{"id":"fa22095b-6876-4cd4-8ba3-c12d83283b74","arxiv_id":"2505.11653","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"low","formal_verification":"none","parameter_count":0,"one_line_summary":"Future linear colliders ILC and CLIC could probe lepton flavor violating tau-mu production up to new physics scales near 50 TeV, surpassing some Belle II projections.","lead":"This paper calculates the rate for electron-positron collisions to produce a tau and a muon, a process that would violate lepton flavor conservation. It estimates that proposed ILC and CLIC colliders could detect or constrain such events better than Belle II in some cases.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eq. (33) appears to have a Jacobian error of factor 2 in the lab-frame conversion; the sensitivity numbers may shift if the sampling uses the stated formula.","rationale":"The reader's weakest assumption focuses on CLIC pion-identification efficiencies and detector resolution tails. These are reasonable detector-performance concerns, but the paper explicitly states the assumption and the reviewer's own rule says disagreement with consensus is not internally inconsistent; the detector efficiencies are an acknowledged approximation. My identified concern is more directly tied to the paper's own derivation: Eq. (33) is a change-of-variables from d sigma/d cos(theta) to d sigma/dp for a boosted two-body final state. The stated prefactor 4 sqrt(s)/(x_- - x_+) does not match the Jacobian obtained from Eq. (32), which gives d cos(theta)/dp = 4/(sqrt(s)(x_- - x_+)). A factor of 2 error in the Jacobian would alter the Monte Carlo sampling of the signal muon momentum distribution, and consequently the cut efficiency epsilon_x^sig and the final sensitivity projections. The Appendix A formula (A2) is the same conversion and should be cross-checked. However, I have not fully re-derived every step with the boosted kinematics including the finite masses; the reader's conditional verdict with a request to fix Eq. (33) is appropriate unless an independent check shows the stated formula is merely a typo in the paper while the Monte Carlo uses the correct Jacobian. Therefore I do not recommend moving to REJECT, and I keep the verdict as CONDITIONAL pending the numerical check.","tokens_in":18866,"tokens_out":1653,"duration_ms":14212,"concrete_test":"Re-derive the Jacobian in Eq. (33) from Eq. (32), or implement the Appendix A convolution numerically with Eq. (A2) and compare the resulting 1/sigma d sigma/dx histogram to the one generated with Eq. (33). If the normalized histograms agree to better than 1%, the concern is moot; if they differ by a factor ~2 in normalization or shift the x-distribution, recompute the projected sensitivities with the corrected Jacobian.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central numerical claims (CLIC reaching ~50 TeV, surpassing Belle II) depend on the Monte Carlo signal model in Section III.A. The lab-frame conversion of the muon momentum distribution, Eq. (33), is suspect. For a two-body final state with beam momenta x_- sqrt(s)/2 and x_+ sqrt(s)/2 (unequal due to ISR), the relation cos(theta) = (4 p / sqrt(s) - x_- - x_+)/(x_- - x_+) (Eq. 32) implies d cos(theta)/dp = 4/sqrt(s) * 1/(x_- - x_+). With x = 2p/sqrt(s), this gives d sigma/dx = (sqrt(s)/2) d sigma/dp = 2/(x_- - x_+) d sigma/d cos(theta). The factor in Eq. (33), 4 sqrt(s)/(x_- - x_+) with d sigma/dp = (4 sqrt(s)/(x_- - x_+)) d sigma/d cos(theta), appears to be a factor 2 too large; the corresponding d sigma/dx would be 2 sqrt(s)/(x_- - x_+) d sigma/d cos(theta) instead of sqrt(s)/(x_- - x_+) d sigma/d cos(theta). If the Monte Carlo samples according to Eq. (33), the signal x-distribution might be distorted, affecting the cut efficiency epsilon_x^sig and hence the projected reach. The reader flagged Eq. (33) only as a minor numerical issue, but the derivation offered in Appendix A appears to contain the same discrepancy and should be checked.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper studies lepton flavor violation in the process e+e- -> tau mu at future linear colliders within SMEFT. The authors derive the cross section for arbitrary electron and positron beam polarizations, including dipole, Z-coupling, and four-fermion operators. They then construct a Monte Carlo model of the signal muon momentum distribution that accounts for beam energy spread, initial-state radiation, and detector resolution, and compare it with an analytic background model for e+e- -> tau+tau- with one tau decaying to a muon. Using ILC and CLIC run parameters, they project 2-sigma sensitivities to Wilson coefficients and to the new physics scale Lambda, concluding that CLIC at 3 TeV can reach Lambda ~ 50 TeV for