{"id":"051d903e-67fb-406a-9f8c-21500daddfc6","arxiv_id":"1908.11653","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"The electron angular asymmetry in muonic-atom mu-e -> e-e decay depends on the chirality and operator type of the flavor violating interaction, and can distinguish them.","lead":"This paper calculates how electrons from a muon decaying inside an atom are emitted when the muon is polarized, for lepton flavor violating new physics. It shows the electron asymmetry reveals the chirality and type of the interaction, which could help future searches like COMET.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The sign-of-chirality claim is derived only under single-operator dominance; with both chiralities present, interference can cancel or reverse the asymmetry, and the paper gives no handle on this.","rationale":"The reader's weakest_assumption concerned the 1s-only approximation for bound electrons. That can shift the numerical FS/FA/FD curves, but the chirality-sign relation would likely survive, as the reader noted. The single-operator concern attacks conclusion item (ii) directly: with both chiralities present, interference can alter or cancel the asymmetry, so the unqualified statement that the sign directly reflects the muon chirality is not established for the general Lagrangian in Eqs. (1)–(3). The manuscript is transparent about restricting the numerical cases to single-operator dominance in Sec. III, so this is a scope limitation rather than an internal error. Still, the abstract and conclusion present the sign mapping as a property of the process, and the proposed ε-sweep is a minimal numerical check using the paper's own formulas. Since the reader already assigned CONDITIONAL partly because of the single-operator assumption, this concern does not change the verdict; it sharpens the condition that would need to be met for the central claim to hold. I therefore recommend keeping the reader's CONDITIONAL verdict.","tokens_in":12455,"tokens_out":12076,"duration_ms":121248,"concrete_test":"Using the multipole formulas of Sec. II.B, compute F(ϵ1,c12) and FD for the two-coupling superposition g1=1, g2=ε (all other couplings zero) at a representative point, e.g., ϵ1=0.7, c12=-0.6, sweeping ε from 0 to 1. Record where the sign of F reverses relative to the ε=0 single-operator value, and likewise for AR=1, AL=ε with gj=0. The parity-conserving combinations ε=1 must give exactly zero; the reversal threshold quantifies how robust the 'sign reflects chirality' claim is against subdominant opposite-chirality operators. If reversal occurs at ε≪1, the central claim is fragile.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's headline physics—'the sign of the asymmetry directly reflects the chirality of the muon involved' (Sec. IV) and the operator-discriminating FS/FA plots (Figs. 2–4)—is computed under the single-operator dominance hypothesis introduced in Sec. III (g1=1, g3=1, g5=1, or AR=1 with all other couplings zero). The general effective Lagrangian in Eqs. (1)–(3) contains both chiralities and both photonic and contact terms. F and FD are ratios of bilinear products of amplitudes, so interference terms between operators of opposite chirality contribute to the numerator and denominator. For a parity-conserving combination (e.g., g1=g2=1 or AR=AL=1), the P·p̂ asymmetry must vanish by parity, so the sign cannot simply be read off from the muon chirality once both chiralities are present. The paper does not estimate how large an opposite-chirality or subdominant photonic admixture can be before the single-operator FS/FA patterns (and hence the model-discrimination claims) break down. Since the conclusion states the sign relation without this qualification, the central claim is not yet established for the full Lagrangian.