{"id":"a215880d-a01a-4c2d-990d-fc2641414372","arxiv_id":"2412.10549","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":6.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"New TQHL1.1 and TQ4Q1.1 fragmentation functions for doubly and fully bottomed tetraquarks are constructed and evolved, yielding first predictions for bottom-tetraquark plus jet distributions at 14 and 100 TeV.","lead":"The authors build new sets of collinear fragmentation functions that describe how a single quark or gluon turns into hypothetical bottom-containing tetraquarks, and they use them to predict tetraquark-plus-jet rates at the LHC and a future 100 TeV collider. The results give experimentalists concrete, NLL/NLO+ resummed cross sections to search for these exotic states.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The T4b predictions inherit their absolute normalization from the unvalidated Eq. (21) LDME Ansatz; its 9th-power sensitivity means a plausible model or lattice correction shifts all T4b rates by orders of magnitude.","rationale":"I read the paper as constructing two model-based VFNS FF families and using them in an established NLL/NLO+ framework to make exploratory predictions. The central claim that the FFs supersede earlier versions is credible as a technical upgrade: the TQHL1.1 normalization is fixed algebraically, and the TQ4Q1.1 quark channel switches from Suzuki to NRQCD inputs. The public LHAPDF release and the JETHAD implementation are concrete independent assets, and the internal structure, including threshold-consistent DGLAP evolution, the EDevo/AOevo split, and linearity in LDMEs, is coherent. The single load-bearing weakness is the T4b normalization: Eq. (21) is a dimensional-analysis extrapolation from T4c with no external anchor. Because Eq. (10) is linear in LDMEs, all T4b predictions in Sec. 4 inherit any error in that ratio, and the ninth power amplifies uncertainties in the input scale choices. This is not merely a disagreement with current consensus; it is a missing validation of an input the paper itself labels an Ansatz. The reader's conditional verdict is therefore appropriate. My recommendation is UNCHANGED: the concern does not call for rejection, but it does require the stated check before the T4b numbers are promoted from model guidance to search benchmarks.","tokens_in":57814,"tokens_out":6658,"duration_ms":65109,"concrete_test":"Recompute the four T4b LDMEs entering Eq. (10) by solving the same Cornell-potential four-body Schrödinger equation used to obtain Eq. (20), with m_b = 4.9 GeV and α_s evaluated at the b-quark Coulomb scale. Compare the resulting ratios ⟨O_T4b⟩/⟨O_T4c⟩ for each [n] channel to Eq. (21). If any ratio deviates by more than 20%, propagate the corrected values through Eq. (10), re-evolve, and rerun the T4b+jet distributions; if the integrated rates shift by more than 50%, the reported absolute predictions are not robust. A minimal interim check is to recompute Eq. (21) with two or three plausible α_s(m_b v_b)/α_s(m_c v_c) choices and quote the spread of the ninth power.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central new physical predictions for fully bottomed tetraquarks (Figs. 13, 16, 17) are not independently normalized. The TQ4Q1.1 T4b FFs are built from T4c LDMEs, Eq. (20), rescaled by Eq. (21), which assumes color-Coulomb binding and replaces m_c α_s^(c) with m_b α_s^(b) in a four-body wave-function-at-origin ratio, quoting a value of 400. Three properties make this the load-bearing point. First, Eq. (10) is linear in each LDME, so any error in the ratio enters the FF and all T4b cross sections linearly, per color channel. Second, Eq. (21) is an input raised to the ninth power: a 15% change in (m_b α_s^(b))/(m_c α_s^(c)), from 1.8 to 2.07, changes the ratio by roughly a factor of 2.6, and the paper does not state which values of α_s, scales, or velocities produce the number 400. Third, there is no anchor: Sec. 2.3.2 explicitly says exact T4b LDMEs have not been computed yet, and no lattice QCD, data, or independent potential-model calculation is used to check Eq. (21). The paper itself labels it \"a reasonable Ansatz.\" The T4c LDMEs also carry model dependence (three potential models are listed in Ref. [104]; only one is used), and that uncertainty is not propagated to T4b either. This is not an internal inconsistency, and the public LHAPDF release is a real asset; however, until Eq. (21) is checked, the absolute normalization of every T4b prediction in Sec. 4 is a model extrapolation rather than a benchmark.