four-fermion operators, surpassing Belle II projections in several scenarios.","tokens_in":19209,"tokens_out":23385,"duration_ms":214610,"significance":"The work extends earlier FCC-ee/CEPC analyses to linear colliders and provides a first-principles SMEFT calculation with arbitrary beam polarizations, which is a genuinely useful handle for disentangling operator chiralities. The signal modeling is detailed and the background treatment is conservative, with no fitted parameters in the derivation. The numerical projections are clearly presented and compared with low-energy tau decay searches, giving a concrete and falsifiable statement about the physics reach of ILC and CLIC. The analytic formulas and the Monte Carlo implementation are cross-checked in Appendix A, which strengthens confidence in the central results.","major_comments":[],"minor_comments":[{"comment":"Equation (33) contains a misprinted Jacobian prefactor. From Eq. (32), d(cosθ)/dp = 4/(√s (x_- - x_+)), so the prefactor should be 4/(√s |x_- - x_+|), not 4√s/(x_- - x_+). The correct normalized expression appears in Appendix A, Eq. (A2). Because the prefactor is constant for fixed x_±, the shape of the Monte Carlo distribution is unaffected, but the equation should be corrected and the code should be confirmed to use the absolute value of the Jacobian.","section":"III.A, Eq. (33)"},{"comment":"The paper assumes that the pion identification efficiencies for the CLIC detectors are the same as those of the ILC without citing a CLIC-specific detector study. Since the projected new physics scale scales roughly as the eighth root of the efficiency, a factor-of-two change would shift Lambda by about 9%, but the assumption should be justified or explicitly caveated.","section":"III.C, after Eq. (39)"},{"comment":"The sensitivity criterion N_sig >= 2√(N_bkg+N_sig) is a simplified Gaussian approximation that does not include systematic uncertainties or Poisson fluctuations; the authors should state this explicitly and note that the quoted '~2σ' sensitivities are therefore approximate.","section":"III.C, Eq. (45)"},{"comment":"There is a typographical error at the start of Section III.C ('backround' instead of 'background'), and the unit 'ab' is used without being defined on first use; please define attobarns when they first appear.","section":"General presentation"}],"recommendation":"minor_revision","confidential_remarks":"The apparent Jacobian inconsistency in Eq. (33) is, in my reading, a typographical error: the wrong prefactor is a constant that cancels in the normalized Monte Carlo distribution, so the numerical projections are not affected. The authors should nonetheless correct Eq. (33) and confirm that the code uses the absolute Jacobian. The CLIC efficiency assumption is the main caveat but has modest impact on the reach. Overall the paper is solid, technically sound, and within scope for the journal."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a solid, incremental study. The authors extend their earlier FCC-ee/CEPC analysis to ILC and CLIC, and the genuinely new piece is the treatment of arbitrary beam polarizations as a handle on the chirality of the LFV operators. The cross-section formulas in Section II look right, the background treatment is conservative, and the conclusion that a 3 TeV CLIC run can push four-fermion operator sensitivity to Lambda ~ 50 TeV, beyond Belle II projections, is reasonable given the s growth of the contact-interaction cross section.\n\nThe stress-test note about Eq. (33) does not land. The prefactor should be 4/sqrt(s), not 4*sqrt(s) — so there is a typo — but the incorrect factor is a constant for a given sqrt(s), independent of p and of the sampled x±. It therefore cancels in any normalized momentum distribution, including the cut efficiency epsilon_x^sig. The Monte Carlo results and the sensitivity numbers are unaffected. The correct Jacobian appears in Appendix A, so the typo is easy to fix and does not require re-running anything.\n\nThe real soft spots are the detector-performance assumptions. Taking CLIC's pion identification efficiencies to be identical to ILC's is a reasonable first approximation, but CLIC's detectors are not the ILC detectors, and at 3 TeV the environment is different. If CLIC's tau ID or muon momentum resolution is worse than assumed, the reach at the highest energy would degrade. The authors are upfront that their analysis is not optimized, so I read the numbers as conservative rather than aggressive. The W+W− background at 3 TeV is noted and handled with the x >= 1 cut; that seems okay.\n\nThe citation pattern is clean. Self-citations to [23] are used for comparison and update, not as input to the derivation, so there is no circularity. The paper is built on a first-principles SMEFT calculation with no fitted parameters.