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First lattice calculation of radiative leptonic decay rates of pseudoscalar mesons
High Energy Physics - Lattice · Submitted 9 Jun 2020
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim Together with the non-perturbative determination of the corrections to the processes $P\to \ell \bar \nu_\ell$ due to the exchange of a virtual photon, this allows accurate predictions at $O(\alpha_{em})$ to be made for leptonic decay rates for pseudoscalar mesons ranging from the pion to the $D_s$ meson.
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The abstract, sentence by sentence
We present a non-perturbative lattice calculation of the form factors which contribute to the amplitudes for the radiative decays $P\to \ell \bar \nu_\ell \gamma$, where $P$ is a pseudoscalar meson and $\ell$ is a charged lepton. Together with the non-perturbative determination of the corrections to the processes $P\to \ell \bar \nu_\ell$ due to the exchange of a virtual photon, this allows accurate predictions at $O(\alpha_{em})$ to be made for leptonic decay rates for pseudoscalar mesons ranging from the pion to the $D_s$ meson. We are able to separate unambiguously and non-pertubatively the point-like contribution, from the structure-dependent, infrared-safe, terms in the amplitude. The fully non-perturbative $O(a)$ improved calculation of the inclusive leptonic decay rates will lead to the determination of the corresponding Cabibbo-Kobayashi-Maskawa (CKM) matrix elements also at $O(\alpha_{em})$. Prospects for a precise evaluation of leptonic decay rates with emission of a hard photon are also very interesting, especially for the decays of heavy $D$ and $B$ mesons for which currently only model-dependent predictions are available to compare with existing experimental data.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a non-perturbative lattice calculation of the form factors which contribute to the amplitudes for the radiative decays $P\to \ell \bar \nu_\ell \gamma$, where $P$ is a pseudoscalar meson and $\ell$ is a charged lepton. | contribution 1.00 | 0.96 | 0.19 | asserted 1.00 |
| s1 | Together with the non-perturbative determination of the corrections to the processes $P\to \ell \bar \nu_\ell$ due to the exchange of a virtual photon, this allows accurate predictions at $O(\alpha_{em})$ to be made for leptonic decay rates for pseudoscalar mesons ranging from the pion to the $D_s$ meson. | result 0.48 | 0.80 | 0.35 | asserted 0.87 |
| s2 | We are able to separate unambiguously and non-pertubatively the point-like contribution, from the structure-dependent, infrared-safe, terms in the amplitude. | result 0.41 | 0.95 | 0.15 | asserted 1.00 |
| s3 | The fully non-perturbative $O(a)$ improved calculation of the inclusive leptonic decay rates will lead to the determination of the corresponding Cabibbo-Kobayashi-Maskawa (CKM) matrix elements also at $O(\alpha_{em})$. | interpretation 0.86 | 0.47 | 0.28 | hedged possibility 0.59 |
| s4 | Prospects for a precise evaluation of leptonic decay rates with emission of a hard photon are also very interesting, especially for the decays of heavy $D$ and $B$ mesons for which currently only model-dependent predictions are available to compare with existing experimental data. | future work 0.89 | 0.09 | 0.05 | hedged possibility 0.69 |
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The paper
Original abstract
We present a non-perturbative lattice calculation of the form factors which contribute to the amplitudes for the radiative decays $P\to \ell \bar \nu_\ell \gamma$, where $P$ is a pseudoscalar meson and $\ell$ is a charged lepton. Together with the non-perturbative determination of the corrections to the processes $P\to \ell \bar \nu_\ell$ due to the exchange of a virtual photon, this allows accurate predictions at $O(\alpha_{em})$ to be made for leptonic decay rates for pseudoscalar mesons ranging from the pion to the $D_s$ meson. We are able to separate unambiguously and non-pertubatively the point-like contribution, from the structure-dependent, infrared-safe, terms in the amplitude. The fully non-perturbative $O(a)$ improved calculation of the inclusive leptonic decay rates will lead to the determination of the corresponding Cabibbo-Kobayashi-Maskawa (CKM) matrix elements also at $O(\alpha_{em})$. Prospects for a precise evaluation of leptonic decay rates with emission of a hard photon are also very interesting, especially for the decays of heavy $D$ and $B$ mesons for which currently only model-dependent predictions are available to compare with existing experimental data.
Human review
References
How the literature uses it
37 arXiv papers cite this in 138 sentences
Papers citing it · 79 sentences without a confident label
Builds on it 3 papers
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Our purpose is therefore to estimate the $B_s →γ$ counterpart of Ref. [ref] , awaiting a direct determination of the same on the lattice.
