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Methods for high-precision determinations of radiative-leptonic decay form factors using lattice QCD
High Energy Physics - Lattice · Submitted 2 Feb 2023
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim The optimal combination of methods yields results for the $D_s^+ \to \ell^+ \nu \gamma$ structure-dependent vector and axial form factors in the entire kinematic range with statistical plus fitting uncertainties of order 5%, using 25 gauge configurations with 64 samples per configuration.
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The abstract, sentence by sentence
We present a study of lattice-QCD methods to determine the relevant hadronic form factors for radiative leptonic decays of pseudoscalar mesons. We provide numerical results for $D_s^+ \to \ell^+ \nu \gamma$. Our calculation is performed using a domain-wall action for all quark flavors and on a single RBC/UKQCD lattice gauge-field ensemble. The first part of the study is how to best control two sources of systematic error inherent in the calculation, specifically the unwanted excited states created by the meson interpolating field, and unwanted exponentials in the sum over intermediate states. Using a 3d sequential propagator allows for better control over unwanted exponentials from intermediate states, while using a 4d sequential propagator allows for better control over excited states. We perform individual analyses of the 3d and 4d methods as well as a combined analysis using both methods, and find that the 3d sequential propagator offers good control over both sources of systematic uncertainties for the smallest number of propagator solves. From there, we further improve the use of a 3d sequential propagator by employing an infinite-volume approximation method, which allows us to calculate the relevant form factors over the entire allowed range of photon energies. We then study improvements gained by performing the calculation using a different three-point function, using ratios of three-point functions, averaging over positive and negative photon momentum, and using an improved method for extracting the structure-dependent part of the axial form factor. The optimal combination of methods yields results for the $D_s^+ \to \ell^+ \nu \gamma$ structure-dependent vector and axial form factors in the entire kinematic range with statistical plus fitting uncertainties of order 5%, using 25 gauge configurations with 64 samples per configuration.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | We present a study of lattice-QCD methods to determine the relevant hadronic form factors for radiative leptonic decays of pseudoscalar mesons. | contribution 1.00 | 0.90 | 0.06 | asserted 0.96 |
| s1 | We provide numerical results for $D_s^+ \to \ell^+ \nu \gamma$. | result 0.51 | 0.95 | 0.09 | asserted 1.00 |
| s2 | Our calculation is performed using a domain-wall action for all quark flavors and on a single RBC/UKQCD lattice gauge-field ensemble. | method 1.00 | 0.93 | 0.02 | asserted 1.00 |
| s3 | The first part of the study is how to best control two sources of systematic error inherent in the calculation, specifically the unwanted excited states created by the meson interpolating field, and unwanted exponentials in the sum over intermediate states. | contribution 0.53 | 0.72 | 0.04 | asserted 0.97 |
| s4 | Using a 3d sequential propagator allows for better control over unwanted exponentials from intermediate states, while using a 4d sequential propagator allows for better control over excited states. | method 0.85 | 0.53 | 0.05 | asserted 0.99 |
| s5 | We perform individual analyses of the 3d and 4d methods as well as a combined analysis using both methods, and find that the 3d sequential propagator offers good control over both sources of systematic uncertainties for the smallest number of propagator solves. | result 0.84 | 0.97 | 0.28 | asserted 1.00 |
| s6 | From there, we further improve the use of a 3d sequential propagator by employing an infinite-volume approximation method, which allows us to calculate the relevant form factors over the entire allowed range of photon energies. | method 0.88 | 0.95 | 0.07 | asserted 0.99 |
| s7 | We then study improvements gained by performing the calculation using a different three-point function, using ratios of three-point functions, averaging over positive and negative photon momentum, and using an improved method for extracting the structure-dependent part of the axial form factor. | method 0.86 | 0.94 | 0.12 | asserted 0.89 |
| s8 | The optimal combination of methods yields results for the $D_s^+ \to \ell^+ \nu \gamma$ structure-dependent vector and axial form factors in the entire kinematic range with statistical plus fitting uncertainties of order 5%, using 25 gauge configurations with 64 samples per configuration. | result 1.00 | 0.97 | 0.73 | asserted 1.00 |
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The paper
Original abstract
We present a study of lattice-QCD methods to determine the relevant hadronic form factors for radiative leptonic decays of pseudoscalar mesons. We provide numerical results for $D_s^+ \to \ell^+ \nu \gamma$. Our calculation is performed using a domain-wall action for all quark flavors and on a single RBC/UKQCD lattice gauge-field ensemble. The first part of the study is how to best control two sources of systematic error inherent in the calculation, specifically the unwanted excited states created by the meson interpolating field, and unwanted exponentials in the sum over intermediate states. Using a 3d sequential propagator allows for better control over unwanted exponentials from intermediate states, while using a 4d sequential propagator allows for better control over excited states. We perform individual analyses of the 3d and 4d methods as well as a combined analysis using both methods, and find that the 3d sequential propagator offers good control over both sources of systematic uncertainties for the smallest number of propagator solves. From there, we further improve the use of a 3d sequential propagator by employing an infinite-volume approximation method, which allows us to calculate the relevant form factors over the entire allowed range of photon energies. We then study improvements gained by performing the calculation using a different three-point function, using ratios of three-point functions, averaging over positive and negative photon momentum, and using an improved method for extracting the structure-dependent part of the axial form factor. The optimal combination of methods yields results for the $D_s^+ \to \ell^+ \nu \gamma$ structure-dependent vector and axial form factors in the entire kinematic range with statistical plus fitting uncertainties of order 5%, using 25 gauge configurations with 64 samples per configuration.
