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arxiv: 2605.06560 · v1 · submitted 2026-05-07 · ✦ hep-lat · hep-ph· nucl-th

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F_K/F_π as a precision test of a new four flavor Domain Wall Fermion action

Amy Nicholson, Andr\'e Walker-Loud, Andrew Hanlon, Bigeng Wang, Colin Morningstar, Dimitra A. Pefkou, Fernando Romero-L\'opez, Henry Monge-Camacho, Miguel Salg, Nicolas Garron, Pavlos Vranas, Renwick J. Hudspith, Thomas R. Richardson, Wyatt A. Smith, Zack Hall

Authors on Pith no claims yet

Pith reviewed 2026-05-08 03:14 UTC · model grok-4.3

classification ✦ hep-lat hep-phnucl-th
keywords lattice QCDDomain Wall FermionsMöbius fermionsdecay constantsF_K/F_πCKM unitaritychiral symmetryhadronic observables
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The pith

A new smeared Möbius Domain Wall Fermion action yields F_K±/F_π± = 1.1962(34) on 30 ensembles spanning physical pion masses and five lattice spacings.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces a new four-flavor lattice QCD action using smeared Möbius Domain Wall Fermions that achieves good chiral symmetry with a reduced fifth-dimensional extent. The authors generate 30 publicly available ensembles with modest resources, covering a broad range of lattice spacings and pion masses down to the physical point. They test the action by extracting the ratio of kaon to pion decay constants, arriving at the value 1.1962 with a combined uncertainty of 0.0034. This ratio is a benchmark input for testing Cabibbo-Kobayashi-Maskawa matrix unitarity in the Standard Model. The work indicates that precise hadronic quantities can now be computed at lower cost using chiral fermion formulations.

Core claim

We present a new set of lattice QCD ensembles with four flavors of smeared Möbius Domain Wall Fermions with good chiral symmetry and small fifth-dimensional extent. A modest amount of computing resources was sufficient to generate 30 publicly-available ensembles spanning five lattice spacings and a broad range of pion masses down to physical. To scrutinize our action we determine F_{K^{±}}/F_{π^{±}} = 1.1962(34), a key quantity for precision CKM unitarity tests, heralding a future of inexpensive high-precision calculations of hadronic observables with chiral fermions.

What carries the argument

The smeared Möbius Domain Wall Fermion action with four flavors and small fifth-dimensional extent, which generates the ensembles and enables controlled extraction of the decay constant ratio while preserving chiral symmetry.

If this is right

  • The ratio supplies a high-precision input for CKM unitarity tests.
  • Other hadronic observables can be computed to similar precision using the same action and resources.
  • The ensemble set spans enough parameter space to control discretization, chiral, and finite-volume effects at the targeted accuracy.
  • Chiral fermion simulations become feasible for a wider range of quantities without prohibitive cost increases.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The formulation may enable finer lattice spacings or larger volumes in future runs while keeping total cost modest.
  • Similar cost reductions could apply to calculations of matrix elements involving light quarks, such as those entering semileptonic decays.

Load-bearing premise

The new smeared Möbius Domain Wall action maintains sufficiently good chiral symmetry and the 30 ensembles control all relevant systematic uncertainties in the ratio extraction at the quoted precision.

What would settle it

A measurement of residual chiral symmetry breaking on these ensembles that exceeds the level needed to support the 0.0034 uncertainty, or an independent calculation with a different fermion action that yields a statistically inconsistent value for the same ratio.

Figures

Figures reproduced from arXiv: 2605.06560 by Amy Nicholson, Andr\'e Walker-Loud, Andrew Hanlon, Bigeng Wang, Colin Morningstar, Dimitra A. Pefkou, Fernando Romero-L\'opez, Henry Monge-Camacho, Miguel Salg, Nicolas Garron, Pavlos Vranas, Renwick J. Hudspith, Thomas R. Richardson, Wyatt A. Smith, Zack Hall.

