The Higgs Boson

All the known forces in the universe are manifestations of four fundamental forces, the strong, electromagnetic, weak, and gravitational forces. But why four? Why not just one master force? Those who joined the quest for a single unified master force declared that the first step toward unification had been achieved with the discovery of the W and Z particles, the intermediate vector bosons, in 1983. This brought experimental verification of particles whose prediction had already contributed to the Nobel prize awarded to Weinberg, Salam, and Glashow in 1979. Combining the weak and electromagnetic forces into a unified "electroweak" force, these great advances in both theory and experiment provide encouragement for moving on to the next step, the "grand unification" necessary to include the strong interaction.

While electroweak unification was hailed as a great step forward, there remained a major conceptual problem. If the weak and electromagnetic forces are part of the same electroweak force, why is it that the exchange particle for the electromagnetic interaction, the photon, is massless while the W and Z have masses more than 80 times that of a proton! The electromagnetic and weak forces certainly do not look the same in the present low temperature universe, so there must have been some kind of spontaneous symmetry breaking as the hot universe cooled enough that particle energies dropped below 100 GeV. The theories attribute the symmetry-breaking to a field called the Higgs field, and it requires a new boson, the Higgs boson, to mediate it.

Illustration courtesy Fermilab, D0 Experiment. 插图 courtesy Fermilab, D0 实验。

Early formulation of the theories estimated that the Higgs boson would have mass energy in excess of 1 TeV, making the energies for discovery almost unattainable on the earth. Now, since the discovery of the top quark, there was tantalizing evidence that the Higgs boson might have energies in the range of a few hundred GeV and therefore within the range of present day accelerators. At Fermilab, data from the D0 detector facility is used with the masses of the W and the T quark to estimate the mass of the Higgs boson. Suggestions that it may have a mass below 200 GeV made it one of the high priorities for high energy physics. 早期的理论估计，希格斯玻色子的质量能量将超过1 TeV，使得在地球上发现它的能量几乎难以实现。现在，由于顶夸克的发现，出现了令人鼓舞的证据，表明希格斯玻色子的能量可能在几百GeV的范围内，因此处于目前粒子加速器的探测范围内。在费米实验室，利用D0探测器设施的数据，结合W夸克和T夸克的质量，来估计希格斯玻色子的质量。有建议指出，如果其质量低于200 GeV，这将成为高能物理研究的优先事项之一。

Searching for the Higgs boson was one of the high priority objectives of the Large Hadron Collider at CERN. At the end of 2011, the LHC results appeared to limit the Higgs to between 114 and 145 GeV if it is to fit in the standard model of particle physics. Then in 2012 a peak at 125 GeV was found by both the Atlas and CMS detectors, and by 2013 there was confidence that a Higgs boson had been found.

The Atlas Evidence for the Higgs

One of the most important goals for the ATLAS detector and CMS detector of the Large Hadron Collider was to search for the Higgs boson. Previous experiments had suggested that the Higgs might have a mass less than 200GeV and might be within the range of the Atlas detector. On July 4, 2012 ATLAS and the CMS detectors at the LHC reported evidence of a particle consistent with the Higgs boson at around 125GeV or 133 times the proton mass. This and subsequent studies are reported in an Atlas bulletin on 4 July 2018. The particle was detected by its decay into two photons and its decay into four leptons. These experiments showed that the properties of the particle and its interactions with other particles were well-matched with the projected properties of the Higgs boson. In March 2013 CERN announced that the new particle was indeed a Higgs boson, and two of the involved theoretical physicists, Peter Higgs and Francois Englert, were awarded the Nobel Prize in Physics for their contributions.

An Atlas bulletin of 26 October 2017 described evidence for the Higgs boson in association with two top quarks.

This plot showing an example of data for the Higgs boson is from the Atlas bulletin of 4 July 2018. Besides the Higgs peak at 125GeV, there is a peak at about 90GeV which is labeled to indicate a decay of the Higgs to a pair of Z bosons (see neutral current) and further decay to four leptons. The 90GeV is in agreement with the mass of the Z intermediate vector boson. 这张图展示了一个希格斯玻色子的数据示例，来源于2018年7月4日的Atlas公报。除了125GeV处的希格斯峰外，还有约90GeV处的一个峰，标注表明希格斯玻色子衰变为一对Z玻色子（见中性流），进一步衰变为四个轻子。90GeV的值与Z中间矢量玻色子的质量一致。

Click on particle for more discussion.

This is modified from Figure 4 of the Atlas Bulletin. It shows data from Atlas and CMS to depict the proportionality of particle mass to the strength of the interaction with the Higgs field. Continuing studies past the 2013 discoveries have shown the Higgs boson to be consistent with the predicted properties: zero spin, no electric charge, no strong force interaction, even parity. Even the proportions of the decay paths have agreed with those predicted.

The Atlas and CMS collaboration continues to work on the exploration of the Standard Model of particle physics, and in a 25 October 2019 Bulletin report a Higgs mass of 125.35 +/- 0.15 GeV.

The Higgs Field

Much attention has been given to the search for and discovery of the Higgs boson, which serves as a confirmation of the Brout-Englert-Higgs (BEH) mechanism by which elementary particles obtain mass. The theory envisions space as filled with the Higgs field, and suggests the elementary particles like leptons and quarks obtain their mass by interaction with the Higgs field. A larger mass for a particle implies that it has a stronger interaction with the Higgs field. The Atlas studies depict a linear relationship of particle mass with the strength of the interaction with the Higgs field. This does not imply that the composite particles (hadrons) obtain all their mass from the Higgs field interaction - the bulk of the mass of a hadron like a proton arises from the strong force interactions.

There are many kinds of fields, such as electric fields and magnetic fields, and one would suppose that at a great distance from the sources of these fields, their values would approach zero. But Carroll describes the Higgs field as "stuck away from zero". All of space is seen as pervaded by this field which has a non-zero value. Carroll quotes this ground state field value as 246 GeV. This is called the "vacuum expectation value" of the Higgs field. "The Higgs boson - the particle discovered at the LHC - is a vibration in that field around its average value." The Higgs field "fills space, breaks symmetries, gives mass and individuality to the other particles of the Standard Model."

The ideas of symmetry and symmetry-breaking in this context are not easily explained. For the weak interaction we have the bosons W⁺, W^-, and Z with the statement that the Higgs boson itself is the fourth member of a boson quartet. It is said that at about 10^-12 seconds after the Big Bang, there was a spontaneous symmetry break from a state in which all four were massless and traveling at the speed of light (i.e., symmetric). Interaction with the Higgs field gave them their distinctive masses and character.

The Higgs field is critical as a source of the basic structure of matter as we know it. Such matter consists of atoms with tiny nuclei surrounded by a much larger regions of space determined by the electrons of the atoms. Ordinary matter including the elements of the periodic table is made up of just three types of fermions, the electron and the up and down quarks. They are responsible for the great difference in scale between the nucleus and the atom. Quantum mechanically, an electron can be considered to be a wave-packet that obtains its relatively small mass by interacting with the Higgs field. The small mass energy translates to a relatively long characteristic wavelength, so the packet is spread out in space. This gives a relatively large size to the atom as a whole. The up and down quarks which make up protons and neutrons in the nucleus have a relatively much larger mass from a stronger interaction with the Higgs field. The characteristic wavelengths of their quantum mechanical wave packets are much smaller. They make up the nucleus as an entity much smaller than the atom. This approach to the scale of the nucleus and atom should be compared to the discussion of particle confinement and the uncertainty principle.