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This paper presents the first computation of the finite-volume '1-quark connected' contributions to the Omega^- baryon two-point function that arise with C-periodic boundary conditions, using a stochastic estimator.

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2026-08-02 20:07 UTC pith:GMO7ULXJ

load-bearing objection First numerical estimate of the C-periodic 1-q connected contribution to the Omega- correlator; the contraction algebra holds up but the signal is noise-dominated and the estimator lacks an independent check. Credible progress report, not yet a physics result. the 4 major comments →

arxiv 2602.23910 v1 pith:GMO7ULXJ submitted 2026-02-27 hep-lat

Baryon masses with C-periodic boundary conditions

Anian Altherr , Isabel Campos , Roman Gruber , Tim Harris , Francesca Margari , Marina Krsti\'c Marinkovi\'c , Letizia Parato , Agostino Patella
show 2 more authors
Sara Rosso Paola Tavella
This is my paper
classification hep-lat
keywords lattice QCDC-periodic boundary conditionsbaryon massesOmega^- baryonisospin breakingstochastic estimatorall-to-all propagatorfinite-volume effects
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

Baryon masses from lattice QCD must include isospin-breaking corrections, including QED, which requires a definition of QED in a finite volume. C-periodic boundary conditions are one such definition, but they introduce extra partially connected terms in baryon correlators that are absent with ordinary periodic conditions. This paper reports the first numerical evaluation of these '1-quark connected' contributions for the Omega^- baryon, using a stochastic estimator for the all-to-all quark propagator. The measured term is small and noise-dominated, but smearing helps; it is expected to vanish exponentially in the infinite-volume limit. The paper also gives improved preliminary proton and Omega masses from 50-60 point sources, with substantially reduced statistical errors compared with earlier calculations.

Core claim

The paper reports the first numerical evaluation of the 1-quark connected contributions to the Omega^- two-point function, a finite-volume artifact of C-periodic boundary conditions that arises from modified quark-quark and antiquark-antiquark propagators. A stochastic estimator for the all-to-all propagator (Eq. 13) is introduced and tested via gauge and translational invariance plus tree-level checks. On a 400 MeV pion mass ensemble, the 1-q correlator is noise-dominated, with errors surpassing the 3-q signal at t=19 without smearing and t=24 with smearing. Preliminary proton and Omega masses from 50-60 point sources are 1170(10) and 1470(20) MeV on the large ensemble, and 1190(15) and 145

What carries the argument

The central machinery is a pair of modified propagator identities (Eq. 3) that C-periodic boundary conditions impose: in addition to the standard quark-antiquark propagator, one obtains quark-quark and antiquark-antiquark propagators that connect a point to its mirror image shifted by one lattice extent, e.g. D^{-1}(x, y+L hat 1) C. These generate the 1-q connected contractions in the baryon two-point function. The computational challenge is the all-to-all propagator from a point to a shifted point; the paper handles it with a stochastic estimator built from independent random numbers per colour-Dirac component per site (Eq. 12), yielding Eq. (13). The estimator's correctness is checked via

Load-bearing premise

The load-bearing assumption is that the stochastic estimator for the all-to-all propagator correctly captures the 1-q connected contributions, which are currently noise-dominated and have not yet been shown to be statistically different from zero; if the estimator or the C-periodic contraction is subtly wrong, the claimed first computation collapses.

What would settle it

On the same ensemble, replace the stochastic estimator with an exact all-to-all propagator (for example by deflation or on a small lattice) and compare the 1-q connected two-point function; a disagreement beyond statistical error would refute the method. Alternatively, measure the term on two volumes and test whether it decays as exp(-mL); absence of the expected decay would contradict the stated infinite-volume limit.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • The 1-q connected finite-volume corrections can now be included in QCD+QED baryon-mass analyses, removing a previously unquantified systematic effect of C-periodic boundary conditions.
  • The use of 50-60 point sources instead of 4-8 visibly reduces statistical noise and yields longer plateaux, making the extracted proton and Omega masses more reliable inputs for scale setting.
  • The stochastic-estimator approach for the all-to-all propagator generalises to other baryons and to QCD+QED ensembles, so the Omega^- result is a proof of principle for a wider set of observables.
  • The documented noise behaviour (error dominance from t=19 to t=24 when smearing is applied) gives a practical guide for choosing smearing levels in future measurements of partially connected terms.
  • Increasing the source count to 100-150 and combining smearing levels in a GEVP analysis should further improve the 3-q connected masses.

