Perturbative breaking of the pseudospin symmetry in the relativistic harmonic oscillator

We show that relativistic mean fields theories with scalar S, and vector V, quadratic radial potentials can generate a harmonic oscillator with exact pseudospin symmetry and positive energy bound states when S = -V. The eigenenergies are quite different from those of the non-relativistic harmonic oscillator. We also discuss a mechanism for perturbatively breaking this, symmetry by introducing a tensor potential. Our results shed light into the intrinsic relativistic nature of the pseudospin symmetry, which might be important in high density systems such as neutron stars.

Spontaneous breaking of a global symmetry in a 3-3-1 model

In a 3-3-1 model in which the lepton masses arise from a scalar sextet it is possible to break spontaneously a global symmetry which implies in a pseudoscalar Majoron-like Goldstone boson. This Majoron does not mix with any other scalar fields and for this reason it does not couple, at the tree level, to either the charged leptons or to the quarks. Moreover, its interaction with neutrinos is diagonal. We also argue that there is a set of parameters in which the model can be consistent with the invisible Z0 width and that heavy neutrinos can decay sufficiently rapid by Majoron emission, having a lifetime shorter than the age of the universe. ©1999 The American Physical Society.

Chiral properties of two-flavour QCD at zero and non-zero temperature

Lattice Quantum Chromodynamics (LQCD) is the preferred tool for obtaining non-perturbative results from QCD in the low-energy regime. It has by nowrnentered the era in which high precision calculations for a number of phenomenologically relevant observables at the physical point, with dynamical quark degrees of freedom and controlled systematics, become feasible. Despite these successes there are still quantities where control of systematic effects is insufficient. The subject of this thesis is the exploration of the potential of todays state-of-the-art simulation algorithms for non-perturbativelyrn$\mathcal{O}(a)$-improved Wilson fermions to produce reliable results in thernchiral regime and at the physical point both for zero and non-zero temperature. Important in this context is the control over the chiral extrapolation. Thisrnthesis is concerned with two particular topics, namely the computation of hadronic form factors at zero temperature, and the properties of the phaserntransition in the chiral limit of two-flavour QCD.rnrnThe electromagnetic iso-vector form factor of the pion provides a platform to study systematic effects and the chiral extrapolation for observables connected to the structure of mesons (and baryons). Mesonic form factors are computationally simpler than their baryonic counterparts but share most of the systematic effects. This thesis contains a comprehensive study of the form factor in the regime of low momentum transfer $q^2$, where the form factor is connected to the charge radius of the pion. A particular emphasis is on the region very close to $q^2=0$ which has not been explored so far, neither in experiment nor in LQCD. The results for the form factor close the gap between the smallest spacelike $q^2$-value available so far and $q^2=0$, and reach an unprecedented accuracy at full control over the main systematic effects. This enables the model-independent extraction of the pion charge radius. The results for the form factor and the charge radius are used to test chiral perturbation theory ($\chi$PT) and are thereby extrapolated to the physical point and the continuum. The final result in units of the hadronic radius $r_0$ is rn$$ \left\langle r_\pi^2 \right\rangle^{\rm phys}/r_0^2 = 1.87 \: \left(^{+12}_{-10}\right)\left(^{+\:4}_{-15}\right) \quad \textnormal{or} \quad \left\langle r_\pi^2 \right\rangle^{\rm phys} = 0.473 \: \left(^{+30}_{-26}\right)\left(^{+10}_{-38}\right)(10) \: \textnormal{fm} \;, $$rn which agrees well with the results from other measurements in LQCD and experiment. Note, that this is the first continuum extrapolated result for the charge radius from LQCD which has been extracted from measurements of the form factor in the region of small $q^2$.rnrnThe order of the phase transition in the chiral limit of two-flavour QCD and the associated transition temperature are the last unkown features of the phase diagram at zero chemical potential. The two possible scenarios are a second order transition in the $O(4)$-universality class or a first order transition. Since direct simulations in the chiral limit are not possible the transition can only be investigated by simulating at non-zero quark mass with a subsequent chiral extrapolation, guided by the universal scaling in the vicinity of the critical point. The thesis presents the setup and first results from a study on this topic. The study provides the ideal platform to test the potential and limits of todays simulation algorithms at finite temperature. The results from a first scan at a constant zero-temperature pion mass of about 290~MeV are promising, and it appears that simulations down to physical quark masses are feasible. Of particular relevance for the order of the chiral transition is the strength of the anomalous breaking of the $U_A(1)$ symmetry at the transition point. It can be studied by looking at the degeneracies of the correlation functions in scalar and pseudoscalar channels. For the temperature scan reported in this thesis the breaking is still pronounced in the transition region and the symmetry becomes effectively restored only above $1.16\:T_C$. The thesis also provides an extensive outline of research perspectives and includes a generalisation of the standard multi-histogram method to explicitly $\beta$-dependent fermion actions.

