Particles - Notes

Elementary Particles Definition of elementary (or fundamental) particle Elementary particle is defined as a subatomic particle without sub structure (or known sub structure), thus not composed of other particles. Particles composed of other particles are called composite particles.

Description of elementary particles Currently, particles that are thought to be elementary include the fundamental fermions (quarks, leptons, antiquarks, and antileptons), which generally are "matter particles" and "antimatter particles", as well as the fundamental bosons (gauge bosons and the Higgs boson), which generally are "force particles" that mediate interactions among fermions.

Below are the list of known (and thought as) elementary particles according to the “Standard Model”. If we were to count the number of elementary particles: a) without counting the antiparticles, we would have 17 (6 quarks, 6 leptons, 4 gauge (vector) bosons and 1 scale bosons (the Higgs-Bosons). This also excludes the hypothetical gauge boson viz. graviton. b) or 38. We have 12 quarks and antiquarks, 12 leptons and antileptons, 13 gauge bosons (W+ boson, W- and Z, 8 gluons, photon and the hypothetical graviton) and 1 scale bosons (the HiggsBosons)

1

Definition of Point Particles A point particle is a particle that does not occupy space at all (zero dimensional entity as it lacks spatial extension).

The use of Point Particles in Physics In physics, a point particle is an idealization of particles with the defining feature that it lacks spatial extension: being zero-dimensional. A point particle is an appropriate representation of any object whose size, shape, and structure is irrelevant in a given context. For example, from far enough away, any finite-size object will look and behave as a point-like object. Examples are point mass and point charge. In the theory of gravity, physicists often discuss a point mass, meaning a point particle with a nonzero mass and no other properties or structure. Likewise, in electromagnetism, physicists discuss a point charge, a point particle with a nonzero charge.

Question: Is an elementary particle a point particle? Although an elementary particle has no internal sub-structure & not composed of other particles (which is the definition of an elementary particle) and treated as point particles (predictive utility), it still occupies non-zero volume!.

The elementary particle e.g. electron (a quantum-mechanical object) still occupies non-zero volume due to de Broglie duality principle. All objects have a wave function which represents the probability of locating that object at a particular point in space. During a collision this wave function momentarily collapses and the particle is truly at one 'point' in space, but it immediately starts to spread out again after the instant of collision. The typical spread of the wave-function of a point particle is given by the Compton wavelength: 𝜆=

ℎ 𝑚𝑐

where, h = 6.62607004 × 10-34 m2kg/s and c = 299792458 m/s This gives  = 2.4e-12 m. The “size” of an electron then, should be at least . This value  has another important meaning. The Compton wavelength is more or less the smallest distance to which you can confine an electron. If you try to squeeze the electron into an even smaller distance, then its momentum will become so large (via the uncertainty principle) that it its kinetic energy will be larger than mc2. In this case, there will be enough energy to create (from the vacuum) a new electron-positron pair, and the newly-created positron can just annihilate the trapped electron while the newly-created electron flies away.

2

This value  is also much larger than its Schwarzschild Radius which is 1.4e-57 m. Hence, electron does not collapse into a black hole! Note that the Schwarzschild Radius is based on General Relativity which breaks down for quantum objects (where quantum mechanics reigns supreme).

For composite particles, the interaction amongst the elementary and non-elementary particles also creates additional field that is observed as a volume. Single elementary particle:

Volume = “field” created by the wavelength spread of the elementary particle.

Composite particle(s):

Volume = “field” created by the motion of the elementary particles as well as the “field” created due to their interactions

3

Details of the Standard Model Elementary Particles

Elementary Fermions

Elementary Bosons

Half Integer Spin Obey Fermi-Dirac Statistics

Integer Spin Obey Bose-Einstein Statistics

Leptons & anti Leptons Spin ½ No color change Electroweak interactions

12

Quarks & anti Quarks

Gauge Bosons

Spin ½ Have color change Strong interactions

Spin 1 Have color change Strong interactions

12

13*

Scale Bosons Spin 0 No color change Electroweak interactions

1

*Including Graviton

Composite Particles Hadrons Hadrons are defined as strongly interacting composite particles. Hadrons are either baryons or mesons. a) Baryons are composite fermions (especially 3 quarks) Examples are the nucleons; protons (uud) and neutrons (udd). b) Mesons are composite bosons (especially 2 quarks). An example is the particle pion π+ is considered to be made up of an up and an anti-down quark

4

5