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The Higgs particle: a useful analogy for physics classrooms

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2010 Phys. Educ. 45 73

(http://iopscience.iop.org/0031-9120/45/1/008)

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The Higgs particle: a usefulanalogy for physics classroomsXabier Cid1 and Ramon Cid2

1 Particle Physics Departament USC, 15706 Santiago de Compostela, A Coruna, Spain2 IES de SAR, 15702 Santiago, A Coruna, Spain

E-mail: xcidvidal@gmail.com and rcid@terra.es

AbstractIn November 2009, the largest experiment in history was restarted. Its primetarget is the Higgs particle—the last remaining undiscovered piece of ourcurrent theory of matter. We present a very simple way to introduce this topicto senior secondary school students, using a comparison with the refractiveindex of light.

The standard modelThe standard model of particle physics is the besttheory that physicists currently have to describethe building blocks of the Universe. It is one ofthe biggest scientific achievements in twentieth-century science.

The standard model describes the Universeusing six quarks and six leptons. There arefour known interactions, each mediated by afundamental particle, known as a carrier particle.

In the 1970s physicists realized that there arevery close ties between two of the four fundamen-tal interactions—namely, the weak interaction andthe electromagnetic interaction.

The two interactions can be described withinthe same theory, which forms the basis of thestandard model. This ‘unification’ implies that theinteraction-carrying particles have no mass.

We know from experiments that this is nottrue. To solve this problem several physicistsproposed the existence of a new field with itscorresponding quantum particle, the Higgs fieldand the Higgs particle.

The Higgs particle has been nicknamed (byNobel Prize-winning physicist Leon Lederman)the ‘God particle’ because of its importance tothe standard model. Detecting this particle is

one of the Large Hadron Collider’s (LHC’s) mainpurposes. The LHC is the world’s largest andhighest-energy particle accelerator, intending tocollide opposing particle beams of either protonsat an energy of 7 TeV per particle or lead nucleiat an energy of 574 TeV per nucleus. It lies in atunnel 27 km in circumference, as much as 100 mbeneath the Franco–Swiss border near Geneva,Switzerland.

The mass of the particlesWhy do particles have mass? Why are the masseswhat they are? Why are the ratios of masses whatthey are?

In the early 1970s, Peter Higgs, FrancoisEnglert, Robert Brout, Gerald Guralnik, DickHagen and Tom Kibble independently proposedthat the Universe is full of a field later called theHiggs field. Disturbances in this field, as particlesmove through it, cause objects to have mass. It isimportant to say that the original basis of Higgs’work came from the Japanese-born theorist and2008 Nobel Prize winner Yoichiro Nambu.

Different ways of explaining this mechanismto a general audience have been proposed. Forexample, the discrete units which stir up the field,Higgs particles, act like a kind of cosmic molasses

0031-9120/10/010073+03$30.00 © 2010 IOP Publishing Ltd P H Y S I C S E D U C A T I O N 45 (1) 73

X Cid and R Cid

which fills all of space. As objects move throughspace they have to ‘wade’ through these Higgsparticles that ‘cling’ to them, causing a drag thatshows up as mass.

Another analogy often cited describes it well:imagine you are at a party. The crowd is ratherthick, and evenly distributed around the room,chatting. When a big star arrives, the peoplenear the door gather around him. By gatheringa fawning cluster of people around him, he hasgained momentum, an indication of mass. He isharder to slow down than he would be without thecrowd. Once he has stopped, it is harder to get himgoing again.

Further analogies have been presented, but weprefer one that is closer to physics.

Comparing refractive index and massWhen light, composed of photons, passes througha transparent material such as water or glass, itsvelocity changes according to the refractive indexof the material. If a beam of light enters thematerial at an angle, it is bent or refracted as aresult of this decrease in velocity.

The reason why photons are slower whenpassing through a transparent material is the effectof electrical fields surrounding the electrons andnuclei of atoms in the material.

The photons are slowed down by interactingwith these electrical fields. The effect is greater inmaterials such as water and glass than it is in air, aresult of their greater relative densities.

The fields almost act like ‘friction’ on thephotons, decreasing their transmission velocity. Itis like trying to walk through a muddy field.

A measure of how much photon speeds arereduced is given by the refractive index of thematerial. The refractive index (i ) of a materialequals the speed of light in a vacuum (c) dividedby the speed of light in the material (v):

i = c/v.

