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Partially connected contributions to baryon masses in QCD+QED

T0 review · 3 major / 4 minor · reviewed 2026-08-09 · deepseek-v4-flash

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Pith's one-line read The paper presents a formula for the one-quark connected contribution to the Omega^- baryon mass in QCD+QED simulations, using point and stochastic source inversions to handle the all-to-all propagator that connects the physical lattice…

desk verdict A clean, implementable formula for the one-quark connected contribution to the Omega^- two-point function under C-periodic boundary conditions, but the planned numerical checks do not verify the sign/index content of the imported Wick identities on which the formula rests. read the letter →

arxiv 2502.03961 v1 pith:Z3D3WMFG submitted 2025-02-06 hep-lat

Anian Altherr , Isabel Campos , Alessandro Cotellucci , Roman Gruber , Tim Harris , Javad Komijani , Jens Lücke , Marina Krstić Marinković
show 4 more authors
Letizia Parato Agostino Patella Sara Rosso Paola Tavella
This is my paper · ORCID
classification hep-lat PACS 12.38.Gc
keywords latticeQCDQCD+QEDC-periodicboundaryconditionsisospinbreakingOmegabaryonmassespartiallyconnecteddiagramsstochasticsources
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

Simulations of QCD coupled to QED must use boundary conditions that allow charged states; C-periodic boundary conditions do this by doubling the lattice and charge-conjugating fields across the boundary. This doubling creates new Wick contractions between two quarks or two antiquarks, which produce partially connected contributions to baryon correlators that vanish in the infinite-volume limit but may be sizable at finite volume. The paper shows how to compute the dominant such contribution for the $\Omega$^- baryon: the one-quark connected diagrams require a propagator from a point to its mirror image, which is all-to-all. Their formula rewrites that propagator as a stochastic-source estimate and combines it with two point-source inversions, giving an implementable expression. If correct, this turns a previously inestimable finite-volume effect into a computable correction that can be compared with the bulk baryon mass measurement.

What carries the argument

The load-bearing object is Eq. (17), the factorized expression for the one-quark connected contribution. It combines three inversions: a point source at the sink point $y$ for the propagator $D^{-1}(y + L_1 \hat{1}, y)$, a point source at $x$ for $D^{-1}(x, y)$, and a stochastic source representing $D^{-1}(x, x + L_1 \hat{1})$ through the identity $(1/N_s) \sum_n [D^{-1}\chi^{(n)}](x) \chi^{(n)\dagger}(x + L_1 \hat{1})$. The stochastic source is what turns the all-to-all propagator between the physical and mirror lattices into a practical computation. The Wick contraction identities (3b) and (3c), imported from earlier work, are what generate the nonzero two-quark contractions that make this diagram exist at all.

What would settle it

Check identities (3b) and (3c) numerically on a small lattice: compute the left-hand contractions and the right-hand Dirac propagators explicitly and compare them element by element; any mismatch would invalidate Eq. (17).

Watch

Extended reading notes

Core claim

On the paper's own terms, the central discovery is that the one-quark connected two-point function for the $\Omega$^- can be written as Eq. (17): two point-source propagators, one evaluated at the source point and one at the sink, contracted with the spin-colour tensor $T$ and the charge-conjugation matrix $C$, times a stochastic estimate of the mirror-lattice propagator $D^{-1}(x; x + L_1 \hat{1})$ given by $(1/N_s) \sum_n [D^{-1}\chi^{(n)}](x) \chi^{(n)\dagger}(x + L_1 \hat{1})$. This expression makes the all-to-all propagator that arises from C-periodic boundary conditions numerically accessible, so that the size of the partially connected correction to the $\Omega$^- mass can be measured on the ensembles used by the collaboration.

Load-bearing premise

The result rests on the Wick contraction identities (3b) and (3c) being exactly right for the orbifold implementation of C-periodic boundary conditions, including the sign of $C$ and the shift by $L_1$; a sign or index error there would change the sign or structure of the whole contribution.

