Modern Physics Letters A

I reflect on some of the basic aspects of present day Beyond the Standard Model particle physics, focusing mostly on the issues of naturalness, in particular on the so-called hierarchy problem. To all of us, physics as natural science emerged with Galileo and Newton, and led to centuries of unparalleled success in explaining and often predicting new phenomena of nature. I argue here that the long-standing obsession with the hierarchy problem as a guiding principle for the future of our field has had the tragic consequence of deviating high energy physics from its origins as natural philosophy, and turning it into a philosophy of naturalness.

New LHCb Collaboration results on pentaquarks with hidden charm¹ are discussed. These results fit nicely in the hadrocharmonium pentaquark scenario.${}^{2,3,}$ In the new data the old LHCb pentaquark $P_c(4450)$ splits into two states $P_c(4440)$ and $P_c(4457)$. We interpret these two almost degenerated hadrocharmonium states with $J^P=1/2^{-}$ and $J^P=3/2^{-}$, as a result of hyperfine splitting between hadrocharmonium states predicted in Ref. 2. It arises due to QCD multipole interaction between color-singlet hadrocharmonium constituents. We improve the theoretical estimate of hyperfine splitting${}^{2,3}$ that is compatible with the experimental data. The new $P_c(4312)$ state finds a natural explanation as a bound state of ${\chi }_{c0}$ and a nucleon, with $I=1/2$, $J^P=1/2^{+}$ and binding energy 42 MeV. As a bound state of a spin-$0$ meson and a nucleon, hadrocharmonium pentaquark $P_c(4312)$ does not experience hyperfine splitting. We find a series of hadrocharmonium states in the vicinity of the wide $P_c(4380)$ pentaquark that can explain its apparently large decay width. We compare the hadrocharmonium and molecular pentaquark scenarios and discuss their relative advantages and drawbacks.

The rare top quark decays mediated by a new neutral massive gauge boson that is predicted in models with extended gauge symmetries are studied. We focus on the processes $t\to cV,uV$ induced at the one loop level, where $V=\gamma ,g$, by considering different extended models. It is found that, within a broad range of mass of the new neutral gauge boson, the models predict branching ratios for the decays in study that are competitive with respect to the corresponding branching ratios in the Standard Model (SM). In order to establish bound on our branching ratios, we consider the recent experimental bounds as $m_{Z^{\prime }}\ge 3.8\text{–}4.5\mathrm{\text{TeV}}$, depending on the model, which also impose restrictions on our calculation. Even in this case, the resulting branching ratios are of the same order of magnitude as that predicted by the SM. It should be noted that for the case of two models studied here, since no experimental bound exists to compare with, the results could be important, as they are, in the best of cases, two orders of magnitude larger than the predicted by the SM.

In this paper, we calculate the quantum anomaly for the longitudinal and the transverse Ward–Takahashi (WT) identities for vector and axial-vector currents in QED₂ theory by means of the point-splitting method. It is found that the longitudinal WT identity for vector current and transverse WT identity for axial-vector current have no anomaly while the longitudinal WT identity for axial-vector current and the transverse WT identity for vector current have anomaly in QED₂ theory. Moreover, we study the four WT identities in massless QED₂ theory and get the result that the four WT identities together give the constraint equation of the vertex function of quantum anomaly. At last, we discuss the Dyson–Schwinger equations in massless QED₂ theory. It is found that the vertex function of the quantum anomaly has corrections for the fermion propagator and Schwinger model.

The degenerate Ferrari-Ibanez solution describes the collision of plane gravitational waves with aligned linear polarization, within the interaction region, the solution is Schwarzschild-like metric, which impels us to be more interesting to analyze the collision process. In this paper, we have considered the electrodynamics effects on the colliding gravitational waves background. Moreover, we have calculated explicitly out the solutions of the electromagnetic waves produced by the plane gravitational wave and the colliding region of plane gravitational waves perturbing a weak magnetic field background. We also work out the solutions of these electromagnetic waves after crossing out a weak magnetic field background.

The aim of this paper is to investigate the existence of stable modes of the Einstein static universe in the background of $f(R)$ theory. For this purpose, we take homogeneous anisotropic perturbations in scale factors as well as matter contents. We construct static and perturbed field equations that are further parameterized by linear equation of state parameter. We obtain the Einstein static solutions for two specific $f(R)$ models and graphically analyze their stable regions. It is concluded that contrary to general relativity, there exists stable Einstein static universe with anisotropic perturbations.

The renormalization program in every renormalized theory should run consistently with the type of boundary condition imposed on quantum fields. To maintain this consistency, the counterterms usually appear in the position-dependent form. In this study, using such counterterms, we calculated the radiative correction to the Casimir energy for massive and massless Lorentz-violating scalar field constrained with Dirichlet boundary condition between two parallel plates in $d$ spatial dimensions. In the calculation procedure, to remove infinities appearing in the vacuum energies, the box subtraction scheme (BSS) supplemented by the cutoff regularization technique and analytic continuation technique was employed. Normally, in the BSS, two similar configurations are defined and their vacuum energies are subtracted from each other in the appropriate limits. Our final results regarding all spatial dimensions were convergent and consistent with the expected physical basis. We further plotted the Casimir energy density for the time-like and space-like Lorentz-violating systems in a number of odd and even dimensions; multiple aspects of the obtained results were ultimately discussed.

In this paper, we consider the $d$-mode $q$-deformed bosonic Newton oscillators. Regarding photon and phonon as the particles obeying the multi-mode $q$-deformed bosonic Newton algebra, we discuss the blackbody radiation and Debye model.

A digital signature with designated verifier (SWDV) makes that only the designated verifier can verify its validity. It can be used to protect the privacy and economic interest of the signer. So, the SWDV schemes have many applications in e-voting, auction and some other fields. To make the SWDV secure against the quantum forger, a quantum signature with designated verifier signature (QSWDV) scheme is proposed. Our QSWDV is robust due to its strong security against forgery attack, inter-resending attacks, impersonation attacks and Trojan horse attacks. Its properties such as non-transferability and hiding source can be guaranteed by the signature simulation of the designated verifier. What is more, our scheme can be proved to be information-theoretically secure, which can guarantee the secrecy of the signer’s private key and the unforgeability of the QSWDV. In the proposed QSWDV scheme, the partners neither need use quantum one-way function nor need perform quantum state comparisons, which can reduce the complexity and improve the efficiency the QSWDV scheme.