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Register a new userReduced uncertainty of the axial $gamma Z$-box correction to the protons weak charge
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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.
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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.
We analyze the low-$Q^2$ behavior of the axial form factor $G_A(Q^2)$, the induced pseudoscalar form factor $G_P(Q^2)$, and the axial nucleon-to-$Delta$ transition form factors $C^A_5(Q^2)$ and $C^A_6(Q^2)$. Building on the results of chiral perturbation theory, we first discuss $G_A(Q^2)$ in a chiral effective-Lagrangian model including the $a_1$ meson and determine the relevant coupling parameters from a fit to experimental data. With this information, the form factor $G_P(Q^2)$ can be predicted. For the determination of the transition form factor $C^A_5(Q^2)$ we make use of an SU(6) spin-flavor quark-model relation to fix two coupling constants such that only one free parameter is left. Finally, the transition form factor $C^A_6(Q^2)$ can be predicted in terms of $G_P(Q^2)$, the mean-square axial radius $langle r^2_Arangle$, and the mean-square axial nucleon-to-$Delta$ transition radius $langle r^2_{ANDelta}rangle$.
It is argued that the dynamics of the elastic scattering of high-energy protons at intermediate transferred momenta changes with the energy increase. It evolves from the multiple scattering at the external layer for energies about 10 GeV to the double scattering at the two subsequent layers within the colliding protons for energies about 10 TeV. The problem of the unitarity is considered in this context.
We review the current status of experimental and theoretical understanding of the axial nucleon structure at low and moderate energies. Topics considered include (quasi)elastic (anti)neutrino-nucleon scattering, charged pion electroproduction off nucleons and ordinary as well as radiative muon capture on the proton.
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.
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