{"id":"b49377a3-6c43-48bd-8abc-72ec2f6ee95c","arxiv_id":"2501.13429","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"A preliminary lattice QCD calculation of twelve proton decay matrix elements at the physical pion mass with Wilson-clover fermions, using updated RI renormalization, agrees mostly with the RBC continuum results.","lead":"This paper computes the hadronic matrix elements that control proton decay rates using lattice QCD on the PACS supercomputer ensembles at physical quark masses. These numbers are needed to turn future proton decay searches at DUNE or Hyper-Kamiokande into constraints on grand unified theories.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The consistency claim rests on a single lattice spacing with the discretization error explicitly excluded from the quoted errors; until an a^2 check is made, the agreement with RBC2022 could be fortuitous.","rationale":"The reader's weakest assumption identifies the same load-bearing concern: the comparison to RBC2022 relies on a single lattice spacing with discretization effects excluded from the error budget. The paper's own text in Section 5 confirms this limitation, so the concern is real but also openly acknowledged. The central claim is weakened only in the sense that the agreement cannot yet be read as a final cross-check; the authors do not overclaim finality. The requested concrete test, a second lattice spacing or a quantitative discretization-error estimate, is the natural and sufficient check. Since the reader already made this the condition for the CONDITIONAL verdict, no verdict adjustment is needed.","tokens_in":8032,"tokens_out":2467,"duration_ms":24602,"concrete_test":"Compute the same twelve W0(q^2=0) values on a second PACS ensemble at a smaller lattice spacing (e.g., a≈0.06 fm, if available) at the same physical pion mass and with the same analysis chain, and perform a two-point a^2 extrapolation. Compare the extrapolated values with the RBC2022 continuum results in Figure 5: if they remain within the quoted errors, the consistency claim stands; if they shift by more than the stated uncertainties, the single-spacing agreement was misleading. A cheaper but weaker check is to compare the PACS a^-1=2.3 GeV points with the RBC2017 coarse-lattice points at a^-1=1.8 GeV and the RBC2022 continuum points to see whether the PACS results lie on a common a^2 trajectory, keeping in mind the different actions and chiral extrapolation.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim is that the twelve renormalized proton decay matrix elements W0 are mostly consistent with the RBC/UKQCD continuum results [7]. For this comparison to be meaningful, O(a^2) discretization effects at a=0.085 fm must be small relative to the quoted errors. The paper does not establish this: it uses a single lattice spacing (Table 1, Section 3) and explicitly states in Section 5 that 'the discretization effect has not been accounted yet.' No bound or estimate for a^2 effects is given, so the agreement seen in Figure 5 could be partially or wholly accidental. The paper itself calls the results preliminary and postpones detailed comparison until after continuum extrapolation, which is honest, but it means the headline comparison cannot yet serve as a precision cross-check of the RBC continuum values. A second lattice spacing, or at least a quantitative discretization-error estimate, is required before the agreement can be interpreted as physical rather than as a cancellation of lattice artifacts.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This proceedings paper reports preliminary lattice QCD results for the twelve proton decay matrix elements W0 at physical kinematics, computed on PACS 2+1 flavor Wilson-clover ensembles at a single lattice spacing a≈0.085 fm (a^{-1}=2.3162(44) GeV). The authors study excited-state contamination by varying the source-sink separation, determine the renormalization constants of the three-quark operators in the RI/MOM scheme (MOM3q and SYM3q) with four intermediate schemes, and quote Z_RL=1.016(5)(41) and Z_LL=1.018(6)(37) in MSbar at 2 GeV. The resulting W0 values are compared with the RBC/UKQCD continuum results of Ref. [7] and are stated to be mostly consistent, while a discrepancy is seen against the older chiral-extrapolated RBC results. The paper explicitly labels the results as preliminary and notes that discretization effects have not yet been accounted for.","tokens_in":8219,"tokens_out":15419,"duration_ms":132048,"significance":"If the results are correct, they provide a second independent lattice action (Wilson-clover physical-point, as opposed to domain-wall) supporting the hadronic matrix elements used to convert proton lifetime bounds into constraints on GUT and SUSY-GUT parameters. The paper's strengths include a clear demonstration of plateaus in the source-sink separation at t_sep≳20, a systematic renormalization-scale study with explicit intermediate-scheme dependence, and an honest acknowledgment that the