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

Area of Science:

• High Energy Physics
• Quantum Chromodynamics
• Nuclear Physics

Background:

• Beta decays are fundamental processes in nuclear and particle physics.
• Precise calculations of electroweak corrections are vital for determining fundamental constants like the CKM matrix elements.
• Gamma-W box diagrams represent a significant electroweak correction that requires accurate computation.

Purpose of the Study:

• To perform the first realistic lattice quantum chromodynamics (QCD) calculation of the gamma-W box diagrams relevant for beta decays.
• To establish a reliable method for computing nonperturbative low-momentum contributions to these diagrams.
• To demonstrate the feasibility of the method using the pion semileptonic decay and to pave the way for neutron decay calculations.

Main Methods:

• A hybrid approach combining lattice QCD simulations for low-momentum regions and perturbative QCD for high-momentum regions.
• Utilizing domain wall fermions at the physical pion mass.
• Employing multiple lattice spacings and volumes to ensure robust results.

Main Results:

• The axial gamma-W box correction to the semileptonic pion decay was calculated as □_{γW}^{VA}|_{π}=2.830(11)_{stat}(26)_{syst}×10^{-3}.
• The total uncertainty for this correction was controlled at approximately 1%.
• The study validates a first-principles method for computing these critical corrections.

Conclusions:

• The developed lattice QCD method is feasible and provides accurate results for gamma-W box diagrams.
• This work is crucial for improving the precision of the determination of the CKM matrix element |V_ud|.
• The methodology is applicable to other processes, including the neutron decay, which is pivotal for |V_ud| calculations.