Where Pith is reading between the lines

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

  • If these 1-q terms are not subtracted, finite-volume baryon masses from C-periodic simulations will carry a bias that scales roughly as exp(-m L); the magnitude reported here suggests this bias is small but not negligible compared with the current statistical errors, so its inclusion may shift central values once the estimator variance is reduced.
  • A direct check of the stochastic estimator against an exact all-to-all computation on a small lattice, where direct inversion is feasible, would provide an independent benchmark that the paper does not currently include.
  • The variance of the estimator does not appear to vanish with volume as quickly as the signal, implying that a hierarchical-probing or deflation-based estimator may be needed to make the 1-q contribution statistically resolvable at larger volumes.
  • The same formalism applies to the proton and to the full octet/decuplet, so the Omega^- measurement is likely the first of a systematic set of finite-volume corrections for all baryons in the C-periodic setup.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper reports preliminary lattice QCD baryon-mass measurements (proton and Omega^-) on two N_f=3+1 ensembles with C-periodic boundary conditions generated by the RC* collaboration. The 3-q connected two-point functions are computed with 50-60 point sources, giving masses 1170(10) MeV and 1470(20) MeV (B400a00b324) and 1190(15) MeV and 1450(25) MeV (A400a00b324). The new element is a stochastic estimator for the '1-q connected' contribution to the Omega^- two-point function, which arises because C-periodic boundary conditions introduce quark-quark and antiquark-antiquark propagators. The authors claim the first numerical evaluation of these contributions, which are expected to vanish exponentially in the infinite volume limit; the presented 1-q correlators are noise-dominated and not shown to be statistically non-zero.

Significance. If the contraction algebra and the stochastic estimator in Eq. (13) are correct, the paper provides a useful technical ingredient for future QCD+QED baryon-mass calculations with C* boundary conditions. The 3-q mass results improve on earlier 4-8 source calculations by using 50-60 sources and longer plateaus. The authors are transparent about the noise problem and state that the 1-q variance is not yet controlled. However, the central claim—the 'first numerical evaluation' of the 1-q connected contribution—currently rests on internal consistency checks that are not sufficient to rule out a biased estimator, and the measured 1-q signal is statistically indistinguishable from zero.