computation is preliminary and that the discretization error is not yet included. The use of physical pion masses avoids the chiral extrapolation that was a major uncertainty in earlier work, and the AMA technique provides reasonable statistical precision. The comparison with RBC/UKQCD, even at the qualitative level, is a useful cross-check for the field.","major_comments":[{"comment":"The central cross-check against the RBC continuum result [7] rests on the assumption that discretization effects at this single lattice spacing are small compared with the quoted uncertainties, yet the paper gives no estimate of their size and explicitly excludes them from the error budget. The conclusion that the results are \"mostly consistent\" (Fig. 5 and Summary) is therefore not yet a quantitative cross-check. Please either provide a quantitative estimate of the O(a^2) effect (for example, by comparing with the RBC point at a^{-1}=1.8 GeV shown in Fig. 5, or with any other available lattice-spacing dependence) or rephrase the consistency claim to make clear that it is provisional pending the planned continuum extrapolation.","section":"§5, Figure 5, and Summary"},{"comment":"The interpolation to the physical kinematics (q^2≈0) is not documented: the fitting function, the number and range of the data points used, and the associated systematic uncertainty are not stated. Since the reported W0(0) values in Fig. 5 are the final quantities, please specify the interpolation procedure and, if possible, the size of the interpolation systematic error.","section":"§5, Figure 4"},{"comment":"The quoted systematic error on the renormalization constant, e.g., 0.041 for Z_RL, is hard to reconcile with the visible spread among the four intermediate schemes in Fig. 2, particularly at low matching scales. Please define the central value (the scale (pa)^2 at which Z is read) and describe how the RMS sum of the systematic contributions (lattice artifacts, IR divergence, perturbative matching, intermediate-scheme dependence) is assembled, so that the quoted total systematic error is reproducible.","section":"§4, Figure 2"}],"minor_comments":[{"comment":"The text states that the configurations at β=1.82 correspond to a lattice spacing of 0.09 fm, but Table 1 and the abstract give a=0.085 fm (a^{-1}=2.3162(44) GeV); please correct the inconsistency.","section":"Section 3, first paragraph"},{"comment":"The word \"nonberturbative\" in the Introduction should be \"nonperturbative.\"","section":"Section 1"},{"comment":"The phrase \"read into\" preceding Eq. (4) should be \"reads.\"","section":"Section 2"},{"comment":"The decay-width formula as displayed appears dimensionally inconsistent if W0 has mass dimension 2 (see Fig. 4's axis label); please verify that the expression matches the convention in Refs. [6,7,9], including any missing mass factor or square on the phase-space bracket that may have been lost in the PDF conversion.","section":"Eq. (5)"},{"comment":"The plateau study is shown for the Gaussian source at m_pi=139 MeV; please clarify whether the same excited-state systematic was checked for the exponential source at 135 MeV, and if so, where the corresponding plot or result is.","section":"Figure 3, Table 1"},{"comment":"The sentence \"those are mostly consistent with ours\" is ambiguous; please rephrase to \"with the PACS results\" or \"with ours (the present work)\" for clarity.","section":"Section 5, last paragraph"}],"recommendation":"major_revision","confidential_remarks":"This is a proceedings contribution, and the requested revisions are largely about framing and documentation rather than about a demonstrable error. The main concern is that the headline comparison to RBC/UKQCD is presented as a consistency check even though the discretization error is not included; a brief quantitative estimate (e.g., from the two RBC lattice spacings visible in Fig. 5) would strengthen the paper considerably. The overlap with the collaboration's earlier proceedings is acceptable; the new elements are the updated renormalization study and the direct comparison with the RBC 2022 continuum results. I do not see improper citation behavior or any reason to question the integrity of the work."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This is a solid proceedings paper from the PACS group, and the main thing to know is that the physics headline is conditional. What is actually new: the first physical-point Wilson-clover numbers for the twelve proton decay W0 matrix elements, plus a fresh evaluation of the RI/MOM renormalization constants using both MOM3q and SYM3q schemes. The extraction looks careful—stable plateaus across t_sep, a systematic study of the renormalization scale dependence, and an honest error budget that separates statistical and systematic pieces. The authors also deserve credit for stating plainly that the discretization effect has not been accounted for, which is exactly the right caveat for a preliminary report.