{"id":"e6aa19f5-8866-492b-9de9-d1f6e141ca6a","arxiv_id":"2607.03249","paper_version":1,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"A 146 GeV scalar explaining the CMS eμ excess prefers Y_eμ ~ 10^{-4.09} and is directly testable by Mu2e, COMET, Mu3e and related cLFV experiments.","lead":"A Bayesian scan of a 146 GeV scalar that could explain the CMS eμ excess finds a preferred Y_eμ near 10^{-4}, already limited by muon conversion. Upcoming low-energy experiments and the HL-LHC will confirm or exclude this interpretation within a decade.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"The non-zero Y_eμ peak is an artifact of treating a 2.8σ global excess as a Gaussian likelihood that is too weak to overcome low-energy nulls.","rationale":"The reader correctly isolates the weakest link: the Gaussian treatment of a 2.8σ global excess (Eqs. 4.3–4.4) that is insufficient to overcome the low-energy null results, producing an artificial secondary mode. The paper itself quantifies that the non-zero mode holds only ~20 % of the 68 % posterior weight, confirming the concern is load-bearing for the abstract’s strongest phrasing. The concrete test (zeroing χ^{2}_146) is decisive and inexpensive. No other technical flaw (K-factor, form factors, prior range) threatens the complementarity conclusion, so the verdict remains CONDITIONAL rather than REJECT; the future-probe statement is robust. Agreement with the reader is complete.","tokens_in":20263,"tokens_out":688,"duration_ms":5267,"concrete_test":"Re-run the identical Zeus MCMC with χ^{2}_146 set identically to zero (or replaced by a one-sided Gaussian upper limit at the 95 % C.L. of the CMS search). If the secondary peak at log10 Y_eμ ≈ -4.09 vanishes and the posterior collapses onto the vanishing-coupling mode, the abstract’s “preferred mode” claim is an artifact of the likelihood construction.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central claim that the MCMC yields a preferred mode peaking at Y_eμ ∼ 10^{-4.09} rests on the construction of χ^{2}_146 in Eqs. (4.3–4.4). The authors center a Gaussian on σ_exp = 3.89 fb with width = 3.89/2.8 fb, thereby converting a 2.8σ global excess into a likelihood that actively pulls the posterior toward non-zero κ_gg Y_eμ. Section 4.2 itself reports that this non-zero mode carries only ~20 % of the 68 % posterior weight; the dominant mode is the vanishing-coupling plateau favored by the low-energy nulls. Because the global significance is already modest and the look-elsewhere effect has been folded in, the Gaussian pull is an over-statement of the evidence. If the CMS term is removed or replaced by a one-sided upper-limit χ^{2} (as done for the μμ/ττ channels), the non-zero peak disappears and the abstract’s “preferred mode” language no longer holds. The complementarity statement for future experiments remains valid, but the claim of a presently preferred non-zero Y_eμ does not.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper studies whether a single real scalar of mass 146 GeV, coupled to gluons via a dimension-5 operator and to all charged-lepton bilinears via seven real Yukawa couplings (Eqs. 1.1/2.1), can accommodate the CMS local excess in pp\toϕ\to eμ while remaining compatible with the full suite of low-energy cLFV bounds. Production is computed in the ggF channel with a heavy-top K-factor (Sec. 3.1); tree-level and one-loop rates for μ−e conversion, muonium oscillation, three-lepton and radiative LFV decays, and semileptonic τ decays are derived in Sec. 3.2. A Bayesian MCMC scan with log-uniform priors (Sec. 4.1) yields a bimodal posterior: a vanishing-coupling mode favored by the null results and a secondary non-zero mode peaking near log10 Yeμ≃−4.09 that is already constrained by current μ−e conversion. Projected sensitivities of Mu2e, COMET, Mu3e, MEG II, Belle II, STCF and the HL-LHC are shown to cover the CMS-selected region, establishing quantitative complementarity between high- and low-energy probes.","tokens_in":20636,"tokens_out":1163,"duration_ms":8904,"significance":"If the CMS excess is real, a model-agnostic map of the seven-parameter space that simultaneously satisfies LHC production and every major low-energy cLFV observable is a useful and timely contribution. The paper supplies explicit, standard formulae for all rates, uses FLAG 2024 form factors, and produces falsifiable projections that future experiments can test within a decade. The bimodal posterior itself is an informative result: it quantifies how weakly a 2.8σ global excess pulls against existing nulls. The analysis is therefore valuable both as a consistency check of the scalar interpretation and as a concrete target list for Mu2e/COMET/Mu3e and HL-LHC.","major_comments":[{"comment":"Abstract and Sec. 4.2: the language “preferred mode with peaked value Yeμ∼10−4.09” overstates the posterior. Sec. 4.2 itself states that the vanishing-coupling mode carries roughly 80 % of the 68 % posterior weight; the non-zero peak is secondary. Because χ^{2}_146 (Eqs. 