First-principles calculation of electroweak box diagrams from lattice QCD

Abstract

We present the first realistic lattice QCD calculation of the $\gamma W$-box diagrams relevant for beta decays. The nonperturbative low-momentum integral of the $\gamma W$ 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 $\gamma W$-box correction to the semileptonic pion decay, ${\square }_{\gamma W}^{VA}{|}_{\pi }=2.830(11{)}_{\mathrm{stat}}(26{)}_{\mathrm{sys}}\times 10^{-3}$, with the total uncertainty controlled at the level of $\sim 1$\%. This study sheds light on the first-principles computation of the $\gamma W$-box correction to the neutron decay, which plays a decisive role in the determination of $|V_{ud}|$.

7 pages, 4 figures; v2, accepted for publication in PRL

References in corpus (14)

• Ab initio calculation of the neutron-proton mass difference
• Adler Function, Bjorken Sum Rule, and the Crewther Relation to Order alpha_s^4 in a General Gauge Theory
• Measurement of the Weak Axial-Vector Coupling Constant in the Decay of Free Neutrons Using a Pulsed Cold Neutron Beam
• Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD+QED
• QED Corrections to Hadronic Processes in Lattice QCD
• $K_L-K_S$ mass difference from lattice QCD
• Finite-Volume QED Corrections to Decay Amplitudes in Lattice QCD
• Determination of light quark masses from the electromagnetic splitting of pseudoscalar meson masses computed with two flavors of domain wall fermions
• Isospin breaking corrections to meson masses and the hadronic vacuum polarization: a comparative study
• Long-distance Contributions to Neutrinoless Double Beta Decay ${\pi }^{-}\to {\pi }^{+}ee$
• Lattice QCD study of the rare kaon decay $K^{+}\to {\pi }^{+}\nu \bar{\nu }$ at a near-physical pion mass
• Toward a First-Principles Calculation of Electroweak Box Diagrams
• A New Theory Framework for the Electroweak Radiative Corrections in $K_{l3}$ Decays
• Calculation of the $K_L-K_S$ mass difference for physical quark masses