Lepton–Gluon Portal Phenomenology

• Lepton–gluon portal is a theoretical framework using effective operators to mediate direct interactions between leptons and gluons, enabling anomalous production at colliders.
• It employs dimension-5 to dimension-7 operators to generate distinctive signals such as lepton+jet resonances and same-sign dilepton events.
• Collider studies at the LHC use high-mass dilepton and lepton+jet analyses to test these portals and distinguish among exotic colored and electroweak states.

The lepton–gluon portal refers to mechanisms, realized within effective field theory (EFT) and specific UV models, whereby new physics states or higher-dimensional operators mediate direct interactions between leptons and gluons in a manner not present at tree level within the Standard Model (SM). This allows single-production or anomalous couplings involving at least one lepton and one gluon, yields an array of exotic collider signals, and probes novel color and electroweak quantum numbers. Originally constrained by high dimension, such portals are rendered phenomenologically relevant by the large gluon and (subdominant) lepton parton densities at modern colliders, especially the LHC (Potter et al., 2012, Almeida et al., 2022, Carpenter et al., 26 Dec 2025).

1. Operator Basis and Quantum Number Structure

The lepton–gluon portal is systematically described by the complete set of effective operators coupling SM leptons to gluons and exotic states up to dimension seven. The generic EFT Lagrangian is: $$\mathcal{L}_{\rm eff}\supset \sum_{n}\frac{C^{(n)}_i}{\Lambda^{n-4}}O^{(n)}_i$$ where $O^{(n)}_i$ includes SM leptons ($\ell$, $L_i$), gluon field strengths ($G^a_{\mu\nu}$), quarks ($u$, $d$, $Q_{L\,i}$), scalar and fermionic exotics ($\phi$, $\psi$), and possibly Higgs insertions. Allowed exotic representations—often labeled “LEX” (Editor’s term)—include color-octet fermions ("lepto-gluons": $(8,1,-1)$ or $(8,2,-1/2)$), anti-triplet scalar leptoquarks, higher multiplets under $SU(3)_C\times SU(2)_L$, and combinations generating same-sign dileptons, hard lepton+jet resonances, or cascade decays (Carpenter et al., 26 Dec 2025).

Dimension-5 (Dipole-type, No Higgs)

Operators such as $G^a_{\mu\nu}\bar\ell\sigma^{\mu\nu}\psi^a$ mediate lepto-gluon single-production. Scalar leptoquarks admit derivative structures $\overline{\ell}\gamma^\mu D_\mu u\,\phi$ (with $X:(\overline{3},1,-5/3)$, etc.).

Dimension-6 (Tensor and Derivative Structures)

Tensor operators with one gluon and two fermions ($$G^a_{\mu\nu}\overline{\ell}\sigma^{\mu\nu}Q_{L\,i}\,\phi^i$$) permit single-production of $SU(3)_C$ multiplet states. Derivative forms such as $G^a_{\mu\nu}D^\mu\overline{\ell}\gamma^\nu\psi^a$ also arise.

Dimension-7 (Two-Gluon Tensors)

Operators of schematic form $G^{a}_{\mu\nu}G^{a\,\mu\nu}\overline{\ell}\psi$ lead to $gg\rightarrow\ell X$ channels and probe even higher representations, e.g. color 10, 27-plets.

2. Collider Phenomenology and Signatures

The portal generates distinctive production and decay signatures at hadron colliders, dominated by the interplay between operator suppression and parton luminosity.

Exotic State	Production Channel	Dominant Signature
Lepto-gluon $(8,1,-1)$	$g\ell\rightarrow X$	$\ell+$jet resonance
Scalar octet	$gg,\,g\ell\rightarrow X$	Dilepton+jet, same-sign dileptons+jet
Higher multiplets	$gq\rightarrow\ell X$	Cascade decays, soft leptons/pions + jet

Hard lepton+jet resonance searches (ATLAS/CMS) constrain $m_X\gtrsim1.2$–1.4 TeV for $C/\Lambda\sim 1/\text{TeV}$, while same-sign dilepton+jet signatures from doubly charged octets exclude $m_\phi\lesssim800$–900 GeV for $C/\Lambda^2\sim1/\text{TeV}^2$ (Carpenter et al., 26 Dec 2025).

