PHY313 - CEI544insti.physics.sunysb.edu/itp/lectures/05-Fall/PHY313/MOM... · 2005. 10. 7. ·...

Peter Paul 10/05/05 PHY313-CEI544 Fall-05 1

PHY313 - CEI544The Mystery of Matter

From Quarks to the CosmosFall 2005

Peter PaulOffice Physics D-143

www.physics.sunysb.edu PHY313


Information about the Trip to BNL

• When and where: Thursday, Nov. 3, 2005 at 5:20 pm pickup by bus (free) inthe traffic circle near the Student Activity Center (SAC). We will drive toBNL and arrive around 6pm (20 miles). We will visit The Relativistic HeavyIon Collider (RHIC) and its two large experiments, Phenix and Star. Expertswill be on hand to explain research and equipment. We will return by about7:30 pm to arrive back at Stony Brook by 8:10 pm.

• What are the formalities? You need to sign up either in class or to my e-mail address [email protected]. by this Friday night. You must bring along avalid picture ID. That’s all! The guard will go through the bus and check thepicture ID’s.

• What about private cars: You will still have to sign up and must bring apicture ID (your drivers license) to the event. You will park your car at thelab gate, join the bus for the tour on-site and then be driven back to your car.

• The extra credit for attending will be a full Home Work equivalent credit.


What have we learned last time• A nuclear fission process can build up a

a chain reaction initiated by neutrons,because each fission process produces~3 neutrons for every one that wasused.

• These neutrons need to be moderated tolow energies to be captured efficiently.

• If enough and sufficiently densenuclear fuel and enough low-energyneutrons are available the reaction canbe hypercritical and take off.

• The chain reaction can be contained oreven stopped by inserting nuclei intothe fuel that have a large capability ofabsorbing neutrons. Boron andCadmium are such nuclei.

• Fission reactors use mostly235Uranium and 239Plutonium as fuel.After a while the fission products fromthe chain reaction poison the fuel.

• Commercial nuclear reactor use light ofheavy water to moderate the neutrons,cool the fuel rods, and produce thesteam that drives a turbine.

• The fusion of deuterium and tritiumdelivers huge amounts of energy/ kg offuel, has an infinite supply of fuel, andproduces no long-lived radioactivewaste.

• However, the fusion reaction requires~100 Million degrees temperature whichposes very difficult technical problems.

• A modern fusion reactor uses magneticfield lines to spool the charged particlesof the plasma around in circles inside adough-nut shaped reactor vessel.

• The next generation Tokamac reactorITER is ready for construction andshould reach ignition.


Quarks

Cosmic Timeline for the Big BangCosmic Timeline for the Big Bang

proton, neutronsdeuterons

He nuclei(α particles)


How are light elements produced in stars• Three minutes after the Big Bang

the universe consisted of75% Hydrogen,25% 4Heless than 0.01% of D, 3He and 7Li.

• The sun began to burn the availableH into additional 4He, as we learnedand heated itself up.

• Once there was sufficient 4Heavailable the reaction4He + 4He+ 4He → 12 C + 8 MeVbecame efficient. It heated the sunup still further


Energy from Fusion in the Sun

!+"+ HeHH312

HHHeHeHe11433++!+

!++"++eHHH

211

!++"++eHHH

211

!! +"+#+ee !! +"+

#+ee

!+"+ HeHH312

4 1H + 2 e- → 4He +2 n + 6 γ + 26.7 MeV


From Helium to Carbon

• When the start has used up its hydrogen, thereaction stops and the star cools and contracts.If the star is heavy enough the contraction willproduce enough heat near the core where the4He has accumulated to start helium burning.

• Because of gravity the heavier elements alwaysaccumulate in the core of the star.

• The star now has 4 layers: at the centeraccumulates the Carbon, surrounded by a Hefusion layer, surrounded by a hydrogen fusionlayer, surrounded by a dilute inert layer ofhydrogen

CHeBe

BeHeHe

1248

844;

!+

!+


The CNO Cycle

• Once sufficient 12C is available it usesH nuclei to produce all the nuclei up to16O in a reaction cycle.

• When sufficient 16O is available and thestar has heated up much more, the starbreaks out of the CNO cycle by captureof a 4He or a proton. This forms all thenuclei up to 56Fe.

• In this process energy is produced toheat the star further because the bindingenergy/ nucleon is still increasing.

• Hans Bethe (Cornell) and Willy Fowler(Caltech) obtained Nobel Prizes forthese discoveries


From 16O to 56Fe

• B/A gives the binding energy pernucleon, i.e. the average energythat must be provided to free up anucleon from inside the nucleus

• The binding energy/nucleon startsvery low in light nuclei, with somespikes at some ”magic numbers”.