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References
How the literature uses it
11 arXiv papers cite this in 19 sentences
Papers citing it · 11 sentences without a confident label
Uses its method or tool 2 papers
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As in our previous work on radiative kaon decays [ref] , we adopt, for the computation of $C_3,W^μν(t_γ, k; t_W)$, the 3d method proposed in Refs. [ref] and [ref] .
Complete lattice QCD calculation of $K^{-}\to \ell^{-}\bar{\nu}_{\ell}\ell^{'+}\ell^{'-}$ form factors · Strategy for the numerical evaluation of the form factors below the $ππ$ threshold · 1.00
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Compared to our previous work, we employed the 3d method [ref] to compute the relevant form factors and have carried out thorough analyses of the systematic errors associated with isolating the initial-state kaon, as well as those arising from the finite temporal extent of the lattice.
Kaon radiative leptonic decay rates from lattice QCD simulations at the physical point · Conclusions · 1.00
Cites it as background 4 papers
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Discussions from the Lattice QCD perspectives on these radiative meson decays can be found in Ref. [ref] .
Constraining inverse moment of $B$-meson distribution amplitude using Lattice QCD data · Introduction · 1.00
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[ref] and it is relevant for decays of pions and kaons into electrons or decays of heavy mesons, while it can be neglected in the calculations of $$ and $$.
Isospin-breaking corrections to weak decays: the current status and a new infrared improvement · QED and isospin-breaking corrections to weak decays · 0.93
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Both approaches have been studied in detail in Ref. [ref] , where they are referred to as the 3d and 4d methods, respectively.
Kaon radiative leptonic decay rates from lattice QCD simulations at the physical point · Form Factors from Euclidean correlation functions · 0.84
What it cites · 49 sentences without a confident label
Builds on 2 papers
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Here we extend our preliminary work [ref] and present a detailed study of nonperturbative lattice methods to extract the structure-dependent form factors contributing to the amplitudes of radiative three-body decays $H →ℓ^- ν̅ γ$.
Controlling unwanted exponentials in lattice calculations of radiative leptonic decays · Introduction · 1.00
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Here we extend our preliminary work [ref] and present a detailed study of nonperturbative lattice methods to extract the structure-dependent form factors contributing to the amplitudes of radiative three-body decays $H →ℓ^- ν̅ γ$.
Radiative leptonic decays on the lattice · Introduction · 1.00
Uses the method or tool of 7 papers
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The charm valence quark is implemented using a Möbius domain-wall action with $L_5/a=12$, $aM_5=1.0$, $am_f=0.6$, and stout-smeared gauge links using three iterations with $ρ=0.1$ [ref] .
SU(3)-breaking ratios for $D_{(s)}$ and $B_{(s)}$ mesons · Lattice parameters · 0.92
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The third method, originally put forth in Ref. [ref] , calculates $F_A,SD$ by exploiting properties of the weak axial-vector three-point function at zero photon momentum.
First lattice calculation of radiative leptonic decay rates of pseudoscalar mesons · Comparing different methods to calculate F_A,SD · 0.89
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All calculations use all-mode averaging [ref] .
Covariant approximation averaging · Lattice parameters · 1.00
Uses data or values from 7 papers
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The sea-quark masses and gauge coupling are $am_u,d=0.005, am_s^sea=0.04, β=2.13,$ and the ensemble has an inverse lattice spacing of $a^-1=1.785(5) GeV$ [ref] .
Domain wall QCD with physical quark masses · Lattice parameters · 1.00
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In this study we make use of one of the “24I” RBC/UKQCD lattice gauge-field ensembles with 2+1 flavors of domain-wall fermions and the Iwasaki gauge action [ref] , with inverse lattice spacing $a^-1 = 1.785 (5)$ GeV and pion mass $m_π= 340 (1)$ MeV [ref] .
Continuum Limit Physics from 2+1 Flavor Domain Wall QCD · Introduction · 0.83
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For the charmed-meson radiative leptonic decays $D^+ →e^+ νγ$ and $D_s^+ →e^+ νγ$, the BESIII collaboration has reported upper limits on the branching fractions with $E_γ^(0) > 10$ MeV of $3.0 ×10^-5$ and $1.3×10^-4$, respectively [ref] .
Search for the Radiative Leptonic Decay $D^{+}\to \gamma e^{+} {\nu}_{e}$ · Introduction · 0.96
Cites as background 38 papers
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According to the well-known Bloch-Nordsieck mechanism [ref] , the integral of the radiative decay rate in the phase space region corresponding to soft photons must be added to the decay rate with no real photons in the final states (the so-called virtual electromagnetic contribution to the decay rate, which has recently been computed on the lattice [ref] ) in order to cancel infrared divergent contributions appearing in unphysical quantities at intermediate stages of the calculations.
Isospin-breaking corrections to light-meson leptonic decays from lattice simulations at physical quark masses · Introduction · 0.85
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According to the well-known Bloch-Nordsieck mechanism [ref] , the integral of the radiative decay rate in the phase space region corresponding to soft photons must be added to the decay rate with no real photons in the final states (the so-called virtual electromagnetic contribution to the decay rate, which has recently been computed on the lattice [ref] ) in order to cancel infrared divergent contributions appearing in unphysical quantities at intermediate stages of the calculations.
Light-meson leptonic decay rates in lattice QCD+QED · Introduction · 0.85
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According to the well-known Bloch-Nordsieck mechanism [ref] , the integral of the radiative decay rate in the phase space region corresponding to soft photons must be added to the decay rate with no real photons in the final states (the so-called virtual electromagnetic contribution to the decay rate, which has recently been computed on the lattice [ref] ) in order to cancel infrared divergent contributions appearing in unphysical quantities at intermediate stages of the calculations.
First lattice calculation of the QED corrections to leptonic decay rates · Introduction · 0.85
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