Articles

The Higgs Boson

Science  21 Dec 2012:
Vol. 338, Issue 6114, pp. 1558-1559
DOI: 10.1126/science.338.6114.1558

The standard model of particle physics describes how elementary particles and a set of forces between them lead to all matter and most higher interactions, thereby providing a basis for understanding much of physics and chemistry. A key prediction of the standard model—that the universe is pervaded by a field that conveys mass—was tested and confirmed this year with the discovery of a particle associated with that field: the Higgs boson. Two separate, complex detectors housed in the largest and most energetic particle accelerator, the Large Hadron Collider (LHC) at CERN near Geneva, Switzerland, identified the characteristic decay products of the Higgs, allowing reconstruction of its mass. These experiments and this discovery were made possible by decades of cutting-edge, publicly supported science, engineering, and construction, and a long-term effort by the physics community worldwide.

In three articles in this issue, the researchers explain their results and the developments that led to the detection. The first presents the history of the search for the Higgs and the experimental approach, and summarizes the results. This is followed by a paper from each of the two detector teams describing their experiments and results in more detail. These papers aim to provide an accessible overview of the two research papers published this summer in Physics Letters B, which are the primary references. We hope that this package and the accompanying glossary give broad access to this discovery that is fundamental to understanding our universe.

Glossary

In the standard model (SM), several fundamental or elementary particles can interact to create all compound forms of matter. Several of these fundamental particles are also used to search for the Higgs boson, because they appear as its decay products. This glossary, developed by the lead authors of the three papers, provides an overview of some of the particles and also indicates some of the important abbreviations, notations, and terms used in particle physics and the papers.

Fundamental Particles

Leptons (ℓ): Fundamental particles that include the electron (e), muon (µ), and τ lepton (τ) that do not combine via the strong interaction.

Quarks: Fundamental particles that can combine via the strong interaction to form composite particles. One of the ways the Higgs boson decays is into a bottom quark and bottom antiquark pair (Hbb¯).

Bosons: Bosons are particles with an integer spin quantum number (0, 1, 2, …); they obey Bose-Einstein statistics, which allows multiple particles to occupy the same quantum state. They can be fundamental or composite particles. Fundamental bosons include the photon (γ), which carries the electromagnetic force; W or Z bosons, which carry the weak force; and gluons, which carry the strong force. All have a spin of 1. The SM also predicts another fundamental boson, the Higgs boson, associated with a field that imparts mass to some of the other fundamental particles. In the SM, the Higgs boson has a spin of 0; the experimental results are consistent with that. Composite bosons include mesons, nuclei with an even number of neutrons and protons, and atoms containing an even number of protons, electrons, and neutrons.

Fermions: Particles with a half-integer spin quantum number (1/2, 3/2, 5/2, …); they obey Fermi-Dirac statistics. Multiple fermions cannot occupy the same quantum state because of the Pauli exclusion principle. They can be fundamental particles (quarks and leptons), composite particles such as the proton or neutron, nuclei containing an odd number of protons and neutrons, or atoms containing an odd number of protons, electrons, and neutrons.

Other Particles

Hadrons: Composite particles made up of quarks and/or antiquarks that are held together by gluons, the carriers of the strong force.

Mesons: Composite particles made up of a quark and an antiquark. All mesons are hadrons. Mesons are short-lived and decay quickly after they are formed.

Baryons: Composite particles made up of three quarks or three antiquarks. All baryons are hadrons. Protons and neutrons are baryons.

Use of natural units (GeV etc.): Einstein's relation linking energy, mass, and momentum is given by E2 = p2c2 + m2c4. Hence, if energy E is measured in electron volts (eV), then momentum p is measured in eV/c and mass m in eV/c2. The electron volt is the amount of energy gained by an electron when traversing a potential difference of 1 V. One GeV is 1,000,000,000 eV. In particle physics, it is common to use a system of “natural units” with c, the speed of light, set equal to 1, so that all three quantities (energy, mass, and momentum) can be expressed in eV.

A reconstructed event in the CMS detector.

The event shows the possible decay of the Higgs boson to a pair of photons (dashed yellow and green lines). Solid yellow lines represent the charged particles also produced in the same collision. The event could also be due to background processes.

