Representation of [Formula: see text]-Bernstein polynomials in terms of [Formula: see text]-Jacobi polynomials.
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ABSTRACT:
SUBMITTER: Soleyman F
PROVIDER: S-EPMC5514192 | biostudies-other | 2017
REPOSITORIES: biostudies-other
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Project description:The experimental value for the isospin amplitude [Formula: see text] in [Formula: see text] decays has been successfully explained within the standard model (SM), both within the large [Formula: see text] approach to QCD and by QCD lattice calculations. On the other hand within the large [Formula: see text] approach the value of [Formula: see text] is by at least [Formula: see text] below the data. While this deficit could be the result of theoretical uncertainties in this approach and could be removed by future precise QCD lattice calculations, it cannot be excluded that the missing piece in [Formula: see text] comes from new physics (NP). We demonstrate that this deficit can be significantly softened by tree-level FCNC transitions mediated by a heavy colourless [Formula: see text] gauge boson with a flavour-violating left-handed coupling [Formula: see text] and an approximately universal flavour diagonal right-handed coupling [Formula: see text] to the quarks. The approximate flavour universality of the latter coupling assures negligible NP contributions to [Formula: see text]. This property, together with the breakdown of the GIM mechanisms at tree level, allows one to enhance significantly the contribution of the leading QCD-penguin operator [Formula: see text] to [Formula: see text]. A large fraction of the missing piece in the [Formula: see text] rule can be explained in this manner for [Formula: see text] in the reach of the LHC, while satisfying the constraints from [Formula: see text], [Formula: see text], [Formula: see text], LEP-II and the LHC. The presence of a small right-handed flavour-violating coupling [Formula: see text] and of enhanced matrix elements of [Formula: see text] left-right operators allows one to satisfy simultaneously the constraints from [Formula: see text] and [Formula: see text], although this requires some fine-tuning. We identify the quartic correlation between [Formula: see text] contributions to [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. The tests of this proposal will require much improved evaluations of [Formula: see text] and [Formula: see text] within the SM, of [Formula: see text] as well as precise tree-level determinations of [Formula: see text] and [Formula: see text]. We present correlations between [Formula: see text], [Formula: see text] and [Formula: see text] with and without the [Formula: see text] rule constraint and generalise the whole analysis to [Formula: see text] with colour ([Formula: see text]) and [Formula: see text] with FCNC couplings. In the latter case no improvement on [Formula: see text] can be achieved without destroying the agreement of the SM with the data on [Formula: see text]. Moreover, this scenario is very tightly constrained by [Formula: see text]. On the other hand, in the context of the [Formula: see text] rule [Formula: see text] is even more effective than [Formula: see text]: it provides the missing piece in [Formula: see text] for [Formula: see text]-[Formula: see text].
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Project description:Dy[Formula: see text]Zr[Formula: see text]O[Formula: see text] a disordered pyrochlore system, exhibits the spin freezing behavior under the application of the magnetic field. We have performed detailed magnetic studies of Dy[Formula: see text]La[Formula: see text]Zr[Formula: see text]O[Formula: see text] to understand the evolution of the magnetic spin freezing in the system. Our studies suggest the stabilization of the pyrochlore phase with the substitution of non-magnetic La along with the biphasic mixture of fluorite and pyrochlore phases for the intermediate compositions. We observed that the spin freezing (T[Formula: see text] [Formula: see text] 17 K) at higher La compositions (1.5 [Formula: see text] [Formula: see text] [Formula: see text] 1.99) is similar to the field-induced spin freezing for low La compositions (0 [Formula: see text] [Formula: see text] [Formula: see text] 0.5) and the well-known spin ice systems Dy[Formula: see text]Ti[Formula: see text]O[Formula: see text] and Ho[Formula: see text]Ti[Formula: see text]O[Formula: see text]. The low-temperature magnetic state for higher La compositions (1.5 [Formula: see text] [Formula: see text] [Formula: see text] 1.99) culminates into a spin-glass like state below 6 K. Cole-Cole plot and Casimir-du Pr[Formula: see text] fit shows the narrow distribution of spin relaxation time in these compounds.
