Modern Physics Letters A

Planck scale physics represents a future challenge, located between particle physics and general relativity. The Planck scale marks a threshold beyond which the old description of spacetime breaks down and conceptually new phenomena must appear. Little is known about the fundamental theory valid at Planckian energies, except that it necessarily seems to imply the occurrence of a minimal length scale, providing a natural ultraviolet cutoff and a limit to the possible resolution of spacetime.

Motivated by String Theory, the models of large extra dimensions lower the Planck scale to values soon accessible. These models predict a vast number of quantum gravity effects at the lowered Planck scale, among them the production of TeV-mass black holes and gravitons. Within the extra dimensional scenario, the minimal length also comes into the reach of experiment and sets a fundamental limit to short distance physics.

We review the status of Planck scale physics in these effective models.

We analyse the CP asymmetry of the B→ϕK_S and B→η'K_S processes in general supersymmetric models. We consider both gluino and chargino exchanges in a model-independent way by using the mass insertion approximation method. We adopt the QCD factorization method for evaluating the corresponding hadronic matrix elements. We show that chromomagnetic type of operator may play an important role in accounting for the deviation of the mixing CP asymmetry between B→ϕK_S and B→J/ψK_S processes observed by Belle and BaBar experiments. We also show that due to the different parity in the final states of these processes, their supersymmetric contributions from the R-sector have an opposite sign, which naturally explain the large deviation between their asymmetries.

A system consisting of an ion and an electron interacting through the Hulthén potential confined in an impenetrable spherical box, with the ion at the centre is considered. Superpotential which is the crucial quantity in supersymmetric quantum mechanics is proposed for the 1s and 2p states. Variational wave functions are thence derived. Energies are calculated from these for different values of the radius of box (R) and these are compared to the exact values; good agreement is shown to exist between the two. The variational wave functions are further employed to calculate the absorption oscillator strength for the 1s→2p transition and the dipole polarizability for different values of R.

A systematic procedure to study one-dimensional Schrödinger equation with a position-dependent effective mass (PDEM) in the kinetic energy operator is explored. The conventional free-particle problem reveals a new and interesting situation in that, in the presence of a mass background, formation of bound states is signalled. We also discuss coordinate-transformed, constant-mass Schrödinger equation, its matching with the PDEM form and the consequent decoupling of the ambiguity parameters. This provides a unified approach to many exact results known in the literature, as well as to a lot of new ones.

We show how, in canonical quantum cosmology, the frame fixing induces a new energy density contribution having features compatible with the (actual) cold dark matter component of the Universe. First we quantize the closed Friedmann–Robertson–Walker (FRW) model in a synchronous reference and determine the spectrum of the super-Hamiltonian in the presence of ultra-relativistic matter and a perfect gas contribution. Then we include in this model small inhomogeneous (spherical) perturbations in the spirit of the Lemaitre–Tolman cosmology. The main issue of our analysis consists in outlining that, in the classical limit, the nonzero eigenvalue of the super-Hamiltonian can account for the present value of the dark matter critical parameter. Furthermore we obtain a direct correlation between the inhomogeneities in our dark matter candidate and those that appear in the ultra-relativistic matter.

A class of exact static solution around a global monopole resulting from the breaking of a global SO(3) symmetry is obtained in the context of Lyra geometry.

Our solution is shown to possess an interesting feature like "wormholes" spacetime. It has been shown that the global monopole exerts no gravitational force on surrounding nonrelativistic matter.

Using the picture of the flux tube model, we propose that the Θ₅ pentaquark as the first candidate of the three-dimensional non-planar hadron with the extremely stable diamond structure. The up and down quarks lie at the corners of the diamond while the anti-strange quark sits in the center. Various un-excited color flux tubes between the five quarks bind them into a stable and narrow color-singlet. Such a configuration allows the lowest state having the negative parity naturally. The decay of the Θ₅ pentaquark into the nucleon and kaon requires the breakup of the non-planar diamond configuration into two conventional planar hadrons, which involves some kind of structural phase transition as in the condensed matter physics. Hence the width of the Θ⁺ pentaquark should be narrow despite that it lies above the kaon nucleon threshold. We suggest that future lattice QCD calculation adopt non-planar interpolating currents to explore the underlying structure of the Θ₅ pentaquark.