4.3–4.4) converts a 2.8σ global excess into a two-sided Gaussian centered on 3.89 fb, the non-zero mode is an artifact of that likelihood construction. The abstract and conclusions should be rewritten to state that the posterior is bimodal, that the dominant mode is vanishing couplings, and that the non-zero peak is only a secondary feature pulled by the modest CMS excess.","section":null},{"comment":"Sec. 4.1, Eqs. (4.3)–(4.4): the treatment of the CMS excess is inconsistent with the treatment of the same-flavor resonance searches (Eq. 4.5). The latter correctly use one-sided upper-limit χ^{2}; the former actively pulls toward a non-zero signal. Given that the global significance is only 2.8σ and the look-elsewhere effect has already been folded in, a more conservative construction (one-sided upper limit, or a mixture that includes the background-only hypothesis) should be shown as a robustness check. If that check eliminates the non-zero peak, the “preferred Yeμ” claim must be dropped.","section":null}],"minor_comments":[{"comment":"Sec. 3.2.3, Eqs. (3.32)–(3.33): the interference terms in τ→eeμ and τ→μμe are dropped “for simplicity.” A short numerical statement that their inclusion does not shift the posterior would strengthen the claim.","section":null},{"comment":"App. B and Fig. 9: the prior-sensitivity test is useful; it would help the reader if the same exercise were repeated for the two-dimensional credible regions of (κgg,Yeμ) that drive the complementarity argument.","section":null},{"comment":"Fig. 5 caption and Table 2: the 68 % HPD intervals for log10 Yeμ are reported as two disjoint intervals, yet the abstract quotes only the non-zero peak. Align the abstract wording with the table.","section":null},{"comment":"Sec. 3.1: the residual model dependence of the SM K-factor for a pure dimension-5 ϕGG operator is stated to be “percent-level”; a one-sentence reference to the finite-mt literature would make the claim fully transparent.","section":null},{"comment":"Typos / notation: “T oy Model” in the contents; occasional missing spaces around ∼ and in “µ−econversion”; “Brth” vs. “Brlim” notation is clear but could be standardized in the tables.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The central technical content is sound and the complementarity projections are useful. The only load-bearing issue is rhetorical over-statement of a secondary posterior mode; once the abstract and Sec. 4.2 are rephrased to match the actual 80/20 weight split, the paper is suitable for publication. No novelty or citation concerns."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The new piece is a seven-parameter Bayesian scan of a single real scalar (M=146 GeV, κ_gg + all lepton Yukawas) that folds the CMS eμ excess together with the full low-energy cLFV suite and same-flavor LHC searches. Earlier papers were UV-specific; this one is deliberately model-agnostic and maps future Mu2e/COMET/Mu3e/MEG-II/Belle-II/HL-LHC reaches onto the same posterior. That is useful and cleanly done.\n\nProduction and decay formulae are standard. The K-factor is taken from the heavy-top SM calculation with the residual uncertainty acknowledged; form factors use FLAG 2024; likelihoods for upper limits are ordinary one-sided Gaussians. Appendices check prior dependence, HPD intervals, and Z→ℓαℓβ loops. The math and citation pattern look solid.\n\nThe soft spot is the language around the “preferred mode.” They center a Gaussian on σ=3.89 fb with width=3.89/2.8, so χ^{2}_146 actively pulls toward non-zero κ_gg Y_eμ. Section 4.2 itself reports that this mode carries only ~20% of the 68% posterior weight; the dominant mode is the vanishing-coupling plateau favored by the nulls. The peak at log10 Y_eμ≈−4.09 is therefore an output of that likelihood construction, not a robust preference. If the CMS term is dropped or replaced by a one-sided limit, the non-zero peak disappears. The abstract’s wording is therefore stronger than the posterior supports. The complementarity statement for future experiments still holds: those experiments will cover the region the excess would select.\n\nThis is for people who work on cLFV phenomenology or who need a ready-made effective-parameter map for the next round of muon and τ experiments. It is not a discovery claim and does not need to be. I would send it to referees; the calculation is transparent and the mapping is worth having. Engage if you are writing on the same excess or on low-energy reach; otherwise it is optional reading.","headline":"Clean model-agnostic MCMC of a 146 GeV cLFV scalar; the non-zero Y_eμ peak is real but carries only ~20% posterior weight under a 2.8σ Gaussian pull, so the abstract overstates preference while the complementarity map remains useful.","tokens_in":21233,"tokens_out":555,"would_cite":true,"duration_ms":5872,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"A 146 GeV scalar that could explain the CMS eμ excess is already under pressure from μ–e conversion and will be settled by low-energy experiments