The Other Fermion Compositeness

TL;DR

This work posits that fermion compositeness consistent with fundamental principles reduces to two calculable EFT patterns: chiral-compositeness with dimension-6 operators and goldstino-compositeness—the latter arising from non-linearly realized SUSY and described by an EFT of ${\cal N}$ Goldstini. The authors construct the Goldstini EFT from a coset geometry, derive the Akulov-Volkov sector, and organize model-independent and model-dependent couplings to composite fields, including maximal $R$-symmetry embeddings that can place SM fermions among Goldstini. They embed leptons and quarks into Goldstini multiplets, predict exotic colored states (quixes) under maximal $R$-symmetry, and analyze explicit SUSY breaking by SM couplings, which generates MFV-consistent dimension-6 and dimension-8 operators. Collider data from the LHC and LEP constrain the corresponding scales $m_*$ and $F$, with significant sensitivity to the dimension-8 goldstino operators; notably, Goldstini-like electrons can be compatible with $m_*$ in the few-TeV range, while full quark completion typically requires higher scales, and the theory also predicts novel color sextets whose phenomenology is actively probed at the LHC. Overall, the paper provides a theoretically robust framework for distinguishing fermion compositeness patterns via high-energy scattering, precision observables, and exotic states, highlighting the energy-dominated reach of goldstino-compositeness and its distinctive collider signatures.

Abstract

We discuss the only two viable realizations of fermion compositeness described by a calculable relativistic effective field theory consistent with unitarity, crossing symmetry and analyticity: chiral-compositeness vs goldstino-compositeness. We construct the effective theory of $\mathcal{N}$ Goldstini and show how the Standard Model can emerge from this dynamics. We present new bounds on either type of compositeness, for quarks and leptons, using dilepton searches at LEP, dijets at the LHC, as well as low-energy observables and precision measurements. Remarkably, a scale of compositeness for Goldstino-like electrons in the 2 TeV range is compatible with present data, and so are Goldstino-like first generation quarks with a compositeness scale in the 10 TeV range. Moreover, assuming maximal $R$-symmetry, goldstino-compositeness of both right- and left-handed quarks predicts exotic spin-1/2 colored sextet particles that are potentially within the reach of the LHC.

Figures (4)

• Figure 1: Some leading diagrams contributing to dimension-6 operators with fermions. Black blobs denote strong interactions, while little red (blue) ones denote SM gauge (Yukawa) couplings that break SUSY explicitly.
• Figure 2: Some leading diagrams contributing to (magnetic) dipole moments and flavor transitions.
• Figure 3: Left: Dijet angular distributions in the highest-energy bin $M_{jj}>5.4 \,\mathrm{TeV}$, for the experimental data with its systematic plus statistical uncertainties (black points), the SM prediction with its theoretical error (blue band), and the BSM predictions for the dimension-8 operator $\mathcal{O}_{dd}$ (solid orange) or the dimension-6 operator $\mathcal{O}_{dd}^{(1)}$Domenech:2012ai (dashed red). The corresponding (positive) coefficients have been chosen to saturate the bounds Eqs. (\ref{['bounds']}) and (\ref{['boundsb']}). Right: Bounds on the scale $m_*$ for a composite $d_R$ with a dimension-8 operator $|c_{dd}| = (4 \pi)^2/2m_*^4$ (orange) or a dimension-6 operator $|c_{dd}^{(1)}| = (4 \pi/m_*)^2$ (red) and for all quarks composite with dimension-8 operators $|c_{ij}| = (4 \pi)^2/2m_*^4$ (black), for different $\chi$ bins (dots) and for all bins combined (lines). The round dots and solid lines correspond to $c > 0$ while square dots and dashed lines to $c < 0$.
• Figure 4: Left: $95\% \, \mathrm{CL}$ upper limits on single- and pair-production cross sections, compared with the theoretical cross sections for single-production (blue) with $m_*/\epsilon = 20$ (solid) or $m_*/\epsilon = 10$ (dashed) and pair-production (dot-dashed red). Right: Exclusion regions at $95\% \, \mathrm{CL}$ from single-production (dark grey; ATLAS:2016lvi solid line and Aaboud:2017yvp dashed line) and double-production (light grey; dot-dashed line). Also shown are lower bounds (red) on the (inverse) coupling of the sextet, $m_*/\epsilon \approx 19 \,\mathrm{TeV}$ (dashed; corresponding to a scale $m_* = 5.4 \,\mathrm{TeV}$, the highest energy of our dijet analysis, and a small parameter $\epsilon = 0.3$), $m_*/\epsilon \approx 27 \,\mathrm{TeV}$ (dot-dashed; same $m_*$, $\epsilon = 0.2$) and $m_*/\epsilon \approx 33 \,\mathrm{TeV}$ (solid; coupling below which pair production dominates the constraints).