{"id":"c905da1e-639b-4518-97ae-ddd61eca1818","arxiv_id":"2602.01332","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"H±→W±Z develops a one-loop CP-violating charge asymmetry in the 2HDM from internal bosonic and fermionic loop interferences, with the purely bosonic part vanishing in the alignment limit when the extra scalars are heavy.","lead":"A charged Higgs boson can decay to W and Z bosons only through quantum loops. This paper computes the resulting CP-violating matter–antimatter asymmetry in the two-Higgs-doublet model and finds new sources beyond earlier work.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Alignment-limit vanishing claim hinges on an unproved analyticity assertion: with m2+m3>mZ only C-1 may be complex; a numerical scan can settle it.","rationale":"The central claim is that one-loop H±→W±Z contains CP-violating charge asymmetries from bosonic self-interference, fermionic self-interference, and boson-fermion interference, with a distinctive alignment-limit prediction: for m2+m3>mZ and no fermionic contributions, the purely bosonic asymmetry vanishes. The manuscript's internal logic is coherent: the physical-coupling parametrization is well documented, the loop amplitudes are tabulated, and the provided Mathematica files are real supporting evidence. The weakest point is exactly the analyticity premise in Section 4.4. The threshold structure makes the assertion plausible — only C-1 has a cut through the neutral-neutral-Z vertex, and the other surviving integrals contain an H± propagator in the relevant channels — but the paper states the conclusion rather than proving it, and no direct numerical scan of the no-fermion alignment-limit asymmetry is shown. This is a genuine load-bearing concern because Eq. (4.13) and the sign-change argument for the vanishing rely on the reality of the involved loop functions. It is, however, testable and likely to pass. No stronger objection surfaced: the spontaneous-CP discussion in Section 7 is explicitly a sketch and peripheral to the main claim; the lack of quantitative comparison with Kanemura-Mura is a presentation issue, not a correctness flaw; and the decomposition into bosonic, fermionic, and interference terms is internally consistent. The reader's CONDITIONAL verdict is therefore appropriate, and my stress-test does not move it.","tokens_in":30905,"tokens_out":27439,"duration_ms":268162,"concrete_test":"Run the provided Mathematica code (or an independent LoopTools/FormCalc implementation) in the exact alignment limit e1=v, e2=e3=0, f1=0, f2=v, f3=-iv, with all rho_X=0, for a dense scan over m_H±, m2, m3, q2, q3 (including complex q_i) satisfying m2+m3>mZ. Compute the charge asymmetry delta of Eq. (1.2); if it is numerically zero everywhere (e.g., <1e-10), the analyticity premise survives. Independently, use LoopTools to evaluate Im[C00] for C-1 and Im[B0], Im[B1] for B-1/B-5/B-8 on the same grid and verify all are exactly zero; any nonzero imaginary part identifies the missing ingredient.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 4.4's central vanishing claim — in the exact alignment limit, with fermionic rho's set to zero and m2+m3>mZ, the purely bosonic charge asymmetry vanishes — rests on the assertion that among the surviving diagrams only C-1 can contain complex loop integrals and that its C00 is real under that mass condition. This is asserted, not derived. The threshold reasoning is plausible: the p1/p2 channels in C-1 and C-2 contain a H± line, so m_H±+m_i > m_W and m_j+m_H± > m_H± force reality; C-2's p3 channel has 2m_H±>m_Z; only C-1 has a neutral-neutral-Z cut. But the paper does not demonstrate this for all Passarino–Veltman coefficients appearing in Table 4.1 (C1, C11, C12, C22 combinations), nor justify that discarded bubble-on-W/Z terms cannot generate an imaginary part. If any of these were complex, Eq. (4.13) (~F_i = -F_i^*, ~G_i = -G_i^*) would fail and a bosonic asymmetry could survive despite m2+m3>mZ. The numerical illustrations in Fig. 8 do not directly plot the no-fermion asymmetry in this limit, so the available numerics do not close the gap.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper computes the one-loop amplitude and charge asymmetry δ for H^± → W^± Z in the general 2HDM, expressing all amplitudes in terms of physical couplings (e_i, f_i, q_i, and the Yukawa matrices ρ̃). The amplitude is split into bosonic and fermionic loop contributions, including fermion tadpoles in the bosonic category. The central claims are: (i) there are CP-violating charge asymmetries from pure-bosonic interference, pure-fermionic interference, and boson–fermion interference; (ii) this qualitatively confirms the Kanemura–Mura result for boson–fermion interference, while also providing new sources; (iii) in the exact alignment limit with no fermionic loops and with