\n\nWho gets value from this: anyone planning the physics case for a future e+e− linear collider, and anyone working on LFV in SMEFT. It is a projection, not a measurement, but it is a useful and honestly presented one. I would send it to a competent referee; the main revision request would be to fix Eq. (33) and add a sentence noting that CLIC tau-ID efficiencies are an assumption that could be revisited with a full detector simulation.","headline":"Solid, incremental SMEFT projection for e+e- -> tau mu at ILC/CLIC; the polarization handle is genuinely useful, the ~50 TeV CLIC reach is plausible, and the flagged Jacobian issue is a harmless typo.","tokens_in":19665,"tokens_out":7068,"would_cite":false,"duration_ms":63171,"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":"CLIC's 3 TeV run would probe tau-mu flavor violation up to ~50 TeV","keywords":["lepton flavor violation","SMEFT","tau-mu production","linear colliders","beam polarization","ILC","CLIC","muon momentum cut"],"falsifier":"At CLIC with $\\sqrt{s}=3$ TeV and 5 ab$^{-1}$, count candidate $e^+e^- \\to \\tau\\mu$ events with one hadronic tau and one muon of momentum fraction $x \\ge 1$. If the observed yield matches the Standard Model tau-pair background within uncertainties, the claimed sensitivity to four-fermion operators at scales around 50 TeV is ruled out for those operators; an excess whose rate fails to grow with $s$ or depend on beam polarization as predicted would likewise falsify the SMEFT interpretation.","tokens_in":1609,"feed_emoji":"⚛️","tokens_out":1871,"duration_ms":77999,"temperature":0.7,"pith_summary":"This paper argues that colliding electrons and positrons to produce a tau and a muon of different flavor is a powerful way to search for lepton flavor violation beyond the Standard Model, complementing rare tau decay experiments. It computes the $e^+e^- \\to \\tau\\mu$ cross section in the Standard Model Effective Field Theory with arbitrary beam polarizations and projects the sensitivities of the ILC and CLIC. The central quantitative claim is that a 3 TeV CLIC run could probe four-fermion lepton-flavor-violating operators up to new physics scales of about 50 TeV, and a 1 TeV ILC run up to about 25 TeV, either matching or exceeding the expected Belle II reach from tau decays. Beam polarization is what lets the two machines separate operators with different chirality structure.","feed_headline":"CLIC could push lepton-flavor-violation reach to ~50 TeV","feed_subtitle":"Polarized e+e- collisions are projected to rival or beat rare tau decay searches for new physics.","key_machinery":"The load-bearing object is the polarized cross section for $e^+e^- \\to \\tau\\mu$, written as a sum over the four electron and positron chirality combinations with coefficients that encode dipole, $Z$-boson, and four-fermion operators (Eqs. 15 and 20). The signal is then characterized by the muon momentum fraction $x = p_{\\rm det}/p_{\\rm beam}$: because the tau and muon carry nearly the full beam energy, the signal is concentrated just below $x = 1$, while the dominant background from $e^+e^- \\to \\tau^+\\tau^-$ with one tau decaying to a muon spreads over lower $x$. A cut at $x \\ge 1$ removes most of the background. The muon momentum distributions are built by Monte Carlo sampling that convolves beam energy spread, initial-state radiation, and detector momentum resolution.","core_discovery":"The authors' main result is that the $e^+e^- \\to \\tau\\mu$ process at future linear colliders provides sensitivity to SMEFT lepton-flavor-violating operators that is at least competitive with, and for four-fermion operators often stronger than, low-energy tau decay searches. Because the four-fermion operator contribution to the cross section grows with the squared center-of-mass energy $s$ while Standard Model backgrounds fall, the high energy of CLIC (3 TeV) is particularly powerful. The calculated polarized cross section shows that different beam chirality combinations pick out different operator classes, so combining runs with different electron and positron polarizations lifts the degeneracies that plague unpolarized measurements. The paper's projected event-level sensitivity uses the muon momentum fraction $x$, whose sharp peak near $x = 1$ for the signal sits above the broad background from tau-pair production.","pith_inferences":["If the energy-growth scaling holds, a null $e^+e^- \\to \\tau\\mu$ result at CLIC would set bounds on four-fermion lepton-flavor-violating operators that are largely independent of the assumptions entering tau decay analyses, giving a cross-check on Belle II.","The predicted polarization asymmetry is a direct chirality test: comparing the $P_- = +0.8$ and $P_- = -0.8$ runs at CLIC could discriminate left-handed from right-handed couplings without needing tau decay angular information.","The same $x$-peak technique could be applied to $e^+e^- \\to \\tau e$ or $e^+e^- \\to \\mu e$, where the backgrounds and operator bases differ but the kinematic separation is analogous.","The ~50 TeV reach depends on CLIC's hadronic tau identification being as efficient as ILC's; a lower efficiency would shrink the reach roughly as the square root of the efficiency, so a dedicated CLIC tau-tagging study would sharpen the projection."],"forward_implications":["A 1 TeV ILC run could constrain four-fermion lepton-flavor-violating operators up to new physics scales of roughly 25 TeV.","A 3 TeV CLIC run could reach about 50 TeV, the strongest projected constraint among the collider and tau-decay options considered in the paper.","Polarized beams allow individual SMEFT operator classes to be constrained separately rather than only in fixed combinations.","The $e^+e^- \\to \\tau\\mu$ search at linear colliders is complementary to Belle II: for some operators the collider wins, for others the rare decay search does.","The same $x \\ge 1$ muon-momentum strategy suppresses the tau-pair background enough that the projected sensitivities hold across the polarization settings."],"supporting_citations":[{"why":"Supplies the SMEFT operator basis, background treatment, and circular-collider sensitivities that this analysis extends.","marker":"[23]"},{"why":"Provides ILC beam energies, luminosities, polarizations, and detector resolution parameters used in the projections.","marker":"[43]"},{"why":"Provides CLIC beam and detector parameters, including momentum resolution.","marker":"[54]"},{"why":"Provides CLIC run energies and integrated luminosities used for the sensitivity estimates.","marker":"[46]"},{"why":"Gives the Belle II projection for tau to mu e e that the collider sensitivities are compared against.","marker":"[10]"},{"why":"Provides the existing Belle bound on tau to mu e e used as the current constraint.","marker":"[64]"},{"why":"Provides the BaBar bound on tau to mu e e used as the current constraint.","marker":"[65]"},{"why":"Supplies the initial-state-radiation distribution used in the signal Monte Carlo.","marker":"[55]"},{"why":"Supplies the hadronic tau identification efficiencies used in the event-count formulas.","marker":"[62]"}],"fun_headline_variants":["Polarized e+e- beams sharpen lepton flavor violation searches","Future colliders could beat Belle II on lepton flavor violation","CLIC's 3 TeV collisions rival tau decays for flavor violation","Beam polarization unlocks chirality tests for lepton flavor violation","High-energy e+e- colliders sharpen lepton flavor violation reach"],"cache_read_input_tokens":21888,"weakest_assumption_plain":"The projected reach assumes that CLIC's detectors can identify a tau decaying into pions as efficiently as ILC's detectors can, and that the beam energy spread and muon momentum resolution match the collider design reports; if either is worse, the signal acceptance drops and the quoted reach numbers shrink.","fun_headline_variants_meta":{"raw":{"variants":["Polarized e+e- beams sharpen lepton flavor violation searches","Future colliders could beat Belle II on lepton flavor violation","CLIC's 3 TeV collisions rival tau decays for flavor violation","Beam polarization unlocks chirality tests for lepton flavor violation","High-energy e+e- colliders sharpen lepton flavor violation reach"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000645,"raw_usage":{"total_tokens":2928,"prompt_tokens":875,"completion_tokens":2053,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":491,"completion_tokens_details":{"reasoning_tokens":1963}},"tokens_in":491,"tokens_out":2053,"duration_ms":14989,"temperature":1.0,"reasoning_tokens":1963,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T20:50:09.773916+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"At CLIC with $\\sqrt{s}=3$ TeV and 5 ab$^{-1}$, count candidate $e^+e^- \\to \\tau\\mu$ events with one hadronic tau and one muon of momentum fraction $x \\ge 1$. If the observed yield matches the Standard Model tau-pair background within uncertainties, the claimed sensitivity to four-fermion operators at scales around 50 TeV is ruled out for those operators; an excess whose rate fails to grow with $s$ or depend on beam polarization as predicted would likewise falsify the SMEFT interpretation.","supporting_citations":[{"cited_title":"Soft photons and second order radiative corrections to e+e−→z0,","cited_arxiv_id":null,"evidence_quote":"Supplies the initial-state-radiation distribution used in the signal Monte Carlo."}],"review_version":1}