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Abstract: The possibility that pairs of quarks will form diquark clusters in the regime above deconfinement transition for hadron matter at finite density is revisited. Here we present the results on the diquark-diquark (dq-dq) interaction in the framework of constituent quark model taking account of spin, isospin and color degrees of freedom in the spirit of generalized Pauli principle. By constructing the appropriate spin and color states of the dq-dq clusters we compute the expectation values of the interaction Hamiltonian involving pairwise quark—quark interaction. We find that the effective interaction between two diquark clusters is quite sensitive to different configurations characterized by color and spin states, obtained after the coupling of two diquark states. The value of the coupling parameter for a particular color—spin state, i.e., -3, 1 is compared to the one obtained earlier by Donoghue and Sateesh,Phys. Rev. D38, 360 (1988) based on the effective Φ4-theory. This new value of λ derived for different color-spin dq-dq states, may lead to several important implications in the studies of diquark star and diquark gas.

Abstract: Motivated by relatively large values of the maximum mass (M = 8.92M⊙) and radius (R = 507 km) obtained for an extended scalar diquark star within the framework of an effective φ4-theory (S K Karnet al [1]) some interesting observations are made with regard to the stability of stellar objects describable in general in terms of the polynomial field theories

Abstract: The construction of invariants up to fourth order in velocities has been carried out for one-dimensional, time-dependent classical dynamical systems. While the exact results are recovered for the first and second order integrable systems, the results for the third and fourth order invariants are expressed in terms of nonlinearpotential equations. Noticing the separability of the potential in space and time variables these nonlinear equations are reduced to a tractable form. A possible solution for the third order case suggests a new integrable systemV(q, t) ∼t −4/3 q 1/2.

A new system of time-dependent anharmonic and anisotropic oscillators in two space-dimensions which corresponds to unequal but related spring constants, having Hamiltonian structure, admitting quadratic invariants and accounting also for the fractional powers in the coupling terms, is found.

The ground state of a class of potentials described byV(x)=a20x2+a1/x2is investigated. This potential possesses some distinct features like that of a symmetric double-well potential, and can be used in modelling the fusion process of two identical nuclei as well.

The construction of the second constant of motion of second order for two-dimensional classical systems is carried out in terms ofz=q1+iq2andq=q1−iq2. As a result a class of Toda-type potentials admitting second order invariants is explored.

With a view to understand the available data on the momentum- and energy-dependences of theJ/Ψsuppression, we compute the suppression rate within the framework of a hydrodynamical evolution model for the quark-gluon plasma (QGP) formation. We make use of an ansatz for the temperature profile function which accounts not only for the space and time evolutions of QGP but also for the possibility of a mixed phase in the boundary region of the deconfined phase. While the predictions are made for the longitudinal momentum- and energy-dependences of the suppression rate, a satisfactory agreement with the available data is found for its dependences on the transverse momentum and the transverse energy.