{"id":"0c820b8b-f5da-48a5-81fd-c00f9fdd18fa","arxiv_id":"1909.00726","paper_version":2,"verdict":"CONDITIONAL","confidence":"HIGH","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":6,"one_line_summary":"In the MSSM with heavy SUSY particles and complex phases, the lightest Higgs mass can vary by up to about 20 GeV with the phase of the trilinear couplings, while its CP-odd admixture drops below 0.5% once the charged Higgs mass exceeds about 260 GeV.","lead":"This paper calculates how the Higgs boson mass and its CP properties change in a supersymmetric model with heavy superpartners and complex phases, using an effective field theory approach. It finds the Higgs mass can shift by several GeV depending on the complex phase, while a measurable CP-odd component appears only for light charged Higgs masses.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The headline 20 GeV phase dependence is computed at |A|=|µ|=3Ms, where one-loop matching corrections to the quartic couplings are comparable to their tree-level values; with two-loop thresholds explicitly omitted, the quantitative claim is not yet controlled.","rationale":"The reader's CONDITIONAL verdict is well placed. The paper is transparent about its approximations and includes a useful internal cross-check of the interpolation method against the 2HDM and SM limits (Fig. 4), and the statement that the CP-odd admixture of the light Higgs falls below 0.5% for MH+ ≈ 260 GeV is stable under the one-loop and resummation variants shown in Fig. 7. The concern I find most load-bearing is therefore not about the CP-odd conclusion but about the quantitative mass swing. The default scenario deliberately uses |A|=|μ|=3Ms to maximize CP violation; at that point the one-loop matching corrections to the quartics are of order 0.1 against tree-level values of order 0.1-0.3, so the threshold loop expansion is not a small perturbation. The phase enters the scalar sector mainly through the loop-induced λ5, λ6 and λ7, so any uncontrolled higher-order piece in exactly those couplings feeds directly into the claimed 20 GeV swing. Since the paper gives no uncertainty estimate and states that two-loop thresholds for complex parameters in the DR scheme are unknown, the quantitative claim should be read as conditional. I agree with the reader that this is the weakest assumption; the check I propose would settle whether omitted two-loop thresholds actually move the phase dependence at the GeV level.","tokens_in":30917,"tokens_out":10346,"duration_ms":122970,"concrete_test":"Implement the two-loop threshold corrections of O(h_t^4 g_s^2) for complex parameters from Ref. [92] in the DR scheme (or with an appropriate MS-to-DR conversion) and rerun the default benchmark |A|=|µ|=3Ms, tanβ=5, MH+=500 GeV of Fig. 5b. If the phase swing Δm_h(φA) changes by more than about 2 GeV relative to the one-loop-threshold result, the omitted two-loop terms invalidate the quantitative claim; if it changes by less than 1 GeV, the concern is resolved.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The most load-bearing problem is not just that two-loop threshold corrections are absent; it is that the benchmark used for the headline number sits where the one-loop matching is already a large correction. In Eqs. (15)-(21), the box contributions scale as κ|A|^4 h_t^4/2; with |A|=3Ms and h_t(Ms)≈0.8 this gives Δλ_i ≈ -0.1, while the tree-level quartics in Eq. (13) are λ_i ≈ 0.1-0.3. The CP-violating couplings λ5, λ6 and λ7 are completely loop-induced and receive exactly these large A-dependent terms, so the phase sensitivity of m_h in Fig. 5b is dominated by threshold corrections that are not parametrically small. Section 4 states that the corresponding two-loop thresholds are unknown for complex parameters in the DR scheme, and no uncertainty estimate is given anywhere. Two-loop terms are suppressed by only one extra loop factor, so the missing O(h_t^4 g_s^2) and O(κ^2 h_t^6 |A|^6) pieces can plausibly shift m_h by more than 1-2 GeV and can change the phase dependence itself, not merely the overall mass. The qualitative conclusion that phases can move m_h by several GeV is likely robust, but the specific 'up to about 20 GeV' and the near-degenerate values around 105 GeV are not controlled by the published calculation.