Unraveling the Secrets of the Strong Force: A New Era of Precision at the LHC

25 March 2026

Photo: Thomas Cridge, Giulia Marinelli, Frank J. Tackmann

Uncertainties in the transverse momentum spectrum, before (yellow band) and after (orange band) employing the new method of profiling Theory Nuisance Parameters (TNPs).

Scientists from the Cluster of Excellence Quantum Universe, University of Hamburg, and DESY are working towards a new era of precision at the Large Hadron Collider (LHC). Their work focuses on understanding the fundamental laws that govern the universe at the smallest scales, where nature is described by quantum physics. Precise measurements of key quantities, such as the strong coupling constant, help test these laws and check whether our current theories correctly describe the quantum universe.

In the subatomic world, nature gives us four fundamental forces. Gravity, electromagnetism, and the weak nuclear force are well-known. But the most difficult to measure experimentally with precision is the strong nuclear force, the interaction that glues quarks together inside protons and neutrons and holds the nucleus of atoms together. Its "strength" is quantified by a single number, the strong coupling constant, or simply α_s.

Knowing the exact value of α_s is crucial for physicists: it's like having a precision ruler for all other predictions in particle physics. Without it, we cannot reliably compare our theories to the results of experiments at CERN's Large Hadron Collider (LHC). Currently, the most precise value of α_s comes from complex computer simulations (called lattice QCD) and has an uncertainty of about 0.6%. Obtaining an equally precise measurement directly from particle collider experiments is one of the grand challenges of modern physics.

At the LHC, when two protons collide, their constituents can interact and produce a Z boson, one of the elementary particles of the Standard Model. It acquires a sideways "kick", called transverse momentum (q_T ). The cause of this kick is the emission of gluons at the moment of the collision. It is precisely in the study of this transverse kick distribution (the q_T spectrum) that α_s reveals itself. The maximum sensitivity to α_s is found in the so-called "peak" region, where the kick is very small. But here's the challenge: the effect of α_s on the shape of the peak is very subtle, and it can be easily masked or mimicked by other physical phenomena. If we don't handle these effects carefully, we risk misinterpreting a spurious effect as a real change in α_s, biasing our extraction.

Theoretical calculations in particle physics are performed using perturbation theory, where we computed quantities as an expansion in powers of α_s. This means our predictions are intrinsically approximate—we can only calculate a finite number of terms in an infinite series. Traditionally, the uncertainty of such calculations is estimated by varying unphysical scales that appear in the calculations themselves. This approach has well-known limitations; especially, it does not provide a statistically meaningful uncertainty, and it fails to capture how the uncertainty at one point in the spectrum is correlated with the uncertainty at another point.

This is crucial: Imagine that if the uncertainty is the same at every point, the shape of the spectrum does not change and the measurement of α_s is unaffected. But if the uncertainty varies from point to point, it can perfectly mimic the effect of α_s itself.

To overcome these limitations, we employ a novel framework based on Theory Nuisance Parameters (TNPs). The idea is simple yet powerful: we define the missing higher-order terms as a set of nuisance parameters with associated uncertainties. These parameters encode distinct sources of theory uncertainty and capture the correct theory correlation across the spectrum.

To test this framework, we studied how well α_s can be extracted using simulated data (called Asimov data) based on the highest available perturbative accuracy. The figure on top shows the uncertainty decomposition for the q_T spectrum in terms of seven independent TNPs (colored lines). Their combined effect gives the total pre-fit uncertainty (yellow band). A key advantage of this approach is that the TNPs can be consistently constrained by the data itself, i.e., profiled in the fit to data. The result is an even more reduced theory uncertainty (orange band).

Our analysis demonstrates that a robust treatment of correlated theory uncertainties is both essential and possible. This sets the stage for a reliable precision determination of α_s, with an expected uncertainty at or below 1%, competitive with the current world average. For a full extraction of α_s additional theory inputs and subleading effects need to be incorporated and their uncertainties carefully assessed, and we are currently working on this.

The TNP framework provides a method to quantify theory uncertainties and their correlations in a systematic, robust, and statistically meaningful way. It confirms that the approach is not only conceptually well-motivated but also experimentally viable at the highest level of precision. By enabling a more faithful treatment of theory uncertainties, this framework opens the door to a new generation of precision studies at the LHC and beyond. It allows fundamental parameters to be extracted with the highest possible accuracy and, just as importantly, with reliable theory uncertainties.