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Register a new userNew formulation of gamma-Z box corrections to the weak charge of the proton
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We present a new formulation of one of the major radiative corrections to the weak charge of the proton -- that arising from the axial-vector hadron part of the $gamma Z$ box diagram, $Re{rm e}, Box_{gamma Z}^{rm A}$. This formulation, based on dispersion relations, relates the $gamma Z$ contributions to moments of the $F_3^{gamma Z}$ interference structure function. It has a clear connection to the pioneering work of Marciano and Sirlin, and enables a systematic approach to improved numerical precision. Using currently available data, the total correction from all intermediate states is $Re{rm e}, Box_{gamma Z}^{rm A} = 0.0044(4)$ at zero energy, which shifts the theoretical estimate of the proton weak charge from $0.0713(8)$ to $0.0705(8)$. The energy dependence of this result, which is vital for interpreting the Q$_{rm weak}$ experiment, is also determined.
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We present the fully up-to-date calculation of the $gamma Z$-box correction which needs to be taken into account to determine the weak mixing angle at low energies from parity-violating electron proton scattering. We make use of neutrino and antineutrino inclusive scattering data to predict the parity-violating structure function $F_3^{gamma Z}$ by isospin symmetry. Our new analysis confirms previous results for the axial contribution to the $gamma Z$-box graph, and reduces the uncertainty by a factor of~2. In addition, we note that the presence of parity-violating photon-hadron interactions induces an additional contribution via $F_3^{gamma gamma}$. Using experimental and theoretical constraints on the nucleon anapole moment we are able to estimate the uncertainty associated with this contribution. We point out that future measurements are expected to significantly reduce this latter uncertainty.
We present a new dispersive formulation of the gamma-Z box radiative corrections to weak charges of bound protons and neutrons in atomic parity violation (APV) measurements on heavy nuclei such as 133-Cs and 213-Ra. We evaluate for the first time a small but important additional correction arising from Pauli blocking of nucleons in a heavy nucleus. Overall, we find a significant shift in the gamma-Z correction to the weak charge of 133-Cs, approximately 4 times larger than the current uncertainty on the value of sin^2(theta_W), but with a reduced error compared to earlier estimates.
The ratio of di-lepton production cross sections on a proton, using the $gamma prightarrow l^+ l^- p$ process, above and below di-muon production threshold allows to extract the effective lepton-proton interaction, which is required to be identical for electrons and muons if lepton universality is exact. To test for a scenario of broken universality at the percent level, of the size which could explain the different proton charge radii extracted from electron scattering and from muonic hydrogen spectroscopy, we evaluate all one-loop QED corrections to this process, including the full lepton mass dependencies. We furthermore show that two-photon exchange processes with both photons attached to the proton line vanish after averaging over di-lepton angles, and estimate the relatively small radiation off the proton. We compare the full one-loop calculation with a soft-photon approximation of the same order, and present estimates for a planned experiment.
Up to now, all charge radius measurements of the proton and deuteron assumed uniform spheroidal charge distribution. We investigate the nuclear deformation effects on these charge radius measurements by assuming a uniform prolate charge distribution for the proton and deuteron. We solve the energy levels of the corresponding muonic and electric atoms with such deformed nucleus and present how the purely quadruple deformation of proton and deuteron affects their Lamb shifts. The numerical results suggest that the deformation of proton and deuteron leads to that the charge radius extracted from the electronic measurement should be smaller than the corresponding one in the muonic measurement which assumed uniform spheroidal charge distribution. If the central values of newest measurements for the proton are adopted, the proton would have a prolate structure with the 0.91 $mathrm{fm}$ long axis and 0.73 $mathrm{fm}$ short axis. Further improved precise charge radius measurements of the proton and deuteron will help us to pin down their shape deformation.
We investigate the contributions of the hadronic structure of the neutron to radiative $O(alpha E_e/m_N)$ corrections (or the inner $O(alpha E_e/m_N)$ RC) to the neutron beta decay, where $alpha$, $E_e$ and $m_N$ are the fine-structure constant, the electron energy and the nucleon mass, respectively. We perform the calculation within the effective quantum field theory of strong low-energy pion-nucleon interactions described by the linear $sigma$-model with chiral $SU(2) times SU(2)$ symmetry and electroweak hadron-hadron, hadron-lepton and lepton-lepton interactions for the electron-lepton family with $SU(2)_L times U(1)_Y$ symmetry of the Standard Electroweak Theory (Ivanov et al., Phys. Rev. D99, 093006 (2019)). We show that after renormalization, carried out in accordance with Sirlins prescription (Sirlin, Phys. Rev. 164, 1767 (1967)), the inner $O(alpha E_e/m_N)$ RC are of the order of a few parts of $10^{-5} - 10^{-4}$. This agrees well with the results obtained in (Ivanov et al., Phys. Rev. D99, 093006 (2019)).
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