# Measuring the strong coupling constant: from the LHC to FCC-ee

The latest advances in the measurement of the coupling of the strong interaction were discussed in a recent workshop on “High precision measurements of α_{s}: from LHC to FCC-ee” held at CERN, 12-13 October 2015. The meeting brought together the leading experts in the field to explore in depth the latest developments on the determination of the strong interaction coupling, presenting results from high-precision measurements and theoretical developments, exploring new ways to measure this coupling in lepton-lepton, lepton-hadron and hadron-hadron collisions, and finally discussing the results expected within the next years at the LHC as well as at the proposed FCC-ee facility.

The strong interaction between coloured quarks and gluons is described by a quantum field theory known as Quantum Chromodynamics (QCD). Its coupling constant as sets the scale of the strength of the strong interaction at a given reference scale (usually taken as the Z boson mass), and it is one of the fundamental parameters of the Standard Model (SM). It is the key quantity for understanding how the fundamental building blocks of matter interact and bound to form hadrons.

The as coupling, known so far with a δα_{s} ≈ ±0.5% uncertainty, is the least precisely known of all fundamental constants in nature, orders of magnitude less well known than the gravitational constant (δG ≈ ±10^{-5}), Fermi (δGF ≈ ±10^{-8}), and the QED fine structure constant (δα ≈ ±10^{−10}). Improving the measurement of as is a prerequisite to reduce the theoretical uncertainties in the calculations of all high-precision perturbative QCD (pQCD) processes whose cross sections or decay rates depend on higher-order powers of a_{s}, as is the case for virtually all the cross-sections measured at the LHC. To address these broader challenges in the field, David d'Enterria and Peter Skands (conveners of the FCC-ee “QCD and g-g” working group), organized this workshop with the aim to address the following three main issues:

• *What is the current state-of-the-art of each one of the α _{s} determination methods, from the theoretical and experimental point of view? What is the current size of the theoretical and experimental uncertainties associated to each*

*α*measurement

_{s}*?*

• *What is the expected uncertainty o*f* α _{s}*measur

*ements in about 10 years from now, taking into account the ongoing theoretical developments as well as the large LHC data sets collected at 13 and 14 TeV?*

•*What are the improvements that a project like FCC-ee could bring in through e ^{+}e^{-} collisions at √ s = 91, 160, 240 and 350 GeV with 10^{12 }Z bosons and jets, and 10^{8} W bosons and leptons collected? What are the systematic errors that the FCC-ee detectors should target in order to match the expected statistical precision, or where that is not possible, what are the important theoretical targets that should be met or exceeded?*

With those goals in mind, the workshop was organized along four sessions. The introductory session, presented the motivations of the workshop, the current status of the world average of the strong coupling, the impact of α_{s} on Higgs cross sections and branching ratios, and on new physics constraints. The uncertainty introduced from α_{s} is currently the second major contributor -after the bottom mass- to the parametric uncertainties of the dominant H -> bb partial decay, and the largest source of uncertainty for the charm-anticharm and gluon-gluon decay modes. An accurate knowledge of the running of α_{s} at large energy scales is also crucial for searches of physics beyond the SM.

The second session of the workshop was devoted to measurements that allow one to extract the QCD coupling at low energies. Those include results from lattice QCD, pion decay factor, τ decays, Upsilon decays, and the evolution of the soft parton-to-hadron fragmentation functions. The comparison of pQCD predictions to computational “data” obtained in lattice QCD calculations, yielding α_{s }= 0.1184±0.0012, still provides the most precise determination of the strong coupling to date, with a δα_{s} ≈ ±1% uncertainty. Theoretical developments in the next 10 years could reduce this uncertainty by a factor of ten. Hadronic decays of the tau lepton result in δα_{s}= ±1.9%, although different theoretical approaches for the perturbative and non-perturbative aspects of the calculations, discussed during the workshop, are still a matter of debate.

The a_{s} determination at higher energy scales –including global fits of parton distribution functions PDFs, hard parton-to-hadron FFs, jets in deep-inelastic and photoproduction processes in e^{±}p collisions, e^{+}e^{-} event shapes, jet cross sections in e^{+}e^{-}, hadronic Z and W decays, and the e^{+}e^{-} hadrons cross section - were the topics covered in the third section of the workshop. The final session of the workshop was dedicated to α_{s} extractions at hadronic colliders. Important theoretical developments for top-quark pair and jets cross sections were reviewed.

The workshop ended with a summary of the discussions given by David d'Enterria who noted that originally, Guido Altarelli had agreed to summarize the results of the workshop. Guido was in touch with the organizers until a few days before he passed away. His loss is an enormous loss for the QCD, and high-energy particle physics, community at large.

The workshop triggered discussions between different groups, offering speakers the opportunity to explain details that have an important impact on the analyses. Novel ideas to extract α_{s}, uncertainties in the combination of different methods, as well issues to be addressed in the experimental design for a future circular collider were also discussed.

It has been a well-attended meeting with more than 40 registered participants, 65 final attendants, and 24 talks covering a wide span of topics. At the end of the workshop, participants were asked to submit written contributions addressing the main goals of the conference that will be published in a short report before the end of the year, and ultimately included into the Conceptual Design Report of the FCC-ee under preparation.

*Slides as well as background reference materials are available on the conference website: *http://indico.cern.ch/e/alphas2015

**The author would like to thank David D’Entreria and Peter Skands for offering valuable insights to this article.**