Repurposing lattice QCD results for composite phenomenology

TL;DR

This work compiles and interprets SU(3) lattice QCD results obtained at moderately heavy quark masses to aid beyond-Standard-Model phenomenology. It emphasizes using dimensionless ratios and physically motivated scale settings, and provides practical parameterizations for spectroscopy and decay constants across a range of quark masses. Key contributions include empirical relations for pseudoscalar and vector masses, linear fits for hadron spectra in intermediate regimes, and lattice determinations of decay constants, sigma terms, and resonance couplings, along with cautions on sum rules and resonance treatment. The findings offer a bridge from lattice results at unphysical points to concrete inputs for composite dark matter, composite Higgs, and other BSM scenarios, enabling more reliable phenomenological modeling and cross-checks with EFT descriptions.

Abstract

A number of proposed extensions of the Standard Model include new strongly interacting dynamics, in the form of SU(N) gauge fields coupled to various numbers of fermions. Often, these extensions allow N = 3 as a plausible choice, or even require N = 3, such as in twin Higgs models, where the new dynamics is a "copy" of QCD. However, the fermion masses in such a sector are typically different from (often heavier than) the ones of real-world QCD, relative to the confinement scale. Many of the strong interaction masses and matrix elements for SU(3) at heavy fermion masses have already been computed on the lattice, typically as a byproduct of the approach to the physical point of real QCD. We provide a summary of these relevant results for the phenomenological community.

Figures (14)

• Figure 1: Squared pseudoscalar meson mass in GeV${}^2$ as a function of the quark mass in MeV. Data are black diamonds from Ref. WalkerLoud:2008bp, red octagons from Ref. Aoki:2008sm, violet crosses from Refs. Alexandrou:2008tnJansen:2009hrBaron:2009wt, blue squares from this work. The square points are likely contaminated by finite-volume systematic effects, as discussed in the text, but they nevertheless show the correct qualitative relationship between $M_{PS}^2$ and $m_q$.
• Figure 2: Edinburgh plot, $M_N/M_V$ vs $M_{PS}/M_V$. Data are black diamonds from Ref. WalkerLoud:2008bp, red octagons from Ref. Aoki:2008sm, violet crosses from Refs. Alexandrou:2008tnJansen:2009hrBaron:2009wt, blue squares from this work. The stars show the physical point and the heavy quark limit.
• Figure 3: Top panel: the ratio $(M_{PS}/M_V)^2$ as a function of the quark mass in MeV. Data are black diamonds from Ref. WalkerLoud:2008bp, red octagons from Ref. Aoki:2008sm, violet crosses from Refs. Alexandrou:2008tnJansen:2009hrBaron:2009wt, blue squares from this work. Bottom panel: the ratio $(M_{PS}/M_V)^2$ as a function of $M_{PS}$ in MeV.
• Figure 4: Meson masses in MeV as a function of the ratio $(M_{PS}/M_V)^2$ (top panel) and quark mass in MeV (bottom panel.) Stars are values of physical particles, obtained as described in the text: gold (silver) stars denote vector (axial-vector) states. The lower densely-populated band is the mass of the isovector vector meson (the rho) and the upper band is the $a_1$. For these particles, the symbols are black diamonds from Ref. WalkerLoud:2008bp, red octagons from Ref. Aoki:2008sm, violet crosses from Refs. Alexandrou:2008tnJansen:2009hrBaron:2009wt, blue squares from this work. The dashed lines show linear fits to the data in certain regimes, as described in the text.
• Figure 5: Nucleon (lower band) and delta baryon (upper band) masses in MeV, as a function of $(M_{PS}/M_V)^2$ (top panel) and quark mass in MeV (bottom panel). Data are black diamonds from Ref. WalkerLoud:2008bp, red octagons from Ref. Aoki:2008sm, violet crosses from Refs. Alexandrou:2008tnJansen:2009hrBaron:2009wt, blue squares from this work. Stars show the physical nucleon and delta masses, and dashed lines show linear fits to the data as described in the text.