{"id":"7da9b849-0ac1-460d-b553-5f9fd0c3d2d8","arxiv_id":"2607.09852","paper_version":1,"verdict":"ACCEPT","confidence":"HIGH","novelty_score":7.0,"correctness_risk":"low","formal_verification":"none","parameter_count":4,"one_line_summary":"Darkly charged ALPs (DALPs) forbid all d=5 ALP-SM operators and admit only two leading d=6 operators (Higgs portal and hypercharge portal), with distinct collider, cooling, and dark-matter phenomenology.","lead":"Axion-like particles that carry conserved dark charges cannot couple to the Standard Model at dimension 5; their leading interactions are two specific dimension-6 operators. This changes how such particles can be searched for and whether they can make up dark matter.","discovery_kind":"extension","skeptic_critique":{"model":"grok-4.5","headline":"No significant objection identified","rationale":"The paper’s strongest claim is a clean group-theoretic and CCWZ statement about the operator basis. The conditions [C1] (RGB contains no H-singlet) and [C2] (antisymmetric bilinear invariant exists) are both necessary and sufficient for the claimed d=5 absence and d=6 content; they are proved in App. A and illustrated by multiple explicit cosets (Sec. 3.5–3.6). The residual modeling choices flagged by the reader—global rather than gauged G, and H-preserving masses—are acknowledged by the authors and affect only the Sec. 4 phenomenology, not the EFT classification. Because the central argument is self-contained, standard, and free of hidden assumptions that would alter the operator count, no load-bearing concern arises and the reader’s ACCEPT verdict stands.","tokens_in":35188,"tokens_out":524,"duration_ms":4446,"concrete_test":"Independently re-derive the lowest-order H-invariant chiral operators of Table 1 (dim ≥ 6 row) from the Maurer–Cartan form u_μ and the branching rule adj G|_H = adj H ⊕ RGB, without using the explicit expansions (3.14)–(3.15); confirm that only the two structures Sij u_i^μ u_j_μ (H†H) and Aij u_i^μ u_j^ν B_μν appear at d=6 when [C1] and [C2] hold.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim—that H-invariance of a non-trivial RGB with no singlet forbids all d=5 ALP-SM operators, leaving precisely the two d=6 operators of Eqs. (2.1)–(2.4)—follows directly from the CCWZ construction (Sec. 3.1–3.2) and the group-theoretic conditions [C1]–[C2] (Sec. 3.3 and App. A). The reader’s weakest assumption (purely global G plus small H-preserving masses) is stated explicitly in the abstract and Sec. 1 and is used only for the phenomenological illustrations of Sec. 4; it does not enter the operator classification itself. No internal inconsistency or hidden assumption that would invalidate the operator basis was found.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.5","summary":"The paper removes the implicit assumption that axion-like particles (ALPs) are singlets under any dark-sector symmetry. For pseudo-Goldstone bosons transforming in a non-trivial representation RGB of an unbroken dark group H (with no H-singlet), H-invariance forbids every d=5 ALP–SM operator. Using the CCWZ construction for a general G→H breaking, the authors show that the leading shift-symmetric EFT contains precisely two d=6 operators coupling DALPs to the SM: a universal Higgs portal Sij(H†H)(∂μai)(∂μaj) and, when an antisymmetric H-invariant exists, a hypercharge portal Aij Bμν(∂μai)(∂νaj). They reformulate the existence conditions [C1]–[C2] in group-theoretic language, classify higher-dimension operators, give concrete coset examples, compute phenomenological constraints (invisible widths, monojet, SN cooling, direct detection) and relic-density mechanisms (freeze-out, freeze-in, misalignment) for a minimal two-DALP case, and supply perturbative UV completions that generate both operators.","tokens_in":35409,"tokens_out":1304,"duration_ms":27055,"significance":"If correct, the result opens a qualitatively distinct corner of ALP parameter space in which the paradigmatic aγγ coupling and all other linear d=5 operators are absent by symmetry, while two d=6 portals become the leading signals. The operator classification is model-independent within the stated assumptions (global G, SM fields neutral under G), the group conditions and CCWZ derivation are clean and standard, and the UV matching calculations (including the non-expanded results in App. B obtained with Matchete) are reproducible. The phenomenology yields falsifiable predictions for invisible Higgs/Z widths, monojet rates, and a DM window that extends to surprisingly large masses via misalignment. These strengths make the work a natural and useful extension of the ALP EFT literature.","major_comments":[{"comment":"Sec. 4 (and Figs. 3–4, 7): the entire phenomenological analysis is performed for a minimal, exactly degenerate two-DALP spectrum. While the authors note that degeneracy follows from an H-preserving explicit G-breaking, the general G→H