Editorial extensions

If this is right

  • The one-quark connected contribution to the Omega^- mass becomes numerically measurable, allowing its size to be compared with the three-quark connected bulk in existing QCD+QED ensembles.
  • If the correction is not negligible at finite volume, it must be included in baryon mass determinations from C-periodic simulations, affecting precision comparisons such as the proton-neutron mass difference.
  • The same point-plus-stochastic decomposition should extend to the partially connected diagrams of other baryon interpolating operators, since the contraction structure is determined by the same C-periodic identities.
  • A successful gauge-invariance test of the implemented formula would provide a strong consistency check that the contractions, indices, and source transformations are correct.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A direct numerical verification of the C-periodic Wick identities (3b) and (3c) on a small volume, independent of the gauge-invariance test, would remove the main residual risk to the formula.
  • The stochastic estimate's noise could be assessed by comparing it at selected points against an exact point-source inversion of $D^{-1}(x, x + L_1 \hat{1})$; this would guide how many stochastic sources are needed for a target precision.
  • Because the correction is expected to vanish in the infinite-volume limit, measuring it at two or three volumes would yield an extrapolation curve, making the finite-volume uncertainty in baryon masses fully controlled.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The manuscript, a Lattice 2024 proceedings contribution, addresses the computation of partially connected ('one-quark connected') contributions to the Omega^- baryon mass in QCD+QED with C-periodic boundary conditions. After reviewing the C-periodic setup and the non-standard Wick contractions it induces, the authors derive an expression for the one-quark connected two-point function in terms of a contraction tensor T and three propagators. They then rewrite one of the propagators, D^{-1}(x, x+L), with stochastic sources and the other two with point sources, obtaining Eq. (17), the central formula they say is implemented in their code. The paper ends with a status report: gauge-invariance testing is in progress; translation-invariance testing and measurements are planned.

Significance. If Eq. (17) is correct, the paper provides a practical decomposition of a finite-volume effect that is otherwise extremely expensive because it requires an all-to-all propagator. The derivation from the Wick contractions to Eq. (17) is clear, and the use of point sources at y combined with stochastic sources for the mirror-to-physical propagator is a sensible algorithmic choice. The paper also makes a falsifiable prediction: these corrections are expected to vanish in the infinite-volume limit, and the proposed method is designed to check that. The main weaknesses are that the derivation rests on two imported identities, Eqs. (3b)-(3c), that are not independently verified, that the stochastic estimator is presented without any noise or variance analysis, and that the paper contains no numerical validation at all. Because these points bear directly on whether the computed quantity is the claimed one, the current version is not yet ready for publication, but the identified gaps appear fixable within the scope of the paper.

major comments (3)
  1. [Section 3, Eqs. (3b), (3c), (10), (17)] The sign and the placement of the charge-conjugation matrix C in the Wick identities (3b) and (3c) are inherited from Ref. [7] without re-derivation or direct numerical verification. These choices are load-bearing: a sign error in (3b) would propagate directly into Eq. (10) and Eq. (17) and would reverse the sign of the predicted mass correction. The consistency checks planned in Section 5, gauge invariance and translation invariance, cannot detect such an error, since an overall sign or a left/right swap of the constant matrix C does not break either symmetry, and the propagator still satisfies the same gauge-covariant transformation. I therefore ask for an explicit independent check of Eqs. (3b) and (3c), for example a direct numerical evaluation of the two-quark Wick contraction on a small lattice or an analytic derivation in an appendix, and a statement of how the sign and C placement are fixed.
  2. [Section 4, Eqs. (12)-(13)] Equation (12) is written as an exact identity for a finite set of N_s stochastic sources, but for actual stochastic source techniques the relation holds only in the expectation over source ensembles, and the finite-N_s estimator in Eq. (13) has a variance that depends on N_s, on the source distribution, and on the spin/colour dilution used. The manuscript does not specify N_s, the noise type, or whether dilution is employed, and it gives no estimate of the variance of the one-quark connected contribution. Since Eq. (17) is the proposed practical method, some noise analysis or at least an empirical variance measurement on a single configuration is needed to establish that the stochastic inversion is feasible and that the signal is not overwhelmed by stochastic noise.
  3. [Section 5] The central claim of the paper is an implementable formula, Eq. (17), but the manuscript reports no numerical results: the gauge-invariance test is still in progress and the translation-invariance test is only planned. Without a single numerical check, an algebraic or index error in the contraction of the Dirac indices in Eq. (17) could go unnoticed. I request that the authors include at least a small-scale validation, for example a comparison of Eq. (17) with a direct point-source evaluation on a few gauge configurations or with the result of computing the Wick contractions numerically on a small lattice, before the method can be considered demonstrated.
minor comments (4)
  1. [Section 3, Eq. (9)] The source point is written as 0 in Eq. (9) but as y in Eqs. (10), (15) and (17); the notation should be unified to avoid confusion.
  2. [Section 4, Eq. (16)] The sums over the intermediate points z and w are not explicitly written; please state clearly that Eq. (15) contains a sum over the full lattice and over the suppressed Dirac and colour indices of the point sources.
  3. [Section 2, Eq. (2)] The overline in the second line of Eq. (2) is a typographical nuisance with the charge-conjugation matrix; a typeset version with unambiguous barred fields would improve readability.
  4. [References] Reference [5] to the openQ*D code gives no version or URL; if a citation of the code is intended, a persistent identifier should be provided.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular derivation: Eq. (17) is a straightforward estimator built from cited Wick identities and standard stochastic-source algebra; no output is fed back as input.

