Next-to-leading order QCD corrections to fully charm tetraquark hadronic decay

Impact Assessment

Core Contribution. This paper computes the next-to-leading order (NLO) QCD corrections to the light-hadron decay channels ($gggg$ and $q\bar{q}q\backslash bar\{q\}$) of fully charm tetraquarks ($T_{4c}T\_\{4c\}$, i.e. $c\bar{c}c\bar{c}c\backslash bar\{c\}c\backslash bar\{c\}$ states such as the observed $X(6900)X(6900)$) within the NRQCD factorization framework. It extends prior leading-order (LO) work by Sang et al. and the authors' own diphoton NLO calculation. The main deliverables are analytic short-distance coefficients for the $0^{++}0^\{++\}$ and $2^{++}2^\{++\}$ states, and numerical predictions for the OZI-suppressed light-hadron decay width ratio ${\mathcal{R}}_{\mathrm{L}\mathrm{H}}\backslash mathcal\{R\}\_\{\backslash mathrm\{LH\}\}$. The headline finding is that NLO corrections are large: +170% for the $0^{++}0^\{++\}$ state and −30% for the $2^{++}2^\{++\}$ state, with the light-hadron rate about three orders of magnitude above the diphoton channel — as expected for a strong-interaction process.

Methodological Rigor. The calculation is technically competent and uses the modern multi-loop toolchain appropriately: spin-singlet/triplet and color projectors, reverse unitarity to convert phase-space integrals into two-loop cut integrals, IBP reduction (Kira/CalcLoop), auxiliary-mass differential equations solved via multiple polylogarithms (weight ≤ 2, reducing to ${\mathrm{L}\mathrm{i}}_2\backslash mathrm\{Li\}\_2$/log), with boundary conditions fixed by AMFlow + PSLQ. A key internal validation is the complete cancellation of IR divergences between real and virtual corrections, a strong consistency check. Seven master integrals are identified and given analytically. The methodology is sound and standard for state-of-the-art NRQCD calculations.

However, the physical robustness of the predictions is limited. The scale dependence is severe — at $\mu =2m_c\backslash mu\; =\; 2m\_c$ the $2^{++}2^\{++\}$ ratio even turns negative, signaling that the perturbative series is poorly convergent and that higher-order corrections remain important. The 170% correction for the $0^{++}0^\{++\}$ undermines confidence in the truncated series. Furthermore, the LDMEs are not independently determined: the $0^{++}0^\{++\}$ matrix elements are simply *assumed* equal to the $2^{++}2^\{++\}$ one (mixing angle $\pi \mathrm{/}4\backslash pi/4$), and results are normalized by the unknown $\mathcal{B}(T_{4c}\to 2J\mathrm{/}\psi )\backslash mathcal\{B\}(T\_\{4c\}\backslash to\; 2J/\backslash psi)$. Thus the absolute predictions carry large, partially uncontrolled uncertainties.

Potential Impact. The topic sits in an active and experimentally vibrant subfield — the fully charm tetraquark family has been established by LHCb/ATLAS/CMS, with CMS recently determining spin-parity of multiple structures. Within this niche, the paper contributes incremental but useful theoretical input. That said, the light-hadron channel is OZI-suppressed and subdominant to the $J\mathrm{/}\psi J/\backslash psi$-pair mode; it is not a channel that experiments currently target, and the small, uncertain branching fractions make near-term experimental confrontation unlikely. The work is more valuable as a demonstration that NRQCD factorization can be applied at NLO to multi-heavy annihilation decays, and as a data point for the total width budget, than as a directly testable prediction.

Timeliness & Relevance. Highly timely. It rides the wave of 2024–2025 experimental developments (CMS Nature paper on spin-parity, ATLAS $J\mathrm{/}\psi \psi (2S)J/\backslash psi\backslash psi(2S)$ observation) and complements a rapidly growing theory literature on $T_{4c}T\_\{4c\}$ production and decay. The authors are clearly embedded in this active program (multiple self-citations to production and diphoton NLO work).

Strengths. (1) First NLO treatment of the light-hadron decay channel — fills a specific gap. (2) Clean analytic results with master integrals provided. (3) Rigorous IR-cancellation validation. (4) Good reproducibility: expressions, integrals, and tool chain are all specified.

Limitations. (1) Large scale dependence and huge $0^{++}0^\{++\}$ K-factor cast doubt on perturbative reliability. (2) Predictions hinge on assumed/borrowed LDMEs and an unknown normalizing branching fraction, so absolute numbers are only indicative. (3) The channel is phenomenologically marginal (OZI-suppressed, hard to measure). (4) Conceptually the work is an expected extension — LO existed, the authors' own production and diphoton NLO calculations supplied the machinery, so the intellectual novelty is modest.

Other observations. The paper is well-organized and clearly written for its audience. The resource barrier is low (small theory group with standard multi-loop software). Its influence will likely be as a routine, citable reference within the $T_{4c}T\_\{4c\}$ phenomenology community rather than a paradigm-shifting result. It neither challenges nor independently corroborates any contested prior claim; it updates an LO calculation.

Overall, this is a solid, competently executed but incremental theoretical contribution of moderate impact confined to a specialized subfield.