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper derives the energy-angular distribution of the two final electrons in the charged lepton flavor violating process μ−e− → e−e− in a muonic atom, for a polarized bound muon. The effective Lagrangian contains photonic dipole and six contact operators of different chiralities. The authors formulate the decay rate in terms of parity-violating asymmetry functions FS and FA and a motion-reversal-odd function FD, first in a plane-wave approximation for the contact interaction and then with a full multipole expansion using Dirac wave functions in a finite nuclear charge distribution. Numerical results for 208Pb are presented for four representative cases: g1, g3, g5, and AR, each under a single-operator dominance hypothesis. The main claims are that the sign of the asymmetry directly reflects the chirality of the muon, that the energy-angle dependence distinguishes operator types, and that FD is generated by final-state interactions even for real couplings at the level of 10^-2 to 10^-1.","tokens_in":12668,"tokens_out":5795,"duration_ms":54827,"significance":"If the central claims hold, this paper provides new observables beyond the total decay rate for identifying the chiral structure of CLFV interactions in muonic atoms. The analytic plane-wave formulas and the multipole expansion are internally cross-checked, and the calculation is parameter-free in the sense that no fitting is involved. The computation of the motion-reversal-odd correlation FD from final-state interactions is a useful, quantitative warning for future CP-violation searches. The analysis is limited by the single-operator dominance assumption and by the lack of truncation/convergence details, but the overall approach is credible and potentially important for COMET and similar programs.","major_comments":[{"comment":"The claim that \"the sign of the asymmetry directly reflects the chirality of the muon involved\" is established only under the single-operator dominance hypothesis used in Eqs. (35)-(38). For the general effective Lagrangian of Eqs. (1)-(3), F and FD are ratios of bilinear products of amplitudes, so interference between opposite-chirality operators contributes to both numerator and denominator. A parity-conserving combination, e.g., g1=g2=1 or AR=AL=1, must have a vanishing P·p̂ term by parity, so the sign is not a direct readout of muon chirality once both chiralities are present. The paper does not quantify how large an opposite-chirality admixture can be before the sign relation or the FS/FA discrimination patterns break down. Please either state the restriction to single-operator dominance in the conclusion and abstract, or provide a robustness analysis with mixed chiralities.","section":"Section IV, finding (ii); Section III, Eqs. (35)-(38)"},{"comment":"The numerical coefficients cF_l and cFD_l in Eqs. (30) and (31) are defined as infinite sums over κ1, κ2, κ1', κ2', J, J', and the expansions in Eqs. (28)-(29) are infinite Legendre series. The manuscript does not state the truncation order used for Figs. 2-5 or provide convergence tests. Because the sharp operator-dependent differences in FS and FA are the central quantitative results, the absence of this information makes the numerical predictions non-reproducible and leaves open the possibility of truncation artifacts. Please state the maximum |κ| and l included and show that the asymmetries are stable under increasing the cutoffs.","section":"Section II.B, Eqs. (28)-(31), Figs. 2-5"}],"minor_comments":[{"comment":"The condition \"gj≠1 = 0\" in Eq. (36) should read \"gj≠3 = 0\", since the case under consideration is g3 = 1.","section":"Section III, case 2, Eq. (36)"},{"comment":"The restriction to 1s bound electrons is stated without a quantitative estimate; adding a sentence on the expected size of higher-n contributions would strengthen the independent-particle-model justification.","section":"After Eq. (5)"},{"comment":"The text says the effect of electron-electron rescattering is much smaller than electron-nucleus scattering because of the large nuclear charge, but no numerical estimate is given; a brief quantitative statement would be helpful for assessing the FD background.","section":"Section III, Fig. 5 discussion"},{"comment":"The figures are only color maps; since the paper makes quantitative claims about the size of asymmetries (e.g., \"large\" for photonic, FD ~ 10^-2 to 10^-1), including numerical tables or contour values for representative kinematics would improve reproducibility.","section":"Figures 2-5"}],"recommendation":"major_revision","confidential_remarks":"The single-operator dominance issue is the main correctness-risk point: the conclusion as stated goes beyond what is derived. If the authors add a qualification or a robustness study, the paper would be suitable for publication."