• The largest binding with 8.8 MeVoccurs in Fe. For higher nuclei theBE decreases again.

• We can build up nuclei from O tothe peak of binding energy byadding more nucleons. Each stepprovides more binding

•Binding energy per nucleon

http://hyperphysics.phy-astr.gsu.edu/hbase/nucene/nucbin.html


Relative Elemental Abundances of the Solar System

1.E-12

1.E-10

1.E-08

1.E-06

1.E-04

1.E-02

1.E+00

1.E+02

0 10 20 30 40 50 60 70 80 90 100

Z

% a

bu

nd

an

ce

8O

26FE/28Ni

82Pb


The Evolution of Matter in Stars

The interplay between gravitational forceand the outward push of the created heatproduces conditions for element formation


The first steps

• Hydrogen forms helium. Thehelium assembles in the core andthe core heats up to ~100 Million K

• There helium forms Carbon• Because of Gravity the heavier

elements concentrate in the core• In the hot core formation of the

heavier elements proceeds, while inthe cooler outer regions the earlierprocesses continue.


Formation up to the Peak of StabilityThe process of element formationcontinues by capture of He nuclei fromOxygen to Iron

16O+4He → 20Ne + 4He → 24Mg24Mg + 4He → 28Si +4He → 32Setc


Heavier Elements formed in Supernova ExplosionAs the heavier elements press on the core the corecollapses. If the star is large enough, the hugeensuing heat produces an outward explosion ofthe massive star. This explosion produces lots ofneutrons that are rapidly captured by the heavyelements.


Summary of Supernova explosion

• When a star has burned allits light fuel, it cools andcontracts under the gravitatio-nal pressure. It then explodes. Duringthe explosion huge numbersof neutrons are produced andcaptured rapidly by the exis-ting elements (r-process).

• Beta decay changes neutrons intoprotons and fills in the elements

• The new elements are blasted into spaceand are collected by newly formed stars.

• Binary stars which are very hot can alsoproduce the heavy elements.


Chart of theChart of theNucleiNuclei

N

Z

““MagicMagic””proton numbersproton numbers

2,8,20,28,50,822,8,20,28,50,82 N=Z

““MagicMagic””neutronneutronnumbersnumbers

...+126...+126

Location of the r-process in the nuclear mass table

The r-process works its wayup the mass table on theneutron-rich side. There areother processes on theproton rich side


Now to Quarks and Gluons !

• After WW-II increasingly powerfulproton accelerators produced manynew “elementary particles” ofincreasingly heavier mass MM = Energy of the collision/c2

• These were all strongly interactingbut some had “strange”characteristics indicating newquantum, numbers.

• It became apparent that this manyparticles could not be allfundamental and there had to be adeeper system explaining all of this.

• In the 1960’s Murray Gell-Mannintroduced a new class ofsubnucleon particles which he calledquarks.

• The Alternating Gradient protonSynchrotron at Brookhavenrevolutionized proton acceleration,reaching 25 GeV in 1962

• This accelerator could produce newparticles with mass as high as 7 GeV


Production of New Elementary Particles

• If we bombard a target of hydrogenwith an accelerated beam, ofprotons, a number of things canhappen:

1. Elastic scattering2. A set of different, but known

particles are produced3. A completely unknown

particle is produced

• The following properties are known tobe conserved:

1. Energy and momentum2. Electric charge3. Baryon Number → number of “heavy

particles

xppp

dpp

pppp

+!+

+!+

+!+

+"

Bubblechamberproduces vividpictures of thereaction


Bubble chamber pictures


Energetics of elementary particle production.

• The kinetic energy of the beam and the reaction products and theenergy contained in all the masses must be conserved, i.e. must add upleft and right: for a stationary target for the three reactions above

• By knowing the masses and Kinetic Energy of the beam and target andmeasuring the KE of all participants, one can determine the mass ofthe new particle x

)()(2)(

)()(2)(

)()(22)(

222

222

22

pKExKEcmcMcMpKE

dKEKEcMcmcMpKE

pKEpKEcMcMpKE

xpp

dp

pP

!+++=•+

+++=•+

!!+!+•=•+

""


“Strange” behavior of new particleshttp://hyperphysics.phy-

astr.gsu.edu/hbase/particles/Cronin.html• In the 1940’s new particles of mass ~ 500

MeV were discovered. Later confirmed atBrookhaven

• They were called Kaons and other particles.• They behaved strangely:1. They decayed into strongly interacting

particles, but with a very slow life time of10-6 to 10-9 s.

