Opposite Parity Research Articles

Rarita-Schwinger field: Dressing procedure and spin-parity of components

We obtain in analytical form the dressed propagator of the massive Rarita-Schwinger field taking into account all spin components. We found that the nearest analogy for dressing the Rarita--Schwinger field in spin--1/2 sector is dressing the two Dirac fermions of opposite parity with presence of mutual transitions. The calculation of the self-energy contributions confirms that besides the leading spin--3/2 component the Rarita--Schwinger field contains also two spin--1/2 components of different parity.

Quark-lepton complementarity relation and neutrino mass hierarchy

Latest measurements have revealed that the deviation from a maximal solar mixing angle is approximately the Cabibbo angle, i.e. QLC relation. We argue that it is not plausible that this deviation from maximality, be it a coincidence or not, comes from the charged lepton mixing. Consequently we have calculated the required corrections to the exactly bimaximal neutrino mass matrix ansatz necessary to account for the solar mass difference and the solar mixing angle. We point out that the relative size of these two corrections depends strongly on the hierarchy case under consideration. We find that the inverted hierarchy case with opposite CP parities, which is known to guarantee the RGE stability of the solar mixing angle, offers the most plausible scenario for a high energy origin of a QLC-corrected bimaximal neutrino mass matrix. This possibility may allow us to explain the QLC relation in connection with the origin of the charged fermion mass matrices.

To a possibility of parity violation measurements in nuclear isomers with the use of internal conversion electrons

Enhancement mechanisms of a weak nucleon- nucleon interaction, which are exist in nuclei, cause observed P-odd effects are several orders higher than that ones in few-nucleon systems. Experiment for search parity violation effects in a nuclear decay of180mHf through the use of electrons of internal nuclear conversion as well as for search a new parity violation mechanism in low-lying states of119mSn, which are not associated with an inteference of close-lying states of opposite parity, are suggested. A P-odd asymmetry\((\vec J\overrightarrow {k_e } )\) at a decay of polarized nuclear isomers180mHf and119mSn through the electrons of internal conversion can be investigated. (Here\(\vec J\) and\(\vec k\) are vectors of a nuclear polarization and a conversion electron momentum, correspondingly).

The thermodynamic characterization of spontaneous electrochemical reactions

We consider whether the association of charged species of opposite parity in a chemical cell constitutes a spontaneous reaction. The initial distributions of the species are modeled as a steady-state phenomenon, characterized by a drift-diffusion system and two coupled constraints: (1) the electroneutrality of net system charge; and, (2) a coupled thermodynamic inequality constraint, reflecting the net decrease of the Gibbs' free energy in the closed system required for any spontaneous chemical reaction leading to uniform association of the species. A useful analytical technique of partial convexity allows the reformulation of thermodynamic compatibility. A control theory interpretation of the Dirichlet boundary conditions allows the selection of a trapping region for the range of the solution components which ensures that the reaction is spontaneous. A specific application is the production of hydrogen in an electrochemical cell. This is contained in a larger modeling context: reduction processes in electrochemistry. The final section describes extensions of the modeling in which an open mathematical problem and a pointer to the nonisothermal case are identified.

A (Not So) Complex Solution to a2 + b2 = cn

(2004). A (Not So) Complex Solution to a2 + b2 = cn. Mathematics Magazine: Vol. 77, No. 4, pp. 300-302.

Chiral doublers of heavy-light baryons

We discuss the consequences of the chiral doubling scenario for baryons built of heavy and light quarks. In particular, we use the soliton description for baryons, demonstrating why each heavy-light baryon should be accompanied by the opposite parity partner. Our argumentation holds both for ordinary baryons and for exotic heavy pentaquarks which are required by the symmetries of QCD to appear in parity doublets, seperated by the mass shift of the chiral origin. Interpreting the recently observed by BaBaR, CLEO and Belle charmed mesons with assignment $(0^+,1^+)$ as the chiral partners of known $D$ and $D^*$ mesons, allows us to estimate the parameters of the mesonic effective lagrangian, and in consequence, estimate the masses of ground states and excited states of both parities. In particular, we interpret the state recently reported by the H1 experiment at HERA as a chiral partner $\tilde{\Theta}_c^0(3099)$ of yet undiscovered ground state pentaquark $\Theta_c^0(2700)$.