MSSM soft terms from supergravity with gauged R-symmetry in de Sitter vacuum

We work out the phenomenology of a model of supersymmetry breaking in the presence of a tiny (tunable) positive cosmological constant, proposed by the authors in arXiv:1403.1534. It utilizes a single chiral multiplet with a gauged shift symmetry that can be identified with the string dilaton (or an appropriate compactification modulus). The model is coupled to the MSSM, leading to calculable soft supersymmetry breaking masses and a distinct low energy phenomenology that allows to differentiate it from other models of supersymmetry breaking and mediation mechanisms.

Possible Unconventional Superconductivity In Substituted Bafe2as2 Revealed By Magnetic Pair-breaking Studies.

The possible existence of a sign-changing gap symmetry in BaFe2As2-derived superconductors (SC) has been an exciting topic of research in the last few years. To further investigate this subject we combine Electron Spin Resonance (ESR) and pressure-dependent transport measurements to investigate magnetic pair-breaking effects on BaFe1.9M0.1As2 (M = Mn, Co, Cu, and Ni) single crystals. An ESR signal, indicative of the presence of localized magnetic moments, is observed only for M = Cu and Mn compounds, which display very low SC transition temperature (Tc) and no SC, respectively. From the ESR analysis assuming the absence of bottleneck effects, the microscopic parameters are extracted to show that this reduction of Tc cannot be accounted by the Abrikosov-Gorkov pair-breaking expression for a sign-preserving gap function. Our results reveal an unconventional spin- and pressure-dependent pair-breaking effect and impose strong constraints on the pairing symmetry of these materials.

CP properties of symmetry-constrained two-Higgs-doublet models

The two-Higgs-doublet model can be constrained by imposing Higgs-family symmetries and/or generalized CP symmetries. It is known that there are only six independent classes of such symmetry-constrained models. We study the CP properties of all cases in the bilinear formalism. An exact symmetry implies CP conservation. We show that soft breaking of the symmetry can lead to spontaneous CP violation (CPV) in three of the classes.

s-wave charmed baryon resonances from a coupled-channel approach with heavy quark symmetry

We study charmed baryon resonances that are generated dynamically within a unitary meson-baryon coupled-channel model that treats the heavy pseudoscalar and vector mesons on equal footing as required by heavy-quark symmetry. It is an extension of recent SU(4) models with t-channel vector-meson exchanges to an SU(8) spin-flavor scheme, but differs considerably from the SU(4) approach in how the strong breaking of the flavor symmetry is implemented. Some of our dynamically generated states can be readily assigned to recently observed baryon resonances, while others do not have a straightforward identification and require the compilation of more data as well as an extension of the model to d-wave meson-baryon interactions and p-wave coupling in the neglected s- and u-channel diagrams. Of several novelties, we find that the Delta c(2595), which emerged as a ND quasibound state within the SU(4) approaches, becomes predominantly a ND* quasibound state in the present SU(8) scheme.