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Project description:The Josephson effect in point contacts between an "ordinary" superconductor [Formula: see text]In[Formula: see text] ([Formula: see text]) and single crystals of the Fe-based superconductor Ba[Formula: see text]K[Formula: see text](FeAs)[Formula: see text] ([Formula: see text]), was investigated. In order to shed light on the order parameter symmetry of Ba[Formula: see text]K[Formula: see text](FeAs)[Formula: see text], the dependence of the Josephson supercurrent [Formula: see text] on the temperature and on [Formula: see text] with [Formula: see text] was studied. The dependencies of the critical current on temperature [Formula: see text] and of the amplitudes of the first current steps of the current-voltage characteristic [Formula: see text] [Formula: see text] on the power of microwave radiation with frequency [Formula: see text] were measured. It is shown that the dependencies [Formula: see text] are close to the well-known Ambegaokar-Baratoff (AB) dependence for tunnel contacts between "ordinary" superconductors and to the dependence calculated by Burmistrova et al. (Phys Rev B 91, 214501 (2015)) for microshorts between an "ordinary" superconductor and a two-band superconductor with [Formula: see text] order parameter symmetry at certain values of the transparency of boundaries and thickness of the transition layer. It is found that the dependencies [Formula: see text] cannot be approximated within the resistively shunted model using the normalized microwave frequencies [Formula: see text] with characteristic voltages [Formula: see text], [Formula: see text]-normal resistance of the contact) found from the low-voltage parts of the current-voltage characteristics. The reasons for this failure are discussed and a method is proposed for accurately determining the value of [Formula: see text], which takes into account all the features of the point contact affecting the period of the dependence [Formula: see text]. An analysis of the [Formula: see text] and [Formula: see text] dependencies shows that the superconducting current of the Josephson contacts under investigation is proportional to the [Formula: see text] of the phase difference [Formula: see text], [Formula: see text]. The implications of these results on the symmetry of the order parameter are also discussed.
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Project description:The temperature-dependent ([Formula: see text]) optical constants of monolayer [Formula: see text], [Formula: see text], [Formula: see text], and [Formula: see text] were investigated through spectroscopic ellipsometry over the spectral range of 0.73-6.42 eV. At room temperature, the spectra of refractive index exhibited several anomalous dispersion features below 800 nm and approached a constant value of 3.5-4.0 in the near-infrared frequency range. With a decrease in temperature, the refractive indices decreased monotonically in the near-infrared region due to the temperature-dependent optical band gap. The thermo-optic coefficients at room temperature had values from [Formula: see text] to [Formula: see text] for monolayer transition metal dichalcogenides at a wavelength of 1200 nm below the optical band gap. The optical band gap increased with a decrease in temperature due to the suppression of electron-phonon interactions. On the basis of first-principles calculations, the observed optical excitations at 4.5 K were appropriately assigned. These results provide basic information for the technological development of monolayer transition metal dichalcogenides-based photonic devices at various temperatures.
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Project description:A search for a massive [Formula: see text] gauge boson decaying to a top quark and a bottom quark is performed with the ATLAS detector in [Formula: see text] collisions at the LHC. The dataset was taken at a centre-of-mass energy of [Formula: see text] and corresponds to [Formula: see text] of integrated luminosity. This analysis is done in the hadronic decay mode of the top quark, where novel jet substructure techniques are used to identify jets from high-momentum top quarks. This allows for a search for high-mass [Formula: see text] bosons in the range 1.5-3.0 [Formula: see text]. [Formula: see text]-tagging is used to identify jets originating from [Formula: see text]-quarks. The data are consistent with Standard Model background-only expectations, and upper limits at 95 % confidence level are set on the [Formula: see text] cross section times branching ratio ranging from [Formula: see text] to [Formula: see text] for left-handed [Formula: see text] bosons, and ranging from [Formula: see text] to [Formula: see text] for [Formula: see text] bosons with purely right-handed couplings. Upper limits at 95 % confidence level are set on the [Formula: see text]-boson coupling to [Formula: see text] as a function of the [Formula: see text] mass using an effective field theory approach, which is independent of details of particular models predicting a [Formula: see text] boson.
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