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper constructs two new families of DGLAP-evolving, VFNS collinear fragmentation functions for tetraquark production: TQHL1.1, describing the fragmentation of a heavy quark into a doubly heavy tetraquark X_{Q\\bar Q q\\bar q} via an improved Suzuki model, and TQ4Q1.1, describing the fragmentation of a gluon or heavy quark into a fully heavy tetraquark T_{4Q} via potential-NRQCD short-distance coefficients and long-distance matrix elements. These FFs are evolved with DGLAP/HF-NRevo and released in LHAPDF format. Using the NLL/NLO+ hybrid factorization implemented in (sym)JETHAD, the authors provide predictions for rapidity-interval and transverse-momentum distributions for bottomoniumlike-state-plus-jet production at 14 TeV LHC and 100 TeV FCC. The central claim is that these FF sets provide usable leading-power, factorized predictions for future searches, superseding the earlier 1.0 versions.","tokens_in":58283,"tokens_out":4658,"duration_ms":44840,"significance":"If the underlying model inputs are accepted, the paper makes a useful and concrete contribution: it provides public, DGLAP-evolved VFNS FFs for doubly and fully bottomed tetraquarks, with transparent symbolic computations through symJETHAD and numerical results through JETHAD. The phenomenology extends the group's established program on high-energy resummation to the exotic bottom sector, and the LHAPDF release is a genuine asset for future experimental and theoretical work. The main scientific value lies in the predictions for tetraquark-plus-jet rates at LHC/FCC energies, which are falsifiable once data on these hypothetical states become available. However, the absolute normalization of the T4b predictions rests on an unvalidated LDME scaling, and the TQHL1.1 shape relies on a heuristic transverse-momentum parameter; these inputs are acknowledged in the text but are not quantified as uncertainties, which limits the strength of the central claim.","major_comments":[{"comment":"The T4b predictions inherit their absolute normalization from the assumption ⟨O_{T4b}⟩/⟨O_{T4c}⟩ ≃ (m_b α_s^{(b)}/(m_c α_s^{(c)}))^9 ≃ 400. Since Eq. (10) is linear in each color-composite LDME, the same factor multiplies every [g→T4b] and [Q→T4b] initial-scale FF and, through the linear convolution in Eq. (33), every T4b cross section shown in Figs. 13, 16, and 17. The ninth-power exponent makes this input extremely sensitive: changing the bracketed ratio from 1.8 to 2.07 changes the ratio by roughly a factor of 2.6, and the paper gives no explicit values of α_s, renormalization scales, or velocities that produce the number 400. The text itself states that exact T4b LDMEs have not been computed and labels Eq. (21) a 'reasonable Ansatz,' with no lattice, data, or independent potential-model value used to anchor it. Please provide an uncertainty band or a sensitivity scan over this ratio, and ideally a cross-check from an alternative LDME model, before presenting the T4b rates as quantitative predictions.","section":"Sec. 2.3.2, Eq. (21)"},{"comment":"The TQHL1.1 ⟨q_T^2⟩ parameter is fixed at 4 GeV² through the relation sqrt(⟨q_T²⟩_{X}) ≈ sqrt(⟨q_T²⟩_{T4Q})/2, where ⟨q_T²⟩_{T4Q}=70 GeV² was itself chosen in Ref. [106] by requiring ⟨z⟩≳0.4 and that the quark channel have the same order of magnitude as the gluon one. This is a heuristic tuning of the peak position, and the statement that the [Q→X_{Q\\bar Q q\\bar q}] FFs peak in the window 0.65<z<0.85 is therefore partly imposed rather than predicted. Since the phenomenological rates in Figs. 12, 14, and 15 depend directly on these FFs, please show how the rapidity-interval and transverse-momentum distributions respond to a variation of ⟨q_T^2⟩ over a plausible range, or justify the chosen value with an independent observable.","section":"Sec. 2.2.1, Eq. (9)"},{"comment":"The paper notes that the [g→T4Q] initial-scale FFs do not vanish as z→1 and acknowledges that this behavior raises questions about compatibility with collinear factorization. Because these FFs enter the convolution in Eq. (33) over a z range that reaches unity, the endpoint region contributes to the cross section. Please estimate the numerical impact of the z→1 region, for instance by comparing with a version of the FF regulated near z=1, or state explicitly the z-range over which the predictions are meant to be trusted.","section":"Sec. 2.3.3, Fig. 7"}],"minor_comments":[{"comment":"The second doubly bottomed state is denoted X_{b\\bar b u\\bar s} in the Summary and Sec. 5, while elsewhere in the paper the same state is denoted X_{b\\bar b s\\bar