MSSM with three right-handed neutrinos.

In this paper, we consider two examples of an entanglement in two-qubit systems and an example of entanglement in quantum field theory (QFT). In the beginning, we study the entanglement of two spin states by a magnetic field. A nonzero entanglement appears for interacting spins. When the coupling between the spins is constant, we study the entanglement by several types of time-dependent magnetic fields. In the case of a constant difference between $z$ components of magnetic fields acting on each spin, we find several time-dependent coupling functions $J(t)$ that also allow us to analyze analytically and numerically the entanglement measure. Considering two photons moving in an electron medium, we demonstrate that they can be entangled in a controlled way by applying an external magnetic field. The magnetic field affecting electrons of the medium affects photons and, thus, causes an entanglement of the photon beams. The third example is related to the effect of production of electron–positron pairs from the vacuum by a strong external electric field. Here, we have used a general nonperturbative expression for the density operator of the system under consideration. Applying a reduction procedure to this density operator, we construct mixed states of electron and positron subsystems. Calculating the von Neumann entropy of such states, we obtain the loss of information due to the reduction and, at the same time, the entanglement measure of electron and positron subsystems. This entanglement can be considered as an example of an entanglement in QFT.