2. They seemed to be produced in pairs:

3. Gell-Mann concluded that a new quantumnumber, which he called Strangeness, mustprohibit (slow down) the decay.

0Kp +!"+

#$

particleneutralK !++"!+ ##0


The Particle Zoo I• Light particles (Leptons) http://hyperphysics.phy-

astr.gsu.edu/hbase/particles/Cronin.html

Very small3 ν’sneutrinos

105.7 MeVµ+, µ-muons

511 keVe+, e-electrons

MassSymbolSpecies

S = 0

S = ± 1S = ± 1

S = 0 S = 0

Strangeness

2.6 keV

1.2 x 10-8s5 x 10-8 , 10-10 s

2.6 x 10-8 s8.3 x 10-17 s

Life time

548.8 MeVηEtas

493.7 MeV497.7 MeV

K+, K-

K0

Kaons

139.6 MeV135 MeV

π+, π-,π0

Pions

MassSymbolSpecies

Medium heavy particles(Mesons). All have…

• Integer spin: 0,1

• Baryon number =0


The Particle Zoo II

S = - 1S = - 1S = - 1S = - 1

S = 0 S = 0

Strangeness

2.6 x 10-10 s0.8 x 10-10

5.8 x 10-20

1.5 x 10-10

>1035 yrs898 s

Life time

1116 MeV1189 MeV1192 MeV1197 MeV

Λ0

Σ+

Σ0

Σ-

Hypernuclei

938.3 MeV939.6 MeV

p+

n0

Nucleons

MassSymbolSpecies

Heavy particles (Baryons): These particles all have

•Half integer spin: ½; 3/2

•Baryon number B = ± 1.


Hidden symmetries reveal themselves

All the “elementary” particles could be arranged in patterns thatdisplayed certain eightfold symmetries: The Eightfold Way

Murray Gell-Mann


The Rock Band Eightfold Way

The beauty of certainsymmetries is recognizedin the popular culture!


Gell-Mann and the Eight-fold Way• In 1961 Gell-Mann and Ne‘eman

proposed a new clasificationscheme to bring simplicity into thiszoo.

1.The Mesons and Baryions interactvia the strong interaction: Hadrons

2. The Mesons have between 1/3 to ½of the mass of the Baryons. Theyhave interger spin (0 and 1)

3.The Baryons are the heaviest group,have half-integer spin (1/2, 3/2)

4.The mesons and the Baryons areseparate groups (B = 0 and B = 1)

5.They all have normal units ofpositive or negative or no charges.

• These and other systematicobservations could be explainbedby a mathematical classificationscheme based on themathematical symmetry groupSU(3). It intro-duced „quarks“ asa mathematical concept.


Quarks as building blocks of Hadrons

• If Quarks are building blocks ofmesons and Baryons must havethe following properties

1.They must have spin ½: the 2quarks can make spin 0 or 1, 3quarks can make ½ and 3/2

2.They must have charges thathave 1/3 or 2/3 the normalcharge of an electron!

3.There must be at least 3 differenttypes: “up”, “down”, and“strange”

4.We need quarks and “antiquarks”

d

-1 0S = 0

-1/3 1/3 -1/3 1/3Q = 2/3B = 1/3

+1 0S = 0

+1/3 -1/3 +1/3 -1/3Q = -2/3B = -1/3

u

u

s

d

s


Simple Quark configurations of hadrons

• Proton uud Q = 2/3+2/3-1/3 = +1 S = 0 B = 1• Neutron udd Q = 2/3 -1/3 - 1/3 = 0 S = 0 B = 1• Λ0 uds Q = 2/3 - 1/3-1/3 = 0 S = -1 B = 1• Σ+ uus Q = 2/3+2/3 -1/3 = +1 S = -1 B = 1• Σ0 uds Q = 2/3 -1/3 – 1/3 = 0 S = -1 B = 1• Σ- dds Q = -1/3-1/3-1/3 = -1 S = -1 B = 1

• π+ udbar Q = =2/3 + 1/3 = 1 S=0 B = 0• π0 uubar + ddbar• π- dubar• K+ usbar Q = 2/3+1/3 = 1 S = +1 B = 0

Here is aproblem

We neglected the fact that quarks with spin ½ are subject to the Pauli Principle


The Omega Particle as Proof

• This quark model predicts that there should be oneparticle that has the simple configuration sss

• This particle has Strangeness S = -3, Charge Q = -1

Baryon Number = -1• When this particle was found in one bubble chamber

picture in 1964 it clinched the quark model.• The reaction was complicated

(S =-1) + (S = 0) → (S = -3) + (S=+1) + (S=+1)• The Ω - and the rest then decayed into many

secondary particles.

0KKpK ++!"+

+##


Feynman Diagramshttp://www2.slac.stanford.edu/vvc/theory/feyn

man.html• Richard P. Feyman invented a pictorial

way to describe the time evolution of areaction based on the exchange offorce particles

• In these diagrams time is movingforward from left to right.