s}; please make the notation uniform.","section":"Summary and Sec. 5"},{"comment":"The caption contains a duplicated phrase: 'ratio between LL/LO or HE-NLO+ or HE-NLO+ and NLL/NLO+ predictions.' Please correct the caption.","section":"Fig. 15 caption"},{"comment":"References [332] and [333] are identical entries for the CMS JINST 16 P02010 paper; one of the duplicates should be removed or replaced with the intended citation.","section":"References"}],"recommendation":"major_revision","confidential_remarks":"The paper is a solid exploratory FF release with a genuine public-code asset, but the T4b normalization issue is load-bearing rather than cosmetic. In my view, the paper should not be accepted before the sensitivity to Eq. (21) and to ⟨q_T^2⟩ is quantified, and before the z→1 endpoint issue is addressed or scoped. The authors' own statements that exact T4b LDMEs are unavailable and that the endpoint behavior is unresolved support this caution. The central machinery and numerical implementation appear sound; the requested additions are feasible within the manuscript's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, the new content is real: TQHL1.1 and TQ4Q1.1 fragmentation functions, an NRQCD-based heavy-quark channel for fully heavy tetraquarks, and the first T4b-plus-jet NLL/NLO+ distributions at 14 and 100 TeV. The framework is inherited from the authors' own earlier TQHL1.0/TQ4Q1.0 papers and the HF-NRevo/JETHAD machinery, so this is an update rather than a new paradigm. Second, the paper is honest about its main vulnerability. Sec. 2.3.2 presents Eq. (21), a color-Coulomb dimensional-analysis estimate for the T4b/T4c LDME ratio, states that exact T4b LDMEs have not been computed, and calls the result \"a reasonable Ansatz.\" Since Eq. (10) is linear in each LDME, any error in this ratio enters every T4b FF and all T4b cross sections linearly, and the ninth-power sensitivity means the factor ~400 is effectively unconstrained. No lattice, data, or independent potential-model check is offered. This is a load-bearing limitation, not an internal inconsistency, and the stress-test note has the right target; its factor of 2.6 for a 15% shift in the mass-coupling ratio is conservative in my own check.\n\nWhat is done well: the DGLAP/HF-NRevo evolution is threshold-consistent; the TQ4Q1.1 vs TQ4Q1.1- comparisons cleanly show the effect of the charm initial-scale input; the sets are publicly released in LHAPDF; and the uncertainty bands from scale variation and integration are reported. The long symbolic SDCs are elaborate and the authors explicitly flag the unresolved z->1 behavior of NRQCD fragmentation functions rather than hiding it.\n\nSofter spots: the TQHL1.1 <q_T^2> = 4 GeV^2 choice is a scanned parameter selected partly to put the FF peak in a desired z-range, so shape statements built on that scan are partly imposed. The T4c LDMEs come from one of three potential models in Ref. [104], and that model uncertainty is not propagated. The citation pattern is self-heavy, but the self-citations point to the actual code and prior releases, which is appropriate for an incremental update.\n\nWho is this for: heavy-flavor QCD phenomenologists planning LHC or FCC exotic-hadron searches, and the BFKL semihard community looking for another stable heavy-flavor tag. It deserves a serious referee. My recommendation: send it to review, and ask the authors to either anchor Eq. (21) with an independent estimate or present T4b predictions both normalized to T4c and with the LDME ratio varied by a plausible factor, plus a <q_T^2> sensitivity scan for TQHL1.1. I would not desk-reject; the released FFs are a concrete, reusable asset.","headline":"A well-executed incremental update with genuinely new T4b FFs and first resummed T4b+jet predictions; the absolute normalization rests on one unvalidated, ninth-power LDME Ansatz.","tokens_in":58803,"tokens_out":4591,"would_cite":false,"duration_ms":41501,"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":"This paper claims that unobserved bottomoniumlike tetraquarks—states containing a bottom-antibottom pair plus either light quarks or a second heavy pair—can be described at high transverse momentum by single-parton fragmentation, and it…","keywords":["bottomoniumlike tetraquarks","fragmentation functions","DGLAP evolution","variable-flavor-number scheme","NRQCD","high-energy resummation","BFKL","LHC and FCC phenomenology"],"falsifier":"A lattice QCD calculation (or an independent potential-model determination) of the ratio $\\langle O_{T_{4b}}\\rangle/\\langle O_{T_{4c}}\\rangle$ for the $0^{++}$ state would settle the normalization claim: if the ratio differs substantially from the $\\simeq 400$ value used in Eq. (21), all $T_{4b}$ cross sections in Section 4 would shift by the same factor. In the charmed sector, a precise high-transverse-momentum measurement of prompt $T_{4c}$ production could already constrain the analogous matrix elements and test the fragmentation picture.","tokens_in":57622,"feed_emoji":"⚛️","tokens_out":9931,"duration_ms":82592,"temperature":0.7,"pith_summary":"Bottomoniumlike tetraquarks—hypothetical particles made of a bottom-antibottom pair plus either two light quarks ($X_{b\\bar{b}q\\bar{q}}$) or a second bottom-antibottom pair ($T_{4b}$)—have not yet been observed, and this paper supplies a calculational framework for how they would form in proton collisions. It claims that at high transverse momentum the dominant production mechanism is the leading-power fragmentation of a single parton into the tetraquark, and it constructs two new families of collinear fragmentation functions, TQHL1.1 and TQ4Q1.1, that describe that splitting and evolve with energy via DGLAP equations in a variable-flavor-number scheme. The initial-scale inputs come from an improved spin-physics-inspired model for the doubly heavy states and from potential nonrelativistic QCD for the fully heavy states. If these functions are right, the paper's next-to-leading-log resummed predictions for tetraquark-plus-jet rates at the LHC and FCC are ready to be compared with future searches.","feed_headline":"Predict bottom tetraquark yields with new fragmentation sets","feed_subtitle":"TQHL1.1 and TQ4Q1.1 turn single-parton splitting into tetraquark-plus-jet predictions.","key_machinery":"The central objects are the two new fragmentation-function families, TQHL1.1 and TQ4Q1.1, each defined by initial-scale inputs at kinematic thresholds—$3m_Q+2m_q$ for the doubly heavy channel, and $4m_Q$ for the gluon and $5m_Q$ for the heavy-quark channel in the fully heavy case—and then evolved with DGLAP using a threshold-consistent heavy-flavor nonrelativistic evolution scheme. The carrying mechanism is the leading-power variable-flavor-number-scheme fragmentation picture, in which a short-distance coefficient for a single parton splitting into the tetraquark Fock state is convoluted with a nonperturbative hadronization matrix element or wave function. The gluon channel plays a dedicated role as a natural stabilizer of the high-energy resummed series, since its smooth scale dependence keeps the next-to-leading-log corrections under control.","core_discovery":"The central claim is that both doubly bottomed tetraquarks $X_{b\\bar{b}q\\bar{q}}$ and fully bottomed $T_{4b}$ (and their charmed analogues) can be treated as produced by collinear fragmentation of a single parton, with initial conditions computed from QCD-based models and then evolved by DGLAP, and that this treatment yields phenomenologically usable predictions. Concretely, the paper releases TQHL1.1 functions for $X_{c\\bar{c}u\\bar{u}}$, $X_{c\\bar{c}s\\bar{s}}$, $X_{b\\bar{b}u\\bar{u}}$, and $X_{b\\bar{b}s\\bar{s}}$, built on a spin-physics-inspired model with a fixed average transverse momentum $\\langle \\vec q_T^2 \\rangle = 4$ GeV$^2$, and TQ4Q1.1 functions for $T_{4c/b}(0^{++})$ and $T_{4c/b}(2^{++})$, built on potential-NRQCD short-distance coefficients and long-distance matrix elements. The fully bottomed rates inherit their absolute normalization from a color-Coulomb scaling Ansatz that sets $\\langle O_{T_{4b}}\\rangle/\\langle O_{T_{4c}}\\rangle \\simeq (m_b\\alpha_s^{(b)}/(m_c\\alpha_s^{(c)}))^9 \\simeq 400$. The resulting rapidity-interval and transverse-momentum distributions for tetraquark-plus-jet production are stable under scale variation and under next-to-leading logarithmic corrections, which the paper interprets as a sign that heavy-flavor fragmentation stabilizes high-energy resummation.","pith_inferences":["The absolute normalization of every $T_{4b}$ prediction rests on the color-Coulomb Ansatz of Eq. (21); a lattice or potential-model computation of the four-body wave function at the origin could rescale all $T_{4b}$ rates by orders of magnitude without changing their shapes.","The same initial-scale inputs could be applied to photoproduction and deep-inelastic channels at an electron-ion collider, where the gluon-initiated fragmentation channel would be probed directly.","Comparing the $T_{4c}$ analogue predictions against existing LHC double-$J/\\psi$ data at high transverse momentum would calibrate the long-distance matrix