force carriers the paradigm of particle physics

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Force Carriersthe paradigm of particle physics

D. Indumathi,

Institute of Mathematical Sciences, Chennai

E-mail: [email protected]

Science Club, Chennai, Oct 7, 2006 – p. 1

What is the world made of?Matter and radiation.

Matter is made up of particles: atoms or molecules. Einstein

proved this in 1905 (Brownian Motion).

Light is made up of waves. It has a wave nature. Established

conclusively by end of 19th century (Maxwell’s equations of

electrodynamics).

Light also behaves as a particle, called photon. The photon is a

light quantum. Its discovery lead to the birth of quantum theory.

Established by Eistein’s explanation of the photoelectric effect

(1905; got 1921 Nobel prize for this. Planck originally proposed

E = hν. Also by Compton in Compton Scattering (1927

Nobel)).

Hence light is said to have a dual nature.Science Club, Chennai, Oct 7, 2006 – p. 2

Flip-flopElectrons also have a dual nature (de Broglie, 1929Nobel).

Quantum mechanics was formulated in 1926 bySchrödinger and Heisenberg. Inconsistent with Specialtheory of relativity.

Dirac, 1928, formulated a new relativistic wave equation:two new ideas: spin and antiparticle.

Matter and antimatter have related properties like samemass, opposite charge, etc. Eg: p+, p−, e−, e+.

Some symmetries surely exist that allow for suchsimilarity. Quantum mechanics + principles of symmetry+ invariance under special relativity = Quantum Fieldtheory. Science Club, Chennai, Oct 7, 2006 – p. 3

What is a quantum field theory?A QFT describes the properties and interaction ofparticles. All particles interact by exchanging otherparticles which are the carriers of the interaction.

Eg: Quantum Electrodynamics QED (Feynman):interaction of charged particles and radiation (photons);most precise theory known today. Eg: two electronsrepel, electron and proton attract.

Interaction Mediator Matter Physical Consequence

EM Photon e, p Atoms formed

Weak W, Z e, µ, quarks Radioactivity

Strong gluons quarks Nucleus formed

Gravity graviton All matter UniverseScience Club, Chennai, Oct 7, 2006 – p. 4

The Standard ModelHence, there are four fundamental forces in nature:gravity, electro-magnetic, strong and weak.

Leptons are those particles that do not experiencestrong forces (which baryons do).

Weak forces are like beta decay or the fusion processesthat power the Sun. (The fusion in a fusion bomb is astrong interaction process.)




Weak forces are like beta decay or the fusion processesthat power the Sun. (The fusion in a fusion bomb is astrong interaction process.)Particle electro-magnetic strong weakp+ ✔ ✔ ✔

e− ✔ ✘ ✔

νe ✘ ✘ ✔





Leptons come in three flavours or types or generations:(

νe

e

) (

νµ

µ

) (

ντ

τ

)

µ and τ heavier versions of e.Reason for their existence (andno. of generations) a mystery.

In order to keep track of this zoo of particles, willrepresent an electron by ε.





Leptons come in three flavours or types or generations:(

νε

ε

) (

νµ

µ

) (

ντ

τ

)

µ and τ heavier versions of e.Reason for their existence (andno. of generations) a mystery.

In order to keep track of this zoo of particles, willrepresent an electron by ε.


More on the Standard ModelHowever, it turns out that Baryons are NOT fundamentalparticles.

Baryons are made up of different quarks, such as u, d,etc. The quarks are considered elementary, just aselectrons are.




Composition of baryons:Particle Quark contentp+ u u dn0 d d u

Why three quarks? Because of quark colour: All quarkscome in three colours, such that the parent baryon iscolourless (from analogy with light).




Baryons also come in three flavours or types orgenerations:(

u

d

) (

c

s

) (

t

b

)

Again, the generations getheavier.

a, b, c, . . . represent quarks.α, β, ε, . . . represent leptons.Both of these are fermions or spin-1/2 particles of whichmatter (both normal and exotic) is made.


More on antiparticlesConsider an atom with an electron(s). When a positronapproaches, they annihilate each other.

Γ

e_

e+

This is Einstein’smass-energy equivalence.

Notion of couplingfrom same diagram:

Γ

e_

Strength of interaction proportional to charge. Here,cross-section depends on α2; α ∼ 1/137 is the finestructure constant.

Hence an exchange force is the exchange of bosons(force carriers) between fermions (matter).


The gauge principle1. Why is this notion called a principle or a paradigm?

2. How is it applied/extended?

1. The spin-1 photon is represented by a vector field(called the vector potential (3, 4 components). What dothese components physically correspond to?

Physical degrees of freedon are the differentpolarisations.

The photon has only two. Example: D-glucose isdextro-rotatory.

The gauge property (symmetry) of the theory removesthe extra d.o.f. → gauge field theories.


Requirements from gauge principleThe consistency of a gauge theory requires that mattercouples to radiation (force carriers) as in the diagrams.

Γ

e_

e_

Γ

e+

Note: No self-interaction of photon.

This is because the photon has no charge and it mediatesthe electro-magnetic force between charged particles.


2. Application to other theoriesLet us start with the weak interaction: Beta decay.

n → p + ε− + νε; the electron is emitted as beta ray.