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"This paper presents an effective-field-theory calculation of the Higgs-boson spectrum in the MSSM with heavy superpartners and complex parameters. The MSSM is matched to a type-III 2HDM at one-loop order at the scale Ms, the 2HDM parameters are evolved down with two-loop RGEs that include complex phases, and the pole masses are computed with several methods: using the 2HDM at MH+, using the 2HDM at mt, matching to the SM for large MH+, and an interpolation method (d) that resums the dominant logarithms while retaining the full 2HDM mass matrix. The central numerical findings are that the mass of the lightest neutral Higgs boson can vary by up to about 20 GeV as the common phase of At and Ab is varied in the extreme benchmark |A|=|µ|=3Ms, tanβ=5, and that the CP-odd admixture of the lightest Higgs boson drops below 0.5% for MH+≈260 GeV in their scenario. The paper also studies the dependence on the gluino phase and the masses and mixings of the heavy Higgs bosons.","tokens_in":31212,"tokens_out":10776,"duration_ms":97732,"significance":"If the quantitative results hold, this work is a valuable step toward next-to-leading-log resummed predictions for the CP-violating MSSM with heavy sfermions. It provides the first complete one-loop matching of the complex MSSM to a type-III 2HDM including field redefinitions, two-loop RGEs with complex phases, and a transparent comparison of different pole-mass schemes. The interpolation method (d) is cross-checked against the pure 2HDM and SM limits for real parameters, and the authors are explicit about the missing two-loop thresholds and the restriction tanβ≤20 without tanβ resummation. The qualitative conclusion that CP phases can shift the lightest Higgs mass by several GeV and can control the size of the CP-odd admixture is plausible and interesting. However, the main numerical claim is made in a benchmark where the one-loop matching is not a small correction, and the absence of any uncertainty estimate limits the quantitative reach of the paper.","major_comments":[{"comment":"The central quantitative claim—that the lightest Higgs mass varies by almost 20 GeV with the phase ϕA—is not controlled by the published calculation. For the benchmark |A|=|µ|=3Ms with h_t(Ms)≈0.8, the one-loop box contributions to the quartics, e.g., Δλ_1^(4) = −κ/2 h_t^4 |µ̂|^4 ≈ −0.1, are comparable to the tree-level values λ_i ≈ 0.1–0.3 in Eq. (13). The CP-violating couplings λ5, λ6, λ7 are entirely loop-induced and receive exactly these A-dependent terms, so the phase sensitivity in Fig. 5(b) is dominated by threshold corrections that are not parametrically small. Section 4 states that two-loop thresholds are unknown for complex parameters in the DR scheme, and no uncertainty estimate is given anywhere. Since two-loop terms are suppressed by only one additional loop factor, the missing O(h_t^4 g_s^2) and O(|A|^6 h_t^6) pieces can plausibly shift m_h by more than 1–2 GeV and can modify the phase dependence itself, not merely the overall mass. The qualitative conclusion that phases can shift m_h by several GeV is likely robust and is a worthwhile result, but the specific magnitude near 20 GeV and the masses close to 105 GeV in Fig. 5(b) are not quantitatively supported. I recommend adding an estimate of the missing higher-order uncertainty, for example by renormalization-scale variation or by using the O(h_t^4 g_s^2) two-loop thresholds of Ref. [92] (converted to DR) as a proxy, and softening the quantitative