• The processes here are scattering ofelectrons and positrons with emissionof a photon

Feynman was oneof the most inventivephysicists alwaysready for a joke

• The process below is the annihilationof a particle (e-) and its antiparticle(e+) with emission of a photon. Thetime axis for an antiparticle runsbackwards.


Deep inelastic scattering: What’s inside a nucleon?http://hyperphysics.phy-

astr.gsu.edu/hbase/nuclear/scatele.html• Deep inelastic scattering of energetic

electrons is the equivalent experimentof Rutherford's α-scattering.

• Energetic electrons interact with thecharged particles (if any) inside theproton.

• The Stanford experiment found suchparticles in 1967, which were calledpartons. Today we know that these arethe quarks.

• They found more than the 3 expectedpartons in a proton because quark-antiquark pairs are constantly formedinside quar

k


Can we see quarks? Jets!• No free quark has ever

been observed. It wouldhave to have 1/3 or 2/3charge

• But quarks and antiquarkscan be seen as a shower ofsecondary particles, whichare called jets. Ecah jetrepresent a quark.

• We show here aspectacular four-jet eventfrom the CDF detector atFermilab.


Schematic description of jet event

The jet production probability can measurethe strength of the strong force as a functionof energy

If more than 2 jets are observedthey could come from Gluons


Gluons

• Gluons are the exchangeparticles between quarks.

• They are neutral particles withspin 1

• They can be seen in 3-jet events,where a quark was struck by anelectron, and then that quarkknocked out a gluon.


The first events from the HERA facility at DESYproving the existence of gluons inside a proton


The Charmed Quark

• In 1974 in a surprising result atBNL and at SLAC a 4th quark wasfound. It was named the CharmedQuark c

• It was much heavier and boundtogether with an charmed antiquarkinto a c-cbar state called J/Ψ.(„hidden charm“)

• This discovery made quarks trulycredible. Since then, two heavierquarks have been found: the b(bottom) quark and the heaviest, thet (top) quark.

http://www.shef.ac.uk/physics/teaching/phy366/j-psi_files/j-psi.pdf

The J/Ψ seen as a peak at 3.1 GeVwith high-energy electron beams →

Sam Ting


Discovery of the Top Quark• The Top Quark was discovered

in 1995 at Fermilab by twocollaborations with strongStony Brook leadership.

• Its mass of 168 TeV is almostequal to the mass of a Goldnucleus.

• It is the heaviest elementaryparticle known so far andcompletes the three quarkfamilies.

In the experiment a proton and an anti-proton beam collide at about 1TeV energy and produce a top-anti-top quark pair. This pair thendecays by emitting six (count them!) jets.


Microscopic Picture of Top Production

• The colliding protons andantiprotons contain 3 quarksand 3 antiquarks, respectively.

• One member of each groupinteracts with a member of theother.

• The quarks and antiquarksthat are produced assemblethemselves into compositemesons as shown, that emergeinto the detector.

• From the energies of theseobserved particles (jets) themass of the top quark (168GeV) is inferred.


Order in the (Quark) Court!

http://hyperphysics.phy-astr.gsu.edu/hbase/particles/quark.html

1/2

1/2

Spin

strange(100 MeV)

charm(1300 MeV)

Second family

-1/2

+3/2

Charge Third familyFirst family

bottom(4,300 MeV)

down(6 MeV)

top(175,000 MeV)

up(3 MeV)

Today we know 3 families of quarks, and 3 antiquark families.


Quark Confinement

• The color interaction between quarksbinds the quarks such that no singlequark can ever be free.

• This is different from two chargedbodies bound by the Coulomb force,but similar to the binding of amagnetic north-pole and a south-pole.

• A quark that emerges from a protonwill “dress itself with other quarks oranti-quarks and emerge as a jet.

• The binding force between quarksrelatively weak when they are closetogether but grows stronger as they arepulled apart.

• At close distances they can almost betreated as free: Asymptotic freedom


Sixth Homework Set, due Oct. 20, 20051. As a star burns its hydrogen and helium fuel and later carbon, oxygen,

magnesium etc. How are the ashes arranged inside the star?2. How does the star produce Carbon? Give some detail.3. How does a star produce the heavy elements past Fe? Describe

environment and process.4. The observed elementary particles can be grouped by their masses in 3

groups. What are the names of these groups and what are typicalmasses in each group?

5. Why are some particles called strange? Name one such strange particle.6. Who invented quarks and where was he employed when he did so?

PHY313 - CEI544insti.physics.sunysb.edu/itp/lectures/05-Fall/PHY313/MOM... · 2005. 10. 7. ·...

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