{"id":"9720a92c-8bda-470f-ae31-57203864283a","arxiv_id":"1908.01274","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"Excited nS and nP heavy quarkonium states contribute tens of percent of the ground-state rate in Higgs semi-exclusive decays, and summing them yields widths of 25.1 keV for Bc-like mesons, 3.23 keV for charmonium, and 2.36 keV for bottomonium.","lead":"This paper calculates how often the Higgs boson decays into a heavy quark-antiquark bound state plus a free quark pair, including excited states of the bound state. The authors find that excited states add large, previously neglected contributions that should be included when measuring Higgs couplings to charm and bottom quarks.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Eqs. (27)-(29) silently assign a 100% cascade branching fraction to every nS/nP state; above open-flavor thresholds charmonium and bottomonium decays bypass the 1S ground state, so the headline widths are upper bounds rather than predictions.","rationale":"The central qualitative result - that high nS/nP Fock states are produced with rates comparable to tens of percent of the 1S ground-state channel - is a standard NRQCD leading-order statement and is supported by the analogous W/Z/t studies cited in the introduction. I do not object to that claim. The load-bearing weakness is the conversion of those production widths into a ground-state width by assuming unit cascade efficiency. The manuscript is unusually honest in writing the conditional, but the abstract's headline numbers and the HE-LHC event yields are quoted without the 'if', and for charmonium/bottomonium the assumption is strongly false for the higher states included in the sum. The reader's weakest assumption identifies exactly this point, so I agree. I also checked the internal consistency: Table IV's [1S] and [1P] entries (14.16 keV, 2.207 keV) do not match the sums from Table I (13.59 keV, 1.48 keV), which makes even the upper-bound sum not fully reproducible; fixing this should accompany the reframing. Neither issue changes the qualitative claim, so the reader's CONDITIONAL verdict remains appropriate.","tokens_in":17273,"tokens_out":8715,"duration_ms":99521,"concrete_test":"Replace the implicit Br=1 in Eqs. (27)-(29) with empirical branching fractions: compute Gamma_eff = sum_n Gamma_prod(n) * Br(n -> ground 1S0) using PDG values for charmonium and bottomonium and potential-model E1/hadronic rates for B_c (or a conservative upper bound). If the charmonium/bottomonium effective widths drop by more than a factor of two, the headline values should be labeled as an upper-bound scenario and the event rates rescaled.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Equations (27)-(29) are not direct widths for producing |(Q Qbar')[1 1S0]>; they are the sums of the production widths for all n1S0, n3S1, n1P1 and n3PJ states with an implicit branching ratio Br([n] -> ground) = 1 for every state. The Conclusions do flag this with 'if almost all ... decay to the ground spin-singlet state', but the Abstract and the event-rate paragraph quote the summed numbers as the widths without repeating the caveat. The physical assumption fails for a large part of the sum: psi(4040), psi(4415) and Upsilon(4S) are above open-flavor threshold and decay predominantly to D/Dbar or B/Bbar, not to the 1S ground state; even psi(2S) and Upsilon(2S) have ground-state branching fractions well below unity. Hence the 25.10, 3.23 and 2.36 keV numbers and the 1.4e7, 1.7e6, 1.3e6 event estimates built on them are upper-bound estimates. The separate qualitative claim that the excited states themselves are produced at sizable rates is not affected by this concern.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper presents a leading-order NRQCD calculation of the semi-exclusive Higgs decay channels H^0 -> |(Q Qbar')[n]> + Qbar Q' for Q,Q' = c,b, considering nS and nP Fock states with n = 1,...,4 and all relevant spin and total-angular-momentum configurations. The authors compute partial widths for |(b cbar)[n]>, |(c cbar)[n]>, and |(b bbar)[n]> production, provide differential distributions in invariant masses and angles, and investigate the sensitivity of the summed widths to five non-perturbative potential models. Their headline results, assuming that all excited Fock states cascade to the ground spin-singlet 1S state, are 25.10 keV for |(b cbar)[n]>, 3.23 keV