Symmetry preserving truncations of the gap and Bethe-Salpeter equations
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Publications and source records attributed to Chang, Lei.
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We describe expressions for pion and kaon dressed-quark distribution functions that incorporate contributions from gluons which bind quarks into these mesons and hence overcome a flaw of the commonly used handbag approximation. The distributions therewith obtained are purely valence in character, ensuring that dressed quarks carry all the meson’s momentum at a characteristic hadronic scale and vanish as ( 1 - x ) 2 when Bjorken- x → 1 . Comparing such distributions within the pion and kaon, it is apparent that the size of S U ( 3 ) -flavor symmetry breaking in meson parton distribution functions is modulated by the flavor dependence of dynamical chiral symmetry breaking. Corrections to these leading-order formulas may be divided into two classes, responsible for shifting dressed-quark momentum into glue and sea quarks. Working with available empirical information, we build an algebraic framework that is capable of expressing the principal impact of both classes of corrections. This enables a realistic comparison with experiment which allows us to identify and highlight basic features of measurable pion and kaon valence-quark distributions. We find that whereas roughly two thirds of the pion’s light-front momentum is carried by valence dressed quarks at a characteristic hadronic scale; this fraction rises to 95% in the kaon; evolving distributions with these features to a scale typical of available Drell-Yan data produces a kaon-to-pion ratio of u -quark distributions that is in agreement with the single existing data set, and predicts a u -quark distribution within the pion that agrees with a modern reappraisal of π N Drell-Yan data. Precise new data are essential in order to validate this reappraisal and because a single modest-quality measurement of the kaon-to-pion ratio cannot be considered definitive.
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Within contemporary hadron physics there are two common methods for determining the momentum-dependence of the interaction between quarks: the top-down approach, which works toward an ab initio computation of the interaction via direct analysis of the gauge-sector gap equations; and the bottom-up scheme, which aims to infer the interaction by fitting data within a well-defined truncation of those equations in the matter sector that are relevant to bound-state properties. We unite these two approaches by demonstrating that the renormalisation-group-invariant running-interaction predicted by contemporary analyses of QCD's gauge sector coincides with that required in order to describe ground-state hadron observables using a nonperturbative truncation of QCD's Dyson–Schwinger equations in the matter sector. This bridges a gap that had lain between nonperturbative continuum-QCD and the ab initio prediction of bound-state properties.
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Upward self-poling phenomenon was observed in PbZr{sub 0.2}Ti{sub 0.8}O{sub 3} ferroelectric films which were grown on (001) SrTiO{sub 3} substrate with either p-type La{sub 0.7}Sr{sub 0.3}MnO{sub 3} or n-type SrRuO{sub 3} buffered layer, or on n-type (001) Nb-SrTiO{sub 3} substrate. Both upward self-poling and epitaxial strain are strong in the super-thin PbZr{sub 0.2}Ti{sub 0.8}O{sub 3} epitaxial films, while they become weak and finally disappear in thick epitaxial films or thin epitaxial films with high-density oxygen vacancies. Besides, both of them disappear in PbZr{sub 0.2}Ti{sub 0.8}O{sub 3} polycrystalline films on Pt/TiO{sub 2}/SiO{sub 2}/Si substrate. Therefore, the main origin of upward self-poling is epitaxial strain rather than p-n/Schottky junction or charged vacancies in PbZr{sub 0.2}Ti{sub 0.8}O{sub 3} epitaxial films here.
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