Ultraheavy Diquark Scalar: Theory & Colliders

Updated 14 February 2026

Ultraheavy diquark scalars are multi-TeV color-sextet particles that couple to pairs of right-handed up-type quarks, playing a pivotal role in both BSM and QCD frameworks.
They are produced via high-energy up-quark collisions and exhibit distinct experimental signatures such as multi-jet final states, same-sign dileptons, and boosted object decays.
Theoretical models use methods like the Schwinger-Dyson formalism and QCD sum rules to predict their mass, decay widths, and coupling-dependent production rates at colliders.

An ultraheavy diquark scalar is a complex scalar particle carrying color, often in the sextet (6) representation of SU(3) $_c$ , that couples directly to pairs of right-handed up-type quarks. Its mass is typically at the multi-TeV scale, making it accessible only at the highest-energy colliders or in fully heavy hadronic systems. This state appears both in extended Standard Model searches (as a hypothesized new resonance) and within QCD-based models for tetraquark or baryon structure. Theoretical frameworks for ultraheavy diquark scalars are motivated by collider phenomenology, QCD dynamics, and possible explanations for anomalies in experimental data.

1. Quantum Numbers, Field Content, and Couplings

Ultraheavy diquark scalars commonly referenced in collider and theoretical studies are color-sextet ($6$ under SU(3) $_c$ ), weak singlet ($1$ under SU(2) $_W$ ), and have hypercharge $Y=+4/3$ , yielding an electric charge $Q=+4/3$ (Dobrescu, 2024, Dobrescu et al., 2018, Dobrescu, 2019). They are described by a field $S_{uu}$ or $\phi_{qq}$ , with the Lagrangian terms: $\mathcal{L} \supset \frac{y_{uu}}{2} K^n_{ij} S_{uu}^n \overline{u}_{R,i} u^c_{R,j} + \text{h.c.}$ where $K^n_{ij}$ are Clebsch-Gordan coefficients for the 3⊗3→6 decomposition, and $y_{uu}$ is the Yukawa coupling controlling both production and decay. Extensions also include couplings to vectorlike quarks $\chi$ : $\mathcal{L} \supset y_{\chi\chi} S_{uu}^{\dagger} \bar{\chi} \chi + \text{h.c.}$ or $S_{uu}\to u\chi$ via $y_{u\chi}$ (Costache et al., 4 Nov 2025, Filip et al., 16 Jan 2026). The quantum numbers and field structure are summarized in Table 1.

Particle	$SU(3)_c$	$SU(2)_W$	$U(1)_Y$	Charge $Q$	Baryon Number $B$
$S_{uu}$	6	1	$+4/3$	$+4/3$	$2/3$
$\chi$ (VLQ)	3	1	$+2/3$	$+2/3$	$1/3$
$A_\chi$	1	1	0	$0$	$0$

2. QCD Dynamics and Mass Generation

The mass of an ultraheavy scalar diquark can arise through several mechanisms. In BSM scenarios, a gauge-invariant bare mass term $M^2 |S_{uu}|^2$ stabilizes the scalar at the TeV scale or above (Rivero, 2011). In QCD dynamics, non-perturbative gluonic effects dynamically generate an effective mass for scalar diquarks, as shown via the Schwinger-Dyson formalism (Imai et al., 2014). The gap equation with RG-improved coupling and a finite-size form factor $f_\Lambda(p^2)$ demonstrates that as the spatial size $R$ decreases (or the bare mass increases), the effective mass function $\Sigma(p^2)$ becomes large— $\Sigma(0)\sim1.4$ –$2.4$ GeV for $R\simeq0.3$ fm, corresponding to the ultraheavy regime.

In the heavy-quark sector, the two-point QCD sum rule analysis of a $bc\bar b\bar c$ scalar tetraquark interpreted as a scalar diquark-antidiquark yields a mass $m_T=(12.7\pm0.09)$ GeV and width $\Gamma \sim 140$ MeV, indicating a broad, non-narrow ultraheavy resonance (Agaev et al., 2024).