From $D_s \to \gamma$ in lattice QCD to $B_s \to \mu \mu \gamma$ at high $q^2$ · Introduction · 0.86
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With respect to Ref. [ref] , several key improvements have been implemented: * For the first time, we go beyond the so-called electroquenched approximation by including quark-disconnected contributions (see Fig. [ref]). * We perform simulations directly at physical light- and strange-quark masses, thereby eliminating the need for chiral extrapolations. * We systematically investigate finite-size effects (FSE) by utilizing ensembles with spatial extents ranging from $L ≃3.8$ fm to $L ≃7.7$ fm. * We carry out a continuum extrapolation using three fine lattice spacings in the range $a ∈[0.08, 0.058]$ fm.
Kaon radiative leptonic decay rates from lattice QCD simulations at the physical point · Introduction · 0.89
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In this paper, we return to the radiative decays of $D_s$ mesons and compute the relevant axial and vector form factors $F_V$ and $F_A$ over the full physical kinematic range and with high statistical accuracy, thus improving significantly upon the previous study of Ref. [ref] .
Lattice calculation of the $D_{s}$ meson radiative form factors over the full kinematical range · Introduction · 0.90
Uses its method or tool 9 papers
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In Sec. III and Appendix B of Ref. [ref] we showed in detail that for the emission of a real photon, the hadronic tensor $H_W^μν$ can be extracted for all values of $x_γ$ from the Euclidean three-point correlation function: [equation] where $T$ is the temporal extent of the lattice [$T$ is not to be confused with $T̂$ which represents "time-ordered".], $ϕ^†_D_s$ is an interpolating operator with the quantum numbers to create the $D_s$ meson, $k=(E_γ, k)$, and $E_γ$ is the energy of the photon.
Lattice calculation of the $D_{s}$ meson radiative form factors over the full kinematical range · Evaluating $F_V$ and $F_A$ from Euclidean lattice correlation functions · 0.87
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In this work we adopt the definition of the vector ($F_V$) and axial-vector ($F_A$) form factors given in Section II of Ref. [ref] (see also Appendix B of Ref. [ref] ).
Comparison of lattice QCD+QED predictions for radiative leptonic decays of light mesons with experimental data · Differential rates for radiative leptonic decays · 0.91
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For $x_k<2m_π/m_K$, the hadronic tensor is reconstructed, following the strategy already applied in previous studies of radiative processes [ref] , directly from the time integration of these correlators (Sec. IV-A of [ref] ).
Rare kaon decays $K^- \to \ell^- \bar{\nu}_\ell \ell'^{+} \ell'^{-}$: Standard Model predictions from lattice QCD · Methods · 0.96
Uses its data or values 6 papers
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In Section [ref] we analyze the LQCD data for $D_s →γℓν$ decays in Ref. [ref] .
From $D_s \to \gamma$ in lattice QCD to $B_s \to \mu \mu \gamma$ at high $q^2$ · Introduction · 0.90
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C_A^K = 0.0370 ±0.0088 , D_A^K = -0.0012 ±0.0074 , where the uncertainties include statistical errors as well as the various sources of systematic errors, except for the QED quenching effect [ref] .
Comparison of lattice QCD+QED predictions for radiative leptonic decays of light mesons with experimental data · Differential rates for radiative leptonic decays · 0.97
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[ref] and the simulation point meson masses and decay constants, together with $F_A^π$ and $F_A^K$ from $χ$PT at $(p^4)$ and $(p^6)$, respectively [ref] .
Isospin-breaking corrections to light-meson leptonic decays from lattice simulations at physical quark masses · Results · 0.85
Compares with it 5 papers
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Concretely, the fit is equivalent to the pole-like fit performed in Ref. [ref] , but we think it has the advantage of providing a plausible physical interpretation.
From $D_s \to \gamma$ in lattice QCD to $B_s \to \mu \mu \gamma$ at high $q^2$ · Application to $V_⊥^D_s$ · 0.95
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We compute the branching ratios for the decays \(π→eν_eγ\), \(K →eν_eγ\), and \(K →μν_μγ\) with or without radiative corrections, and compare them with the previous lattice calculations [ref] and experimental measurements [ref] .
Lattice Calculation of Light Meson Radiative Leptonic Decays · Conclusions · 0.99
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Combining statistical and systematic uncertainties, we obtain [equation] to be compared with our previous determination $R_γ^ETMC-21 = 1.74 (21) ×10^-5$ [ref] .
