Abstract
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}|.
Highlights
We present the first realistic lattice QCD calculation of the γW-box diagrams relevant for beta decays
The calculation is performed at the physical pion mass with various lattice spacings and volumes, which allows us to control the systematic effects in the lattice results
Where the first uncertainty is statistical, and the remaining errors account for perturbative truncation and higher-twist effects, lattice discretization effects, and lattice finitevolume effects by comparing the 24D and 32D results
Summary
It has been proposed to use the Feynman-Hellmann theorem to calculate the γW-box contribution [36,37]. We opt for a more straightforward way to perform the lattice calculation. The calculation is performed at the physical pion mass with various lattice spacings and volumes, which allows us to control the systematic effects in the lattice results. Combining the results from lattice QCD together with the perturbative. QCD, we obtain the axial γW-box correction to pion decay amplitude with a relative ∼1% uncertainty. The γW-box contribution.—In the theoretical analysis of the superallowed nuclear beta decay rates, the dominant uncertainty arises from the nucleus-independent electroweak radiative correction ΔVR, which is universal for both nuclear and free neutron beta decay [1]. Among various contributions to ΔVR, Sirlin established [2] that only the axial γW-box contribution is sensitive to hadronic scales; see Fig. 1 for the γW diagrams.
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