full rationale

The paper's central claim is a computational strategy, not a numerical prediction. The one-quark-connected two-point function in Eq. (10) follows by applying the C-periodic Wick identities (3b) and (3c) from Ref. [7] to the contraction sum (9). This is a derivation, not a fitting or a definitional equivalence: the target Eq. (17) is not an input to those identities, and the identities do not assume the result being computed. They are parameter-free consequences of the boundary conditions in Eq. (2), derived in a prior publication; even though the author lists overlap (A. Patella is a co-author of both papers), the citation is real independent evidence under the stated criteria: it is derivable, parameter-free, and externally checkable, rather than a fitted parameter or an ansatz adopted only by fiat. The stochastic-source identity (12) is also an exact/unbiased algebraic identity, and Eq. (13) is just its application to one column of D^{-1}; no fitted input is renamed as a prediction. The infinite-volume expectation stated in the abstract and Section 5 is motivational and is not used to derive Eq. (17). The unverified sign/index content of (3b)-(3c), and the fact that the planned gauge/translation tests cannot detect such an error, is a correctness risk, not a circularity: it means the derivation may rest on an imported premise, but that premise is external to this paper's derivation chain and is not equivalent to the paper's own output. Therefore no circular step is present.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

The paper introduces no fitted parameters and no new entities. Its derivation rests on previously established C-periodic Wick contractions, a standard stochastic source identity, and an unproven expectation about the infinite volume limit. No free parameters are fitted to data.

assumptions (4)
  • domain assumption C-periodic boundary conditions implemented via an orbifold doubling with charge-conjugated mirror fields (Eq. (2))
    This is the RC* collaboration's established setup, cited from [5] and [6]; the paper builds on it rather than re-deriving it.
  • domain assumption Wick contraction identities (3a)-(3c) for quark fields under C-periodic boundary conditions
    Taken from Lucini et al. [7]; these identities create the non-zero quark-quark contractions that define the one-quark connected contribution. They are cited, not derived or verified in this paper.
  • standard math Stochastic source identity (12): the ensemble average of chi chi-dagger equals the identity
    Standard property of random noise fields used in Eq. (13); stated without proof or noise analysis.
  • domain assumption One-quark connected contributions vanish in the infinite volume limit
    Stated as an expectation in the abstract and Section 5; it motivates the study but is not used in the derivation of Eq. (17).

