Resonant and nonresonant new phenomena of four-fermion operators for experimental searches

TL;DR

This paper explores new phenomena related to four-fermion operators within the Standard Model framework, analyzing their potential experimental signatures at high-energy colliders and their role in symmetry-breaking and particle compositeness.

Contribution

It introduces the study of resonant and nonresonant effects of four-fermion operators in the Einstein-Cartan theory, highlighting their experimental signatures and implications for SM symmetry dynamics.

Findings

Resonant phenomena of composite Dirac particles could be observed in collider experiments.

Nonresonant effects influence Higgs boson production and decay rates at high energies.

Four-fermion operators may impact neutrino oscillation experiments.

Abstract

In the fermion content and gauge symmetry of the standard model (SM), we study the four-fermion operators in the torsion-free Einstein-Cartan theory. The collider signatures of irrelevant operators are suppressed by the high-energy cutoff (torsion-field mass) $\Lambda$, and cannot be experimentally accessible at TeV scales. Whereas the dynamics of relevant operators accounts for (i) the SM symmetry-breaking in the domain of infrared-stable fixed point with the energy scale $v\approx 239.5$ GeV and (ii) composite Dirac particles restoring the SM symmetry in the domain of ultraviolet-stable fixed point with the energy scale ${\mathcal E}\gtrsim 5$ TeV. To search for the resonant phenomena of composite Dirac particles with peculiar kinematic distributions in final states, we discuss possible high-energy processes: multi-jets and dilepton Drell-Yan process in LHC $p\,p$ collisions, the resonant cross-section in $e^-e^+$ collisions annihilating to hadrons and deep inelastic lepton-hadron $e^-\,p$ scatterings. To search for the nonresonant phenomena due to the form-factor of Higgs boson, we calculate the variation of Higgs-boson production and decay rate with the CM energy in LHC. We also present the discussions on four-fermion operators in the lepton sector and the mass-squared differences for neutrino oscillations in short baseline experiments.