m2 + m3 > mZ, the purely bosonic asymmetry vanishes; and (iv) away from alignment, or with fermionic loops, a charge asymmetry can survive. Extensive one-loop amplitudes are tabulated, cross-checked with FormCalc and by hand, and code is made available on GitHub.","tokens_in":31285,"tokens_out":11174,"duration_ms":122445,"significance":"If the claims are correct, this work is a valuable addition to 2HDM phenomenology: it isolates contributions to CP violation in H^± → W^± Z in terms of physical couplings rather than potential parameters, and it identifies new sources of the charge asymmetry beyond those studied by Kanemura and Mura. The paper has notable strengths: the analytic tabulation of loop amplitudes is detailed and machine-checked, the physical-coupling parametrization makes the phase structure transparent, the CPT/Cutkosky discussion gives a useful consistency check, and the GitHub repository provides reproducible analytic results. However, the alignment-limit vanishing claim — which is highlighted in the abstract — rests on an analyticity assertion that is not proven, and one of the analyticity statements in the fermionic section is incorrect as written. These issues are local and fixable, but they directly affect the paper's central claims.","major_comments":[{"comment":"The alignment-limit vanishing claim is load-bearing for the abstract, but it rests on the unproved assertion that 'it turns out that only diagram C-1 can possibly contain loop integrals with an imaginary part' and that its C00 is real for m2+m3>mZ. The surviving amplitudes in Table 4.1 also involve the combinations C1, C11, C12, C22 for C-1 and C-2, as well as B0 and B1 for the bubbles. No analyticity argument is given for these coefficients, and the numerical illustrations in Fig. 8 include fermionic tadpoles; they do not plot the no-fermion asymmetry in the exact alignment limit. Please provide a complete proof, or a numerical scan of the imaginary parts of all surviving Passarino–Veltman coefficients, together with a no-fermion asymmetry plot in the alignment limit. Without this, Eq. (4.13) and the abstract conclusion remain conditional.","section":"Section 4.4, Eq. (4.13)"},{"comment":"The statement 'Since the loop integrals involved in the H amplitudes are all real' is not correct. For the tb triangles in Table 5.4, the coefficients C0 and C1 become complex when m_H± > m_t + m_b, which is precisely the region where the fermionic F and G amplitudes develop their imaginary parts. The conclusion that the H amplitude does not contribute to the charge asymmetry can instead be justified by the fact that the H+ and H- amplitudes are proportional to ρ^* Z and ρ Z with a common loop factor Z for diagonal ρ, so |H+|^2 = |H-|^2. The erroneous analyticity claim should be removed and replaced by this argument.","section":"Section 5.1, just before Eqs. (5.3)"}],"minor_comments":[{"comment":"The symbol ρ is used both for the kinematic tadpole factor in Eq. (4.10) and (in the form ρ̃) for the Yukawa matrices. This is confusing in Tables 4.3 and 4.4. Please rename one of them.","section":"Notation, Eq. (4.10) and Section 2.3"},{"comment":"The phrase 'the thin curves below do not' is ambiguous. Please specify exactly which contributions are omitted in the thin curves.","section":"Figure 8 caption"},{"comment":"There is a typo: 'threshol' should be 'threshold'.","section":"Section 4.5"},{"comment":"The paper says it 'qualitatively confirms' Kanemura and Mura, but no quantitative comparison or parameter-overlap plot with Ref. [4] is provided. Please add one, so that the confirmation claim can be checked and the differences identified in Sections 4.6 and 5.3 are put in context.","section":"Abstract / Comparison with Ref. [4]"},{"comment":"The remark that 'i' in the K_d column denotes the imaginary unit should be made in the table caption, not only in a footnote in the text.","section":"Table 4.1"}],"recommendation":"major_revision","confidential_remarks":"The calculation appears largely sound and the paper is in scope for a hep-ph journal. The main blocker is the missing proof or numerical verification of the alignment-limit vanishing claim in Section 4.4; this is a central assertion in the abstract. The Section 5.1 claim that the H-amplitude loop integrals are real is plainly wrong as stated, though the final conclusion may survive once the argument is corrected. Both issues are fixable with additional analysis or a numerical scan, so I recommend major revision rather than rejection."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"I've read through this carefully. Short version: this is a solid, genuinely additive one-loop calculation, and the central claim about the alignment limit has a real but addressable gap.