The mass of a top

Standard

by Peter Skands from Nature 514, 174–176 (09 October 2014) doi:10.1038/514174a

A measurement of the mass of the heftiest-known elementary particle, the top quark, which exists for less than a trillionth of a trillionth of a second, sheds light on the ultimate fate of our Universe, although ambiguities cloud its interpretation.

Writing in Physical Review Letters, researchers working in the D0 experiment (Abazov et al.(1)) at the Tevatron accelerator at Fermilab near Chicago, Illinois, report the most precise single measurement so far of the mass of the heaviest-known elementary particle, the top quark. The result concludes an exciting 20-year saga — from the joint discovery of the top quark by the D0 Collaboration(2) and its competitor the CDF Collaboration(3), to a measurement of the top quark’s mass with a precision better than 0.5%. A similar result from the CDF experiment is to be expected, updating their 2012 result(4).
The top quark is one of six types of quark predicted by the standard model of particle physics; quarks are elementary particles that make up composite particles such as protons and neutrons. The top quark existed in the extremely hot conditions of the early Universe and can be recreated artificially by large particle accelerators such as the Tevatron. The D0 experiment takes its name from its location on the accelerator ring. According to the D0 measurement, a top quark weighs 187.85 ± 0.82 atomic units (174.98 ± 0.76 gigaelectronvolts c−2 in particle-physics units, with c being the speed of light), just shy of the mass of a gold atom. Unlike atoms, however, the top quark is elementary, and acquires its mass by interacting with the elusive, omnipresent Higgs field, the telltale evidence of which — the Higgs boson — was famously discovered(5, 6) in 2012.
Briefly stated, the presence of the Higgs field in the Universe causes an increase in the potential energy of all particles except photons, gluons and possibly neutrinos. The extra potential energy is equivalent to a mass, and the size of this mass is proportional to the strength of the Higgs field (called its vacuum expectation value, a universal constant) and to the size of each particle’s ‘Higgs charge’, which determines how strongly each particle interacts with the Higgs field. For the top quark, this charge is called the top-quark Yukawa coupling, named after the Japanese physicist and Nobel laureate Hideki Yukawa.
The fact that the top quark has by far the largest mass among elementary particles implies that it has by far the largest Yukawa coupling, and this in turn gives rise to some of the most significant quantum fluctuations in nature. At the quantum level, the Higgs field constantly fluctuates into pairs of ‘virtual’ particles and antiparticles, which are allowed a brief existence by Heisenberg’s uncertainty principle. Because of the huge top-quark Yukawa coupling, the fluctuations involving the top quark affect the shape of the Higgs potential (which describes the potential energy of the Higgs field as a function of the field strength). In fact, making the strong assumption that there are no as-yet-undiscovered particles, the Higgs field seems to exist in a local minimum of the potential(7), which would make the Universe as we know it unstable. Fortunately, the calculated lifetime of the Universe comfortably exceeds its present age. So, rest assured, the Universe will not decay tomorrow. But the desire to ascertain its ultimate fate is a key reason for accurately determining the top-quark mass: differences of just 5% in this mass make the difference between stability and instability. With modern experimental measurements such as that from D0 reaching precisions better than 1%, it is now largely a matter of improving the delicate theoretical calculations to settle the issue.
The measurement is far from trivial. First, in collisions of protons and antiprotons at the Tevatron, top quarks are created predominantly by the strong nuclear force, which conserves ‘quark number’, and so they must be created in pairs (top plus antitop). And they decay within one-trillionth of a picosecond (1 picosecond is 10−12 s) into bottom quarks and W bosons, the latter being elementary particles that mediate the weak nuclear force. Bottom (b) quarks undergo a process called fragmentation and turn into jets: sprays of nuclear particles (hadrons) arranged in fractal-like patterns. D0 identifies these ‘b-quark jets’ with around 65% efficiency by using the fact that b-quarks travel about one centimetre before decaying, leaving a detectable ‘displaced vertex’. The W bosons decay immediately, either to a charged lepton (electron, muon or tauon) accompanied by a neutrino or an antineutrino, or to a quark jet and an antiquark jet. Putting all this together, the final states are therefore complex and are classified into three main categories according to the decay products of the two W bosons: all-jets, leptons and jets, and dileptons.