Kaon radiative leptonic decay rates from lattice QCD simulations at the physical point · Introduction · 0.97
Cites it as support 1 paper
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As predicted by $χPT$ [ref] and confirmed by lattice calculations [ref] , structure-dependent contributions are negligible for the decay channels studied in this work, namely the decay of pions or kaons into muons and neutrinos, and therefore at our level of precision we can reliably consider $Γ_1(Λ_IR)≃Γ_1^pt(ω_γ^max,Λ_IR)$, where $ω_γ^max$ is the maximum photon energy kinematically allowed.
Isospin-breaking corrections to light-meson leptonic decays from lattice simulations at physical quark masses · Introduction · 1.00
Cites it as background 12 papers
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The hadronic tensor $H^μν_W$ can be decomposed in terms of a “point-like" contribution $H_pt^μν$ (i.e. the expression obtained by treating the $D_s$ meson as a point-like particle) and four structure-dependent (SD) scalar form factors, $F_V, F_A, H_1$ and $H_2$ [ref] [Here, we use the dimensionless definitions of $H_1,2$ introduced in Ref. [ref] which differ by simple factors from those used in our earlier papers [ref] .
Lattice calculation of the $D_{s}$ meson radiative form factors over the full kinematical range · Definition of the form factors · 0.87
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Since then, a lattice calculation of radiative leptonic decays was published in [ref] , where the authors use what we call the 4d-method.
Controlling unwanted exponentials in lattice calculations of radiative leptonic decays · Introduction · 0.81
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Previous lattice-QCD studies of radiative corrections to light-meson leptonic decays have focused mainly on the muon channels and the related $K_μ2/π_μ2$ ratio [ref] , as well as on the radiative decays $P→ℓνγ^(*)$ [ref] .
First Lattice QCD Determination of Lepton-Flavor-Universality Ratios in Light-Meson Leptonic Decays · Introduction · 0.93
What it cites · 34 sentences without a confident label
Uses the method or tool of 4 papers
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The procedure to evaluate the term in the first parentheses, $Γ_0(L) - Γ_0^pt(L)$, is explained in detail in Ref. [ref] , where the explicit expression for the term in the second parentheses, $Γ_0^pt(μ_γ) + Γ_1^pt(ΔE_γ, μ_γ)$, can also be found.
QED Corrections to Hadronic Processes in Lattice QCD · Expressions for the decay rates in terms of $F_V$ and $F_A$ · 0.86
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Renormalisation of the corresponding axial-vector and vector currents with Twisted Mass Fermions gives $F_A = Z_V F^0_A$ and $F_V =Z_A F^0_V$ where $F^0_A$ and $F^0_V$ are the unrenormalised quantities as explained in Eq. ([ref]), $Z_A$ has been computed with method M2 and $Z_V$ with the WI [ref] .
Up, down, strange and charm quark masses with Nf = 2+1+1 twisted mass lattice QCD · Numerical results · 0.90
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Here we use the lattice size $L$ as the intermediate infrared regulator by working in the QED$_L$ formulation of QED in a finite volume [ref] but any other consistent formulation of QED on the lattice can also be used.
QED in finite volume and finite size scaling effect on electromagnetic properties of hadrons · Expressions for the decay rates in terms of $F_V$ and $F_A$ · 0.99
Uses data or values from 2 papers
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The results in Eqs. ([ref]) and ([ref]) can be combined with the values of the decays constants computed in Ref. [ref] and [ref] [equation] to compute the differential or total decay rate using the expressions given in Appendix [ref].
Leptonic decay constants fK, fD and fDs with Nf = 2+1+1 twisted-mass lattice QCD · Numerical results · 0.99
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The results in Eqs. ([ref]) and ([ref]) can be combined with the values of the decays constants computed in Ref. [ref] and [ref] [equation] to compute the differential or total decay rate using the expressions given in Appendix [ref].
Up, down, strange and charm quark masses with Nf = 2+1+1 twisted mass lattice QCD · Numerical results · 0.99
Cites as background 3 papers
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A non-perturbative calculation of the radiative decay rates can be particularly important for heavy mesons since, unlike the case of pions and kaons where such decays have been studied using Chiral Perturbation Theory (ChPT) [ref] , no model-independent calculations have ever been performed.
On the Radiative Pion Decay · introduction · 0.81
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A non-perturbative calculation of the radiative decay rates can be particularly important for heavy mesons since, unlike the case of pions and kaons where such decays have been studied using Chiral Perturbation Theory (ChPT) [ref] , no model-independent calculations have ever been performed.
Form Factors in the radiative pion decay · introduction · 0.81
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A non-perturbative calculation of the radiative decay rates can be particularly important for heavy mesons since, unlike the case of pions and kaons where such decays have been studied using Chiral Perturbation Theory (ChPT) [ref] , no model-independent calculations have ever been performed.
Kaon Decays in the Standard Model · introduction · 0.81
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