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Fundamental interactions in particle physics

U. Straumann, Aarau, 25.3.06

Forces and fundamental interactions

Contents: 1. Gravitation and Electrostatics 2. Electrodynamics: Electric and Magnetic united 3. More forces: weak and strong 4. Principle of the scattering experiment 5. Quantummechanical complications 6. Example experiment 7. Grand unification? Summary and outlook

U. Straumann, Aarau, 25.3.06

1. Gravitation and Electrostatics (1) Newton and Coulomb

Newton's law: Force of gravitation between two bodies 1 and 2:

m1m2 F = 2 R

Coulomb's law: Electrical force between two bodies 1 and 2, carrying electric charge qi

1 q 1q 2 F= 2 4 0 R

Same formula, but two different constants!

1. Gravitation and Electrostatics (2): 2 ­ particles bound states:

Earth ­ Moon:

m 1m2 E pot =- R


Hydrogen atom: Proton ­ Electron same drawing, same formula, different constants (and QM, see later)




1. Gravitation and Electrostatics (3): comparison in more detail:

Strength: Compare electrostatic and gravitation force of two bodies with mass mP and unity electrical charge e: They are equal, if =>

m Pm P 1 ee = 2 2 4 0 R R (Planck mass) m P =21.77 g

electrical charge exists only in whole numbers of e E: attractive or repulsive, G: always attractive (incl. antimatter) G: mT=mS mass of inertia = mass of gravity, thus all bodies feel the same acceleration (Galilei's law of free fall).

2. Electrodynamics (1): magnetostatic forces:

Experimental evidence very old complicate laws: proportional to R3 ,also torque

2. Electrodynamics (2): unification of electr. and magn. forces:

by Faraday and Maxwell in 19th century Magnetic fields are created by moving electrical charges or time ­ varying electrical fields Time ­ varying magnetic fields generate electrical fields A set of 4 equations (Maxwell equations) describe all electromagnetic effects consistently. Electric and magnetic forces are two different phenomena which have their origin in the same physics law There is only one fundamental constant: c

2. Electrodynamics (3): explains new effects:

Maxwell's equations explain also electromagnetic waves, for instance light. Speed of light is constant = c, independent of speed of source or speed of observer => theory of special relativity (Einstein 1905) Maxwell's electrodynamics is probably the best theory we have: it truely unifies two forces it explains additional effects, like light it predicts correctly the theory of special relativity.

3. More interactions: weak and strong force(1): What is the proton made of?

Protons and Neutrons are made of three quarks each. u quark: q=2/3 e d quark: q=-1/3 e proton: uud neutron: udd q=+1 q=0


eps e -> k

! ing ris

The forces between the quarks are due to the strong interaction The "charges" on which the strong force interacts are called "colors": There are three colors: red green blue. -> Quantum chromo dynamics, QCD.


3. More interactions: weak and strong force(2): What makes the sun shining?

There are many processes, most importantly: Protons (Hydrogen) are melt together to form He-4. He-4 nucleus = ppnn

need to change some p into n. u quark into d quark d e u = weak interaction (" rays")

3. More interactions: weak and strong force(3): Properties of weak interaction

The weak interaction is also responsible for radioactivity. It has a very short range:

1 - R E pot ~ - e R

with = 1/0.002 fm The only interaction with this short range. At very small R same formula as the other interactions, but different const.

Epot R

3. More interactions (4): Four fundamental interactions

As of today, we know four fundamental interactions: "classical" description: Gravity Electric Strong Weak infinite range infinite range confinement short range



Each of them has its own interaction constant. Do they become similar at small R?

4. How to measure ? The scattering experiment: Conceptual idea

Basic setup: Beam energy determines Rmin, i.e. the resolution

Particle Detector

Target object

particle beam


Measure probability of scattered particle as a function of: - energy - scattering angle (often colliding beams are used)

4. The scattering experiment(2): Determine interaction law

Example 1: "hard ball" interaction at surface for instance neutrons.


Example 2: Electrically charged particles, for instance electron and quark (inside proton)


1 sin 4 /2



Epot R

1 R



4. The scattering experiment(3): What we can learn in addition:

From overall scattering probability -> coupling constant From energy of scattered particle -> momentum of target particle Energy of beam particle determines, how close we can come: Rmin -> "resolution" of experiment -> need large energy to determine law at small distances Often additional particles produced -> more detail about nature of interaction.

5. Complication: Quantummechanics (1)

1. Discrete energy and angular momentum states in bound systems, for instance Hydrogen atom. 2. Interaction field comes in quanta as well, "interaction carriers", "exchange particles", "propagator" are also particles. Example: El-mag. interaction: Photon

"Quantum field theory" (QFT)

5. Complication: Quantummechanics (2) field quanta for fundamental interactions

Standard model of particle physics is a QFT, describing: Elektromagnetism Photon Weak Interaction Strong Interaction W, Z Gluon mass = 0 electrical charge

mass 90 GeV weak hypercharges mass = 0 color charge

The propagators transfer energy and momentum. Each interaction has its own coupling constant

6. Example experiment: electron proton collider at DESY, Hamburg

circumference 6.5 km electron 29 GeV proton 920 GeV collide at two positions

Experiment H1 p

measure direction and energy of all particles produced


Some members of the H1 Collaboration

Work at the innermost parts of the H1 detector

HERA e-p scattering events observed in the H1Detector


A NC-DIS event with two jets

ep e Jet 1 Jet 2






Jet2 e Jet1






7 Grand Unification Coupling constants are not exactly constant:

Coupling Constants

They vary slowly with energy ( = 1 / Rmin) Theoretically predicted


on g


Do they meet at high energy? = Unified interaction

netic electromag

Energy, ~1 / Rmin 100 GeV Todays experiments 1016 GeV

7 Grand Unification: Experimental result on strong interaction

Strong Coupling Constant

Energy, ~1/R

7. Grand Unification: extrapolation to very high energies

Experimental result:

1 / (Coupling Constants)

Coupling constants do NOT excactly meet at high energy, but almost. If they would meet, we would have unified the interactions! May be there is new physics, new interactions? What about Gravity?

Energy, ~1/R

Summary Forces and interactions

Long distance (low energy): Fundamental forces are described by their potential energy. We know 4 fundamental forces: Gravity, electromagnetic, strong and weak

Epot R

Short distance (high energy): Fundamental interactions are described by Quantum Field Theory (QFT), with exchange particles. The standard model (SM) of particle physics is a QFT describing three different interactions: Electromagnetic, strong and weak. Same formalism, but different constants. Are the three SM forces different, low-energy phenomena of the same fundamental interaction? Can we unify them at very high enery?


From 2008 a new collider (pp) at CERN, called LHC, will search for new physics and new interactions. Open questions on fundamental interactions: - Is there new physics, which would allow to exactly unify the interactions at high energies? - "Dark Matter" in the universe asks for new particles and interaction in the mass region, reachable by LHC - How to include gravity in a consistent QFT of all interactions?


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