The collisions of protons (p) and antiprotons (p−) in the Tevatron accelerator can, among many other possible reactions, produce a pair of top quarks, one top quark (t) and one antitop quark (t−), which both decay rapidly to lighter particles. By measuring the energies and momenta of these particles accurately, the masses of the original top quarks can be reconstructed. The specific decay pattern shown here corresponds to the 'leptons + jets' channel used by the D0 Collaboration measurement(1), in which the top and the antitop each decay differently. The antitop quark decays into a negatively charged W boson (W−), which in turn decays to a charged lepton (l; an electron, muon or tauon) and an antineutrino (ν−). The top quark decays into a positively charged W boson (W+), which decays into quark (q) and antiquark (q−) jets. Both decays also produce a bottom (b)-quark jet.

The collisions of protons (p) and antiprotons (p) in the Tevatron accelerator can, among many other possible reactions, produce a pair of top quarks, one top quark (t) and one antitop quark (t), which both decay rapidly to lighter particles. By measuring the energies and momenta of these particles accurately, the masses of the original top quarks can be reconstructed. The specific decay pattern shown here corresponds to the ‘leptons + jets’ channel used by the D0 Collaboration measurement(1), in which the top and the antitop each decay differently. The antitop quark decays into a negatively charged W boson (W), which in turn decays to a charged lepton (l; an electron, muon or tauon) and an antineutrino (ν). The top quark decays into a positively charged W boson (W+), which decays into quark (q) and antiquark (q) jets. Both decays also produce a bottom (b)-quark jet.

The all-jets category represents half of the events, but there are significant non-top ‘multi-jet’ backgrounds, and accurate energy calibrations of the measured particle jets are challenging. Dileptons can be measured very precisely, but they occur only 4% of the time, and the two escaping neutrinos (one of which is actually an antineutrino) leave an irreducible ambiguity in the determination of the top-quark mass.
The best of both worlds is obtained in the ‘leptons + jets’ channel, which was used by the D0 Collaboration. The rate of occurrence of this channel (30%) is reasonable, there are fewer jets and lower non-top backgrounds than in the all-jets case, and momentum conservation accurately constrains the energy and direction of the single escaping neutrino.
The masses of the original top quarks are encoded in the energies and momenta of their decay products. The calibration techniques to extract the ‘true’ top-quark mass from the raw data have evolved enormously since 1995. In the D0 analysis, the set of measured variables is compared with state-of-the-art theoretical calculations of the likelihood of combined signal and background events for several reference top-quark mass values, to find the one that maximizes the overall likelihood.
The accuracy of the theoretical calculations therefore affects the measurement precision, and elaborate cross-checks are necessary to estimate the added uncertainty. Imperfections in the description of the jet-fragmentation process and the modelling of the energies and momenta of the top quarks and their decay products are especially important. The D0 analysis achieves an unprecedented systematic uncertainty (experimental plus theoretical) of just 0.5 GeV c−2.
The Tevatron collider was shut down in 2011, and this measurement is the final word from D0 on the leptons + jets channel, comprising about 2,500 collision events. Meanwhile, the ATLAS and CMS experiments at the Large Hadron Collider (LHC) at CERN near Geneva, Switzerland, have already published(8, 9) measurements rivalling those of CDF(4) and D0. When the LHC starts up again in 2015, top-quark production rates will skyrocket to thousands of times the Tevatron level.
Given the high precision being attained by these experiments, it is ironic that theorists are not quite sure how to interpret the measured values. In quantum field theory, particle masses can be defined in many slightly different ways, and currently there is no consensus about exactly which definition the experimental measurements correspond to, leaving a 1% ambiguity when converting between the measured mass and the Yukawa coupling. Because this is larger than the precision on the raw measurement, this is an issue that urgently needs to be resolved before we can truly claim that we know the mass of a top.


(1) Abazov, V. M. et al. Phys. Rev. Lett. 113, 032002 (2014).
(2) Abachi, S. et al. Phys. Rev. Lett. 74, 2632–2637 (1995).
(3) Abe, F. et al. Phys. Rev. Lett. 74, 2626–2631 (1995).
(4) Aaltonen, T. et al. Phys. Rev. Lett. 109, 152003 (2012).
(5) ATLAS Collaboration et al. Phys. Lett. B 716, 1–29 (2012).
(6) CMS Collaboration et al. Phys. Lett. B 716, 30–61 (2012).
(7) Elias-Miró, J. et al. Phys. Lett. B 709, 222–228 (2012).
(8) The ATLAS Collaboration. Eur. Phys. J. C 72, 2046 (2012).
(9) The CMS collaboration. J. High Energy Phys. 105, 1212 (2012).

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