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Finite-volume effects in long-distance processes with massless leptonic propagators
High Energy Physics - Lattice · Submitted 17 Sep 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim We demonstrate that, in spite of the presence of the propagator of an almost massless electron, such an infinite-volume reconstruction procedure can be used to obtain the amplitude for the rare kaon decay $K^+\to\pi^+\nu\bar\nu$ from a lattice quantum chromodynamics computation with only exponentially small finite-volume corrections.
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The abstract, sentence by sentence
In Ref. [1], a method was proposed to calculate QED corrections to hadronic self energies from lattice QCD without power-law finite-volume errors. In this paper, we extend the method to processes which occur at second-order in the weak interaction and in which there is a massless (or almost massless) leptonic propagator. We demonstrate that, in spite of the presence of the propagator of an almost massless electron, such an infinite-volume reconstruction procedure can be used to obtain the amplitude for the rare kaon decay $K^+\to\pi^+\nu\bar\nu$ from a lattice quantum chromodynamics computation with only exponentially small finite-volume corrections.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In Ref. [1], a method was proposed to calculate QED corrections to hadronic self energies from lattice QCD without power-law finite-volume errors. | background 1.00 | 0.03 | 0.03 | asserted 1.00 |
| s1 | In this paper, we extend the method to processes which occur at second-order in the weak interaction and in which there is a massless (or almost massless) leptonic propagator. | contribution 1.00 | 0.80 | 0.07 | asserted 0.96 |
| s2 | We demonstrate that, in spite of the presence of the propagator of an almost massless electron, such an infinite-volume reconstruction procedure can be used to obtain the amplitude for the rare kaon decay $K^+\to\pi^+\nu\bar\nu$ from a lattice quantum chromodynamics computation with only exponentially small finite-volume corrections. | result 0.97 | 0.93 | 0.92 | asserted 1.00 |
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The paper
Original abstract
In Ref. [1], a method was proposed to calculate QED corrections to hadronic self energies from lattice QCD without power-law finite-volume errors. In this paper, we extend the method to processes which occur at second-order in the weak interaction and in which there is a massless (or almost massless) leptonic propagator. We demonstrate that, in spite of the presence of the propagator of an almost massless electron, such an infinite-volume reconstruction procedure can be used to obtain the amplitude for the rare kaon decay $K^+\to\pi^+\nu\bar\nu$ from a lattice quantum chromodynamics computation with only exponentially small finite-volume corrections.
Human review
How the literature uses it
11 arXiv papers cite this in 16 sentences
Papers citing it · 10 sentences without a confident label
Uses its method or tool 2 papers
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The infinite volume reconstruction (IVR) method [ref] is defined as [equation] Here we only consider the calculation of $t<0$ time ordering.
Finite-volume formalism for physical processes with an electroweak loop integral · Avoiding cusp effect by IVR method · 0.99
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There will be no terms with exponentially growing time dependence since the calculation is performed in Minkowski space and the unwanted term that oscillates at large times can be isolated in this analytic calculation and dropped as was done in Ref. [ref] .
Radiative corrections to leptonic decays using infinite-volume reconstruction · Electromagnetic corrections to $𝐊_ℓ3$ decays · 0.81
Cites it as background 3 papers
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The examples include kaon mixing [ref] , rare kaon decays [ref] , double beta decays [ref] , inclusive $B$-meson decays [ref] , as well as the electromagentic and radiative corrections to the weak decays [ref] .
Lattice QCD calculation of the electroweak box diagrams for the kaon semileptonic decays · Introduction · 0.92
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It has since been used in studies including: long distance contributions to neutrinoless double-$β$ decay [ref] , rare kaon decays [ref] ; the width for the decay $K→ℓν(ℓ^' +ℓ^' -)$, where $ℓ$ and $ℓ^'$ represent charged leptons [ref] ; the $π^+$ - $π^0$ mass splitting [ref] ; the two-photon exchange contribution to the muonic-hydrogen Lamb shift [ref] and the contribution from a light sterile neutrino to neutrinoless double-$β$ decay [ref] .
Radiative corrections to leptonic decays using infinite-volume reconstruction · Introduction · 0.84
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Besides the references in [ref] , we acknowledge later progress in the massive-photon-QED approach [ref] , and in the infinite-volume-QED approach [ref] .] In our long-term research program, aiming at a precise calculation of the aforementioned gold-plated quantities, we use an approach fully consistent with the basic principles of quantum field theory.
First results on QCD+QED with C* boundary conditions · Introduction · 0.96
What it cites · 13 sentences without a confident label
Builds on 1 paper
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In this work, we extend the infinite-volume reconstruction method proposed in Ref. [ref] to long-distance processes with massless (or almost massless) leptonic propagators.
QED self energies from lattice QCD without power-law finite-volume errors · Conclusion · 1.00
Uses the method or tool of 2 papers
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To completely remove the power-law finite-volume effects induced by the massless electron or neutrino, we adopt the infinite-volume reconstruction (IVR) method proposed in Ref. [ref] , which has been used to eliminate such effects in QED corrections to hadronic self energies.
QED self energies from lattice QCD without power-law finite-volume errors · Introduction · 0.98
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Following Ref. [ref] , where the $K_L$-$K_S$ mixing is analysed as an example, one can correct for such potentially large finite-volume effects.
Effects of finite volume on the $K_L$-$K_S$ mass difference · Introduction · 0.80
Cites as background 46 papers
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As explained in Ref. [ref] , the $K^+→π^+ν_ℓν̅_ℓ$ decay amplitude, where $ℓ$ represents the lepton quantum number, contains contributions from both $Z$-exchange diagrams and $W$-$W$ diagrams.
Prospects for a lattice computation of rare kaon decay amplitudes II $K\to\pi\nu\bar{\nu}$ decays · Finite-volume effects in $K^+→π^+ν_ℓν̅_ℓ$ decays · 0.88
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Examples include $K_L$-$K_S$ mixing [ref] and $ϵ_K$ [ref] , rare kaon decays [ref] , neutrinoless double-beta decays [ref] , electroweak box contributions to semileptonic decays [ref] , inclusive $B$-meson decays [ref] , nucleon Compton amplitudes [ref] , as well as isospin-breaking effects in hadronic spectra [ref] , the hadronic vacuum polarization function [ref] , leptonic decays [ref] and $K→ππ$ decays [ref] .
Electromagnetic mass splittings of the low lying hadrons and quark masses from 2+1 flavor lattice QCD+QED · Introduction · 0.93
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Examples include $K_L$-$K_S$ mixing [ref] and $ϵ_K$ [ref] , rare kaon decays [ref] , neutrinoless double-beta decays [ref] , electroweak box contributions to semileptonic decays [ref] , inclusive $B$-meson decays [ref] , nucleon Compton amplitudes [ref] , as well as isospin-breaking effects in hadronic spectra [ref] , the hadronic vacuum polarization function [ref] , leptonic decays [ref] and $K→ππ$ decays [ref] .
Full QED+QCD Low-Energy Constants through Reweighting · Introduction · 0.93
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