Numerical consistency check between two approaches to radiative corrections for neutrino masses and mixings

We briefly outline the two popular approaches on radiative corrections to neutrino masses and mixing angles, and then carry out a detailed numerical analysis for a consistency check between them in MSSM. We find that the two approaches are nearly consistent with a discrepancy factor of 4.2% with running vacuum expectation value (VEV) (13% for scale-independent VEV) in mass eigenvalues at low-energy scale but the predictions on mixing angles are almost consistent. We check the stability of the three types of neutrino models, i.e., hierarchical, inverted hierarchical and degenerate models, under radiative corrections, using both approaches, and find consistent conclusions. The neutrino mass models which are found to be stable under radiative corrections in MSSM are the normal hierarchical model and the inverted hierarchical model with opposite CP parity. We also carry out numerical analysis on some important conjectures related to radiative corrections in the MSSM, viz., radiative magnification of solar and atmospheric mixings in the case of nearly degenerate model having same CP parity (MPR conjecture) and radiative generation of solar mass scale in exactly two-fold degenerate model with opposite CP parity and non-zero Ue3 (JM conjecture). We observe certain exceptions to these conjectures. We find a new result that both solar mass scale and Ue3 can be generated through radiative corrections at low energy scale. Finally the effect of scaledependent vacuum expectation value in neutrino mass renormalisation is discussed

On a Problem of D. H. Lehmer and General Kloosterman Sums

Let q ≥ 3 be an odd number, a be any fixed positive integer with (a, q) = 1. For each integer b with 1 ≤ b < q and (b, q) = 1, it is clear that there exists one and only one c with 0 < c < q such that bc ≡ a (mod q). Let N(a, q) denote the number of all solutions of the congruent equation bc ≡ a (mod q) for 1 ≤ b, c < q in which b and c are of opposite parity, and let $$ E{\left( {a,q} \right)} = N{\left( {a,q} \right)} - \frac{1} {2}\phi {\left( q \right)} $$ . The main purpose of this paper is to study the distribution properties of E(a, q), and give a sharper hybrid mean-value formula involving E(a, q) and general Kloosterman sums.

Line broadening studies for U 3+ and U 4+ ions in RbY 2Cl 7 single crystals

Temperature-dependent line broadening measurements of emission and excitation transitions for two intrinsic sites U(1) and U(2) of U 3+ ions doped in a RbY 2Cl 7 single crystals as well as of U 4+ ions have been performed. Values of the electron phonon (EP) coupling parameter α ̄ were determined by a fit of experimentally observed line widths to an equation containing the temperature dependent broadening term due to the Raman two-phonon process. The α ̄ parameters for U 3+ ions in RbY 2Cl 7 are larger than those determined for this ion in LaCl 3 host crystals. This is due to shorter M–Cl distances in RbY 2Cl 7 which leads to a stronger interaction of uranium with the chlorine ions and to an increase of covalency. The relatively large α ̄ value determined for the 2H2 11/2 multiplet of U 3+ in RbY 2Cl 7 may result from the proximity of opposite parity 5 f 26 d 1 states. The α ̄ parameters obtained for the U 3+ ions are larger than those for U 4+. The latter ones are affected by a stronger crystal-field (CF), however the position of the first 5 f 26 d 1 or 5 f 16 d 1 states, which for U 3+ is observed at an energy of ∼15,000 cm −1 lower than for U 4+, is the dominating one among the factors influencing the EP coupling strength. The EP coupling parameters for all investigated transitions of the U 3+ ions are larger for U(2) than for U(1), which results mainly from the larger crystal field strength observed for the U(2) site. The differences in the EP coupling strength of the U 3+ ions in the U(1) and U(2) sites are in accordance with decay times observed for emission for both sites from the 4F 9/2 multiplet.