elements and thereby sharpen the $T_{4b}$ predictions.","The transverse-momentum parameter that fixes the doubly heavy fragmentation functions is chosen by heuristic peak scans rather than data; a data-driven determination of this parameter would convert the fragmentation functions from model-guided into measured inputs."],"forward_implications":["Predictions are now available for $X_{b\\bar{b}u\\bar{u}}$, $X_{b\\bar{b}s\\bar{s}}$, $T_{4b}(0^{++})$, and $T_{4b}(2^{++})$ plus a jet in rapidity-interval and transverse-momentum bins at 14 TeV LHC and 100 TeV FCC, with rates from about 1 pb down to $10^{-5}$ pb.","The gluon fragmentation channel, though smaller than the heavy-quark one, controls the stability of the resummed distributions, so future data can test the natural-stability picture directly.","The released machine-readable sets let other groups compute single-inclusive and semi-inclusive bottom-tetraquark observables without redoing the model inputs.","Variants evolved without the initial heavy-quark input differ from the full sets by factors of 1.5 to 10 in the heavy-quark channel, so precision measurements could discriminate the initial condition.","Cross sections grow by roughly an order of magnitude from LHC to FCC energies, which would make a future 100 TeV collider a substantially more sensitive discovery channel."],"supporting_citations":[{"why":"Supplies the original heavy-quark fragmentation calculation from which the doubly heavy tetraquark initial-scale input is adapted.","marker":"[94]"},{"why":"Provides the NRQCD short-distance coefficients for gluon fragmentation into fully charmed tetraquarks, extended to bottom in this work.","marker":"[104]"},{"why":"Provides the potential-NRQCD heavy-quark channel inputs for the fully heavy tetraquark fragmentation functions.","marker":"[105]"},{"why":"Defines the superseded 1.0 version of the doubly heavy tetraquark functions that TQHL1.1 extends.","marker":"[95]"},{"why":"Defines the superseded 1.0 version of the fully heavy tetraquark functions that TQ4Q1.1 extends.","marker":"[106]"},{"why":"Supplies the threshold-consistent heavy-flavor nonrelativistic DGLAP evolution scheme used to build the released sets.","marker":"[115, 116]"},{"why":"Furnishes the color-Coulomb scaling Ansatz, Eq. (21), that fixes the overall normalization of the fully bottomed tetraquark predictions.","marker":"[209]"},{"why":"Provides the NLO light-hadron emission function whose form is used in the resummed tetraquark-plus-jet cross section.","marker":"[320]"}],"fun_headline_variants":["TQHL1.1 and TQ4Q1.1: new fragmentation for bottom tetraquarks","Bottom tetraquark plus jet predictions from single-parton splitting","Stable high-energy tetraquark+jet rates from new fragmentation","Doubly and fully bottom tetraquarks via DGLAP+resummation","Predict tetraquark+jet at 14 and 100 TeV with TQHL1.1"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the color-Coulomb scaling Ansatz of Eq. (21), which sets the ratio of bottom- to charm-tetraquark nonperturbative matrix elements to about 400, correctly fixes the overall normalization of all fully bottomed tetraquark rates.","fun_headline_variants_meta":{"raw":{"variants":["TQHL1.1 and TQ4Q1.1: new fragmentation for bottom tetraquarks","Bottom tetraquark plus jet predictions from single-parton splitting","Stable high-energy tetraquark+jet rates from new fragmentation","Doubly and fully bottom tetraquarks via DGLAP+resummation","Predict tetraquark+jet at 14 and 100 TeV with TQHL1.1"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000883,"raw_usage":{"total_tokens":3918,"prompt_tokens":1152,"completion_tokens":2766,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":768,"completion_tokens_details":{"reasoning_tokens":2656}},"tokens_in":768,"tokens_out":2766,"duration_ms":18441,"temperature":1.0,"reasoning_tokens":2656,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T15:51:16.472767+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"A lattice QCD calculation (or an independent potential-model determination) of the ratio $\\langle O_{T_{4b}}\\rangle/\\langle O_{T_{4c}}\\rangle$ for the $0^{++}$ state would settle the normalization claim: if the ratio differs substantially from the $\\simeq 400$ value used in Eq. (21), all $T_{4b}$ cross sections in Section 4 would shift by the same factor. In the charmed sector, a precise high-transverse-momentum measurement of prompt $T_{4c}$ production could already constrain the analogous matrix elements and test the fragmentation picture.","supporting_citations":[],"review_version":1}