for |(c cbar)[n]>, and 2.36 keV for |(b bbar)[n]>, with corresponding event-rate estimates at the HE-LHC. The main claim is that high excited Fock states contribute sizably and should be included in studies of Higgs couplings to heavy quarks.","tokens_in":17537,"tokens_out":5958,"duration_ms":62187,"significance":"If the results are correct, the paper provides a useful systematic extension of NRQCD calculations for Higgs semi-exclusive decays to excited quarkonia, complementing direct searches such as H -> J/psi gamma and H -> Upsilon(nS) gamma. The inclusion of excited nS and nP states and the differential distributions are valuable for future Higgs factories and high-energy LHC studies. The paper is transparent in separating perturbative short-distance coefficients from non-perturbative matrix elements, and it compares five potential models. The independent qualitative point that excited quarkonium Fock states are produced at rates comparable to the 1S state is plausible and not affected by the concerns below. However, the numerical inconsistency in the central table and the implicit 100% cascade assumption must be resolved before the quantitative claims can be taken at face value.","major_comments":[{"comment":"There is an internal numerical inconsistency in the central results for the |(b cbar)[n]> channel. Table I gives Gamma(H -> |(b cbar)[1S0]> + cbar b) = 5.736 keV and Gamma(H -> |(b cbar)[3S1]> + cbar b) = 7.857 keV, so the [1S] sum is 13.593 keV; the corresponding [1P] sum from Table I is 0.2761 + 0.1838 + 0.6706 + 0.3521 = 1.483 keV. Table IV, however, lists [1S] = 14.16 keV and [1P] = 2.207 keV. The other n entries in Table IV match Table I, so this is not a rounding issue. Consequently, the sum of the Table I entries is 23.81 keV, not the 25.10 keV quoted in Eq. (27), Table IV, the uncertainty range, and the event-rate estimate of 1.4e7 events in Sections III.B and IV. The authors must reconcile Table I with Table IV and recompute all quantities that depend on the summed width.","section":"III.B, Tables I and IV"},{"comment":"The sums in Eqs. (27)-(29) implicitly assign a 100% branching fraction for each excited nS and nP state to decay to the ground spin-singlet state |(Q Qbar')[1 1S0]>. This assumption is stated conditionally in the abstract and conclusions, but the widths and the event rates quoted in Section III.B and IV are presented without the caveat. For charmonium and bottomonium the assumption is strongly violated: states such as psi(4040), psi(4415), and Upsilon(4S) are above open-flavor threshold and decay predominantly to D/Dbar or B/Bbar, while even psi(2S) and Upsilon(2S) have ground-state branching fractions well below unity. The quoted 25.10 keV, 3.23 keV, and 2.36 keV numbers, and the corresponding event estimates of 1.4e7, 1.7e6, and 1.3e6, are therefore upper bounds rather than predictions for observable ground-state quarkonium production. The qualitative statement that excited states are produced at sizable rates is unaffected, but the paper should either compute or model realistic cascade efficiencies, or explicitly relabel the summed widths and event rates as upper bounds.","section":"III.B (Eqs. (27)-(29)) and IV"}],"minor_comments":[{"comment":"The abstract contains the phrase \"non-perturbative hadronic non-perturbative matrix elements\" with a duplicated word, and the sentence beginning \"In addition to the lower-level Fock states ... continent\" has an apparent typo (“continent” should likely be “contributions”).","section":"Abstract"},{"comment":"The caption for Fig. 4 lists the lines as “|(b cbar)[2S]>” while the figure shows bottomonium states; this should read “|(b bbar)[2S]>”.","section":"Figure 4 caption"},{"comment":"There are minor typographical errors: “charmonium” appears as “charmonim” in Section III.C, and “proposed” appears as “purposed” in the Conclusions.","section":"III.C and IV"},{"comment":"The notation [n] is overloaded: in Tables I-III it denotes individual spin states, while in Tables IV-VI and Eqs. (27)-(29) it denotes sums over all nS and nP states. The text defines this usage, but a more explicit notation such as [nS] and [nP] would improve readability.","section":"II and III.A"}],"recommendation":"major_revision","confidential_remarks":"The numerical inconsistency between Table I and Table IV for the |(b cbar)[n]> channel is the most serious issue and must be corrected before the paper can be considered for publication. The cascade-branching concern also needs to be addressed explicitly, either by including realistic branching fractions or by presenting the summed widths as upper bounds. The underlying NRQCD calculation is standard, and the qualitative point about sizable excited-state production is likely salvageable."