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nWorth knowing: this is a real, useful calculation, not a paradigm shift. Kuno et al. take their established unpolarized μ⁻e⁻→e⁻e⁻ rate formalism and add muon-polarization dependence, deriving parity-violating asymmetry functions F_S, F_A, and the T-odd F_D for each CLFV operator. The genuinely new piece is operator/chirality discrimination: for a single dominant operator, the sign of F_S/F_A follows the muon chirality, and the eps1-c12 shape distinguishes contact from photonic. The F_D estimate from final-state interactions is also a useful background estimate for future CP studies.\n\nWhat's done well: The plane-wave analytic formulas in Sec. IIA are cross-checked against the full multipole expansion, and the internal consistency is credible. The derivation is not fitted or tuned; couplings are set to 1 as conventions. The Z-dependence of the previous rate work is properly cited and extended.\n\nSoft spots, in order of importance:\n\n1. The chirality-sign statement in the conclusion (item ii) is too strong. It holds only under single-operator dominance, stated in Sec. III but not carried into the conclusion. With an admixture of opposite chirality (e.g., g1+g2 or AR+AL), parity allows the asymmetry to vanish or change sign, and the paper does not quantify how much mixing can be tolerated before the sign diagnostic breaks. This is not a flaw in the per-operator calculation, but the interpretive claim needs an explicit caveat. The stress-test concern lands here.\n\n2. No numerical tables or convergence details for the multipole sums. For a paper whose results live entirely in figures, a reader can't easily reproduce or check the κ sums. Minor, but it weakens the paper as a reference.\n\n3. The 1s-only assumption for bound electrons is stated but not justified numerically; if higher shells contribute a few percent, the asymmetry curves shift somewhat. The chiral-sign relation likely survives, but a quantitative bound would be better.\n\nWho it's for: theorists and experimentalists in CLFV phenomenology, especially COMET Phase-I; anyone needing polarized-muon observables for μ-e conversion in atoms. It deserves real refereeing—the math is involved and the result is relevant to upcoming experiments.\n\nRecommendation: send it to peer review, but ask the authors to (a) soften the conclusion to single-operator dominance, (b) add a short paragraph quantifying opposite-chirality mixing, and (c) ideally include a small table of asymmetry values or public code. The core calculation is probably correct.","headline":"Solid, useful extension of their unpolarized rate work to spin-dependent asymmetries; the chirality-sign claim needs the single-operator caveat made explicit.","tokens_in":13209,"tokens_out":2571,"would_cite":true,"duration_ms":24448,"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":"A polarized muon in a muonic atom yields a parity-violating electron asymmetry whose sign encodes the chirality of the lepton-flavor-violating interaction, and whose energy-angle pattern distinguishes photonic from contact operators.","keywords":["charged lepton flavor violation","muonic atom","muon polarization","electron angular asymmetry","parity violation","chiral structure","final state interaction","motion-reversal-odd correlation"],"falsifier":"A polarized-muon muonic-atom experiment (for example on a heavy nucleus such as $^{208}$Pb) that measures $F_S$, $F_A$, and $F_D$ as functions of $\\epsilon_1$ and $c_{12}$ would settle the claim: if the sign of the parity-violating asymmetry for the assumed dominant operator is opposite to the template, or if $F_D$ falls far outside the $10^{-2}$ to $10^{-1}$ range for real couplings, the chiral-sign relation and the final-state-interaction estimate would be refuted. A calculation that includes 2s or 2p bound electrons and checks whether the $g_1$-versus-$g_2$ sign relation survives would also directly test the paper's core prediction.","tokens_in":12237,"feed_emoji":"⚛️","tokens_out":6789,"duration_ms":61462,"temperature":0.7,"pith_summary":"This paper works out what a polarized muon adds to searches for charged lepton flavor violation in muonic atoms. Its central claim is that in a muonic atom, the decay $\\mu^- e^- \\to e^- e^-$ produces a parity-violating angular asymmetry of the two emitted electrons whose sign is set by the chirality of the muon coupling, and whose dependence on electron energy and opening angle tells