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Symmetric Mass Generation

Anna Hasenfratz, Oliver Witzel

TL;DR

This work investigates symmetric mass generation (SMG) in a four-dimensional SU(3) gauge theory with $N_f=8$ fundamental fermions, testing whether SMG can occur without chiral symmetry breaking and potentially provide a UV completion of the Standard Model. Using a Pauli–Villars–improved lattice action with nHYP-smeared staggered fermions, the authors access strong coupling and analyze the hadron spectrum, hyperscaling, and finite-size scaling to map a phase diagram featuring a weak-coupling conformal region and a strong-coupling SMG phase. They find no evidence of chiral symmetry breaking in the chiral limit and observe a continuous transition between the two phases, with parity doubling in correlation functions and hyperscaling behavior consistent with a nontrivial fixed point. If confirmed, these results imply a UV-complete continuum QFT for $SU(3)$ with $N_f=8$ and open avenues for beyond-Standard-Model physics through SMG dynamics and higher-dimensional operators.

Abstract

In recent years tantalizing signs for a novel phase have been reported that is chirally symmetric but nevertheless exhibits massive bound states. The necessary condition for such a phase, referred to as Symmetric Mass Generation (SMG), is the cancellation of all (continuous and discrete) 't~Hooft anomalies. In 3+1 dimensions this occurs in systems containing a multiple of 16 massless Weyl fermions. SMG was originally discovered in lower dimensional condensed matter systems. We present results investigating four dimensional field theories with gauge group SU(3). Our findings suggest that SU(3) with $N_f=8$ fundamental fermions exhibits an SMG phase not only on the lattice but also in the infinite cutoff continuum limit. If confirmed, SMG could provide a new UV completion of the standard model and give rise to new scenarios for beyond standard model physics.

Symmetric Mass Generation

TL;DR

This work investigates symmetric mass generation (SMG) in a four-dimensional SU(3) gauge theory with fundamental fermions, testing whether SMG can occur without chiral symmetry breaking and potentially provide a UV completion of the Standard Model. Using a Pauli–Villars–improved lattice action with nHYP-smeared staggered fermions, the authors access strong coupling and analyze the hadron spectrum, hyperscaling, and finite-size scaling to map a phase diagram featuring a weak-coupling conformal region and a strong-coupling SMG phase. They find no evidence of chiral symmetry breaking in the chiral limit and observe a continuous transition between the two phases, with parity doubling in correlation functions and hyperscaling behavior consistent with a nontrivial fixed point. If confirmed, these results imply a UV-complete continuum QFT for with and open avenues for beyond-Standard-Model physics through SMG dynamics and higher-dimensional operators.

Abstract

In recent years tantalizing signs for a novel phase have been reported that is chirally symmetric but nevertheless exhibits massive bound states. The necessary condition for such a phase, referred to as Symmetric Mass Generation (SMG), is the cancellation of all (continuous and discrete) 't~Hooft anomalies. In 3+1 dimensions this occurs in systems containing a multiple of 16 massless Weyl fermions. SMG was originally discovered in lower dimensional condensed matter systems. We present results investigating four dimensional field theories with gauge group SU(3). Our findings suggest that SU(3) with fundamental fermions exhibits an SMG phase not only on the lattice but also in the infinite cutoff continuum limit. If confirmed, SMG could provide a new UV completion of the standard model and give rise to new scenarios for beyond standard model physics.

Paper Structure

This paper contains 3 sections, 4 figures.

Table of Contents

  1. Introduction
  2. Numerical setup and results
  3. Summary

Figures (4)

  • Figure 1: Sketch of the phase structure for SU(3) with $N_f=8$ fundamental flavors. A similar phase structure was identified for SU(2) gauge with $N_f=4$ in Ref. Butt:2024kxi.
  • Figure 2: Left: lightest pseudoscalar mass $aM_{PS}$ in lattice units vs. the bare gauge coupling $\beta_b$. Right: Test for conformal hyper-scaling by plotting $L\cdot M_{PS}$ vs. $\beta_b$.
  • Figure 3: Pseudoscalar and scalar correlators on $24^3\times 48$ lattices at strong coupling ($\beta_b=8.60$) on the left and weak coupling ($\beta_b=9.20$) ont the right.
  • Figure 4: Curve-collapse fits to explore the nature of the phase transition using data near the critical point. The left plot tests the hypotheses of a 1st or 2nd order phase transition, whereas the plot on the right tests for a BKT transition.