statements in the abstract and Section 7 accordingly.","section":"Section 4, Eqs. (15)–(21), Fig. 5(b)"}],"minor_comments":[{"comment":"There is a typo in the sentence describing the loop-function evaluation: \"evalued\" should be \"evaluated\".","section":"Section 4"},{"comment":"The symbol \"γreum\" is a typo for \"γresum\".","section":"Eq. (56)"},{"comment":"Please clarify that the notation P^2_{i3} in the CP-odd percentage definition denotes |P_{i3}|², since the mixing matrix is in general complex.","section":"Section 6.5"},{"comment":"The abstract quotes the phase dependence as \"on the order of a couple of GeV,\" while Fig. 5(b) shows almost 20 GeV for the extreme benchmark |A|=|µ|=3Ms. Please state both the typical and maximal values, and explicitly connect the maximal value to the benchmark at the boundary of the calculation’s validity.","section":"Abstract and Section 6.4"}],"recommendation":"major_revision","confidential_remarks":"The paper is a solid EFT calculation, but the headline numerical claim is presented without an uncertainty estimate. I would ask the authors to add a scale-variation or scheme-comparison estimate of the missing two-loop thresholds, or to reword the abstract and conclusions so that the ~20 GeV effect is clearly presented as an upper bound of an approximation whose quantitative accuracy is not yet controlled. The work is within the scope of the journal and the central derivation is internally consistent, so this is fixable within a major revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"You should know this is a careful, honest EFT calculation, not a breakthrough. It computes the MSSM Higgs spectrum with heavy SUSY and complex phases by matching to a type-III 2HDM at one loop, running with two-loop complex RGEs, and resumming NLLs. That specific combination is new relative to Refs. [64,65,92], and the numerical study of phase dependence and CP-odd admixtures is useful. The paper is also unusually candid about its limitations—Section 4 explicitly says two-loop thresholds are unknown for complex parameters in DR, and the omission of tanβ resummation is stated.\n\nThe technical core looks sound. The one-loop matching formulas are given in detail and agree with Ref. [92] up to gauge terms; the RGEs are checked against Ref. [106]; the interpolation method (d) is cross-checked against the 2HDM and SM limits. The three pole-mass options are sensible, and the authors explain when each is applicable. The qualitative results—phase dependence of several GeV at low tanβ, and a CP-odd admixture that drops below 0.5% for MH+ above about 260 GeV in the benchmark—are likely robust.\n\nThe soft spot is the quantitative headline. The 20 GeV phase dependence shown in Fig. 5b is calculated at |A|=|µ|=3Ms, where the one-loop box corrections to the quartic couplings are comparable to their tree-level values. The CP-violating couplings λ5-λ7 are loop-induced and receive exactly these large A-dependent terms, so the phase sensitivity is driven by a threshold correction that is not parametrically small. With two-loop thresholds omitted and no uncertainty estimate given, a shift of several GeV in mh is plausible. The authors do not overclaim—they say \"sizeable\" and \"couple of GeV\"—but the specific numbers in Fig. 5b should be treated as uncontrolled until the missing pieces are estimated.\n\nThe remaining issues are minor. The non-iteration of the 125.15 GeV input in footnote 6 is acceptable. The tanβ≤20 restriction is conservative. No code or external benchmark against existing public tools is provided, which makes independent verification harder.