[Paper Review] Ab-initio calculation of the proton and the neutron's scalar couplings for new physics searches

Sz. Borsányi, Z. Fodor+5 more|arXiv (Cornell University)|Jul 7, 2020

Dark Matter and Cosmic PhenomenaPhysics and Astronomy1 references17 citations

TL;DR

This paper presents a fully controlled, ab-initio calculation of proton and neutron scalar couplings (σ-terms) to the six quark flavors using lattice QCD and heavy-quark effective theory. It achieves sub-15% accuracy for all six quark contributions, providing critical inputs for interpreting dark matter and flavor-violating searches.

ABSTRACT

Many low-energy, particle-physics experiments seek to reveal new fundamental physics by searching for very rare scattering events on atomic nuclei. The interpretation of their results requires quantifying the non-linear effects of the strong interaction on the spin-independent couplings of this new physics to protons and neutrons. Here we present a fully-controlled, ab-initio calculation of these couplings to the quarks within those constituents of nuclei. We use lattice quantum chromodynamics computations for the four lightest species of quarks and heavy-quark expansions for the remaining two. We determine each of the six quark contributions with an accuracy better than 15%. Our results are especially important for guiding and interpreting experimental searches for our universe's dark matter.

Motivation & Objective

• To provide precise, first-principles predictions of nucleon σ-terms for all six quark flavors, essential for interpreting low-energy new physics experiments.
• To overcome systematic uncertainties in previous lattice and phenomenological determinations by employing high-statistics, fully controlled lattice QCD simulations.
• To extend the calculation to heavy quarks (charm, bottom, top) using heavy-quark effective theory (HQET), ensuring consistency across the quark mass spectrum.
• To deliver a complete, correlated set of quark content values for arbitrary linear combinations, enabling flexible use in experimental analyses.

Proposed method

• Perform high-statistics lattice QCD simulations on four-fermion ensembles with four lightest quarks (u, d, s, c), using multiple lattice spacings and volumes to control finite-volume and discretization effects.
• Apply continuum extrapolation and infinite-volume limits using a comprehensive set of 24 analysis procedures, with systematic error estimated via AIC-weighted combination of fits.
• Use heavy-quark effective field theory (HQET) to compute σ-terms for b and t quarks, with perturbative expansions valid up to O((Λ_QCD/m_Q)^2) corrections.
• Input lattice results for light and strange quarks into HQET expressions to compute b and t contributions, with errors combined in quadrature.
• Develop a C routine that computes arbitrary linear combinations of quark contents with full correlation information, enabling flexible use in Higgs-nucleon coupling and dark matter direct detection analyses.
• Validate results using crosschecks: HQET prediction for charm quark σ-term agrees with direct lattice result within uncertainties.

Experimental results

Research questions

• RQ1 What are the precise scalar couplings of the proton and neutron to the u, d, s, c, b, and t quarks, with controlled systematic errors?
• RQ2 How can lattice QCD and heavy-quark effective theory be combined to reliably compute σ-terms across the full quark mass spectrum?
• RQ3 To what extent do different fitting procedures, scale-setting methods, and continuum extrapolation schemes affect the final σ-term values?
• RQ4 How do the results compare with existing phenomenological and lattice estimates, and what improvements do they bring in terms of precision and control?
• RQ5 Can a unified, correlated framework be provided for computing arbitrary linear combinations of quark contents relevant to Higgs-nucleon couplings and dark matter searches?

Key findings

• The u, d, s, and c quark σ-terms for both proton and neutron are computed with an accuracy better than 15%, using high-statistics lattice QCD simulations.
• The charm quark σ-term is validated via a crosscheck using heavy-quark effective theory, yielding f_c^N = 0.07323(61)(65), in excellent agreement with the direct lattice result.
• The bottom quark σ-term is computed as f_b^N = 0.08748(13) - 0.10129(39) × f̄_4, with the dominant uncertainty arising from lattice inputs of light quarks.
• The top quark σ-term is computed as f_t^N = 0.09169(4) - 0.09840(10) × f̄_5, with the error primarily driven by uncertainties in the light quark contributions.
• The systematic error is dominated by the continuum extrapolation procedure, with the fit quality averaging Q̄ = 0.60 across all analyses.
• A public C routine is released that computes arbitrary linear combinations of quark contents with full correlations, enabling flexible use in Higgs and dark matter coupling studies.