High-precision calculation of the quark–gluon coupling from lattice QCD | Nature

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Subjects

- Phenomenology

- Theoretical particle physics

Abstract

The outcomes of modern particle physics experiments, such as proton–proton collisions at the Large Hadron Collider at CERN (European Organization for Nuclear Research), depend crucially on the precise description of the scattering processes in terms of the fundamental forces. Among all the known forces that contribute, the limited understanding of the strong nuclear force is a key source of inaccuracy. At the fundamental level, the strong force is described by quantum chromodynamics, the theory of quarks and gluons. Their coupling, αs, becomes weaker at high energies (asymptotic freedom), enabling power series expansions in αs, but the confinement of quarks in hadronic bound states usually requires additional model assumptions. Consequently, determinations of αs from experiment mostly remain with large systematic theory errors1,2. Here we report the model-free determination of αs with unprecedented precision from low-energy experimental input combined with large-scale numerical simulations of the first-principles formulation of quantum chromodynamics on a space–time lattice. The uncertainty, about half that of all other results combined3, originates predominantly from the statistical Monte Carlo evaluation and has a clear probabilistic interpretation. The result for αs describes both low-energy hadronic physics with the help of lattice quantum chromodynamics and high-energy scattering using the perturbative expansion. By removing a source of theoretical uncertainty, our estimate of αs could enable markedly improved analyses of many high-energy experiments4. This will contribute to the likelihood that small effects of yet unknown physics are uncovered, as well as enable stringent precision tests of the Standard Model.

Main

At the fundamental level, the strong nuclear force between nucleons arises from quantum chromodynamics (QCD), a quantum field theory formulated in terms of their ‘colour-charged’ elementary constituents, the quarks and gluons. The interaction between these constituents is characterized by being weak at very high energies and short distances, a phenomenon known as asymptotic freedom5,6, whereas, in contrast to the other forces, it is so strong at nuclear distances that thinking of quarks and gluons as individual particles makes no sense at all. We speak of ‘confinement’: fundamental quarks and gluons cannot be directly observed, but instead, only composite ‘colour-neutral’ states, such as protons, neutrons or π-mesons, are observed in experiments. This fact poses several challenges, including the fundamental question of how to determine the strength of the interaction between quarks and gluons at high energy.

The quark–gluon coupling, αx(μ), depends on the energy scale, μ, of the interaction and also on its detailed definition, summarized as the ‘scheme’, x. Owing to confinement, we cannot collide quarks with quarks or gluons and determine αx(μ), directly in experiments. Instead, phenomenological estimates of the strong coupling are obtained by examining different processes, such as electron–positron or proton–proton collisions at various energy scales. After decades of theoretical and experimental efforts to parameterize the effects of confinement and to identify observables in which these effects are minimized, significant uncertainties persist. In particular, in determining a world average of αx(μ), notably by the Particle Data Group (PDG), different categories still exhibit uncertainties in the range of 1.5–3% (compare ref. 3 and Fig. 5). In fact, in most cases, these are not simply due to the limited precision of the experimental data, but include significant systematic uncertainties originating from the lack of an analytic understanding of confinement. In this situation, we cannot profit much from having more experimental data in reducing the uncertainty in αx(μ).

The inaccuracy of αx(μ) limits the potential of current experiments that test the fundamental laws of nature4. Even when all phenomenology extractions of the strong coupling are combined, they lead to an error of about 1%. This uncertainty propagates, for example, into a 2–4% uncertainty in the rate of production of Higgs particles by gluon fusion7 or its decay into gluons8. Furthermore, reducing the current uncertainty in the strong coupling by a factor of 2 turns out to be crucial9 for finding out whether the vacuum of the Standard Model is stable10 and to constrain extensions of the Standard Model, which cure the possible instability11,12.

A first-principles, robust, free of modelling uncertainties determination of the strong coupling avoids the limitations of extractions from experimental data and will affect ongoing searches for new physics.

Here we provide such a determination. We analyse the scale dependence of the strong coupling, as described by its β-function:

$$\mu \frac{{\rm{d}}}{{\rm{d}}\mu }{\alpha }_{{\rm{x}}}(\mu )={\bet