3. Partonic and Hadronic Cross Sections

For dimension-5 dipole operators ($g\ell\rightarrow X$),

$$\hat\sigma(g\ell\rightarrow X)\simeq \frac{\pi}{4m_X^2}\left|\frac{C}{\Lambda}\right|^2\delta(\hat{s}-m_X^2)$$

Dimension-6 operators ($gq\rightarrow\ell X$): $$\hat\sigma(gq\rightarrow\ell X)\propto \frac{\alpha_s}{16\pi}\frac{|C|^2}{\Lambda^4}\hat{s}\left(1-\frac{m_X^2}{\hat{s}}\right)^2$$ Dimension-7 ($gg\rightarrow\ell X$) scales as $\propto \alpha_s^2|C|^2\hat{s}^2/\Lambda^6$.

For $\Lambda=5$ TeV, $C=1$, and $m_X\lesssim1.5$ TeV, integrated hadronic cross sections are typically $1$–$100$ fb (Carpenter et al., 26 Dec 2025).

4. Lepton-Gluonic Couplings and Dilepton Production

In the SM-symmetric EFT, lepton–gluon interactions appear first at dimension eight. The basis couplings for charged leptons are: $$\mathcal{L}_{\rm eff}\supset \frac{g_s^2}{\Lambda^4}\left[c\,G^A_{\mu\nu}G^{A\,\mu\nu}\bar L_\ell\ell_R\phi + \tilde{c}\,G^A_{\mu\nu}\widetilde{G}^{A\,\mu\nu}\bar L_\ell\ell_R\phi \right]+\text{h.c.}$$ After EWSB, these induce lepton currents coupled to gluon tensors. The partonic cross section for $gg\to\ell^+\ell^-$ reads: $$\hat{\sigma}(gg\to\ell^+\ell^-)= (|c|^2 + |\tilde{c}|^2)\frac{v^2g_s^4}{\Lambda^8}\frac{\hat{s}^2}{32\pi}$$ The hadronic cross section is integrated over gluon PDFs, with LHC $gg$ luminosity greatly enhancing sensitivity. For $\sqrt{s}=13\text{–}14$ TeV, LHC searches in the high-mass dilepton tail ($m_{\ell\ell}>120\,\text{GeV}$) can be competitive with traditional $q\bar q$ Drell–Yan modes, probing $c/\Lambda^4\gtrsim0.7/(1\,\text{TeV})^4$ (Potter et al., 2012).

5. Spin Discrimination and Exotic State Identification

Resonant production via the lepton–gluon portal enables robust discrimination between candidate new states. Specifically, color-octet fermionic leptogluons (spin-$1/2$) can be distinguished from scalar or vector leptoquarks using multi-observable template fits (6-dimensional distributions) or single-variable asymmetry tests based on the Collins–Soper angle. $\sim 80$ signal events suffice for 95% CL separation even with up to 20% systematics (Almeida et al., 2022).

6. Existing Constraints and Future Prospects

Limits from LEP-II and Tevatron are weak: $|c|\lesssim80$ for $\Lambda=2$ TeV. LHC projections estimate $|c|\gtrsim0.7$ for $\Lambda=1$ TeV at 14 TeV with 10 fb$^{-1}$, with sensitivity scaling as $c\sim(\Lambda/1\,\text{TeV})^4$ (Potter et al., 2012). Resonant leptogluon searches at the LHC can exclude masses up to $m_{\ell_8}\simeq3.5$ TeV for $\Lambda/a_L\sim 1$–$4$ TeV and discover up to $m_{\ell_8}\approx3$ TeV at HL-LHC (3 ab$^{-1}$) (Almeida et al., 2022). Current color-octet, di-lepton+jet, and same-sign dilepton searches exclude slices of parameter space, but higher $SU(3)\times SU(2)$ multiplets catalogued in (Carpenter et al., 26 Dec 2025) remain largely unexplored.

7. Outlook and Theoretical Implications

The lepton–gluon portal systematically expands the landscape of possible SM extensions, enabling single-production mechanisms, novel signatures, and high-multiplet representations accessible only via gluonic couplings. The smoking-gun collider sign—an enhancement in the high-mass tail of dilepton (or lepton+jet) spectra with characteristic $s^2$ growth—would signal dimension-eight or higher lepton–gluon new physics. Further study at ATLAS and CMS should cover $\tau$-flavor, lepton-flavor violation, full detector simulations, and exploitation of CP-odd observables to disentangle operator structures (Potter et al., 2012, Almeida et al., 2022, Carpenter et al., 26 Dec 2025). A plausible implication is that lepton–gluon couplings remain among the least-constrained “asymmetric portals” at the TeV scale and could uncover broad classes of exotic colored or electroweak states at the next LHC runs.