CROSSING SYMMETRY

LECTURE 5-6 (PARTICLE PHYSICS )

Title :CROSSING SYMMETRY +THE EIGHTFOLDWAYS

In Particle physics their is a general principle that goes under the name of crossing symmetry .

If a particle interaction is like this

, then related interactions can be anticipated from the fact that any of the particles can be replaced by its antiparticle on the other side of the interaction. This is commonly known as “crossing symmetry”.

Any of these can be crossed over to the other side of the equation and become an anti particle the cross section is possible calculation of these processes are identical important thing is the conservation of energy can forget some of the reactions.

The observation of the above interaction implies the existence of the following interactions

The overbar indicates the antiparticle. Crossing symmetry applies to all known particles, including the photon which is its own antiparticle. One example of the crossing principle is that of the relation between Comptons scattering  and electron -positron annihilation .

Compton scattering / comptons effect :  γ + e^– → e^– + γ

pair production : γ + γ → e^– + e⁺

Pair annihilation:   e^– + e⁺ → γ + γ

Another example of crossing symmetry may have led  Reines and Cowan  to their experiment for the detection of the neutrino. If you take the electron product from the neutron decay reaction to the other side and convert it into a positron, then you have the reaction which they used.

The “Eightfold Way” is a term used in the context of particle physics, specifically in the classification of particles known as hadrons. Proposed by Murray Gell-Mann and independently by Yuval Ne’eman in the early 1960s, the Eightfold Way provided a systematic framework for organizing the plethora of newly discovered particles observed in high-energy experiments.

Title :THE EIGHTFOLDWAYS (1961-1964)

The Mendeleev of elementary particle physics are Murray Gell-Mann ,who introduced the so called Eightfold Ways in 1961 .The eightfold ways arranged the baryons and mesons into weird geomatrical pattern , according to their charge and strangeness .The eight lightest baryons fit into a hexagonal array , with two particles at the center .

Here are the key points about the Eightfold Way:

1. Classification of Hadrons:

• The Eightfold Way focused on categorizing hadrons, which are composite particles made up of quarks bound together by the strong nuclear force.
• Hadrons are classified into two main categories: baryons (composed of three quarks) and mesons (composed of a quark and an antiquark).

2. SU(3) Symmetry:

• The Eightfold Way is based on the symmetry group SU(3), which describes the possible transformations of quarks under the strong force.
• SU(3) symmetry allows for the classification of hadrons into multiplets based on their properties such as mass, spin, and charge.

3. Organization into Octets and Decuplets:

• The Eightfold Way organizes hadrons into two main groupings: octets and decuplets.
• Octets consist of eight particles, while decuplets consist of ten particles.
• Each multiplet represents a specific combination of quarks that obey the rules of SU(3) symmetry.

4. Predictions and Discoveries:

• The Eightfold Way made predictions about the existence of certain particles based on the symmetries observed within the multiplets.
• Several particles predicted by the Eightfold Way were later discovered experimentally, validating the framework’s predictive power.

5. Contribution to Quark Model:

• The Eightfold Way laid the groundwork for the development of the quark model, which proposes that hadrons are composed of combinations of fundamental particles called quarks.
• Quarks were introduced as the building blocks of hadrons, and the Eightfold Way provided insight into their possible combinations.

6. Legacy and Impact:

• The Eightfold Way revolutionized the way physicists thought about particle classification and organization.
• It provided a systematic framework for understanding the relationships between different hadrons, paving the way for further developments in particle physics.

Title :THE QUARK MODEL :

All the hadrons are infact composed of elementary particles which Gell-man named as Quark .The Quarks comes in three types (or” flavors”) ,forming a triangular ” Eightfold-Way ” pattern :

The Quark model asserts that :

1. Every baryon is composed of three quarks (and every antibaryon is composed of three antiquarks ).
2. Every meson is composed of a quark of and a antiquark.

If baryons and mesons are made of up of quarks then they should be easy to produce. It is also for known lightest particle with fractional charge let no one has ever found a single confinement .i.e quark or absolutely confined within baryon and mesons till we are unable to discover the mechanism responsible for confinment we can still study quarks stuck inside hadrons using same technique as Rutherford uses inside and atom i. e by firing something into it .Using higher energy electrons at standford linear accelerators. Counter slack (SLAC) same process is repeated again by using your beam at CERN and now using proton result of the inelastic scattering experiments are same as obtained by Rutherford.

Strong support that hadrons contains sub -structure

u⁷u⁶d_⁸

still there is Pauli’s Exclusion Principal which say that for example delta++ consists of u u u in the same state with spin [1/2] .Same is true for delta – .so Greeberg suggest that quark also same in colour also with a flavour in red green and blue so quantum number are thus not included.

• A red colour is one of unit of redness .
• A blue colour quark carries one unit of blueness.
• A gree in colour carries the one unit of greenness.

All naturally occurring particles are colourless . i.e q_red q_blue ,q_green .