major comments (4)
  1. [§3.2, Eq. (13)] The code is validated only by gauge/translational invariance and a tree-level check. These tests are necessary but not sufficient for the central claim: a sign or index-ordering error in the C-matrix contraction (Eq. 3b) or in the handling of stochastic sources on the mirror lattice can cancel in the tree-level amplitude while biasing the full correlator. Since the 1-q signal is noise-dominated (errors exceed the central value from t=19 without smearing and t=24 with smearing; Figs. 4-5), such a bias is invisible. The authors should benchmark the estimator against an exact all-to-all propagator on a small volume or one configuration, and/or compare two independent noise/dilution schemes. Without this, 'first numerical evaluation' is not established.
  2. [§3.2 and Conclusions] The text says the 1-q contributions were 'computed for the first time', but the plotted 1-q correlators are everywhere consistent with zero: the error bars are much larger than the central values in the plateau region and no effective mass or fit is shown for the 1-q term alone. The conclusion should state explicitly that the contribution is not yet resolved and that the paper provides an upper bound or exploratory estimate, not a measurement. This qualification belongs in the abstract, which currently implies a successful computation.
  3. [§2, Eqs. (8)-(11)] The contraction algebra leading to Eq. (11) is not shown. In particular, the index flow from the epsilon tensors to the propagator D^{-1}(x,x+L1)^{BA}_{b\alpha} C_{\alpha a} and the sign from Eq. (3b) should be written out explicitly. As written, a reader cannot verify that the correct C-matrix ordering and the correct placement of the L1 shift are used. Given that the central claim is the first evaluation of this term, the derivation should be self-contained.
  4. [§3.2] The exponential suppression of the 1-q term in the infinite-volume limit is attributed to [4], which addresses charged hadrons in QED+QCD with C* boundary conditions. For the present QCD-only C-periodic ensembles, the mechanism should be argued explicitly or the citation should be shown to cover this case. Moreover, no estimate is given of the expected signal-to-noise ratio; the statement in Conclusions that a variance-reducing estimator is still being developed further underlines that the current numerical evaluation has no demonstrated significance.
minor comments (5)
  1. [Fig. 4] The label 'CO' in the left panel should be 'C_Ω'; the zoom panels have axis tick labels concatenated without spaces and would benefit from clearer axis labels.
  2. [Eq. (12)] Specify the distribution of the stochastic noise (e.g., Z2 or Gaussian) and whether the 12 random numbers per site are real or complex components. The identity holds for any normalized distribution, but reproducibility requires this detail.
  3. [§3.1] Clarify that the 50-60 point sources are used for the mass results, while the 3-q comparison in Figs. 4-5 uses only 10 point sources. The text states both numbers without explicitly distinguishing the two analyses.
  4. [References] Reference [14] is cited as 'PoS Science466'; include an arXiv identifier or DOI for reproducibility.
  5. [Abstract/Conclusions] The abstract says 'we are computing for the first time' while the conclusions say 'we also computed for the first time'; align the tense and qualification with the actual status of the 1-q contribution.

Circularity Check

0 steps flagged

No significant circularity: reported masses and 1-q connected estimator are not fit to the quantities they claim.

full rationale

The central numerical outputs are measurements: the 3-q masses come from plateau fits (Figs. 2-3, Table 2) and the 1-q connected contribution is a direct stochastic estimator (Eq. 13) derived algebraically from the C-periodic propagator identities (Eq. 3) and the standard noise-source identity (Eq. 12). No parameter is fitted to the final masses or to the 1-q correlator: scale setting uses the external CLS value sqrt(8 t0)=0.415 fm and c_sw=2.18859 from [6]. The self-citations ([1,2] code, [5] ensembles, [14] previous work) provide tools and context, not the numerical claim, and [4] is used only for the formal expectation that the 1-q terms vanish exponentially; that formal QED_C result is an external, parameter-free input to the physical interpretation, not an output of the present fit. The paper's own statements that the 1-q estimator is noise-dominated and that a variance-reducing definition is still under investigation are statistical limitations, not circular reductions. The validation by gauge/translational invariance and tree-level tests is an internal consistency check; insufficient validation would be a correctness risk, but it does not make the derivation equivalent to its inputs by construction.

Axiom & Free-Parameter Ledger

2 free parameters · 5 axioms · 0 invented entities

The computation uses the RC* collaboration's openQxD code and the C* boundary-condition formalism of [4]; no new physical entities are introduced. The only hand-tuned inputs are smearing parameters and plateau choices; physical scale and clover coefficient are taken from prior literature.

free parameters (2)
  • Gaussian smearing parameters kappa, N = not stated; chosen from best parameters of [5]
    Chosen by hand to minimize statistical noise; the mass values and 1-q/3-q comparison depend on this analysis choice.
  • Plateau fit intervals = not quoted numerically
    Plateaux are selected visually in Figs. 2-3; the quoted masses depend on this subjective choice and no systematic error is assigned.
axioms (5)
  • domain assumption C* modified propagator identities (Eq. 3): quark-quark and antiquark-antiquark propagators get contributions shifted by one lattice spacing
    Taken from [4]; this is the core mechanism generating the 1-q connected terms and is not re-derived in this paper.
  • domain assumption 1-q connected contributions vanish exponentially in the infinite-volume limit
    Used to interpret the 1-q signal as a finite-volume artifact; cited from [4], no in-paper derivation or numerical check.
  • standard math Stochastic estimator identity (Eq. 12) gives an unbiased estimate of the all-to-all propagator
    Standard noise-source identity; used to estimate the last Dirac inverse in Eq. 13.
  • domain assumption CLS value sqrt(8t0)=0.415 fm and c_sw=2.18859 from [6], [7]
    Physical scale and O(a) improvement coefficient are taken from literature; masses in Table 2 inherit their uncertainties.
  • domain assumption openQxD code with orbifold construction correctly implements C* boundary conditions
    The paper relies on the code's published implementation [1,2]; code is tested for gauge/translational invariance and tree-level, but not independently verified here.

