Muon and electron g−2 and proton and cesium weak charges implications on dark Zd models

M Cadeddu,N Cargioli,F Dordei,E Picciau,C Giunti

doi:10.1103/physrevd.104.l011701

Abstract

Theories beyond the standard model involving a sub-GeV-scale vector ${Z}_{d}$ mediator have been largely studied as a possible explanation of the experimental values of the muon and electron anomalous magnetic moments. Motivated by the recent determination of the anomalous muon magnetic moment performed at Fermilab, we derive the constraints on such a model obtained from the magnetic moment determinations and the measurements of the proton and cesium weak charge, ${Q}_{W}$, performed at low-energy transfer. In order to do so, we revisit the determination of the cesium ${Q}_{W}$ from the atomic parity violation experiment, which depends critically on the value of the average neutron rms radius of $^{133}\mathrm{Cs}$, by determining the latter from a practically model-independent extrapolation from the recent average neutron rms radius of $^{208}\mathrm{Pb}$ performed by the PREX-2 Collaboration. From a combined fit of all the aforementioned experimental results, we obtain rather precise limits on the mass and the kinetic mixing parameter of the ${Z}_{d}$ boson, namely ${m}_{{Z}_{d}}={47}_{\ensuremath{-}16}^{+61}\text{ }\text{ }\mathrm{MeV}$ and $ϵ={2.3}_{\ensuremath{-}0.4}^{+1.1}\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$, when marginalizing over the $Z\ensuremath{-}{Z}_{d}$ mass mixing parameter $\ensuremath{\delta}$.

Highlights

Theories beyond the standard model involving a sub-GeV-scale vector Zd mediator have been largely studied as a possible explanation of the experimental values of the muon and electron anomalous magnetic moments
Motivated by the recent determination of the anomalous muon magnetic moment performed at Fermilab, we derive the constraints on such a model obtained from the magnetic moment determinations and the measurements of the proton and cesium weak charge, QW, performed at low-energy transfer
In order to do so, we revisit the determination of the cesium QW from the atomic parity violation experiment, which depends critically on the value of the average neutron rms radius of 133Cs, by determining the latter from a practically model-independent extrapolation from the recent average neutron rms radius of 208Pb performed by the PREX-2 Collaboration

Summary

Another consequence of the existence of this additional

Besides the modification of the lepton magnetic moment, would be the introduction of a new source of parity violation that could be tested by experiments sensitive to the weak charge, QW, of both protons and nuclei. [60,61] there was not any cesium neutron radius measurement, the correction on Q1W33Cs;PDG due to the difference between Rnð133CsÞ and Rpð133CsÞ, the average proton rms radius, could only have been estimated exploiting hadronic probes, using an extrapolation of data from antiprotonic atom x-rays [62]. From these data, the value of the so-called neutron skin, ΔRnp ≡ Rn − Rp, has been measured for a number of elements, from which the extrapolated neutron skin value for each nucleus was found assuming a linear dependence on the asymmetry parameter, I 1⁄4 ðN − ZÞ=A, where A is the mass number, leading to the empirically fitted function. The weak charge of Cs is extracted from the ratio of the parity violating amplitude, EPNC, to the Stark vector transition polarizability, β, and by calculating theoretically EPNC in terms of Q1W33Cs;SM, leading to

ImEPNC β exp

Findings

This result can be compared to the current one presented in