The CMS experiment achieves the most precise determination of the strength of the strong nuclear force using the rates of production of jets at several centre-of-mass energies.

The strengths of the fundamental interactions in Nature drive the evolution of our universe, and a precise knowledge of their values affects our understanding of this evolution.

Formally, these strengths are encoded in coupling constants. While we can calculate the energy dependence of these couplings in the standard model of particle physics, experimental measurements are needed to extract their values at a particular scale. Out of the three known coupling constants relevant for particle physics, the least well known is the strength of the strong nuclear force.

The constituents of the atomic nuclei, protons and neutrons, are made of quarks, interacting through the strong force by exchanging gluons. The presence of these gluons is responsible for the generation of most of the visible mass in our universe. The strength of this force is governed by the fundamental constant of nature α_S, which in fact is not a constant, but depends on the energy (or distance), at which we probe matter!

This fundamental quantum property of the strong interaction has been predicted theoretically and confirmed experimentally. At high energies, the strong force becomes very weak and we talk about “asymptotic freedom” of quarks. At small energies, in contrast, α_S becomes very large and the force becomes very strong. This property is known as confinement, which manifests itself in the non-observation of free quarks. Instead, once a quark is kicked out of a proton e.g. in proton-proton collisions at the LHC, it gives birth to a collimated spray of particles, called jets. Jets preserve the direction and energy of the particle that initiated them and their production rate is proportional to the value of α_S. Jets are produced abundantly at the LHC. We reconstruct them by combining the responses of different sub-detectors of the CMS detector.

Previously, the CMS experiment measured the rates of events in which at least one highly energetic jet is produced in proton-proton collisions at different centre-of-mass energies of 2.76, 7, 8 and 13 TeV. Now, for the first time, all these measurements are analyzed together, accurately assessing the correlations of the systematic uncertainties among the different measurements. Valentina Guglielmi from DESY, the leading author of this study, says: “This is very tedious work, basically going back in time and investigating the calibrations and assumptions made for each measurement. I felt a bit like an archaeologist, but ultimately this study did not only improve the accuracy of our results but can also be applied in future interpretations of our data by theorists.”

Comparing these measurements to theory predictions at the highest precision possible to date, we extracted the value of the strong coupling. An additional challenge in the determination of α_S from jet production in proton-proton collisions comes from the structure of the protons themselves. The so-called parton distribution functions (PDFs), which describe how the momenta of the quarks and gluons are distributed in the proton, are an important ingredient when calculating jet rates. As a result, there is a strong correlation between α_S and the PDFs when predicting jet rates, and the uncertainties in the PDFs affect the precision of the resulting value of α_S. In the CMS analysis, this tricky correlation is mitigated through a simultaneous extraction of PDFs and the value of α_S.

Above: The value of α_S(m_Z) obtained in this analysis (red marker), compared with previous CMS results obtained by using different methods (black markers) with their total uncertainties (horizontal error bars). The world average (dashed line) together with its uncertainty (shaded band) is also shown.

Furthermore, by applying this method in intervals of jet transverse momenta, serving as the energy scale for the measurement, the energy dependence of the strong coupling, its so-called running, can be precisely probed (below).

Above: The running of the strong interaction coupling. The results of this analysis (black markers) are shown with their total uncertainties (vertical error bars). For comparison, the theory prediction is shown using the current world-average value α_S(m_Z) = 0.1180 ± 0.0009 (red line) together with its associated total uncertainty (shaded band).

This result prominently illustrates the weakening of the strong force between quarks with increasing energy towards their asymptotic freedom.

These new results represent the most precise determination of α_S and its running from jet data to date.

Read more about these results:

• CMS Publication (SMP-24-007): "Determination of the strong coupling and its running from measurements of inclusive jet production"

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