Authors

• Sehar Ajmal (sehar.ajmal@…)
  • Department of Physics and Geology, University of Perugia, Italy
• Matteo Presilla (matteo.presilla@…)
  • Institute for Experimental Particle Physics (ETP), Karlsruhe Institute of Technology (KIT), Wolfgang-Gaede-Straße 1, 76131 Karlsruhe, Germany
• Orlando Panella (orlando.panella@…)
  • INFN, Section of Perugia, Via A. Pascoli, I-06123, Perugia, Italy
• She Sheng Xue (xue@…)
  • ICRANet, Piazzale della Repubblica, 10-65122, Pescara, Italy
  • Physics Department, Sapienza University of Rome, Piazzale Aldo Moro 5, 00185 Roma, Italy
  • INFN, Section of Perugia, Via A. Pascoli, I-06123, Perugia, Italy
  • ICTP-AP, University of Chinese Academy of Sciences, Beijing, China

Model Description

The model utilizes four-fermion interactions in its Lagrangian to characterize interactions among Standard Model (SM) elementary fermions at the ultraviolet (UV) cutoff. These interactions, following the Nambu–Jona-Lasinio (NJL) or Einstein-Cartan type, effectively represent more fundamental interactions in the UV completion. The incorporation of effective four-fermion interactions stems from a theoretical inconsistency observed between the bilinear Lagrangian of the SM chiral (parity-violating) gauged fermions and the UV regularization of unidentified dynamics. This inconsistency hints at the presence of four-fermion interactions at the UV cutoff.
The model is grounded in a strong four-fermion coupling UV fixed point at TeV scales, giving rise to massive composite particles as bound states of SM fermions. Bound states are classified into bosons and fermions called as Composite Bosons and Composite Fermions, with Composite Bosons engaging in interactions with Lepton-Quark and Quark-Quark pairs. Composite Fermions consist of either 3 Quarks, 3 Leptons, or mixed combination (of three of them). The SM chiral gauge symmetries remain intact, and composite particles interact with SM gauge bosons. As the energy scale decreases and composite particles disintegrate, the model undergoes a first-order phase transition involving the breaking of SM chiral gauge symmetries. It transitions to a weak four-fermion coupling infrared (IR) fixed point at the electroweak scale, where the low-energy SM is realized. The energetically favorable symmetry-breaking ground state leads to the generation of the top quark mass through spontaneous symmetry breaking, and the masses of other fermions follow a hierarchy via explicit symmetry breaking through family mixing see ​2 and ​3.
Previously, there has been a phenomenological investigation related to the composite fermions and bosons see ​4.
In this implemented scenario, only composite boson leptoquarks Contact and Gauge interactions have been integrated across the entire spectrum of composite particles. There exist four Leptoquarks (LQs) exhibiting coupling within the generation, possessing a baryon number (B) of 1/3 and a lepton number (L) of -1, for details see ​1. Interactions involving other particles are reserved for future implementations.

References

1. ​https://arxiv.org/pdf/2311.18472.pdf
2. ​https://doi.org/10.1007/JHEP05%282017%29146
3. ​https://doi.org/10.1016/j.nuclphysb.2023.116168
4. ​https://doi.org/10.1140/epjc/s10052-020-7822-0

Model Files

• ​NJL_Model_LQ.fr: This file contains the definitions of Particle Classes and parameters specifically tailored for Leptoquark Interactions within the NJL composite model.

• ​NJL_Model_LQ.nb: This is a Mathematica notebook that incorporates the Lagrangian of the NJL composite model. The notebook is designed to load the model and perform calculations related to Feynman rules for Leptoquark Interactions.

Matrix element generator files

• ​NJLCompositeModel-LQ_UFO.zip: The model files in Universal FeynRules Output (UFO) format for leptoquark interactions (e.g. for MadGraph5_aMC@NLO).