pith-pipeline@v1.3.0-alltime-deepseek · 8254 in / 11084 out tokens · 105597 ms · 2026-08-02T20:07:18.498511+00:00 · methodology

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read the original abstract

Isospin-breaking corrections pose a significant challenge to lattice simulations, both because of the splitting between the up and down quark masses and, in particular, the need to include QED effects. The RC* collaboration has developed the openQxD code, based on openQCD, which enables fully dynamical QCD+QED simulations through the implementation of C-periodic boundary conditions. We use this code to measure baryon masses, with a special focus on the {\Omega^-} baryon mass, whose precise determination is especially important since it has been used to set the scale of lattice simulations. Due to the use of C-periodic boundary conditions, the two-point function of the {\Omega^-} baryon gets additional partially connected contributions, which vanish in the infinite-volume limit and which we are computing for the first time. We will present preliminary results for baryon masses obtained on QCD ensembles with C-periodic boundary conditions, at an unphysical pion mass of approximately 400 MeV.

Figures

Figures reproduced from arXiv: 2602.23910 by Agostino Patella, Anian Altherr, Francesca Margari, Isabel Campos, Letizia Parato, Marina Krsti\'c Marinkovi\'c, Paola Tavella, Roman Gruber, Sara Rosso, Tim Harris.

Figure 1
Figure 1. Figure 1: 2-dimensional section of a 4-dimensional lattice representing the orbifold construction used to implement C-periodic boundary conditions. Figure taken from [2] . in the extended lattice, as shown by the domains of different colours in the figure. C-periodic boundary conditions modify the structure of the quark propagators, leading to non￾zero contributions not only for the quark–antiquark propagator, but a… view at source ↗
Figure 2
Figure 2. Figure 2: Proton and Ω− effective masses together with the selected plateaux and the fits to a constant for the ensemble B400a00b324. Values in MeV are obtained by using the reference value (8𝑡0) 1/2 = 0.415 fm. where 𝐻𝑡(𝑥, 𝑦) is the spatial hopping operator 𝐻𝑡(𝑥, 𝑦) = ∑︁ 3 𝑗=1 [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Proton and Ω− effective masses together with the selected plateaux and the fits to a constant for the ensemble A400a00b324. Values in MeV are obtained by using the reference value (8𝑡0) 1/2 = 0.415 fm. 3.2 1-q connected contributions In this section, we focus on the Ω− , detail the implementation of the 1-q connected contributions and show some preliminary results for this quantity measured on the A400a00b… view at source ↗
Figure 4
Figure 4. Figure 4: Results for the Ω− 2-point function with no smearing. In the left plot are the 3-q connected contributions, in red, and the 1-q connected, in black, with a zoom of the high 𝑡 region. In the right plot is a comparison of the 3-q correlator with the absolute error on the 1-q correlator, in a logarithmic scale for the y axis. We measured these contributions for 40 decorrelated configurations, spaced 50, of th… view at source ↗
Figure 5
Figure 5. Figure 5: Results for the Ω− 2-point function with maximum smearing on the source and none on the sink. In the left plot are the 3-q connected contributions, in red, and the 1-q connected, in black, with a zoom of the high 𝑡 region. In the right plot is a comparison of the 3-q correlator with the absolute error on the 1-q correlator, in a logarithmic scale for the y axis. 4. Conclusions and outlook We provide comput… view at source ↗

discussion (0)

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Forward citations

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