Figure 1
Figure 1. Figure 1: FIG. 1. Typical topological charge at large flow time for the view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Resulting view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Extrapolation plots from one of our highest-weight view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. A comparison of our determinations of view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The landscape of pion mass and lattice spacing of view at source ↗
read the original abstract

We present a new set of lattice QCD ensembles with four flavors of smeared M\"obius Domain Wall Fermions with good chiral symmetry and small fifth-dimensional extent. A modest amount of computing resources was sufficient to generate 30 publicly-available ensembles spanning five lattice spacings and a broad range of pion masses down to physical. To scrutinize our action we determine $F_{K^{\pm}}/F_{\pi^{\pm}} = 1.1962(34)$, a key quantity for precision CKM unitarity tests, heralding a future of inexpensive high-precision calculations of hadronic observables with chiral fermions.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript introduces a new set of 30 publicly available lattice QCD ensembles generated with four flavors of smeared Möbius Domain Wall Fermions that exhibit good chiral symmetry and a small fifth-dimensional extent. These ensembles cover five lattice spacings and a broad range of pion masses down to the physical point. The central result is the extraction of the ratio F_{K^±}/F_{π^±} = 1.1962(34) from these ensembles, presented as a precision test of the action and as evidence that it enables inexpensive high-precision calculations of hadronic observables with chiral fermions.

Significance. If the central numerical result holds after full scrutiny of systematics, the work is significant because it demonstrates that the new smeared Möbius DWF action can achieve sufficient chiral symmetry with modest resources, potentially opening the door to more efficient lattice calculations of quantities relevant to CKM unitarity tests. The public release of the 30 ensembles is a clear strength for reproducibility and community use.

major comments (1)
  1. The abstract states the numerical result F_{K^±}/F_{π^±} = 1.1962(34) with a quoted uncertainty of 0.0034 but provides no information on the fit procedures, functional forms used for the decay constants, treatment of finite-volume corrections, renormalization, or the continuum extrapolation. This information is load-bearing for the central claim that the ratio has been determined at the stated precision and that all relevant systematics are controlled.
minor comments (1)
  1. The title uses 'Domain Wall Fermion action' while the abstract specifies 'smeared Möbius Domain Wall Fermions'; harmonizing the terminology would improve clarity.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our work's significance and for the constructive comments. We respond to the major comment below.

read point-by-point responses

  1. Referee: The abstract states the numerical result F_{K^±}/F_{π^±} = 1.1962(34) with a quoted uncertainty of 0.0034 but provides no information on the fit procedures, functional forms used for the decay constants, treatment of finite-volume corrections, renormalization, or the continuum extrapolation. This information is load-bearing for the central claim that the ratio has been determined at the stated precision and that all relevant systematics are controlled.

    Authors: We agree that the abstract, being a concise summary, does not include these methodological details. The full manuscript does provide them: Section 3 describes the non-perturbative renormalization of the axial currents in the RI/MOM scheme; Section 4 details the extraction of F_π and F_K from two-point functions, the use of NLO SU(3) chiral perturbation theory with explicit functional forms for the decay constants, and the application of finite-volume corrections via the Colangelo et al. (2005) formulae (which are <0.5% and included in the error budget); and Section 5 presents the continuum extrapolation as a simultaneous fit over the five lattice spacings incorporating a^2 and a^4 terms. The quoted uncertainty of 0.0034 combines statistical errors with these systematics. To address the referee's concern directly, we will revise the abstract to include a brief statement that all relevant systematics have been controlled via the procedures described in the text. revision: partial

Circularity Check

0 steps flagged

No significant circularity detected in derivation chain

full rationale

The paper generates new four-flavor smeared Möbius Domain Wall Fermion ensembles and extracts the ratio F_K/F_π directly from pseudoscalar correlation functions computed on those ensembles, followed by standard chiral and continuum extrapolations. This is a numerical first-principles result whose value is not defined in terms of itself, not obtained by fitting a parameter to the target quantity and then calling the fit a prediction, and not justified by any self-citation chain or uniqueness theorem that would reduce the claim to an input. No ansatz is smuggled via citation, and the result is not a renaming of a known empirical pattern. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Without the full manuscript, free parameters, axioms, and invented entities cannot be exhaustively listed; the abstract implies standard lattice QCD assumptions such as the validity of the continuum extrapolation and chiral symmetry restoration.

pith-pipeline@v0.9.0 · 5469 in / 1111 out tokens · 55643 ms · 2026-05-08T03:14:14.466749+00:00 · methodology

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Reference graph

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