First sight of the running of the top-quark mass

The coupling between quarks and gluons depends strongly on the energy scale of the process. The same is true for the masses of the quarks. This effect – the so‑called “running” of the strong coupling constant and the quark masses – is described by the renormalisation group equations (RGEs) of quantum chromodynamics (QCD). The experimental verification of the RGEs is both an important test of the validity of QCD and an indirect search for unknown physics, as physics beyond the Standard Model could modify the RGEs at scales probed by the Large Hadron Collider. The running of the strong coupling constant has been established at many experiments in the past, and, over the past 20 years, evidence for the running of the masses of the charm and bottom quarks was demonstrated using data from LEP, SLC and HERA, though the running of the top‑quark mass has hitherto proven elusive.

CMS has probed the running of the mass of the top quark for the first time

The CMS collaboration has now, for the first time, probed the running of the mass of the top quark. The measurement was performed using proton–proton collision data at a centre‑of‑mass energy of 13 TeV, recorded by the CMS detector in 2016. The top quark’s mass was determined as a function of the invariant mass of the top quark–antiquark system (the energy scale of the process), by comparing differential measurements of the system’s production cross section with theoretical predictions. In the vast majority of the cases, top quarks decay into a W boson and a bottom quark. In this analysis, candidate events are selected in the final state where one W boson decays into an electron and a neutrino, and the other decays into a muon and a neutrino.

One-loop agreement

The cross section was determined using a maximum‑likelihood fit to multi‑differential distributions of final‑state observables, allowing the precision of the measurement to be significantly improved by comparison to standard methods (figure 1). The measured cross section was then used to extract the value of the top‑quark mass as a function of the energy scale. The running was determined with respect to an arbitrary reference scale. The measured points are in good agreement with the one‑loop solution of the RGE, within 1.1 standard deviations, and a hypothetical no‑running scenario is excluded at above 95% confidence level.

This novel result supports the validity of the RGEs up to a scale of the order of 1 TeV. Its precision is limited by systematic uncertainties related to experimental calibrations and the modelling of the top‑quark production in the simulation. Further progress will not only require a significant effort in improving the calibrations of the final‑state objects, but also substantial theoretical developments.