\n\nThe soft spot is the one the stress-test note emphasizes: the central consistency claim with the RBC/UKQCD continuum results rests on a single lattice spacing at a=0.085 fm, with no estimate of O(a^2) effects. The agreement in Figure 5 could be fortuitous, and the authors themselves postpone a detailed comparison until after continuum extrapolation. That is not a hidden flaw—it is disclosed—but it does mean the headline \"mostly consistent\" should not be used as a final cross-check. The discrepancy against the older chiral-extrapolated RBC band is interesting, but again it cannot be interpreted as evidence for nonlinear chiral behavior until the continuum limit is taken. In a proceedings contribution, this is an acceptable stopping point, but it is not a finished precision result.\n\nWho is this for? Lattice practitioners working on proton decay and people in the GUT-phenomenology community who want an independent check of the hadronic input. A serious referee should engage with it, mostly to make sure the systematic error budget is transparent and that the comparison plots are not over-read. The paper is honest and the methods are sound; the only real request is a quantitative bound on discretization error, which the authors already plan. I would not cite this as a final number yet, but I would bring it to a reading group to discuss what counts as a meaningful cross-check at one lattice spacing. Verdict: send to peer review as a proceedings, but make clear in any report that the consistency claim is preliminary.","headline":"A clean, honest preliminary Wilson-clover calculation of proton decay matrix elements; the consistency with RBC2022 is suggestive but cannot be a precision cross-check until a second lattice spacing is included.","tokens_in":8776,"tokens_out":1357,"would_cite":false,"duration_ms":15632,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"Two independent lattice QCD actions now give consistent proton decay matrix elements at the physical point.","keywords":["proton decay","lattice QCD","matrix elements","Wilson-clover fermions","physical pion mass","renormalization","Rome-Southampton scheme","grand unification"],"falsifier":"Repeat the calculation on one or more finer ensembles, for example a = 0.06 fm with the same action, and take the continuum limit; if the extrapolated values move outside the reference continuum band by more than the combined quoted errors, the reported agreement is an artifact of the single lattice spacing.","tokens_in":7825,"feed_emoji":"⚛️","tokens_out":6620,"duration_ms":66575,"temperature":0.7,"pith_summary":"The paper reports a first calculation of proton decay matrix elements with the Wilson-clover action directly at the physical pion mass, on a $64^{4}$ lattice with a = 0.085 fm. These matrix elements convert a measured proton lifetime into constraints on grand-unified-theory parameters, so a second independent lattice result is a useful cross-check. The paper's twelve renormalized form factors W0 at physical kinematics are mostly consistent with the recent continuum physical-pion result obtained with domain-wall fermions, while they visibly deviate from the older chiral-extrapolated result. The paper describes the work as preliminary and notes that the discretization effect has not yet been included in the quoted uncertainties.","feed_headline":"Proton decay inputs now backed by two lattice methods","feed_subtitle":"A Wilson-clover calculation at the physical pion mass matches the domain-wall continuum result, tightening GUT predictions.","key_machinery":"The central objects are the renormalized three-quark matrix elements $W_0$ for proton-to-pseudoscalar transitions through baryon-number-violating operators, evaluated at physical kinematics. They are extracted from three-point functions at several source-sink separations around 1.7 fm to control excited-state contamination, then renormalized nonperturbatively via the Rome-Southampton method in both the MOM3q and SYM3q schemes (three-quark RI schemes with equal momenta, or with equal-magnitude momenta summing to zero), converted to the MS scheme at 2 GeV using RI/SMOM intermediate schemes. All-mode averaging with a deflated Schwarz-preconditioned solver suppresses statistical noise. This chain turns raw lattice correlators into $W_0$ values that can be compared across different lattice fermion actions and inserted into the proton partial-width formula.","core_discovery":"The central claim is that Wilson-clover fermions on $64^{4}$ lattices at a = 0.085 fm can produce renormalized proton decay matrix elements $W_0^{RL}$ and $W_0^{LL}$ for the twelve relevant modes at $q^2 \\simeq 0$, and that these are consistent with the recent continuum domain-wall result. The paper attributes the tension with the older chiral-extrapolated band to nonlinear chiral behavior near the physical pion mass. Explicitly, the updated renormalization constants are $Z_{RL}^{\\rm MS}(2\\,\\mathrm{GeV}) = 1.016(5)(41)$ and $Z_{LL}^{\\rm MS}(2\\,\\mathrm{GeV}) = 1.018(6)(37)$, with