whether the new interaction is photonic or contact-like. That matters because decay-rate measurements alone can determine the interaction type but not its handedness. The paper also computes the size of a motion-reversal-odd correlation generated by final-state scattering even when all couplings are real, which must be counted as background in any future CP-violation search.","feed_headline":"Polarized muon reveals chirality of flavor-violating new physics","feed_subtitle":"The sign of the electron asymmetry reveals left- vs right-handed new physics; its shape identifies the operator.","key_machinery":"The organizing object is the spin-correlation decomposition of the differential decay rate: $$\\frac{d\\Gamma}{d\\epsilon_1 d\\Omega_1 d\\Omega_2} = \\frac{1}{8\\$pi^{2}$}\\, \\frac{d\\Gamma_{\\rm unpol.}}{d\\epsilon_1 dc_{12}}\\left[1 + F_S\\,P\\cdot \\hat{p}_{12} + F_A\\,P\\cdot \\hat{q}_{12} + F_D\\,P\\cdot (\\hat{p}_1\\times \\hat{p}_2)\\right].$$ The coefficients are built from multipole-expanded Dirac amplitudes for bound and scattered leptons in the Coulomb potential of a finite nuclear charge distribution; in the plane-wave limit the asymmetry functions reduce to radial integrals ($I_{gg}$, $I_{fg}$, $I_{gf}$, $I_{ff}$) and are proportional to the handedness parameter $h_a$ of the operator. That proportionality is what carries the argument: the sign of the asymmetry directly reflects the chirality of the muon coupling.","core_discovery":"The paper establishes, using Dirac wave functions in the Coulomb field of a finite nuclear charge distribution, that the differential decay rate for $\\mu^- e^- \\to e^- e^-$ with a polarized muon factorizes into the unpolarized rate times three polarization terms. The coefficients $F_S$ and $F_A$ are parity-violating asymmetries; their sign flips when the chirality of the muon operator flips, and their pattern in $\\epsilon_1$ and $c_{12}$ differs between contact and photonic operators, with the photonic case giving the largest asymmetries. The third coefficient $F_D$ is parity-even but motion-reversal-odd; although the couplings are taken real, final-state Coulomb distortion generates $F_D$ at the level $10^{-2}$ to $10^{-1}$, largest for the photonic interaction. The calculation uses a 1s muon and a 1s electron in the initial state, and treats the emitted electrons as distorted waves including the finite nuclear size.","pith_inferences":["Inference: The same formalism could be used to optimize the choice of target nucleus, since lighter nuclei would suppress the final-state-interaction-induced $F_D$ background while heavier nuclei amplify the finite-size effect that makes the parity-violating asymmetry visible.","Inference: The chiral-sign relation may extend to other bound-state CLFV transitions initiated by polarized muons, such as muon-to-electron conversion in atoms, but the authors do not perform that calculation here; testing it would require an analogous distorted-wave analysis.","Inference: The paper's templates assume a single dominant operator; a practical experimental analysis could fit mixtures of operators and treat 2s or 2p bound-electron contributions as a systematic uncertainty, which the paper mentions as a possible extension of its multipole formulas.","Inference: If the sign-chirality relation survives inclusion of higher-n bound electrons and electron-electron rescattering, the asymmetry could serve as a model-independent handedness diagnostic even when the overall rate is dominated by several competing operators."],"forward_implications":["The measured sign of $F_S$ and $F_A$ would assign a left- or right-handed muon coupling to the dominant CLFV operator, information that the decay rate alone cannot provide.","The $\\epsilon_1$ and $c_{12}$ dependence separates the photonic dipole case from contact scalar and vector cases, and distinguishes same-chirality contact operators ($g_1$/$g_3$) from opposite-chirality ones ($g_5$).","A finite nuclear charge distribution is not a minor correction: for $g_1$–$g_4$ type interactions the asymmetry would essentially vanish for a point-like nucleus, so realistic nuclear wave functions are required for any asymmetry measurement.","The motion-reversal-odd coefficient $F_D$ is predicted to be nonzero at $10^{-2}$ to $10^{-1}$ even for real couplings, with the largest value for photonic interactions, so any CP-violation