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The complete gauge-invariant set of the one-loop QED corrections to theparity-nonconserving (PNC) amplitude in cesium and francium is evaluated to allorders in $\alpha Z$ using a local form of the Dirac-Fock potential. Thecalculations are performed in both length and velocity gauges for the absorbedphoton and the total binding QED correction is found to be $-$0.27(3)% for Csand $-$0.28(5)% for Fr. Moreover, a high-precision calculation of theelectron-correlation and Breit-interaction effects on the 7$s-8s$ PNC amplitudein francium using a large-scale configuration-interaction Dirac-Fock method isperformed. The obtained results are employed to improve the theoreticalpredictions for the PNC transition amplitude in Cs and Fr. Using an averagevalue from two most accurate measurements of the vector transitionpolarizability, the weak charge of $^{133}$Cs is derived to amount to $Q_W=-72.65(29)_{\rm exp}(36)_{\rm theor}$. This value deviates by $1.1\sigma$from the prediction of the standard model. The values of the $7s$-$8s$ PNCamplitude in $^{223}$Fr and $^{210}$Fr are obtained to be $-$15.49(15) and$-$14.16(14), respectively, in units of i$\times 10^{-11}(-Q_W)/N$ a.u.Comment: 28 pages, 8 tables, 2 figure

Radiative and correlation effects on the parity-nonconserving transition amplitude in heavy alkali-metal atoms