3. Production and Decay in Hadron Colliders

Production of $S_{uu}$ predominantly occurs through the $uu\to S_{uu}$ $s$ -channel process, capitalizing on valence up-quark PDFs. The leading-order partonic cross-section is: $\hat{\sigma}(uu\to S_{uu}) = \frac{\pi}{6 \hat{s}}\,|y_{uu}|^2\,\delta(\hat{s}-M_S^2)$ with hadronic cross-section scaling with $|y_{uu}|^2$ and the up-quark luminosity evaluated at $M_S$ (0909.2666, Dobrescu, 2019, Costache et al., 4 Nov 2025). Next-to-leading-order QCD corrections introduce a K-factor, with values $K\approx1.22$ –1.32 for color-sextet diquarks at the LHC (0909.2666). For $M_S=8$ –$10$ TeV and $y_{uu}=1$ , the NLO cross-section at $\sqrt{s}=14$ TeV is 0.2–0.031 fb (Dobrescu, 2019), enabling tens of events at high-luminosity LHC.

Decay phenomenology is controlled by the available channels and coupling hierarchy. For $M_S>2m_\chi$ , the diquark decays as $S_{uu} \to \chi\chi$ , $S_{uu} \to u\chi$ , and $S_{uu} \to uu$ , with partial widths

$\Gamma(S_{uu}\to uu) = \frac{y_{uu}^2 M_S}{32\pi}$

$\Gamma(S_{uu} \to \chi\chi) = \frac{y_{\chi\chi}^2 M_S}{32\pi}(1-2m_\chi^2/M_S^2)\sqrt{1-4m_\chi^2/M_S^2}$

$\Gamma(S_{uu}\to u\chi) = \frac{M_S}{16\pi} |y_{u\chi}|^2 \left(1 - \frac{m_\chi^2}{M_S^2}\right)^2$

Branching ratios depend on the coupling ratios and phase space; for $y_{\chi\chi}\gg y_{uu}$ , decays to vectorlike quarks dominate (Costache et al., 4 Nov 2025, Filip et al., 16 Jan 2026).

4. Collider Phenomenology and Signatures

The characteristic collider signatures of an ultraheavy diquark scalar reflect its decay chains:

Six-jet final states: $pp \to S_{uu} \to \chi\chi \to (W^+b)(W^+b) \to (jjb)(jjb)$ ; jet kinematics are characterized by $p_T \sim$ TeV, multiple $b$ -tags, and large scalar $H_T$ (Costache et al., 4 Nov 2025, Duminica et al., 21 Mar 2025).
Four-jet (or higher multiplicity) cascades: In models with further cascade via lighter colored states ( $\chi_1$ , $\chi_2$ ), $S_{uu}\to\chi_2\chi_2\to (uA_\chi)(uA_\chi)\to 4j$ or similarly $(\chi_1A_\chi)(uA_\chi)\to 5j$ (Dobrescu, 2024).
Paired dijet and multijet signatures: Paired dijet masses clustered at $m_{\chi_1}, m_{\chi_2}$ on an overall $M_{4j}\sim M_S$ resonance, especially when $S_{uu}$ accumulates in a narrow 4-jet invariant-mass window.
Boosted tops, $W$ , $Z$ , $h$ signatures: When $\chi$ decays via mixing, $S_{uu}\to u\chi\to u(Wb)$ or $u(h t)$ , leading to multi-jet events with highly boosted substructure (Filip et al., 16 Jan 2026, Dobrescu, 2019).
Same-sign dileptons: When decays favor top-rich final states, positively charged same-sign leptons without anti-particle counterparts can arise (Dobrescu, 2019).