\n\nThe new content: the paper confirms the Kanemura–Mura boson–fermion interference and then adds two sources they missed—interference purely among bosonic loops and purely among fermionic loops. The decomposition of the asymmetry into three pieces is clean, and expressing everything in terms of physical couplings (the e_i, f_i, q_i, ρ couplings) makes the relevant phases transparent. The amplitude tables are detailed and cross-checked with FormCalc plus by hand, and the Mathematica files on GitHub give other people a way to reuse or check the analytic results. That is reproducible work in the sense that matters.\n\nThe weak spot is Section 4.4. The abstract's headline claim—in the alignment limit, no fermion loops, m2+m3>mZ, the purely bosonic CP asymmetry vanishes—rests on the assertion that among the surviving diagrams only C-1 can have an imaginary part, and that its C00 is real under that condition. The paper says 'it turns out' and gives a plausible threshold argument for why the other channels are forced real, but it does not systematically check every PV coefficient in Table 4.1, and it does not explicitly rule out an imaginary part from the discarded bubble-on-W/Z terms. The numerics do not close the gap either: Figure 8 does not isolate the pure-bosonic asymmetry in that limit with fermionic ρ set to zero. So a careful referee should ask for either a proof or a numerical scan showing that the asymmetry goes to zero. It is an addressable issue, not a sign the calculation is wrong; the rest of the paper stands regardless.\n\nTwo minor quibbles: the spontaneous-CP-violation discussion is explicitly only sketched, despite the abstract saying the calculation covers it. And there is no quantitative comparison with Kanemura–Mura's numbers for overlapping benchmarks, which would make the 'we qualitatively confirm' statement easier to verify.\n\nThis is a paper for people working on 2HDM collider phenomenology and CP violation. It deserves a serious referee. I would send it out, with a request to tighten or numerically substantiate the alignment-limit claim.","headline":"Competent, genuinely additive one-loop 2HDM calculation; the alignment-limit vanishing claim has an addressable but real analyticity gap.","tokens_in":31729,"tokens_out":3838,"would_cite":true,"duration_ms":41202,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["12.60.Fr","11.30.Er"],"model":"deepseek-v4-flash","headline":"The one-loop H±→W±Z amplitude in the two-Higgs-doublet model carries a CP-violating charge asymmetry that decomposes into bosonic, fermionic, and interference parts, and in the alignment limit only the fermionic part survives when the addit","keywords":["CP violation","two-Higgs-doublet model","charged Higgs boson","charge asymmetry","H±→W±Z vertex","alignment limit","Yukawa phases","loop-induced decay"],"falsifier":"Compute the full one-loop bosonic amplitude numerically in the exact alignment limit for a scalar spectrum with m2+m3>mZ, without imposing the 'only C-1 is complex' premise; if the imaginary parts of any other triangle or bubble integrals are non-zero, the claim that the asymmetry vanishes is refuted. A more direct experimental falsifier would be a measured non-zero charge asymmetry in a parameter region where fermionic contributions are kinematically or parametrically suppressed (e.g., mH± < mt+mb and |ρ| → 0).","tokens_in":30857,"feed_emoji":"⚛️","tokens_out":6370,"duration_ms":62317,"temperature":0.7,"pith_summary":"The paper tries to prove that the one-loop decay H± → W±Z in the two-Higgs-doublet model carries a CP-violating charge asymmetry that can be decomposed into three independent sources: interference inside the purely bosonic loops, inside the purely fermionic loops, and between bosonic and fermionic loops. It further shows that in the alignment limit, the purely bosonic contribution to the asymmetry disappears as long as the two additional neutral scalars satisfy m2 + m3 > mZ, leaving fermionic loops and their tadpoles as the only possible origin of a surviving asymmetry. This is worth knowing because the entire calculation is expressed in terms of physical masses and couplings, so a measured charge asymmetry would translate directly into constraints on the complex phases of the underlying scalar and Yukawa sector, without needing to fix the scalar potential. The authors argue the mechanism is generic to any CP-violating multi-Higgs-doublet model.","feed_headline":"Charge asymmetry in H±→W±Z probes CP violation","feed_subtitle":"Three loop families generate it; in the alignment limit only fermion loops keep it alive.","key_machinery":"The argument is carried by a reparametrisation of the 2HDM in terms of physical couplings rather than potential parameters: the neutral-scalar couplings to vector boson pairs (ei, with e1²+e2²+e3² = v²), the charged-Higgs–neutral-scalar–W couplings (fi, with phases fixed by the ei), the neutral-scalar–charged-pair