the second bracketed error collecting lattice artifacts, infrared effects, perturbative conversion, and scheme dependence.","pith_inferences":["A continuum extrapolation at finer lattice spacings could shift $W_0$ by an amount comparable to the quoted errors, so the consistency with the earlier continuum result should be treated as provisional until that extrapolation exists.","The agreement between Wilson-clover and domain-wall actions at the physical point suggests that discretization artifacts may be subdominant in current error budgets, but it also implies that future precision will be limited by renormalization-scale and excited-state systematics rather than statistics.","If the disagreement with the older chiral-extrapolated band is truly nonlinear chiral behavior, the same effect should appear in other physical-point baryon observables that were previously obtained by chiral extrapolation; testing those correlations could confirm the interpretation."],"forward_implications":["A second independent lattice discretization now backs the hadronic matrix elements used to turn proton-lifetime limits into GUT parameter exclusions.","Computing at the physical point removes the need for chiral extrapolation in this quantity, so nonlinear chiral behavior near the physical pion mass can be seen directly.","The reported $W_0$ values can be inserted into the partial-width formula to update model-specific proton lifetime predictions.","The planned continuum extrapolation on finer lattices will decide whether the agreement with the domain-wall result persists at the percent level.","The renormalization constants evaluated with two RI schemes provide a cross-check for any Wilson-clover calculation of baryon-number-violating operators."],"supporting_citations":[{"why":"Recent continuum physical-pion domain-wall computation; provides the benchmark with which this paper's $W_0$ values are compared.","marker":"[7]"},{"why":"Older chiral-extrapolated calculation whose discrepancy with the physical-point result motivates the nonlinear-chiral-behavior discussion.","marker":"[9]"},{"why":"Framework for nucleon decay matrix elements from lattice QCD and their renormalization, defining the quantities used here.","marker":"[5]"},{"why":"Defines the MOM3q three-quark renormalization scheme and the $3\\times3$ mixing matrix used for $W_0$.","marker":"[6]"},{"why":"Sets the RI/SMOM renormalization conventions and the wavefunction renormalization used to convert to MS at 2 GeV.","marker":"[11]"},{"why":"The Rome-Southampton method underlying the nonperturbative renormalization step.","marker":"[21]"},{"why":"Perturbative three-loop renormalization for the SYM3q scheme used in the conversion.","marker":"[22]"},{"why":"All-mode-averaging variance reduction that makes the physical-point statistical errors affordable.","marker":"[14]"}],"fun_headline_variants":["Clover lattice matches domain-wall proton decay","Wilson-clover proton decay inputs confirmed","Proton decay matrix elements: two methods agree","Physical-point clover run verifies proton decay","New lattice computation tightens proton decay rates"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The result stands on the assumption that discretization effects at the single lattice spacing of 0.085 fm are small compared with the quoted errors, since no continuum extrapolation is made and the discretization effect is explicitly left out of the reported error budget.","fun_headline_variants_meta":{"raw":{"variants":["Clover lattice matches domain-wall proton decay","Wilson-clover proton decay inputs confirmed","Proton decay matrix elements: two methods agree","Physical-point clover run verifies proton decay","New lattice computation tightens proton decay rates"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000169,"raw_usage":{"total_tokens":1193,"prompt_tokens":806,"completion_tokens":387,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":422,"completion_tokens_details":{"reasoning_tokens":320}},"tokens_in":422,"tokens_out":387,"duration_ms":4467,"temperature":1.0,"reasoning_tokens":320,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T15:57:21.452348+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Repeat the calculation on one or more finer ensembles, for example a = 0.06 fm with the same action, and take the continuum limit; if the extrapolated values move outside the reference continuum band by more than the combined quoted errors, the reported agreement is an artifact of the single lattice spacing.","supporting_citations":[{"cited_title":"Proton decay matrix elements with domain-wall fermions","cited_arxiv_id":"hep-lat/0607002","evidence_quote":"Defines the MOM3q three-quark renormalization scheme and the $3\\times3$ mixing matrix used for $W_0$."},{"cited_title":"Three loop renormalization of 3-quark operators in QCD","cited_arxiv_id":"1208.5619","evidence_quote":"Perturbative three-loop renormalization for the SYM3q scheme used in the conversion."}],"review_version":1}