Lattice QCD Calculation of Electroweak Box Contributions to Superallowed Nuclear and Neutron Beta Decays.

We present the first lattice QCD calculation of the universal axial γW-box contribution □_{γW}^{VA} to both superallowed nuclear and neutron beta decays. This contribution emerges as a significant component within the theoretical uncertainties surrounding the extraction of |V_{ud}| from superallowed decays. Our calculation is conducted using two domain wall fermion ensembles at the physical pion mass. To construct the nucleon four-point correlation functions, we employ the random sparsening field technique. Furthermore, we incorporate long-distance contributions to the hadronic function using the infinite-volume reconstruction method. Upon performing the continuum extrapolation, we arrive at □_{γW}^{VA}=3.65(7)_{lat}(1)_{PT}×10^{-3}. Consequently, this yields a slightly higher value of |V_{ud}|=0.973 86(11)_{exp}(9)_{RC}(27)_{NS}, reducing the previous 2.1σ tension with the CKM unitarity to 1.8σ. Additionally, we calculate the vector γW-box contribution to the axial charge g_{A}, denoted as □_{γW}^{VV}, and explore its potential implications.

First-Principles Calculation of Electroweak Box Diagrams from Lattice QCD.

We present the first realistic lattice QCD calculation of the γW-box diagrams relevant for beta decays. The nonperturbative low-momentum integral of the γW loop is calculated using a lattice QCD simulation, complemented by the perturbative QCD result at high momenta. Using the pion semileptonic decay as an example, we demonstrate the feasibility of the method. By using domain wall fermions at the physical pion mass with multiple lattice spacings and volumes, we obtain the axial γW-box correction to the semileptonic pion decay, □_{γW}^{VA}|_{π}=2.830(11)_{stat}(26)_{syst}×10^{-3}, with the total uncertainty controlled at the level of ∼1%. This study sheds light on the first-principles computation of the γW-box correction to the neutron decay, which plays a decisive role in the determination of |V_{ud}|.

γW Box Inside Out: Nuclear Polarizabilities Distort the Beta Decay Spectrum.

I consider the γW-box correction to superallowed nuclear ß decays in the framework of dispersion relations. I address a novel effect of a distortion of the emitted electron energy spectrum by nuclear polarizabilities and show that this effect, while neglected in the literature, is sizable. The respective correction to the ß^{+} spectrum is estimated to be Δ_{R}(E)=(1.6±1.6)×10^{-4}E/MeV assuming a conservative 100% uncertainty. The effect is positive definite and can be observed if a high-precision measurement of the positron spectrum is viable. If only the full rate is observed, it should be included in the calculated Ft values of nuclear decays. I argue that this novel effect should be included in the analyses of nuclear beta decay experiments to ensure the correct extraction of V_{ud} from decay rates, and of the Fierz interference term from precision measurements of decay spectra.

Reduced Hadronic Uncertainty in the Determination of V_{ud}.

We analyze the universal radiative correction Δ_{R}^{V} to neutron and superallowed nuclear ß decay by expressing the hadronic γW-box contribution in terms of a dispersion relation, which we identify as an integral over the first Nachtmann moment of the γW interference structure function F_{3}^{(0)}. By connecting the needed input to existing data on neutrino and antineutrino scattering, we obtain an updated value of Δ_{R}^{V}=0.02467(22), wherein the hadronic uncertainty is reduced. Assuming other standard model theoretical calculations and experimental measurements remain unchanged, we obtain an updated value of |V_{ud}|=0.97370(14), raising tension with the first row Cabibbo-Kobayashi-Maskawa unitarity constraint. We comment on ways current and future experiments can provide input to our dispersive analysis.

New Sum Rule for the Nuclear Magnetic Polarizability.

The well-known Levinger-Bethe photonuclear sum rule relates the strength of the photoexcitation of the giant dipole resonance in a nucleus to the number of nucleons in that nucleus. I extend this sum rule to the case of virtual photons and relate the size of the magnetic polarizability of a nucleus to the Q^{2} slope of the transverse virtual photoabsorption cross section integrated over the energy in the nuclear range. I check this sum rule for the deuteron where necessary data is available, discuss possible applications and connection with other sum rules postulated in the literature.

Low-energy theorem for virtual compton scattering and generalized sum rules of the nucleon.

We formulate the low-energy theorem for virtual Compton scattering off a nucleon and examine its consequences for generalized nucleon polarizabilites. As a result of a new, model-independent definition of the low-energy limit for doubly virtual Compton scattering, all generalized sum rules of the nucleon have a continuous limit for real photons and obtain contributions from the t channel that were not included previously.