search using $F_D$ must first subtract this final-state-interaction background.","Combining the asymmetry observables with the atomic-number dependence of the decay rate from the authors' previous work gives a two-pronged strategy for identifying the new-physics operator behind charged lepton flavor violation.","When the next-generation muon experiments search for $\\mu^- e^- \\to e^- e^-$, the polarization asymmetry provides a concrete, background-labeled observable to include in the experimental design."],"supporting_citations":[{"why":"Proposes the muonic-atom $\\mu^- e^- \\to e^- e^-$ process as a CLFV search channel and gives the simple $(Z-1)^3$ rate estimate that this paper refines.","marker":"[10]"},{"why":"Supplies the Dirac wave-function treatment and unpolarized transition rate for $\\mu^- e^- \\to e^- e^-$ on which the asymmetry formulas are built.","marker":"[11]"},{"why":"Provides the multipole-expansion amplitudes and the energy-angular distribution of emitted electrons that this paper extends to a polarized muon.","marker":"[12]"},{"why":"Shows how muon polarization can expose the chiral structure of CLFV, motivating the same idea for the muonic-atom process.","marker":"[13]"},{"why":"Develops polarized-muon chiral-discrimination observables for related CLFV decays that the authors adapt conceptually.","marker":"[14]"},{"why":"Defines motion-reversal-odd correlations, the category to which the coefficient $F_D$ belongs.","marker":"[15]"},{"why":"Demonstrates that final-state interactions generate such motion-reversal-odd correlations even without CP violation, the background mechanism estimated here.","marker":"[16]"}],"fun_headline_variants":["Electron asymmetry flips with new-physics chirality","Parity-violating electron pairs expose CLFV operator","Asymmetry sign tells left from right in muonic atom","Operator shape of CLFV revealed by electron asymmetry"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes that only the 1s bound muon and 1s bound electron contribute to the initial state and that electron-electron rescattering is negligible, so if higher-n bound electrons or electron-electron rescattering contribute significantly, the computed asymmetry curves would shift.","fun_headline_variants_meta":{"raw":{"variants":["Electron asymmetry flips with new-physics chirality","Parity-violating electron pairs expose CLFV operator","Asymmetry sign tells left from right in muonic atom","Operator shape of CLFV revealed by electron asymmetry"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000633,"raw_usage":{"total_tokens":2900,"prompt_tokens":901,"completion_tokens":1999,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":517,"completion_tokens_details":{"reasoning_tokens":1934}},"tokens_in":517,"tokens_out":1999,"duration_ms":13460,"temperature":1.0,"reasoning_tokens":1934,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T10:09:19.200330+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A polarized-muon muonic-atom experiment (for example on a heavy nucleus such as $^{208}$Pb) that measures $F_S$, $F_A$, and $F_D$ as functions of $\\epsilon_1$ and $c_{12}$ would settle the claim: if the sign of the parity-violating asymmetry for the assumed dominant operator is opposite to the template, or if $F_D$ falls far outside the $10^{-2}$ to $10^{-1}$ range for real couplings, the chiral-sign relation and the final-state-interaction estimate would be refuted. A calculation that includes 2s or 2p bound electrons and checks whether the $g_1$-versus-$g_2$ sign relation survives would also directly test the paper's core prediction.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Shows how muon polarization can expose the chiral structure of CLFV, motivating the same idea for the muonic-atom process."},{"cited_title":"Koike, Y","cited_arxiv_id":null,"evidence_quote":"Develops polarized-muon chiral-discrimination observables for related CLFV decays that the authors adapt conceptually."},{"cited_title":"Uesaka, Y","cited_arxiv_id":null,"evidence_quote":"Defines motion-reversal-odd correlations, the category to which the coefficient $F_D$ belongs."},{"cited_title":"Uesaka, Y","cited_arxiv_id":null,"evidence_quote":"Demonstrates that final-state interactions generate such motion-reversal-odd correlations even without CP violation, the background mechanism estimated here."}],"review_version":1}