Composite quarks and leptons with embedded QCD

TL;DR

This work develops a concrete preon-based model in which an $SU(15)_{ m p}$ gauge interaction confines chiral preons while the preons are also charged under a weakly-coupled $SU(4)_{ m PS} \times SU(2)_L \times SU(2)_R$ group that embeds QCD and breaks down to the SM. The model yields three generations of SM fermions as 3-preon bound states, and a dynamical origin for the Higgs sector as 6-preon bound states, with a rich spectrum including composite vectorlike leptons near the TeV scale. The gauge sector remains perturbative up to high scales thanks to the PS embedding and preon-induced effects, with potential unification in a larger group such as $SO(10)$; $\Lambda_{ m PS}$ is in the $30$–$100$ TeV range, and $\Lambda_{ m pre}$ around $3\times10^3$ TeV, while the vectorlike leptons have current experimental bounds near $\sim$TeV. The framework predicts distinctive collider signatures, notably multi-Higgs sectors and dilepton states, and highlights the importance of nonperturbative dynamics in the $SU(15)_{ m p}$ sector for precise mass spectra and vacuum structure.

Abstract

We construct a model of quark and lepton compositeness based on an $SU(15)$ gauge interaction that confines chiral preons, which are also charged under the weakly-coupled $SU(4)_{\rm PS} \times SU(2)_L\times SU(2)_R$ gauge group. The breaking of the latter, down to the Standard Model group, is achieved by scalar $SU(15)$ bound states at a scale in the $30 - 100$ TeV range. The embedding of the QCD gauge group in $SU(4)_{\rm PS} $ slows down the running of $α_s$ in the UV. We estimate the effects of the strongly-coupled $SU(15)$ dynamics on the running of the $SU(4)_{\rm PS} \times SU(2)_L\times SU(2)_R$ gauge couplings, which likely remain perturbative beyond the compositeness scale of about $10^3 - 10^4$ TeV, and even above a unification scale. A composite vectorlike lepton doublet acquires a mass in the TeV range probed at future colliders, and an extended Higgs sector arises from 6-preon bound states.

Figures (6)

• Figure 1: Preon exchange diagram inducing the $\phi_{15\text{-}4_i}^\dagger \, \phi_{10\text{-}\bar{4}_i}$ bilinear terms in the scalar potential, which are responsible for vacuum alignment along the $SU(4)_{\rm PS} \times SU(2)_{\rm R}$ space. Gray bubbles represent the prebaryons (see Table \ref{['table:PSprebaryons']}): ${\cal P}_{15}$ and ${\cal P}_{\bar{4}}^i$ form the $\phi_{15\text{-}4_i}$ di-prebaryons, while ${\cal P}_{10}$ and ${\cal P}_{\bar{4}}^i$ form the $\phi_{10\text{-}\bar{4}_i}$ di-prebaryons.
• Figure 2: Preon exchange diagram inducing the effective Yukawa interaction of the $\phi_{10\text{-}\overline{10}}$ scalar (a gauge-singlet bound state of the ${\cal P}_{10}$ and ${\cal P}_{\overline{10} }$ prebaryons) to a pair of ${\cal P}_{1,2}$ prebaryons.
• Figure 3: Effective Yukawa interaction of the $\phi_{15\text{-}15}$ di-prebaryon (a gauge-singlet bound state of two ${\cal P}_{15}$ prebaryons) to a pair of ${\cal P}_{1,2}$ prebaryons, induced by an $SU(4)_{\rm PS}$ gauge boson exchange.
• Figure 4: Main process for pair production of composite vectorlike leptons at the LHC, yielding a $5\tau \!+\! E_T \space\slash$ final state, provided that the mass of the composite pseudoscalar $A_{\cal L}$ satisfies $2m_\tau < M_{A} < m_{\cal L}$. For $M_{A} < 2m_\tau$, $A_{\cal L}$ predominantly decays into $\gamma\gamma$ or $\mu^+\mu^-$, so similar diagrams lead to $4\gamma + \tau \!+\! E_T \space\slash$ or $4\mu + \tau \!+\! E_T \space\slash$ final states.
• Figure 5: Effective Yukawa coupling induced by preon interactions: the $H_u$ Higgs doublet (a 6-preon bound state) couples to the second-generation SM quark doublet ($q_{2_L}$) and up-type quark singlet ($u^c_2$), producing the charm quark mass. The antisymmetric scalars ${\cal A}$ and ${\cal A}'$ couple to different preon flavors as in Eq. (\ref{['eq:Apsipsi']}). The preon $\psi_{\! _Q}$ is the color-triplet component of $\Psi_W$, while the preon $\psi_{\! _U}$ is the color-antitriplet and upper-$SU(2)_R$ component of $\Psi_{W'}$.