\n\nThis paper deserves a serious referee and probably a conditional accept. I would ask for an uncertainty estimate, a benchmark at a less extreme |A|/Ms, and a comparison with FeynHiggs or FlexibleSUSY in the real-parameter limit. It will be useful for people working on MSSM Higgs EFT and CP violation in the Higgs sector.","headline":"A careful, honest NLL EFT calculation of the complex MSSM Higgs sector that is new in combination, but the headline 20 GeV phase effect sits on large one-loop thresholds with no two-loop control.","tokens_in":31778,"tokens_out":2700,"would_cite":true,"duration_ms":159731,"reading_group":"yes","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"This paper predicts that, in the MSSM with heavy superpartners and complex phases, the lightest Higgs mass swings by almost 20 GeV when the trilinear phase varies, while the CP-odd admixture falls below 0.5% for charged Higgs masses above…","keywords":["MSSM Higgs mass","CP violation","complex phases","two-Higgs-doublet model","effective field theory","two-loop RGEs","next-to-leading logarithms","CP-odd admixture"],"falsifier":"Compute the missing two-loop threshold corrections for the complex MSSM in the same scheme and re-evaluate $m_h$ as a function of $\\phi_A$ at $\\tan\\beta = 5$ and $|A| = |\\mu| = 3M_s$; if the almost-20 GeV swing collapses to below the few-GeV level, the central claim would be refuted, and on the experimental side an HL-LHC measurement of the tau-Yukawa CP angle $\\phi_\\tau$ would decide whether the predicted admixture near $\\phi_\\tau \\simeq 4^\\circ$ for $M_{H^\\pm} \\sim 500$ GeV is present or excluded.","tokens_in":30652,"feed_emoji":"⚛️","tokens_out":14139,"duration_ms":121688,"temperature":0.7,"pith_summary":"The paper sets out to predict the Higgs sector of the Minimal Supersymmetric Standard Model (MSSM) in the regime where all superpartners are heavy, the two Higgs doublets are light, and the MSSM parameters can be complex. Its central result is that the phase of the common trilinear coupling, $\\phi_A$, is not a minor detail: at $\\tan\\beta = 5$ and $|A| = |\\mu| = 3M_s$, varying $\\phi_A$ moves the predicted lightest-Higgs mass by almost 20 GeV, and even at $\\tan\\beta = 20$ the shift reaches about 5 GeV. The calculation carries this through a one-loop matching of the MSSM onto a type-III two-Higgs-doublet effective theory at the SUSY scale, followed by two-loop renormalization-group running that keeps all complex phases, so that next-to-leading logarithms of the heavy scale are resummed. A second finding is that the CP-odd admixture of the lightest Higgs boson falls below half a percent once the charged Higgs mass exceeds roughly 260 GeV in the studied scenario. The paper matters because it delimits how much CP violation from the heavy SUSY sector can survive in the 125 GeV Higgs boson and how strongly the Higgs-mass prediction depends on the unknown phases.","feed_headline":"CP phase swings MSSM Higgs mass by up to 20 GeV","feed_subtitle":"Complex-phase two-loop running predicts GeV-size phase effects and a tiny CP-odd component for heavy charged Higgs.","key_machinery":"The load-bearing object is the effective-field-theory chain from the MSSM to a low-energy type-III two-Higgs-doublet model, i.e. a two-Higgs-doublet model in which both doublets couple to up- and down-type fermions. At the SUSY scale $M_s$, one-loop matching produces complex quartic couplings $\\lambda_5,\\lambda_6,\\lambda_7$ and 'wrong'-Yukawa couplings $h'_t,h'_b$ from box, triangle, and wave-function-renormalization diagrams; the field redefinition in Eq. (30) ensures canonically normalized kinetic terms. The two-loop RGEs for the 2HDM carry all phases, and the 'top-down' iterative solution fixes the high-scale MSSM couplings so that SM couplings match their measured values at $M_t$. The pole masses are then computed by one of three methods: (a) one-loop-corrected 2HDM mass matrix at $M_{H^\\pm}$, (b) the same at $m_t$, (c) matching to the SM and evaluating a SM pole mass for large $M_{H^\\pm}$. The default option (d) adds $\\gamma_{\\mathrm{resum}}$ to the (1,1), (1,2), and (2,2) entries of the Higgs-basis mass matrix before rotating back, resumming $\\ln(M_{H^\\pm}/m_t)$ while retaining the full 2HDM mixing information; this is the mechanism that produces the quoted interpolated masses and the CP-odd admixtures.","core_discovery":"In the paper's own terms, the claim being established is an extension of existing heavy-SUSY Higgs predictions to include CP violation: after one-loop matching of the complex MSSM to a type-III two-Higgs-doublet model and two-loop phase-keeping RGE evolution, the phase $\\phi_A$ of the common trilinear coupling is a controlling parameter for the spectrum. For $\\tan\\beta = 5$ and $|A| = |\\mu| = 3M_s$, $m_h$ changes by almost 20 GeV as $\\phi_A$ runs from $0$ to $360^\\circ$; at $\\tan\\beta = 20$ the variation shrinks to about 5 GeV, and the sign of the effect depends on the ratio $|A|/M_s$. The gluino phase $\\phi_{M_3}$ moves $m_h$ by at most about 1.3 GeV, while the heavy neutral Higgs masses shift by roughly 3.5 GeV ($H_2$) and 1.5 GeV ($H_3$) with $\\phi_A$, and their CP-odd content is exchanged between the two states. The CP-odd component of the lightest Higgs is computed from the mixing matrix in the rotated basis; it is maximal near $\\phi_A \\approx 120^\\circ$ and drops below 0.5% already for $M_{H^\\pm} \\simeq 260$ GeV in the benchmark scenario. The paper also claims that the interpolating pole-mass approximation, which adds the resummed correction $\\gamma_{\\mathrm{resum}} = v^2(m_t)\\lambda_{\\rm SM}(m_t) - v^2(M_{H^\\pm})\\lambda_{\\rm SM}(M_{H^\\pm})$ to the Higgs-basis mass matrix, agrees well with the pure 2HDM determination at small $M_{H^\\pm}$ and with the decoupled-SM determination at large $M_{H^\\pm}$, making it a reliable default.","pith_inferences":["Editorial inference: the missing two-loop thresholds are the main caveat; if they are approximately phase-independent, the quoted differences—like the 20 GeV swing—survive, but if they are phase-sensitive they could either enhance or erase the effect.","Editorial inference: the low-scale phases of $\\lambda_5,\\lambda_6,\\lambda_7$ generated by complex RGE running feed directly into electric-dipole-moment predictions, so the same calculation provides a route to map which high-scale CP phases are experimentally allowed; the paper explicitly leaves this EDM check for future work.","Editorial inference: combining the fast drop of the CP-odd component with LHC bounds on low $M_{H^\\pm}$ and high $\\tan\\beta$ suggests that a measurably CP-violating 125 GeV Higgs in this heavy-SUSY setup would require a low charged-Higgs mass or a smaller $M_s$ than the 30 TeV benchmark; an HL-LHC $\\tau\\tau$ measurement could test this directly.","Editorial inference: a natural testable extension is to recompute the benchmark with the missing two-loop thresholds and $\\tan\\beta$ resummation included, or to port the same matching-and-running machinery to the next-to-minimal supersymmetric standard model, and check whether the phase swing remains of order several GeV."],"forward_implications":["At $\\tan\\beta = 5$ with $|A| = |\\mu| = 3M_s$, the phase $\\phi_A$ changes the predicted lightest-Higgs mass by almost 20 GeV, so fixed-phase scans miss a controlling parameter of the heavy-SUSY Higgs sector.","The same phase dependence shrinks to about 5 GeV at $\\tan\\beta = 20$, and its sign depends on $|A|/M_s$, meaning that the CP-phase correction cannot be absorbed into a universal shift.","The gluino phase $\\phi_{M_3}$ shifts $m_h$ by at most about 1.3 GeV in the considered scenarios, so it is a subleading source of CP-driven mass uncertainty.","For the heavy neutral Higgs bosons, $\\phi_A$ moves $m_{H_2}$ by about 3.5 GeV and $m_{H_3}$ by about 1.5 GeV, and the two states exchange their CP-odd character as $\\phi_A$ varies, with only weak dependence on $M_{H^\\pm}$.","The CP-odd component of the lightest Higgs falls below 0.5% once $M_{H^\\pm} \\gtrsim 260$ GeV in the benchmark scenario, so for the experimentally preferred $M_{H^\\pm} \\geq 500$ GeV the predicted admixture is just below the expected LHC reach of roughly $\\phi_\\tau \\simeq 4^\\circ$."],"supporting_citations":[{"why":"Supplies the two-Higgs-doublet effective-field-theory setup for heavy supersymmetry with an intermediate charged-Higgs scale that this work extends to complex phases.","marker":"[67]"},{"why":"Provides the earlier one-loop complex threshold results for heavy MSSM Higgs scenarios; the paper's thresholds agree with these up to gauge contributions to the quartic couplings.","marker":"[92]"},{"why":"Supplies the matching conditions and the wave-function/mixing-angle prescription used to keep the kinetic terms canonical.","marker":"[77]"},{"why":"Found that the lightest-Higgs CP-odd component drops rapidly with increasing heavy-Higgs mass, the behaviour this paper maps in detail.","marker":"[91]"},{"why":"Sets the high-luminosity LHC sensitivity to the tau-Yukawa CP angle used to judge observability of the predicted admixture.","marker":"[120]"},{"why":"Supplies the Standard-Model input parameters and running conventions used to fix the low-scale boundary conditions.","marker":"[110]"},{"why":"Provides the real-case gauge contributions to the quartic couplings that complete the complex one-loop matching conditions.","marker":"[61]"}],"fun_headline_variants":["CP phase shifts MSSM Higgs mass by up to 20 GeV","Two-loop CP effects move Higgs mass by 20 GeV","Complex phase controls MSSM Higgs mass variation","MSSM Higgs mass swings 20 GeV with CP phase"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the omitted two-loop threshold corrections—which are not yet available for complex MSSM parameters in the dimensional-reduction scheme—are small enough not to change the quoted GeV-level phase dependence; the paper does not estimate their size.","fun_headline_variants_meta":{"raw":{"variants":["CP phase shifts MSSM Higgs mass by up to 20 GeV","Two-loop CP effects move Higgs mass by 20 GeV","Complex phase controls MSSM Higgs mass variation","MSSM Higgs mass swings 20 GeV with CP phase"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000577,"raw_usage":{"total_tokens":2831,"prompt_tokens":1162,"completion_tokens":1669,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":778,"completion_tokens_details":{"reasoning_tokens":1602}},"tokens_in":778,"tokens_out":1669,"duration_ms":12018,"temperature":1.0,"reasoning_tokens":1602,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T05:39:01.418009+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Compute the missing two-loop threshold corrections for the complex MSSM in the same scheme and re-evaluate $m_h$ as a function of $\\phi_A$ at $\\tan\\beta = 5$ and $|A| = |\\mu| = 3M_s$; if the almost-20 GeV swing collapses to below the few-GeV level, the central claim would be refuted, and on the experimental side an HL-LHC measurement of the tau-Yukawa CP angle $\\phi_\\tau$ would decide whether the predicted admixture near $\\phi_\\tau \\simeq 4^\\circ$ for $M_{H^\\pm} \\sim 500$ GeV is present or excluded.","supporting_citations":[{"cited_title":"Higgs Bosons in Heavy Supersymmetry with an Intermediate $m_A$","cited_arxiv_id":"1508.00576","evidence_quote":"Supplies the two-Higgs-doublet effective-field-theory setup for heavy supersymmetry with an intermediate charged-Higgs scale that this work extends to complex phases."},{"cited_title":"Precise prediction of the MSSM Higgs boson masses for low MA","cited_arxiv_id":"1805.00867","evidence_quote":"Supplies the matching conditions and the wave-function/mixing-angle prescription used to keep the kinetic terms canonical."},{"cited_title":"CP-odd component of the lightest neutral Higgs boson in the MSSM","cited_arxiv_id":"1502.02210","evidence_quote":"Found that the lightest-Higgs CP-odd component drops rapidly with increasing heavy-Higgs mass, the behaviour this paper maps in detail."}],"review_version":1}