couplings (qi), and the generic Yukawa matrices ρ~ that carry independent phases for up-type, down-type and lepton sectors. The charge asymmetry is organised by writing the one-loop amplitude as a sum over diagrams with a common prefactor fi or ρ~, so that complex conjugation of the external charge reverses only these coupling phases while leaving the Passarino–Veltman integrals un","core_discovery":"The central claim is that the charge asymmetry δ = (Γ(H+→W+Z) − Γ(H−→W−Z)) / (Γ(H+→W+Z) + Γ(H−→W−Z)) arises at one loop from three distinct interference families. In addition to the previously identified interference between bosonic and fermionic amplitudes, the paper identifies CP violation generated entirely within the bosonic loops (through the complex phases of the couplings fi that link each neutral Higgs to the charged Higgs and W) and entirely within the fermionic loops (through relative phases among the Yukawa couplings ρ~). All amplitudes are written directly in terms of the physical couplings ei, fi, qi and ρ, with loop integrals identical for both charge states. In the exact align","pith_inferences":["A dedicated numerical scan that drops the analyticity premise of section 4.4 could test whether subleading bosonic diagrams develop imaginary parts below the m2+m3>mZ threshold; if they do, the vanishing of the bosonic asymmetry in the alignment limit would be an artifact of the assumption.","The same charge-asymmetry variable could be adapted to H±→W±γ, where the photon coupling forbids the scalar-mediated diagrams but shares the WZ gauge structure; a combined measurement of both asymmetries would help isolate the fermionic contribution.","One could use the relation between the asymmetry and the CP-odd invariants ImJi to design sum rules linking the asymmetry size to known collider constraints on e2, e3 and qi, turning a future observation into a measurement of the invariants themselves."],"forward_implications":["If the decomposition is correct, a measured charge asymmetry in H±→W±Z directly constrains combinations of physical phases (phases of fi, phases of ρ, and the relative boson–fermion phase), not just the parameters of the scalar potential.","In the alignment limit with m2+m3>mZ, any observed asymmetry is evidence of CP violation in the fermionic couplings or in the fermion-tadpole sector, since the purely bosonic contribution is predicted to vanish.","The three sources of asymmetry can in principle be separated by scanning the charged-Higgs mass: fermionic amplitudes become complex immediately above the tb threshold, while bosonic amplitudes require the heavier mHi + mW threshold.","The construction extends trivially to any multi-Higgs-doublet model, suggesting the charge asymmetry is a generic signature of extended scalar sectors, not a special feature of the 2HDM."],"fun_headline_variants":["Three loop families generate CP violation in H±→W±Z","Bosonic loop phases alone yield CP violation in 2HDM","In alignment limit, CP asymmetry needs fermion loops","New CP sources from bosonic and fermionic loop interference"],"cache_read_input_tokens":2304,"weakest_assumption_plain":"The vanishing of the purely bosonic asymmetry in the alignment limit rests on the premise, stated in section 4.4, that for m2+m3>mZ the only potentially complex loop integral among the surviving bosonic diagrams is C00 of diagram C-1, with all others real; if any other diagram or subleading term acquires an imaginary part, the asymmetry need not vanish.","fun_headline_variants_meta":{"raw":{"variants":["Three loop families generate CP violation in H±→W±Z","Bosonic loop phases alone yield CP violation in 2HDM","In alignment limit, CP asymmetry needs fermion loops","New CP sources from bosonic and fermionic loop interference"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.00123,"raw_usage":{"total_tokens":4867,"prompt_tokens":695,"completion_tokens":4172,"prompt_tokens_details":{"cached_tokens":256},"prompt_cache_hit_tokens":256,"prompt_cache_miss_tokens":439,"completion_tokens_details":{"reasoning_tokens":4102}},"tokens_in":439,"tokens_out":4172,"duration_ms":31999,"temperature":1.0,"reasoning_tokens":4102,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-03T05:41:26.558379+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the full one-loop bosonic amplitude numerically in the exact alignment limit for a scalar spectrum with m2+m3>mZ, without imposing the 'only C-1 is complex' premise; if the imaginary parts of any other triangle or bubble integrals are non-zero, the claim that the asymmetry vanishes is refuted. A more direct experimental falsifier would be a measured non-zero charge asymmetry in a parameter region where fermionic contributions are kinematically or parametrically suppressed (e.g., mH± < mt+mb and |ρ| → 0).","supporting_citations":[],"review_version":1}