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the quick take: this is a straightforward NRQCD leading-order extension of the authors' previous ground-state Higgs-to-quarkonium calculations to nS and nP states up to n=4, for bc, cc, and bb. The new content is the set of production widths and differential distributions for those excited Fock states, plus a five-potential-model uncertainty scan. The qualitative result—that excited states contribute tens of percent of the ground-state rate, and in some cases more—is credible and consistent with their earlier W, Z, and top-quark studies. That part is solid and worth having on record.\n\nThe soft spots are real but patchable. First, Table IV is internally inconsistent with Table I for (b cbar): the n=1 [1S] entry is 14.16 keV in Table IV but 13.593 keV from Table I, and [1P] is 2.207 vs 1.483. The headline 25.10 keV total inherits this discrepancy; using Table I the bc total would be about 23.8 keV. The authors need to find which table is right and quote consistent numbers in the abstract and conclusions.\n\nSecond, the stress-test point is on target. Equations (27)–(29) sum production widths for all n1S0, n3S1, n1P1, and n3PJ states and implicitly take Br(state -> ground 1S0) = 1. The abstract and conclusions do flag the 'if all excited states decay to ground' condition, but the event-rate numbers (1.4e7, 1.7e6, 1.3e6) are quoted right after without repeating the caveat. Above open-flavor threshold, states like psi(4040), psi(4415), and Upsilon(4S) decay dominantly to D/Dbar or B/Bbar, not to the ground state; even the 2S states have ground-state branching fractions well below unity. So the summed widths and the event rates built on them are upper bounds, not central predictions. The paper should say that explicitly.\n\nThe potential-model uncertainties (the +0%/-51.6%, etc.) are honestly presented, though they only cover one source of uncertainty; alpha_s and quark masses are fixed, and the leading-order nature is stated. Not a big deal for this kind of paper.\n\nThe citation pattern is fine; using their earlier wave-function paper [35] is standard practice, and the self-citations are to prior calculations they are extending, not a red flag.\n\nBottom line: the qualitative message survives—excited states matter for Higgs-to-quarkonium channels. But the specific numbers need a correction and a more careful upper-bound framing. I'd send it to peer review with a request for those fixes. It's a legitimate calculation, not a desk reject.","headline":"A useful but imperfect extension of the authors' own ground-state NRQCD calculations; the excited-state contributions are plausibly sizable, but the headline numbers are compromised by a table inconsistency and an unstated upper-bound assumption.","tokens_in":18108,"tokens_out":3095,"would_cite":false,"duration_ms":30719,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":["12.38.Bx","14.40.Gx","14.80.Bn"],"model":"deepseek-v4-flash","headline":"Excited quarkonium Fock states contribute sizably to Higgs decays, summing to 25.10 keV for Bc-like mesons, 3.23 keV for charmonium, and 2.36 keV for bottomonium.","keywords":["Higgs boson decays","heavy quarkonium","NRQCD","excited Fock states","B_c meson","charmonium","bottomonium","HE-LHC"],"falsifier":"Measure the inclusive $J/\\psi$ and $\\Upsilon$ yields from Higgs decays at a high-luminosity Higgs factory; if the observed yield is substantially below the predicted summed widths of 3.23 keV (charmonium) and 2.36 keV (bottomonium), the cascade assumption would fail. The same test could be sharpened by measuring the cascade branching fractions of the $2S$, $3S$, $4S$, $1P$, $2P$, $3P$, and $4P$ states into the ground $1S$ state: a product well below unity would directly invalidate the summed-width claim.","tokens_in":17005,"feed_emoji":"⚛️","tokens_out":8946,"duration_ms":82757,"temperature":0.7,"pith_summary":"The paper asks whether Higgs boson decays into a heavy quark pair produce quarkonium mesons mostly in the ground state or also in excited nS and nP