Manifestation of the pairing symmetry in the vortex core structure in iron-based superconductors

The superconducting gap is a basic character of a superconductor. While the cuprates and conventional phonon-mediated superconductors are characterized by distinct d- and s-wave pairing symmetries with nodal and nodeless gap distributions respectively, the superconducting gap distributions in iron-based superconductors are rather diversified. While nodeless gap distributions have been directly observed in Ba1–xKxFe2As2, BaFe2–xCoxAs2, LiFeAs, KxFe2–ySe2, and FeTe1–xSex, the signatures of a nodal superconducting gap have been reported in LaOFeP, LiFeP, FeSe, KFe2As2, BaFe2–xRuxAs2, and BaFe2(As1–xPx)2. Due to the multiplicity of the Fermi surface in these compounds s± and d pairing states can be both nodeless and nodal. A nontrivial orbital structure of the order parameter, in particular the presence of the gap nodes, leads to effects in which the disorder is much richer in dx2–y2-wave superconductors than in conventional materials. In contrast to the s-wave case, the Anderson theorem does not work, and nonmagnetic impurities exhibit a strong pair-breaking influence. In addition, a finite concentration of disorder produces a nonzero density of quasiparticle states at zero energy, which results in a considerable modification of the thermodynamic and transport properties at low temperatures. The influence of order parameter symmetry on the vortex core structure in iron-based pnictide and chalcogenide superconductors has been investigated in the framework of quasiclassical Eilenberger equations. The main results of the thesis are as follows. The vortex core characteristics, such as, cutoff parameter, ξh, and core size, ξ2, determined as the distance at which density of the vortex supercurrent reaches its maximum, are calculated in wide temperature, impurity scattering rate, and magnetic field ranges. The cutoff parameter, ξh(B; T; Г), determines the form factor of the flux-line lattice, which can be obtained in _SR, NMR, and SANS experiments. A comparison among the applied pairing symmetries is done. In contrast to s-wave systems, in dx2–y2-wave superconductors, ξh/ξc2 always increases with the scattering rate Г. Field dependence of the cutoff parameter affects strongly on the second moment of the magnetic field distributions, resulting in a significant difference with nonlocal London theory. It is found that normalized ξ2/ξc2(B/Bc2) dependence is increasing with pair-breaking impurity scattering (interband scattering for s±-wave and intraband impurity scattering for d-wave superconductors). Here, ξc2 is the Ginzburg-Landau coherence length determined from the upper critical field Bc2 = Φ0/2πξ2 c2, where Φ0 is a flux quantum. Two types of ξ2/ξc2 magnetic field dependences are obtained for s± superconductors. It has a minimum at low temperatures and small impurity scattering transforming in monotonously decreasing function at strong scattering and high temperatures. The second kind of this dependence has been also found for d-wave superconductors at intermediate and high temperatures. In contrast, impurity scattering results in decreasing of ξ2/ξc2(B/Bc2) dependence in s++ superconductors. A reasonable agreement between calculated ξh/ξc2 values and those obtained experimentally in nonstoichiometric BaFe2–xCoxAs2 (μSR) and stoichiometric LiFeAs (SANS) was found. The values of ξh/ξc2 are much less than one in case of the first compound and much more than one for the other compound. This is explained by different influence of two factors: the value of impurity scattering rate and pairing symmetry.

Optical and Thermal Properties of Diethyl-(2R, 3R) (1)-tartrate Based Chiral Polyurethanes with Main Chain Amido Chromophores

The toluene diisocyanate based optically active chiral polyurethanes were synthesized according to the symmetry conditions. The noncentrosymmetric (both charge asymmetry and spatial asymmetry) environment were attained by the incorporation of the chiral units (diethyl-(2R,3R)(þ)-tartrate) and donor-acceptor building blocks in the main chain which induce a helical conformation in the macromolecular chain. A series of optically active polyurethanes containing chiral linkages in the polymer back bone have been synthesized by using DBTDL catalyst by incorporating the amido diols which were obtained by the aminolysis of e-caprolactone by using the diamines, diaminoethane, diaminobutane, and diaminohexane respectively. The effect of incorporation of the chiral molecule diethyl-(2R,3R)(þ)-tartrate on the properties of polyurethanes was studied by changing the chromophores and also by varying the chiral-chromophore composition. Various properties of polyurethanes were investigated by UV, Fluorescence, TG/DTA, XRD, polarimetric techniques, Kurtz-Perry powder techniques, etc.