A very important detail is that the speed of light ina transparent material depends on the wavelength(i.e. momentum) of the photons. For instance,consider visible light in water, the refractiveindices for the different colours are:

Blue(486.1 nm)

Yellow(589.3 nm)

Red(656.3 nm)

1.337 1.333 1.331

‘Yellow’ photons travel through water faster thanblue, and red photons are even faster. Youcould say that blue photons have greater difficultymoving in water than yellow and red photons. Youcould say that blue photons behave as if they havemore ‘inertia’, i.e. more ‘mass’. Refractive indexgives a measure of the interaction between photonsand a material medium through which they travel;it could also be considered an ‘index of mass’,since the bigger its value the lower the photonspeed.

In a vacuum, all photons travel with identicalspeed but, if the Universe were filled with water,photons corresponding to different wavelengthswould travel with different speeds.

As has been said before, they would appear tohave ‘different masses’. So you would pass froma symmetrical situation to a nonsymmetrical one.This is what in particle physics is called symmetrybreaking.

Now we are ready to establish our compari-son.

The standard model suggests that all particleswere massless just after the big bang but, as theUniverse cooled and the temperature fell below acritical value, an invisible field called the ‘Higgsfield’ appeared, filling all space. You couldalso say that the Higgs field was created at thebeginning of the Universe, but it only showed itsinfluence once the Universe cooled down enough.The massless symmetry of particles was broken.

Unlike magnetic or gravitational fields, whichvary from place to place, the Higgs field is exactlythe same everywhere. What varies is how thedifferent fundamental particles interact with thefield and are given mass. Of course, other kinds ofinteraction, such as the electromagnetic, weak orstrong interaction may also contribute significantlyto the resulting mass. Moreover, the degree ofresistance of the Higgs field is different dependingon the fundamental particle, and this generates,for example, the difference in mass between anelectron and a quark.

Now, suppose a quark or electron is moving(making up composite particles such as protons,neutrons or various atoms) in a uniform Higgsfield. If these atoms (or molecules) change theirvelocities, that is, if they accelerate, and if theHiggs field exerts a certain amount of resistanceor drag, then this is the origin of inertial mass.

74 P H Y S I C S E D U C A T I O N January 2010

The Higgs particle: a useful analogy for physics classrooms

The situation is similar to refraction, dis-cussed above. The Higgs field acts as a ‘transpar-ent material’ with a specific ‘refractive index’ foreach kind of fundamental particle. In this way, theHiggs field gives each different particle its charac-ter, what physics calls ‘mass’.

For instance, when a proton interacts with anelectron, it undergoes an effect almost 2000 timessmaller than the electron, because the ‘index’ inthe Higgs field for protons is almost 2000 timesgreater.

The analogy only works if you consider lightas particles, and not as waves. The refraction oflight happens only in a material medium, whichthe Higgs field is certainly not. Provided theselimitations are made explicit and clear, we thinkthe refraction analogy can help secondary studentsto understand the Higgs field.

From a quantum point of view, however,you can only stir up the Higgs field in discreteunits. The smallest possible disturbance is dueto a Higgs particle, or more precisely, a Higgsboson. ATLAS and CMS are general-purposeLHC detectors designed to see a wide rangeof particles and phenomena produced in LHCcollisions. The Higgs boson, possibly hundreds oftimes heavier than a proton, could be created in theproton collisions in the centre of their detectors.

More than 4000 physicists from about 40countries will be using the data collected from bothcomplex detectors to search for Higgs particles. Itis widely believed that they exist or at least somesort of Higgs-like particle which plays that role.But there is no real guarantee that the LHC willfind it. It should find it, at least in the simplestmodels, but the simplest models are not alwaysright.

Anyway, following Professor Hawking, evena failure would be exciting, because that wouldpose new questions about the laws of nature. So, ifit turns out that we cannot find the Higgs particle,this will leave the field wide open for physiciststo develop a completely new theory to explain theorigin of particles’ mass.

AcknowledgmentsThe authors would like to thank Abraham GallasTorreira and Diego Martınez Santos for theirhelpful comments and corrections to this article.Received 28 August 2009, in final form 15 October 2009doi:10.1088/0031-9120/45/1/008

Further readingTaking a closer look at LHC http://lhc-closer.esHigh school teachers at CERN teachers.web.cern.ch/

teachers/CERN www.cern.chLHC lhc.web.cern.ch/lhc/Detector CMS cmsinfo.cern.ch/outreach/Detector ATLAS atlas.ch

Xabier Cid Vidal graduated in physics in2007. He is currently doing his PhD onexperimental particle physics, taking partin the LHCb collaboration at CERN withthe University of Santiago’s group.

Ramon Cid graduated in physics andchemistry and has taught physics atsecondary school since 1980. Heparticipated in the HST programme atCERN in 2003. He has coordinatedvarious European teaching projects andseveral annual ENCIGA (Association ofScience Teachers of Galicia) scienceteachers’ congresses.

January 2010 P H Y S I C S E D U C A T I O N 75