within a decade.","keywords":["charged lepton flavor violation","146 GeV scalar","CMS eμ excess","μ–e conversion","Bayesian MCMC","effective Lagrangian","Mu2e","COMET"],"falsifier":"A null result from Mu2e or COMET at the projected 10^{-16}–10^{-17} conversion sensitivity would exclude the entire non-zero Yeμ peak preferred by the CMS excess.","tokens_in":21160,"feed_emoji":"⚛️","tokens_out":1043,"duration_ms":8524,"temperature":0.7,"pith_summary":"CMS has reported a 2.8σ excess consistent with a 146 GeV scalar decaying to an electron-muon pair. The paper asks whether any such scalar can also survive the full suite of existing low-energy charged-lepton-flavor-violation bounds. It introduces a minimal effective description with seven free couplings (one gluonic, six Yukawa) that control both the LHC rate and every low-energy process, then maps the allowed region with a Bayesian MCMC scan. The posterior is bimodal: one mode clusters near vanishing flavor-violating couplings, the other peaks at Yeμ ≈ 10^{-4.09} and is already grazed by present μ–e conversion limits. Projected reaches of Mu2e, COMET, Mu3e, MEG II, Belle II, STCF and the HL-LHC cover essentially the entire non-zero mode, so the scalar interpretation of the excess will be confirmed or excluded within roughly ten years.","feed_headline":"146 GeV scalar for CMS excess faces μ–e conversion limits","feed_subtitle":"Next-decade muon experiments will confirm or kill the interpretation","key_machinery":"The seven-parameter effective Lagrangian of Eq. (1.1)/​(2.1) together with a Bayesian MCMC likelihood that folds the CMS 3.89 fb excess, same-flavor di-lepton resonance limits, and the complete set of low-energy cLFV branching-ratio bounds into a single posterior.","core_discovery":"A single real scalar of mass 146 GeV coupled to gluons and to all charged-lepton bilinears yields a preferred posterior mode with Yeμ ∼ 10^{-4.09} that simultaneously accommodates the CMS eμ excess and existing cLFV null results; that mode is already cut by current μ–e conversion and lies fully within the projected sensitivity of the next generation of low-energy experiments.","pith_inferences":["Because the non-zero mode is already grazed by present conversion limits, even a modest improvement in SINDRUM-II-style data could have shifted the posterior weight decisively toward vanishing couplings.","The same seven-parameter scaffold can be reused for any future resonance claim in a different di-lepton channel without committing to a specific ultraviolet completion.","A parallel lepton-PDF production analysis would test whether the excess can be rescued by a purely leptophilic production mechanism that evades the gluonic conversion bound."],"forward_implications":["Mu2e and COMET will cover almost the entire CMS-favored Yeμ island, leaving at most a narrow surviving strip.","Mu3e will independently close the same island through the three-electron channel.","MEG II will tighten the product Yeτ Yμτ by an order of magnitude, further restricting the τ-sector plane.","HL-LHC same-flavor di-lepton searches will push the diagonal Yukawas Ye e, Yμμ, Yττ well below their present loose upper limits.","If the excess is real, a heterogeneous data set from muon experiments, τ factories and the HL-LHC will pin down the seven couplings within a decade."],"fun_headline_variants":["146 GeV scalar fits CMS eμ excess but hit by μ–e conversion","CMS 146 GeV excess scalar already cut by current μ–e limits","Preferred Yeμ∼10^{-4.09} for CMS excess within next muon reach","Low-energy cLFV probes test 146 GeV scalar for CMS anomaly","Single 146 GeV scalar accommodates CMS excess yet faces μ–e cuts"],"cache_read_input_tokens":16512,"weakest_assumption_plain":"Treating the CMS 2.8σ global excess as a Gaussian likelihood centered on 3.89 fb while still allowing a vanishing-coupling mode, so the non-zero peak is only as strong as that modest excess.","fun_headline_variants_meta":{"raw":{"variants":["146 GeV scalar fits CMS eμ excess but hit by μ–e conversion","CMS 146 GeV excess scalar already cut by current μ–e limits","Preferred Yeμ∼10^{-4.09} for CMS excess within next muon reach","Low-energy cLFV probes test 146 GeV scalar for CMS anomaly","Single 146 GeV scalar accommodates CMS excess yet faces μ–e cuts"]},"model":"grok-4.5","effort":"low","cost_usd":0.00388,"raw_usage":{"total_tokens":1288,"prompt_tokens":866,"num_sources_used":0,"completion_tokens":108,"cost_in_usd_ticks":38800000,"prompt_tokens_details":{"text_tokens":866,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":314,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":866,"tokens_out":108,"duration_ms":3390,"temperature":1.0,"reasoning_tokens":314,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-12T03:48:32.825377+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"A null result from Mu2e or COMET at the projected 10^{-16}–10^{-17} conversion sensitivity would exclude the entire non-zero Yeμ peak preferred by the CMS excess.","supporting_citations":[],"review_version":1}