examples of Sec. 3.5 (e.g. SU(3)→U(1)×U(1)) produce several multiplets with generically different masses and decay constants. The invisible-width formulae (4.1), (4.4), the monojet rates, and the relic-density curves then change. A short paragraph quantifying how the bounds and the DM windows generalize (or stating that they are representative only) is needed for the claim of “model-independent phenomenological implications” to hold beyond the minimal case.","section":null},{"comment":"Sec. 4.3: the supernova-cooling window for OBa is obtained by rescaling the fermionic vector-portal bounds of Ref. [76] via averaged production and capture cross sections (4.10)–(4.12). The authors note that bosonic versus fermionic statistics differ by O(1) factors, but the radial averaging and the neglect of possible DALP self-interactions inside the SN introduce a systematic uncertainty that is not quantified. Because this window is competitive with collider bounds in Fig. 4, a brief estimate of that uncertainty (or a statement that the blue region should be regarded as indicative) is required for the exclusion to be robust.","section":null}],"minor_comments":[{"comment":"Abstract and Sec. 2: the phrase “just two d=6 operators” is accurate for the leading SM portals of mass dimension two, but Table 1 shows that other d=6 structures exist once higher-dimension SM operators are allowed. A clarifying clause (“two operators that start at d=6 with the lowest-dimension SM singlets”) would prevent misreading.","section":null},{"comment":"Eq. (2.1) and Fig. 1: the notation Sij versus eSij (kinetic versus portal) is introduced only later; defining both tensors already in Sec. 2 would improve readability for readers who skip Sec. 3.","section":null},{"comment":"Sec. 3.5.2, Eq. (3.37): the relation between the three decay constants and the adjoint VEV components is useful; a short remark that the most general Sij need not coincide with the kinetic-term combination would make the subsequent discussion of independent portal coefficients clearer.","section":null},{"comment":"Figs. 3, 4 and 7: the gray “EFT breakdown” line is drawn but never defined quantitatively in the text. Stating the criterion used (e.g. fa/√c ≳ ETmax or 4πfa) would help the reader.","section":null},{"comment":"Sec. 5.1, Table 3: the present bound on CH□ is quoted from a global SMEFiT fit; a one-sentence reminder that the bound assumes no other new physics would be useful for non-SMEFT readers.","section":null},{"comment":"App. A.2: the sufficient condition involving the center of H is elegant; a one-line example showing that it recovers the U(1) factor criterion already stated in Sec. 3.3 would make the appendix self-contained.","section":null},{"comment":"References: a few recent multi-axion and dark-pion papers (e.g. on freeze-in of multiple axions) are cited, but the connection of OBa to the operator already noted in Ref. [34] could be flagged more explicitly in Sec. 4.4.","section":null}],"recommendation":"minor_revision","confidential_remarks":"The manuscript is a clean, well-executed conceptual advance that fits JHEP’s scope. The two major comments are local and easily addressable; they do not threaten the central EFT claim. I see no novelty or citation issues."},"author_rebuttal":null,"desk_editor":{"model":"grok-4.5","letter":"The punchline is simple: if ALPs transform non-trivially under an unbroken dark H with no H-singlet, every linear d=5 ALP-SM operator is forbidden by charge conservation, and the leading shift-symmetric EFT collapses to exactly two d=6 operators—one universal Higgs portal and one antisymmetric hypercharge portal. That is new relative to the standard ALP literature and to multi-axion setups that still allow d=5 terms.\n\nThey do the technical work carefully. The CCWZ construction (Sec. 3), the group-theoretic conditions [C1]–[C2] (and their pure-group reformulations in App. A), the classification of higher operators up to d=9, and the matching calculations for the SO(3)→SO(2) UV examples are all standard and clean. The phenomenology section is also solid: invisible widths, monojet, SN cooling, freeze-in/misalignment relic curves, and direct-detection bounds are computed with the usual tools and plotted against the two free coefficients. The observation that misalignment can work up to hundreds of MeV because the lightest DALP is charge-stabilized is a nice concrete payoff.\n\nSoft spots are minor and mostly declared. They restrict to global G (no dark gauge bosons) and to a small H-preserving mass term that keeps the DALPs light and, for the plots, degenerate. That is fine for the operator basis itself; it only limits the phenomenological illustrations. The freeze-out region is almost entirely excluded, as expected for d=6 operators, and the SN bound is a rescaling rather than a full re-calculation—neither is load-bearing. Citation pattern looks normal; no circularity.