On nuclear states of [`(K)] \bar K mesons

The search for nuclear states of $ \bar K $ \bar K mesons poses interesting problems for the nuclear and low energy hadron physics: the behavior of tightly bound nuclear systems with strongly correlated impurities, the new kind of binding mechanisms and the extension of effective low energy theories to the strange sector. These problems are briefly presented and a method of variational calculation of the binding energies is discussed.     

On the superfield effective potential in three dimensions

We develop the superfield approach to the effective potential in three dimensions and calculate the one-loop and two-loop Kählerian effective potential in commutative and noncommutative cases.     

Preparation of quantum states of two spin-12 particles in the form of the Schmidt decomposition

We consider a system of two spins that are coupled via an isotropic Heisenberg Hamiltonian. For the first time, a two-step method for the preparation of an arbitrary quantum state of two qubits in the form of the Schmidt decomposition is proposed. The simplified version of this method is applied to the physical system of an atom with a nuclear spin 1/2 and one valence electron. As an example, the preparation of two-spin quantum states in the ³¹P system is considered.     

PT\mathcal{PT}-Symmetry in (Generalized) Effect Algebras

We show that an η ₊-pseudo-Hermitian operator for some metric operator η ₊ of a quantum system described by a Hilbert space H{\mathcal{H}} yields an isomorphism between the partially ordered commutative group of linear maps on H{\mathcal{H}} and the partially ordered commutative group of linear maps on H_r+{\mathcal{H}}_{\rho_{+}}. The same applies to the generalized effect algebras of positive operators and to the effect algebras of c-bounded positive operators on the respective Hilbert spaces H{\mathcal{H}} and H_r+{\mathcal{H}}_{\rho_{+}}. Hence, from the standpoint of (generalized) effect algebra theory both representations of our quantum system coincide.     

K*0 and φ meson production in proton–nucleus interactions at ?s=41.6\textGeV\sqrt{s}=41.6\text{GeV}

The inclusive production cross sections of the strange vector mesons K^*0, K̄^*0, and φ have been measured in interactions of 920 GeV protons with C, Ti, and W targets with the HERA-B detector at the HERA storage ring. Differential cross sections as a function of rapidity and transverse momentum have been measured in the central rapidity region and for transverse momenta up to p_T = 3.5 GeV/c. The atomic number dependence is parametrised as σ_pA=σ_pN*A^α, where σ_pN is the proton–nucleon cross section. Within the phase space accessible, α(K^*0)=0.86±0.03, α(K̄^*0)=0.87±0.03, and α(φ)=0.96±0.02. The total proton–nucleon cross sections, determined by extrapolating the differential measurements to full phase space, are σ_pN→K*0=(5.06±0.54) mb, σ_pN→K̄*0=(4.02±0.45) mb, and σ_pN→φ=(1.17±0.11) mb. For all resonances the Cronin effect is observed; compared to the measurements of Cronin et al. for K^± mesons, the measured values of α for φ mesons coincide with those of K⁺ mesons for all transverse momenta, while the enhancement for K^*0/K̄^*0 mesons is smaller.     

Spherical-separability of Non-Hermitian Hamiltonians and Pseudo- PT\mathcal{PT} -symmetry

Non-Hermitian but -symmetrized spherically-separable Dirac and Schr?dinger Hamiltonians are considered. It is observed that the descendant Hamiltonians H _r , H _θ , and H _φ play essential roles and offer some “user-feriendly” options as to which one (or ones) of them is (or are) non-Hermitian. Considering a -symmetrized H _φ , we have shown that the conventional Dirac (relativistic) and Schr?dinger (non-relativistic) energy eigenvalues are recoverable. We have also witnessed an unavoidable change in the azimuthal part of the general wavefunction. Moreover, setting a possible interaction V(θ)≠0 in the descendant Hamiltonian H _θ would manifest a change in the angular θ-dependent part of the general solution too. Whilst some -symmetrized H _φ Hamiltonians are considered, a recipe to keep the regular magnetic quantum number m, as defined in the regular traditional Hermitian settings, is suggested. Hamiltonians possess properties similar to the -symmetric ones (here the non-Hermitian -symmetric Hamiltonians) are nicknamed as pseudo- -symmetric.     

Two-loop graviton scattering relation and IR behavior in supergravity

We derive an ABDK-like relation between the one- and two-loop four-graviton amplitudes in supergravity. Specifically we show that the infrared-divergent part of the two-loop amplitude is one-half the square of the one-loop amplitude, suggesting an exponential structure for IR divergences. The difference between the two-loop amplitude and one-half the square of the full one-loop amplitude is therefore finite, and expressible in a relatively simple form. We give arguments for generalizations to higher loops and n-point functions, suggesting that the exponential of the full one-loop amplitude may be corrected, to low orders, by only simple finite terms.     

Description of Heavy Quark [`(MS)]\overline{MS} Mass by Lippmann-Schwinger Equation

Quark masses are of great prominence in high-energy physics. In this paper, we have studied the heavy meson systems via solving the Lippmann-Schwinger equation by using the Martin potential for heavy quark masses. We have also attempted to use Martin potential to find an acceptable mass spectrum for heavy quarkonia. We obtained this spectrum via minimal phenomenological model (Melles in Phys. Rev. D. 62:074019, 2000).