CREDIT: CMS COLLABORATION/CERN

Decay channel and final state: Many particles produced in proton-proton collisions at the LHC are unstable and decay almost instantaneously into other particles, which may themselves decay further. Just as a vending machine might return the same amount of change using different combinations of coins, a particle can decay into different combinations of other particles. These sets of secondary particles represent different decay channels. Detectors such as ATLAS and CMS may not observe the original particles at all, but rather the detectable collection of secondary particles from their decays that exists long enough to be detected. This detectable collection of particle species is called the final state. The Higgs particle, for example, is unstable and has many decay channels, each having a certain probability to occur called the branching ratio or branching fraction. The sum of all branching ratios is equal to 1. The branching ratios of the Higgs boson depend on the mass of the Higgs boson and are precisely predicted in the SM. For example, for a SM Higgs boson (H) of mass 125 GeV, the discovery decay channels H→WW, H→ZZ, and H→γγ have branching ratios of B(H→WW) = 0.14, B(H→ZZ) = 0.016, and B(H→γγ) = 0.0023. Other channels studied include decays to bb¯ and τ+τ, which have branching ratios B(Hbb¯)=0.58 and B(H→τ+τ) = 0.064.

Invariant mass: Particle physicists use the word “mass” to refer to the quantity m both in Newton's second law of motion, F = ma, and in Einstein's equation, E = mc2 (in which E must be interpreted as the energy of the particle in its rest frame and c is the speed of light in vacuum). When a particle decays and hence no longer exists, its mass before the decay can be calculated from the energies and momenta of the decay products. The inferred mass is independent of the reference frame in which the energies and momenta are measured, so that the mass is called “invariant.”

Cross section: A quantity proportional to the probability for a specified reaction (such as the creation of a new particle) to occur; for example, when the two proton beams collide as in the LHC. The name reflects the origin of the concept in classical mechanics (geometrical cross-sectional area of an object, which could be hit by a beam), but in particle physics the probabilities are determined from quantum mechanics. At the LHC, cross sections are typically expressed in nanobarns (nb), picobarns (pb), and femtobarns (fb). One barn corresponds to a cross-sectional area of 10−28 m2. For example, the cross section for the production of a SM Higgs boson of mass 125 GeV at the LHC in proton-proton collisions at the center-of-mass energy of 7 TeV is about 15 pb: σ(pp→H) = 15 pb = 15,000 fb. At the center-of-mass energy of 8 TeV, the cross section is about 25% higher.

Luminosity: Instantaneous luminosity ℒ gives a measure of the rate of collisions occurring in a particle collider, based on how intense the circulating beams of particles are and how squeezed in space they are at the point of collision. Although it does not mean that all those particles will collide, squeezing more particles into a narrower space makes it more likely that they will. Instantaneous luminosity is measured in units of cm−2 s−1. Integrated luminosity is obtained by summing the product of a given time interval with the instantaneous luminosity in that interval, over time: L = ∫ℒ dt. Integrated luminosity L is often measured in a unit called inverse femtobarn (fb−1 = 10−39 cm−2), which is equivalent to about 100 trillion (1014) proton-proton collisions at the LHC. The number of events (N) produced in these collisions for a given process is calculated as the product of the cross section σ for that process multiplied by the integrated luminosity L (N = L·σ). For example, for a proton-proton collision run at 7 TeV resulting in an integrated luminosity of L = 1 fb−1, the average number of SM Higgs bosons produced in the process pp→H followed by the decay H→γγ is N(H→γγ) = L × σ(pp→H) × B(H→γγ) = 1 fb−1 × 15,000 fb × 0.0023 = 34.5 (a dimensionless quantity since fb−1 cancels with fb). In a real experiment, the number of observed events will fluctuate around the average value of 34.5, according to Poisson statistics.

A reconstructed Higgs boson decay event in the ATLAS detector.

This event has two muons (red) and two electrons (green). The inset shows the reconstructed proton-proton collision vertices.

CREDIT: ATLAS COLLABORATION/CERN

Significance and the look-elsewhere effect: The probability for a background fluctuation to be at least as large as the observed maximum excess is termed the local P value, and the probability for an excess anywhere in a specified mass range is the global P value. This probability can be evaluated by generating sets of simulated data incorporating all correlations among analyses optimized for different Higgs boson masses. The global P value (for the specified region) is greater than the local P value, and this fact is often referred to as the look-elsewhere effect. Both the local and global P values can be expressed as a corresponding number of standard deviations using the one-sided Gaussian tail convention. For example, a 5σ significance tells us that the probability of the background alone fluctuating up locally by the amount observed or more is about 1 in 3 million. In particle physics, this criterion has become a convention to claim discovery but should not be interpreted literally.

Subjects

Navigate This Article