\n\nThis is for people who work on ALP EFTs, light DM, or future collider/direct-detection strategies. It opens a qualitatively distinct search corner without claiming to rewrite the field. I would send it to a serious referee without hesitation; the math and the logic hold. Worth reading and, for anyone writing on multi-ALP or charged dark scalars, worth citing.","headline":"Clean, self-contained EFT paper that kills the entire d=5 ALP Lagrangian once ALPs carry dark charge, isolates two d=6 operators, and maps their distinct collider/DM phenomenology.","tokens_in":36015,"tokens_out":517,"would_cite":true,"duration_ms":7635,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.5","headline":"ALPs that carry dark charges lose every ordinary d=5 coupling and interact with the Standard Model only through two d=6 operators.","keywords":["axion-like particles","dark charges","effective field theory","Goldstone bosons","Higgs portal","hypercharge portal","dark matter","CCWZ"],"falsifier":"An observation of a single ALP decaying to two photons, or a non-zero linear ALP–Higgs or ALP–fermion coupling at dimension five, would immediately rule out the dark-charge premise.","tokens_in":36131,"feed_emoji":"🌑","tokens_out":596,"duration_ms":5042,"temperature":0.7,"pith_summary":"Standard axion-like particles are assumed to be singlets under every dark symmetry as well as under the Standard Model. This paper drops that assumption. Once the ALPs transform non-trivially under an unbroken dark group H, charge conservation immediately forbids every linear, dimension-five ALP–SM operator, including the celebrated ALP–photon coupling. The leading shift-symmetric effective theory then starts at dimension six and contains only two operators: a universal Higgs-portal interaction and a single hypercharge-portal interaction that requires an antisymmetric H-invariant. The authors construct the full non-linear chiral Lagrangian for a general G\to H breaking, give group-theoretic conditions that guarantee the two operators exist, map the resulting collider, astrophysical and dark-matter phenomenology, and supply concrete ultraviolet completions. The result is a qualitatively different search strategy: look for invisible Higgs and Z decays, monojets, and freeze-in or misalignment dark matter rather than photon signals.","feed_headline":"Dark-charged ALPs kill every ordinary d=5 coupling","feed_subtitle":"Only two d=6 operators remain, rewriting collider and dark-matter searches","key_machinery":"The CCWZ chiral Lagrangian for a general coset G/H, together with two group-theoretic conditions: RGB contains no H-singlet (so d=5 operators are absent) and the antisymmetric product of RGB with itself contains an H-singlet (so the Bμν operator is allowed).","core_discovery":"When ALPs transform in a non-trivial representation RGB of an unbroken dark symmetry H that contains no H-singlet, every d=5 ALP–SM operator is forbidden by H-invariance, and the lowest-order shift-symmetric Lagrangian consists of precisely two d=6 operators: the universal Higgs portal Sij(H†H)(∂μai)(∂μaj) and the antisymmetric hypercharge portal Aij Bμν(∂μai)(∂νaj).","pith_inferences":[],"forward_implications":[],"fun_headline_variants":["Dark charges ban every d=5 ALP-SM operator","Only two d=6 portals remain for charged ALPs","Unbroken dark H forbids all ordinary d=5 ALP couplings","Darkly charged ALPs leave just Higgs and hypercharge d=6","No H-singlet ALPs kill every shift-symmetric d=5 term"],"cache_read_input_tokens":32896,"weakest_assumption_plain":"The dark symmetry is purely global and any explicit breaking that gives the ALPs a small mass still preserves the unbroken dark group, so the particles remain light and (in the minimal case) mass-degenerate.","fun_headline_variants_meta":{"raw":{"variants":["Dark charges ban every d=5 ALP-SM operator","Only two d=6 portals remain for charged ALPs","Unbroken dark H forbids all ordinary d=5 ALP couplings","Darkly charged ALPs leave just Higgs and hypercharge d=6","No H-singlet ALPs kill every shift-symmetric d=5 term"]},"model":"grok-4.5","effort":"low","cost_usd":0.004862,"raw_usage":{"total_tokens":1365,"prompt_tokens":784,"num_sources_used":0,"completion_tokens":93,"cost_in_usd_ticks":48620000,"prompt_tokens_details":{"text_tokens":784,"audio_tokens":0,"image_tokens":0,"cached_tokens":128},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":488,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":784,"tokens_out":93,"duration_ms":4870,"temperature":1.0,"reasoning_tokens":488,"cache_read_input_tokens":128,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-07-14T15:01:56.799132+00:00","model_set":{"reader":"grok-4.5"},"falsifier":"An observation of a single ALP decaying to two photons, or a non-zero linear ALP–Higgs or ALP–fermion coupling at dimension five, would immediately rule out the dark-charge premise.","supporting_citations":[],"review_version":1}