Isosorbide based chiral polyurethanes: optical and thermal studies

A new class of chiral polyurethanes containing amido linkages in the polymer backbone have been synthesized by reacting toluene diisocyanate with isosorbide (IS) chiral moiety and the chromophores [N,N0-ethane- 1,2-diyl bis(6-hydroxy hexanamide), N,N0-butane-1,4-diyl bis(6-hydroxy hexanamide) and N,N0-hexane-1,6-diyl bis (6-hydroxy hexanamide)]. The corresponding chromophores were obtained by the aminolysis of e-caprolactone by using the diamines, diaminoethane, diaminobutane and diaminohexane, respectively. All the polymers were synthesized according to the symmetry conditions so as to obtain the non-centrosymmetric environment. A series of polyurethanes were synthesized by varying the chiral– chromophore composition. The polyurethanes developed were characterized by optical and thermal methods.

The chemistry of intrinsically chiral surfaces

Intrinsically chiral metal and mineral surfaces show enantioselective behaviour without modifiers. Examples are artificial high-Miller-index surfaces of metal single crystals with cubic bulk lattice symmetry, which have no mirror planes and are therefore chiral, or surfaces of naturally occurring crystallites of some common minerals, such as alpha-quartz or calcite. Recent findings with regards to the surface geometry, reactivity and thermal stability of intrinsically chiral surfaces are discussed. A number of enantioselective effects have been reported in connection with the adsorption of small chiral molecules (e.g. alanine, cysteine) on intrinsically chiral surfaces under well-defined conditions. From a combination of experimental surface science techniques and theoretical ab initio model calculations it emerges that these effects are due to a combination of attractive and repulsive adsorbate-substrate and inter-adsorbate interactions.

Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator

We solve the generalized relativistic harmonic oscillator in 1+1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative quadratic potentials and discuss in detail their bound-state solutions for fermions and antifermions. The main features of these bound states are the same as the ones of the generalized three-dimensional relativistic harmonic oscillator bound states. The solutions found for zero pseudoscalar potential are related to the spin and pseudospin symmetry of the Dirac equation in 3+1 dimensions. We show how the charge conjugation and gamma(5) chiral transformations relate the several spectra obtained and find that for massless particles the spin and pseudospin symmetry-related problems have the same spectrum but different spinor solutions. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with scalar, vector, and isoscalar tensor interactions and discuss the conditions in which one may have both nucleon and antinucleon bound states.

Discrete symmetries, invisible axion, and lepton number symmetry in an economic 3-3-1 model

We show that Peccei-Quinn and lepton number symmetries can be a natural outcome in a 3-3-1 model with right-handed neutrinos after imposing a Z(11)circle timesZ(2) symmetry. This symmetry is suitably accommodated in this model when we augment its spectrum by including merely one singlet scalar field. We work out the breaking of the Peccei-Quinn symmetry, yielding the axion, and study the phenomenological consequences. The main result of this work is that the solution to the strong CP problem can be implemented in a natural way, implying an invisible axion phenomenologically unconstrained, free of domain wall formation, and constituting a good candidate for the cold dark matter.

Gravitation and duality symmetry

By generalizing the Hodge dual operator to the case of soldered bundles, and working in the context of the teleparallel equivalent of general relativity, an analysis of the duality symmetry in gravitation is performed. Although the basic conclusion is that, at least in the general-case, gravitation is not dual symmetric, there is a particular theory in which this symmetry shows up. It is a self dual (or anti-self dual) teleparallel gravity in which, due to the fact that it does not contribute to the interaction of fermions with gravitation, the purely tensor part of torsion is assumed to vanish. The ensuing fermionic gravitational interaction is found to be chiral. Since duality is intimately related to renormalizability, this theory may eventually be more amenable to renormalization than telepaxallel gravity or general relativity.