CHROMODYNAMICS

Fundamental Forces/Fields• Strong Force• Electromagnetic Forces• Weak Nuclear Force• Gravitational Force

• There is no definite way to define a field, except mathematically, in which it is defined as the ‘……function of position in space, relative to a point in space-time.’

• Classical Fields are continuous.• Paul Dirac combined Theory of Relativity and Quantum Mechanics, to

solve for quantized fields. This is known as the Second Quantization Revolution.

• According to Quantum Field Theory:- fields are everywhere.- particles are manifestations of field localized excitations/vibrations.(Basically, I am not over-sized. The field around me has more excitations!)

• These fields interact with one another and explain how particles are created and destroyed.

• A particle senses the presence of another particle through the exchange of messenger particles.

A simple example in Quantum Electro-Dynamics of electron-electron repulsion.

DIMENSIONAL HEIRARCHY

The Eight-fold Way

• There are Eight Baryons(‘Heavier-ones’) with spin quantum number ½.

• If we plot strangeness of these baryons against their charge quantum numbers. We get a hexagon, with two baryons at it’s center.

• Developed in 1961, independently by Murray Gell-Mann and Yuval Ne’eman.

• Similar to the Periodic Table. Suggest an underlying structure for Baryons and Mesons.

Quark Model• Gell-Mann and George Zweig in 1964 pointed out that the eightfold

way patterns can be understood in a simpler way.• They suggested that the Hadrons are built up of sub-units, namely

quarks.• Each of these quarks are spin-½ particles, carrying fractional charges:

+2/3e or -1/3 e• Quarks are always bound up together in two’s or three’s to form

Mesons and Baryons, respectively.

Quark Model(Contd.)The idea is simple:• Each hadron comprises of quarks, buzzing around at very high speeds

comparable to speed of light.• These buzzing particles are bound together by a very ‘strong’ force that

overcomes their ridiculously large velocity.With all due respect, particle physicists should not be allowed to name

things! • Nearly all of Baryon mass is due to internal energies of (i)the quark

motion (ii) the Strong Field.• The mediating particles are known as ‘GLUONS’.

Another Quantum Number• Gell-Mann & Zweig proposed three quarks- up(u), down(d) and strange(s)

to explain the composition of Baryons and Mesons.• That leads to 10 possible combinations for Baryons, including uuu, ddd &

sss.• But obviously, Pauli’s deceased spirit, would have had a problem with that

because of the violation of the Exclusion Principle.• Oscar ‘Wally’ Greenberg adds a little ‘color’ and comes to the comes to the

rescue! • Force acting between two quarks is called the color force and the

underlying theory by analogy to QED is called Quantum Chromo-Dynamics.

Some Rules:• The quarks have an added quantum characteristic: ‘color’.• They can exist in three possible color states: Red, Blue or Green.• Correspondingly, there are also anti-quarks in three colors: anti-red, anti-blue

or anti-green.• All physically existing particles are, as per se, are color neutral/colorless or

color singlets.• Color neutrality can be achieved through two ways:

-Red + Green + Blue for Baryons.-(Red + Anti-Red) or (Blue + Anti-Blue) or (Green+ Anti-Green) for Mesons.• Gluons are formed by a quark + anti-quark combination and carry color charge.

QED & QCD:

Comparison QED

• Describes interaction of ‘charged’ particles.• Mediator particle: photon.• Coupling constant,• Single charge.• Symmetry group: U(1).

QCD• Describes interaction of ‘colored’

particles.• Mediator particle: gluon.• Coupling constant, • Three charges.• Symmetry group: SU(3)

A top quark was first detected during a high energy collision of a proton and an anti-proton, even though it weighs about 186 times the mass of a proton. How does that happen?

Gluons• Each gluon carries one unit of color and one unit of

anti color. • By this, there should be nine species of gluons. • In terms of SU(3) symmetry, these nine gluons

constitute a “color octet”:

There is also a “color singlet” state that is possible but forbidden(?):

It is forbidden because, if the singlet gluon existed, it would be as conspicuous and common as the photon#.

As we know already all naturally occurring particles have to be color singlets. This explains why the octet gluons never appear as free particles. But if |9) exists as a

mediator it should also occur as free particle.

Moreover, it could be exchanges between two color singlets (a proton and a neutron, say), giving rise to long range force with strong coupling*, whereas we

know that strong forces are of very short range.

Quick question: What if this singlet gluon is the photon? Things will go pretty wild, won’t they?

Gluons(Contd.)• As stated before, gluons have color charge. Hence, unlike photons,

they can interact with other gluons. • This leads to gluon-gluon vertices, other than quark-gluon vertices. As

of now we have two kinds of gluon vertices: three gluon and four gluon vertices:

This gluon-gluon coupling makes QCD far more complex than QED, but far more richer, allowing, the existence of glueballs.

A green quark emits a green-antiblue gluon to convert into a blue quark.

A few Important Terms to Recognize

• Confinement:-At large distances, the coupling between quarks is large, resulting in confinement.-Hence, free quarks are not observed in nature.-Also, no naturally occurring particle can carry color. Why? How?• Asymptotic Freedom:

-At short distances, the effective coupling between quarks decreases logarithmically.-Under such conditions, the quarks are quasi-free.• Chiral Symmetry:

-Connected with quark masses.-When confined, the quarks have large masses- constituent mass.-In small coupling units, some quarks have small masses- current mass.

A few Important Terms to Reconcile with

• Confinement:-At large distances, the coupling between quarks is large, resulting in confinement.-Hence, free quarks are not observed in nature.-Also, no naturally occurring particle can carry color. Why? How?• Asymptotic Freedom:

-At short distances, the effective coupling between quarks decreases logarithmically.-Under such conditions, the quarks are quasi-free.• Chiral Symmetry:

-Connected with quark masses.-When confined, the quarks have large masses- constituent mass.-In small coupling units, some quarks have small masses- current mass.

Beta functions encode the dependence of coupling parameter(g) in the energy scale.

The Beta function is negative for QCD, which is positive for QED.

Which means that, although at relatively large distances characteristic of nuclear physics, the coupling is very big; at short distances(less than the size of the proton), it becomes very small. This phenomenon is known as the Asymptotic Freedom.

Simply put, it means that inside the proton or a pion, quarks rattle around at very high speeds, without interacting much.

A few new things to be amazed at…..

Quick Question:What is the hottest thing you can imagine?

Hint: It’s not Emma Watson….

Sorry, to crush your expectations; but Physicists have found something much hotter. She is a close second, though.

The Quark-Gluon Plasma• Something exciting happened at the RHIC

particle accelerator at the Brookhaven National Laboratory, when two high energy beams of gold nuclei collided head on. At that spot, the Kinetic Energy of the particles was so large that it matched the kinetic energy of the particles that were present soon after the beginning of the universe. It was 30 GeV.

• This much energy literally, melted the protons and the neutrons to form momentarily a gas of individual quarks and gluons.

• This gas was called the Quark-Gluon Plasma. This was repeated at the LHC, yielding same results as before. Have a look….

References:• David J. Griffiths, Introduction to Elementary Particles, Wiley-VCH

Publications, 2004.• Robert Resnick, David Halliday, Jearl Walker, Fundamentals of Physics,

Wiley Publications, 8th Edition, 2010.• Lewis H. Ryder, Quantum Field Theory, Cambridge University Press,

2001.• Arthur Beiser, Concepts of Modern Physics, McGraw Hill Publications,

6th Edition.• Feynman, Leighton and Sands, The Feynman Lectures on Physics, Vol. 2,

Pearson Publications.

ANY DOUBTS?