Fock states. Using the NRQCD factorization framework, it computes the semi-exclusive decay channels $H^0\\to |(Q\\bar{Q}')[n]\\rangle + \\bar{Q}Q'$ for $Q=c$ or $b$ and finds that the excited states contribute tens of percent of the ground-state width: for charmonium, the $2S$, $3S$, $4S$, $1P$, $2P$, $3P$, and $4P$ states add up to about 47%, 32%, 25%, 24%, 12%, 15%, and 16% respectively. Summing all states and assuming they cascade to the ground $1\\,^1S_0$ state, the total widths are 25.10 keV for $(b\\bar{c})$, 3.23 keV for $(c\\bar{c})$, and 2.36 keV for $(b\\bar{b})$, with uncertainties from five potential models. If correct, these sizable excited-state contributions mean future Higgs factories and the 27 TeV LHC should search for quarkonia in these channels and include the excited states in coupling measurements.","feed_headline":"Excited quarkonia add up to 25 keV to Higgs decay width","feed_subtitle":"If excited states cascade to the ground state, Higgs decays yield millions of quarkonium events at a 27 TeV LHC.","key_machinery":"The central machinery is NRQCD factorization, which splits each decay width into a perturbative short-distance coefficient $\\hat\\Gamma(H^0 \\to |(Q\\bar{Q}')[n]\\rangle + \\bar{Q}Q')$ and a non-perturbative vacuum matrix element; the color-singlet matrix elements are identified with the radial wave function at the origin for $nS$ states and its first derivative at the origin for $nP$ states. To handle the lengthy amplitudes for massive final-state particles, especially the $P$-wave projectors, the paper uses the 'improved trace technology,' which manipulates Dirac traces at the amplitude level, and it evaluates the wave-function inputs under five potential models (BT, Richardson, Igi-Ono, Chen-Kuang, and Cornell) to quantify theoretical uncertainty.","core_discovery":"Within the NRQCD factorization framework, the paper computes the semi-exclusive Higgs decay channels $H^0 \\to |(Q\\bar{Q}')[n]\\rangle + \\bar{Q}Q'$ for $Q^{(\\prime)}=c$ or $b$ and for quarkonium Fock states $n\\,^{1}S_0$, $n\\,^{3}S_1$, $n\\,^{1}P_1$, and $n\\,^{3}P_J$ with $n=1,2,3,4$. It finds that the high excited $nS$ and $nP$ states contribute sizably relative to the ground $1S$ state: for charmonium, for example, the $2S$, $3S$, $4S$, $1P$, $2P$, $3P$, and $4P$ widths are about 47%, 32%, 25%, 24%, 12%, 15%, and 16% of the $1S$ width, and similar or larger ratios hold for bottomonium. Summing all these Fock states and assuming they cascade to the ground spin-singlet state through electromagnetic or hadronic interactions, the total decay widths are $25.10^{+11.6\\%}_{-51.6\\%}$ keV for $|(b\\bar{c})[n]\\rangle$, $3.23^{+0\\%}_{-62.2\\%}$ keV for $|(c\\bar{c})[n]\\rangle$, and $2.36^{+0\\%}_{-57.1\\%}$ keV for $|(b\\bar{b})[n]\\rangle$, with uncertainties from five non-perturbative potential models. The paper concludes that the high excited Fock states should be taken seriously in Higgs-to-quarkonium studies and estimates that at the HE-LHC ($\\sqrt{s}=27$ TeV, 15 ab$^{-1}$) about $1.4\\times10^7$ $(b\\bar{c})$, $1.7\\times10^6$ $(c\\bar{c})$, and $1.3\\times10^6$ $(b\\bar{b})$ quarkonium events could be produced through Higgs decays.","pith_inferences":["If the cascade assumption is confirmed, the charmonium channel could provide a comparatively clean probe of the Higgs-charm Yukawa coupling, since the quarkonium-plus-two-jets final state is more distinctive than inclusive $H\\to c\\bar c$.","The same excited-state summation could be applied to other rare Higgs decays, such as $H\\to Z+$ quarkonium or $H\\to\\gamma+$ quarkonium, where higher Fock states may also boost the predicted rates.","The 50–60% spread across potential models suggests that lattice-QCD determinations of the relevant radial wave functions and derivatives would be the most direct way to sharpen these predictions."],"forward_implications":["Excited $nS$ and $nP$ Fock states should be included in NRQCD predictions for quarkonium production in Higgs decays; their contributions are tens of percent of the ground-state width, not negligible.","Adding all states that cascade to the ground $1\\,^1S_0$ state gives total widths of 25.10 keV for $(b\\bar{c})$, 3.23 keV for $(c\\bar{c})$, and 2.36 keV for $(b\\bar{b})$.","Event-rate estimates at the HE-LHC (27 TeV, 15 ab$^{-1}$) yield about $1.4\\times10^7$, $1.7\\times10^6$, and $1.3\\times10^6$ events for $(b\\bar{c})$, $(c\\bar{c})$, and $(b\\bar{b})$ quarkonia from Higgs decays, making these channels experimentally searchable.","The differential distributions $d\\Gamma/ds_1$, $d\\Gamma/ds_2$, $d\\Gamma/d\\cos\\theta_{12}$, and $d\\Gamma/d\\cos\\theta_{23}$ show the excited states contribute throughout the phase space, so kinematic cuts for background rejection will not remove their contribution."],"supporting_citations":[{"why":"Establishes the NRQCD factorization formalism that separates short-distance coefficients from non-perturbative matrix elements.","marker":"[28]"},{"why":"Supplies the radial wave functions and their derivatives for nS and nP quarkonium states under the five potential models used in the numerical evaluation.","marker":"[35]"},{"why":"Provides the earlier calculation of B_c meson production in Higgs decays, the baseline whose leading-order 1S results the present work reproduces.","marker":"[32]"},{"why":"Gives the previous study of P-wave and color-octet configurations in the same Higgs semi-exclusive channels, which the present work extends to high excited states.","marker":"[33]"},{"why":"Introduces the improved trace technology used to derive compact analytic amplitudes for massive final-state particles, especially the P-wave projectors.","marker":"[37]"},{"why":"Defines the BT potential model, the default potential whose wave functions give the central-value decay widths.","marker":"[46]"},{"why":"Provides the 27 TeV gluon-fusion Higgs production cross section of 151.6 pb used for the event-rate estimates.","marker":"[6]"}],"fun_headline_variants":["Excited quarkonia add up to 25 keV to Higgs width","High nS and nP quarkonia in Higgs decay yield 25 keV","Excited quarkonia from Higgs: millions at 27 TeV LHC","Excited quarkonia cascade to ground, widening Higgs to 25 keV","Up to 25 keV from Higgs to excited quarkonium"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The headline summed widths assume that almost all high excited quarkonium Fock states decay, electromagnetically or hadronically, all the way down to the ground spin-singlet $|(Q\\bar{Q}')[1\\,^1S_0]\\rangle$ state; if that cascade efficiency is noticeably below one, the summed numbers are upper limits rather than predictions.","fun_headline_variants_meta":{"raw":{"variants":["Excited quarkonia add up to 25 keV to Higgs width","High nS and nP quarkonia in Higgs decay yield 25 keV","Excited quarkonia from Higgs: millions at 27 TeV LHC","Excited quarkonia cascade to ground, widening Higgs to 25 keV","Up to 25 keV from Higgs to excited quarkonium"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001518,"raw_usage":{"total_tokens":6349,"prompt_tokens":1479,"completion_tokens":4870,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":1095,"completion_tokens_details":{"reasoning_tokens":4776}},"tokens_in":1095,"tokens_out":4870,"duration_ms":39921,"temperature":1.0,"reasoning_tokens":4776,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-14T15:18:00.180613+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Measure the inclusive $J/\\psi$ and $\\Upsilon$ yields from Higgs decays at a high-luminosity Higgs factory; if the observed yield is substantially below the predicted summed widths of 3.23 keV (charmonium) and 2.36 keV (bottomonium), the cascade assumption would fail. The same test could be sharpened by measuring the cascade branching fractions of the $2S$, $3S$, $4S$, $1P$, $2P$, $3P$, and $4P$ states into the ground $1S$ state: a product well below unity would directly invalidate the summed-width claim.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Establishes the NRQCD factorization formalism that separates short-distance coefficients from non-perturbative matrix elements."},{"cited_title":"Jiang and C","cited_arxiv_id":null,"evidence_quote":"Provides the earlier calculation of B_c meson production in Higgs decays, the baseline whose leading-order 1S results the present work reproduces."},{"cited_title":"improved trace technology","cited_arxiv_id":null,"evidence_quote":"Gives the previous study of P-wave and color-octet configurations in the same Higgs semi-exclusive channels, which the present work extends to high excited states."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Introduces the improved trace technology used to derive compact analytic amplitudes for massive final-state particles, especially the P-wave projectors."}],"review_version":1}