Eigenvalue decomposition of meson correlators

Euclidean space hadronic correlators are computed in quenched QCD at a small quark mass using truncations of quark propagators which include or exclude low eigenvalue eigenmodes of the Dirac operator. High modes provide the dominant contribution to parity averaged correlators, especially at short distances. Differences of correlators of opposite parity receive most of their contributions from low modes and are much smaller in size than parity averages at short distances. The pion propagator in any correlator to which it couples receives a large contribution from low modes, while the tensor meson correlator receives a tiny contribution from low eigenmodes.

Magnetic Linear Birefringence in Rare Earth Systems. II. Third-Order Approach

The theory of linear magnetic birefringence of rare earth ions in crystals is extended here by the contributions that represent a direct perturbing influence of the crystal field potential surrounding the central ion. The basic assumptions of the theoretical model are the same as in the previous analysis of second-order terms. The third-order contributions introduced here break the free ionic system approximation, and they represent the impact due to configuration interaction. The effective operators include the perturbing influence of the excitations from the 4f shell to one-electron states of the same parity (as previously at the second order), and in addition, the excitations to states of opposite parity. All contributing terms are expressed by the effective operators that are defined within the perturbed function approach. The tensorial structure of these operators is discussed, and special attention is directed to newly defined radial integrals. The values of all radial integrals that are necessary for the third-order numerical analysis are presented in the case of all lanthanide ions.

Compact supercell method based on opposite parity for Bragg fibers

The supercell- based orthonormal basis method is proposed to investigate the modal properties of the Bragg fibers. A square lattice is constructed by the whole Bragg fiber which is considered as a supercell, and the periodical dielectric structure of the square lattice is decomposed using periodic functions (cosine). The modal electric field is expanded as the sum of the orthonormal set of Hermite-Gaussian basis functions based on the opposite parity of the transverse electric field. The propagation characteristics of Bragg fibers can be obtained after recasting the wave equation into an eigenvalue system. This method is implemented with very high efficiency and accuracy.

Pentaquark hadrons from lattice QCD

We study spin 1/2 isoscalar and isovector candidates in both parity channels for the recently discovered \Theta^+(1540) pentaquark particle in quenched lattice QCD. Our analysis takes into account all possible uncertainties, such as statistical, finite size and quenching errors when performing the chiral and continuum extrapolations and we have indications that our signal is separated from scattering states. The lowest mass that we find in the I^P=0^- channel is in complete agreement with the experimental value of the \Theta^+ mass. On the other hand, the lowest mass state in the opposite parity I^P=0^+ channel is much higher. Our findings suggests that the parity of the \Theta^+ is negative.

A study of γ decays and octupole bands in 21Ne and 21Na

The reactions 16O(7Li, 2n) and 16O(7Li, np) populating 21Na and 21Ne have been studied at EL=27 MeV using the GASP γ-detector array. The level schemes for 21Na and 21Ne have been extended to higher spin. The population of the bands with K=3/2 and 1/2, forming parity doublets, are compared. Preferential E1 decay between bands of opposite parity is observed in agreement with the octupole scenario. The structure of these bands can be interpreted as consisting of an instrinsic asymmetric (4He + 16O) structure with octupole deformation.

Opposite-parity orthonormal function expansion for efficient full-vectorial modeling of holey optical fibers.

An improved full-vectorial method exploiting the opposite-parity property of eigenmodes based on orthonormal-functions expansion is proposed to solve the wave equation for holey optical fibers. By use of the parity property of eigenmodes in symmetric structures, the number of orthonormal function integrals involved in the calculation is reduced, and the computation efficiency is greatly enhanced. The coupling between the two transverse field components is considered, and both dominant and minor field components can be calculated for the accurate modeling of fiber modes. This method is useful for efficiently modeling holey fibers, especially those with large air holes, in which the coupling effect that is due to refractive-index discontinuities is strong.