Machine learning classifiers (Random Forest or BDTs) employing multi-observable event shapes and jet substructure variables have been crucial in maximizing signal-background separation for these signatures (Costache et al., 4 Nov 2025, Duminica et al., 21 Mar 2025, Filip et al., 16 Jan 2026).

5. Experimental Reach and Statistical Sensitivity

High-luminosity LHC projections indicate:

$M_S \sim 7$ –$8.5$ TeV can be discovered or excluded at $5\sigma$ or 95%~C.L. for moderate $y_{uu} B(\chi \to Wb)\gtrsim0.1$ with 3000 fb $^{-1}$ at 13.6–14 TeV (Costache et al., 4 Nov 2025, Duminica et al., 21 Mar 2025, Filip et al., 16 Jan 2026).
$M_S$ reach extends to $\sim 10$ TeV for dijet or background-free multilepton channels in favorable coupling regimes (Dobrescu, 2019).
Anomalous 4-jet events observed by CMS at $M_{4j}\sim8$ TeV with paired dijet masses at $\sim2$ TeV are consistent with $M_S\sim8.5$ TeV, $m_{\chi_2}\sim2.1$ TeV, $y_{uu}\sim0.8$ , $y_{\chi}\sim1$ (Dobrescu, 2024). The extremely low QCD background at such large $M_{4j}$ enables $S/B\gg1$ even for cross sections $\lesssim0.2$ fb.

Advanced jet substructure, $b$ -tagging, and high-threshold event selection are needed to operate in the ultraheavy regime. Machine learning approaches yield AUC~0.95 and improve discovery significance by factors of $\sim2$ over cut-based methods. At a 27 TeV HE-LHC, the accessible mass range can be extended to $M_S\sim12$ –$15$ TeV, and to $M_S\sim30$ TeV at 100 TeV (Costache et al., 4 Nov 2025).

6. Theoretical and QCD-Based Models

In QCD-based approaches, ultraheavy scalar diquarks act as effective degrees of freedom in multi-quark systems:

In the $bc\bar b\bar c$ system, a scalar diquark-antidiquark model yields $m_T=(12.7\pm0.09)$ GeV with $\Gamma_T\sim140$ MeV. The mass lies well above hadronic thresholds, resulting in broad resonant structures rather than narrow states (Agaev et al., 2024).
The Schwinger-Dyson formalism demonstrates that the scalar diquark acquires a large dynamical mass from gluonic dressing effects, enhanced for small spatial sizes, and does not require chiral symmetry (Imai et al., 2014).
Path-integral hadronization in the NJL model yields effective actions, Ward identities, and Isgur-Wise-type weak transition functions for diquark-based baryonic systems (Shi, 2020).

These QCD treatments indicate that in the heavy sector, scalar diquarks do not form narrow, stable objects, but can dominate as effective, strongly-coupled constituents in multi-quark resonance phenomenology.

7. Extensions, Constraints, and Open Directions

Extensions of the $S_{uu}$ scenario include additional colored or uncolored exotics (e.g., multiple vectorlike quarks, light pseudoscalars) (Dobrescu, 2024), as well as flavor- or baryon-number-protecting symmetries (Rivero, 2011, Dobrescu, 2019). Collider constraints stem from:

Dijet resonance, multijet, and vectorlike quark searches (setting $M_S\gtrsim5$ TeV for large $y_{uu}$ ).
Low energy processes (e.g., $D^0$ – $\bar D^0$ mixing: $|y_{uu} y_{cc}| \left(\frac{10\,\text{TeV}}{M_S}\right)^2 \lesssim 3.7\times10^{-4}$ ).
Non-observation of same-sign top pairs and paired dijet resonances.

Scenarios with prompt $\chi \to uA_\chi$ or $A_\chi \to gg$ decays are plausible for certain coupling windows. Complementary searches in channels with single or paired boosted objects, lepton charge asymmetries, and mixed decay topologies will further test the validity of the ultraheavy diquark scalar hypothesis.