The underlying quark-level (elementary) process is

d → u + ε− + νε

Conservation laws:B: 1 → 0 + 1 + 0L: 0 → 0 − 1 + 1Q: −1/3 → 2/3 − 1 + 0

Easier νε + d → u + ε:

W

ud

ν e

“Flavour” changes

Charge changes

Mediator of weak interactions is a charged spin-1 bosoncalled W. Science Club, Chennai, Oct 7, 2006 – p. 10

Neutral weak interactionsNeed not have change in

electric charge in a weak interaction.

Mediator of neutral weak interactions

is a neutral spin-1 boson called Z.

Z

dd

ν,ε ν,ε

The flavour “charge” is involved in weak interactions.

All matter has flavour charge so experience weak interaction.

W and Z are massive so the interaction is short-ranged.

(Explanation).

Something new: self-coupling

WWZ and ZZZ vertices appear


The weak carriersWe have seen an annihilation diagram

Γ

e_

e+

The final state particle can be a Z boson.

The momenta of ε and its antiparticle get converted intothe mass of the Z, which is very large:

mZ = 91, 190MeV ∼ (pε− + pε+)/2; mε ∼ 1/2MeV.

Call (pε− + pε+)/2 =√

s . When√

s = mZ , the Z particlecan be produced as a resonance.

QM tells us that any energy level (not ground state) hasa finite width because of decay. Esp true for heavy Z.

Z → ε+ε−, Z → µ+µ−, Z → qq, etc.Science Club, Chennai, Oct 7, 2006 – p. 12

Width/Inverse lifetime of Z-state6 40. P lots of cross sections and related quantities

σ and R in e+e− Collisions

10-8

10-7

10-6

10-5

10-4

10-3

10-2

1 10 102

ρ

ωφ

ρ

J/ψ ψ(2S)

Z

σm

b

10 2

10 3

ωφ

J/ψ ψ(2S)ZR


http://pdg.ihep.su/xsect/contents.html

Lifetimes and strengths of interactionsWe know that Γ ∼ 1/τ . We can calculate Γ ∼ α2 from thetheory and compare with experiment.

Consider ∆ → pπ: Lifetime τ ∼ 10−23 seconds.τ ∼ R/c where R is a typical size of the baryons. Thisgives R ∼ 1fm.

Consider π0 → γγ: Observed τ ∼ 10−16 seconds.

τEM

τstr∼ 104to106 .

Since αEM = 1/137, this means αstr ∼ 1.

Repeat for weak decay τwk ∼ 10−10 seconds. Getαwk ∼ 10−6.


The scale of interactionsConclude that decay rates or lifetimes are of the order10−23, 10−16 and greater than 10−10 seconds for strong,electromagnetic and weak interactions.

The model predicts that the coupling (alphas) of matterto the corresponding force carriers is 1 : 10−2 : 10−5.

Hence the names strong, electromagnetic (?!) and weakinteractions.

On this scale, the coupling to gravity is ∼ 10−29 and sostandard model does not include gravity.


Back to Z decays at LEP


Z → µµ


Z → qq


Something new happens


Newer still


Lessons learned from LEPDecays as expected; rates as expected.

Quarks seen as “jets.”

q → qG seen as 3 and 4 jets.

Consistency check on width of Z indicates there arethree flavours of neutrinos.

So LEP has information on weak, strong andelectromagnetic interactions!


Other decaysLet us return to beta decay:d → u + ε + νε . We can also haveµ → νµ + ε + νε . Recall(

u

d

) (

νµ

µ

)

The coupling in weak interactions ∼ αwk/M2N ≡ G.

Gµ = (1.16632 ± 0.00002) × 10−5 GeV−2.

Gβ = (1.136 ± 0.003) × 10−5 GeV−2.

Is this an error or a signal of new physics?


Quark mixing and CP violationIt turns out that the difference in the weak coupling constant

obtained from different experiments is real and arises because we

can have both u → dW and u → sW .

So there is mixing between the quarks d and s.

If consider all three generations, then the mixing between the

flavours is no longer real and allows for a phase.

Physically this means that the interactions of quarks and their

antiquarks is no longer the same: CP violation.

Good, because of baryon asymmetry in the universe. Where is the

anti-matter in universe?

This may happen in lepton sector as well: observed as neutrino

mixing.

Lots of work on CP.Science Club, Chennai, Oct 7, 2006 – p. 23

Digression: Strong force mediatorMediator is called gluon.

Charge here is colour charge.

Gluon is electric charge neutral but has colour charge.So it also experiences self interaction.

Leads to asymptotic freedom. One way to understandthis is to realise that the coupling constants are notreally constant!

αstr decreases as the energy scale of interactionincreases.

This prompts people to wonder whether there is a grandunified theory that unifies EM, strong and weakinteractions.


Beyond the standard model

Quark-lepton universality: GUTs

Why are there three generations?

W and Z are massive, not photon. Why? What is theorigin of fermion masses? (Related issue is the particlecalled Higgs that LHC will search for and a theory calledsupersymmetry).


Beyond the standard modelHow is asymptotic freedom related to no free colourbeing observed? Quark confinement.

How to incorporate gravity? (String theory? next talk.)

Bottom line: Apart from neutrino masses and mixing, nofirm experimental evidence for any physics beyond thestandard model. However, Standard model brings nodeep understanding of the fundamental issues inparticle physics. It is just a good working model.


force carriers the paradigm of particle physics

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