A problem of D.H. Lehmer and its mean square value formula

Let q be an odd positive integer and let a be an integer coprime to q. For each integer b coprime to q with 1⩽ b< q, there is a unique integer c coprime to q with 1⩽ c< q such that bc≡a( mod q) . Let N( a, q) denote the number of solutions of the congruence equation bc≡a( mod q) with 1⩽ b, c< q such that b, c are of opposite parity. The main purpose of this paper is to use the properties of Dedekind sums, the properties of Cochrane sums and the mean value theorem of Dirichlet L-functions to study the asymptotic property of the mean square value ∑′ a=1 q(N(a,q)− 1 2 φ(q)) 2 , and give a sharp asymptotic formula.

Can radiative magnification of mixing angles occur for two-zero neutrino mass matrix textures?

Neutrino Majorana masses and mixings can be generated from a dimension-5 operator within the standard model particle content. After a review of the mechanism of radiative enhancement of the mixing angle in a two-neutrino case, we consider three-flavour mass matrices of two-zero texture generated from such an operator and investigate the possibility of implementing the mechanism here. We observe that radiative magnification of only the solar angle is consistent with oscillation data on masses and mixings, and that too for nearly degenerate neutrinos, with two of them having opposite CP parities, while for hierarchical masses the mechanism does not work. In supersymmetry or in an extra-dimensional scenario the above features are qualitatively unchanged.

Dual Aharonov–Casher effect in singlet-exciton systems

Dual Aharonov–Casher (DAC) phase (or He–McKellar–Wilkens phase), which is defined as a quantum topological phase acquired by a neutral particle only with an electric dipole moment μ E being taken on a closed path around a magnetic monopole wire, is theoretically investigated in singlet-exciton systems. In the Sangster's interference scheme, a moving 2s exciton in magnetic fields feels an effective electric field in co-moving frame, which causes a superposition of opposite parity states, i.e., |2s〉 and |2p〉, due to the motional Stark effect. The superposition gives rise to a nonvanishing electric dipole moment required for the DAC effect to the exciton. The accumulated phase is determined by detecting photon emissions from 2p states as a function of applied magnetic fields.

Do parity doublets in the baryon spectrum reflect restoration of chiral symmetry?

We discuss the mass spectrum of highly-excited nucleon and Δ∗ resonances. The spectrum exhibits parity doublets, pairs of resonances of identical total angular momentum J but of opposite parity. It has been proposed that the parity doublets evidence restoration of chiral symmetry at large baryon excitation energies. We compare this conjecture with the possibility that high-mass states are organized into (L,S)-multiplets with defined intrinsic quark spins and orbital angular momenta. The latter interpretation results in a better description of the data. There is however a small trend possibly indicating the onset of chiral symmetry restoration.

Global fitting of line intensities of acetylene molecule in the infrared using the effective operator approach

The method of effective operators has been applied to the global fitting of line intensities of the acetylene molecule in the middle infrared. Simultaneous fittings of recently observed line intensities in the cold and hot bands lying in the 13.6, 7.8, and 5 μm regions have been performed. The eigenfunctions of the effective Hamiltonian developed for the global treatment of the vibration–rotation line positions of acetylene [O.M. Lyulin, V.I. Perevalov, S.A. Tashkun, J.-L. Teffo, in: Leonid N. Sinitsa (Ed.), 13th Symposium and School on High Resolution Molecular Spectroscopy, Proceedings of SPIE, vol. 4063, 2000, pp. 126–133] have been used in the calculations. The sets of effective dipole moment parameters obtained reproduce the observed line intensities within the experimental accuracy. The importance of l-type resonance, responsible for some large differences between intensities of the same lines in subbands having opposite parities, is exhibited and discussed.