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Cite this review

Pith. "Pith review of Partially connected contributions to baryon masses in QCD+QED." pith.science (2026). https://pith.science/paper/Z3D3WMFG

@misc{pith2026250203961,
  author       = {Pith},
  title        = {Pith review of: Partially connected contributions to baryon masses in QCD+QED},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/Z3D3WMFG}},
  note         = {Machine review of arXiv:2502.03961}
}
abstract

Full QCD+QED simulations allow to evaluate isospin breaking corrections to hadron masses. With the openQxD code, we are able to perform these simulations employing C-periodic boundary conditions, implemented through a doubling of the physical lattice along one spatial direction. The use of these boundary conditions introduces non-zero Wick contractions between two quark or two antiquark fields, that, in the case of the computation of baryon masses, lead to partially connected additional contributions that we expect to vanish in the infinite volume limit. These contributions are challenging because they involve an all-to-all propagator connecting one point in the physical lattice and one in the mirror lattice. We present a way to compute these corrections to the $\Omega^-$ baryon mass using a combination of point and stochastic source inversions. This work is part of the program of the RC* collaboration.

Figures

Figures reproduced from arXiv: 2502.03961 by the authors.

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 [6] . quark of flavour 𝑓 . These boundary conditions allow equation (1) to have a non zero result because the operation of charge conjugation changes the sign of the electric field, which now becomes anti-periodic at the boundaries. The boundary conditions are im… view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Baryon masses with C-periodic boundary conditions

    hep-lat 2026-02 conditional novelty 4.0 of 10

    First numerical estimates of the C-periodic 1-q connected contributions to the Omega-minus two-point function, plus preliminary proton and Omega masses at m_pi ~ 400 MeV.

Reference graph

Works this paper leans on

7 extracted references · 2 canonical work pages · cited by 1 Pith paper

  1. [7]

    Lucini, A

    B. Lucini, A. Patella, A. Ramos, N. Tantalo, Charged hadrons in local finite-volume QED+QCD with C* boundary conditions, JHEP02(2016) 076 [1509.01636] 7

    arXiv 2016

  2. [1]

    Borsanyi, S

    S. Borsanyi, S. Durr, Z. Fodor, C. Hoelbling, S. D. Katz, S. Krieg, L. Lellouch, T. Lippert, A. Portelli, K. K. Szabo, and B. C. Toth,Ab initio calculation of the neutron-proton mass difference, Science347 (2015) 1452 [1406.4088]

    arXiv 2015

  3. [2]

    T.Blum,P.A.Boyle,N.H.Christ,J.Frison,N.Garron,R.J.Hudspith,T.Izubuchi,T.Janowski, C. Jung, A. Jüttner, C. Kelly, R.D. Kenway, C. Lehner, M. Marinkovic, R.D. Mawhinney, G. McGlynn, D.J. Murphy, S. Ohta, A. Portelli, C.T. Sachrajda, and A. Soni,Domain wall QCD with physical quark masses, Phys. Rev. D93(2016) 074505 [1411.7017]

    arXiv 2016

  4. [3]

    Miller, L

    N. Miller, L. Carpenter, E. Berkowitz, C. Cheng Chang, B. Hörz, D. Howarth, H. Monge- Camacho„E.Rinaldi,D.A.Brantley,C.Körber,C.Bouchard,M.A.Clark,A.SinghGambhir, C.J.Monahan,A.Nicholson,P.VranasandA.Walker-Loud, ScalesettingtheMöbiusdomain wallfermionongradient-flowedHISQactionusingtheomegabaryonmassandthegradient- flow scales𝑡0 and𝑤0 Phys. Rev. D103 (20...

    arXiv 2021

  5. [4]

    Bushnaq, I

    L. Bushnaq, I. Campos, M. Catillo, A. Cotellucci, M. Dale, P. Fritzsch, J. Lücke, M. Marinković, A. Patella, N. Tantalo,First results on QCD+QED with C* boundary condi- tions, JHEP03(2023) 012 [2209.13183]

    arXiv 2023

  6. [5]

    RC* collaboration,openQ*Dcode

    work page

  7. [6]

    I.Campos,P.Fritzsch,M.Hansen,M.Marinković,A.Patella,A.Ramos,N.Tantalo, openQ*D code: aversatiletoolforQCD+QEDsimulations ,Eur.Phys.JC 80(2020)195[ 1908.11673]

    work page Pith review arXiv 2020

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