Abstract
In a recent Letter [B. K. Sahoo, B. P. Das, and H. Spiesberger, Phys. Rev. D 103, L111303 (2021)], a calculation of the parity violating 6S-7S E1 amplitude in Cs is reported, claiming an uncertainty of just 0.3%. In this Comment, we point out that key contributions have been omitted, and the theoretical uncertainty has been significantly underestimated. In particular, the contribution of missed QED radiative corrections amounts to several times the claimed uncertainty.
Highlights
The 6S–7S atomic parity violation (APV) amplitude in Cs may be expressed as h7fSjDzj6fSi, where Dz is the z component of the electric dipole (E1) operator, and j6fSi and j7fSi are weak-interaction-perturbed atomic states; the source of this interaction is Z-boson exchange between the electrons and the nucleus
Qw ρðrÞγ5 is the parity-violating weak interaction operator, with GF the Fermi constant, Qw the nuclear weak charge, ρ the nuclear density, and γ5 the Dirac matrix, and n runs over all p1=2 states including the core; see
We again use the radiative potential method and find it gives a correction of −1.2%, 3 times too large compared to rigorous quantum electrodynamics (QED) calculations [29,33], confirming the importance of the omitted effects
Summary
The 6S–7S atomic parity violation (APV) amplitude in Cs may be expressed as h7fSjDzj6fSi, where Dz is the z component of the electric dipole (E1) operator, and j6fSi and j7fSi are weak-interaction-perturbed atomic states; the source of this interaction is Z-boson exchange between the electrons and the nucleus. The accuracy of the calculation is determined by account of many-body effects and smaller corrections including higher-order relativistic effects. [6,7,8,9], was the recognition of the importance of quantum electrodynamics (QED) radiative corrections and the formulation of methods to account for them in precision calculations for heavy atoms [10,11,12,13,14,15,16,17] (see [18,19,20,21]). The treatment of QED radiative corrections omits important contributions to EPV, which amount to several times the theoretical uncertainty claimed in Ref. The treatment of QED radiative corrections omits important contributions to EPV, which amount to several times the theoretical uncertainty claimed in Ref. [22]
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