Seminar: Quarkonia-boundstatesofQCD,messengersofQGP … · 2007. 11. 5. · Motivation - History...

Motivation - HistoryQuarks - the Elementary Particles

Group Theory - the Symmetry of the QuarksSummary and Outlook

The quark structure of matter - an introductionSeminar: Quarkonia - bound states of QCD, messengers of QGP

Christopher Bauer

Winter term 2007/08

25.10.2007

Christopher Bauer Quark structure



1 Motivation - History

2 Quarks - the Elementary ParticlesOverview - the FlavorsColor - the Charge of the Strong InteractionGluons

3 Group Theory - the Symmetry of the QuarksSU(2) GroupsSU(3) Groups

4 Summary and Outlook




History

Steps through the structure of matter:

1897 "Discovery" of the electron e(J.J. Thomson)1905 Photon is a particle (A. Einstein)1911 Discovery of the nucleus (Rutherford)1919 Discovery of the proton p (Rutherford)1932 Discovery of the neutron n(Chadwick)

↪→ Structure of the atoms is understood




History

1928 Prediction of the positron (Dirac)1930 Prediction of the neutrino (Pauli)1933 Discovery of the positron (Anderson and Neddermeyer)

↪→ Explanation of the β decay↪→ Open question: What keeps the nucleus together?

1935 First theory of the strong interaction (Yukawa)proton and neutron interact via pion exchange1947 Discovery and identification of the pion1947 Electromagnetic interaction described in QED




History

1949ff Discovery of many other strong interaction particles("hadrons"):

mesons (bosons, integer spin), e.g. pion πbaryons (fermions, half integer spin), e.g. proton and neutron




History

1964 Quark model (Gell-Mann, Neeman, Zweig)hadrons consist of quarks q:baryons = qqq and mesons = qqthree "Flavours": up (u), down (d) and strange (s)further quarks:charm (c, 1974), bottom (b, 1977), top (t, 1995)

1973 Theory of the strong interaction: "Quantumchromodynamics" (QCD) by Weinberg, Fritzsch, Gell-Mann,Leutwylerquarks interact via exchange of gluons




Overview - the FlavorsColor - the Charge of the Strong InteractionGluons









Background of the Word "Quark"

Word "quark" was coined by Murray Gell-Mann, having been takenfrom the phrase "Three quarks for Muster Mark" in FinnegansWake by James JoyceGell-Mann: "Quarks are merely convenient mathematicalconstructs, not real particles."





Overview

Gen. Weak Isospin Flavor Name Symbol Charge e Mass [MeV /c2]1 +1/2 Iz = +1/2 Up u +2/3 1.5− 3

−1/2 Iz = −1/2 Down d -1/3 3− 72 −1/2 S = −1 Strange s -1/3 70− 120

+1/2 C = 1 Charm c +2/3 1150− 13503 −1/2 B′ = −1 Bottom b -1/3 4100− 4400

+1/2 T = 1 Top t +2/3 170900± 1800

all quarks have spin 1/2 and baryon number 1/3for each quark a corresponding antiparticlequarkonium (pl. quarkonia) = a flavorless meson (quark andits own antiquark)





Why Quarks need Color

Combinations as proton (uud) and neutron (udd) etc.

∆++ = uuu with J = Ml = 32 would have three identicalfermions u in a completly symmetric ground state↪→ forbidden by the Pauli exclusion principleWhat about the the other possibilities such as qq, qq or singlequarks?

⇒ Introduction of a new quantum number for quarks: "Color"Christopher Bauer Quark structure




The Color of the Quarks

Quarks come in three primary colors:red (R), green (G), blue (B)all particle states observed in natureare postulated to be colorless/whitethis solves problem for the ∆++

explains also the existence ofbaryons (RGB)antibaryons (RGB)mesons (RR + GG + BB)

and that the others do not exist





Quark-Confinement

Quarks themselves are colored → not visibleexist just as constituents of hadrons → confinementHadrons carry no color charge





Overview

Gluons are the quanta of thecolor field, that

bind quarks in nucleonsand also nucleons in nuclei

EM: electrons interact byexchange of virtual photonsQCD: quarks interact by gluonexchange (strong interaction)Non-abelian gauge theory:gluons carry charge





Screening of the Electric Charge

⇓





Anti-Screening of the Color Charge - Asymptotic Freedom





Momentum Space

Coupling constant in momentumspace:

αs(q2) =αs(µ

2)

1 + αs(µ2)b ln(|q|2/µ2)

b =33− 2Nf

12π





Closer Look on Gluons

Gluons can interact with themselves (6= EM interaction)carry color charge: bicolored objects

9 bicolored states: RR,RG ,RB,GR,GG ,GB,BR,BG ,BBRR + GG + BB is a color singlet, no net color charge

⇒ 8 gluons in QCD instead of the single photon in QED↪→ in accordance with gauge theories for QED and QCD




SU(2) GroupsSU(3) Groups









The Group SU(2)

Special unitary group in 2 dimensions(j = 12) is lowest-dimension nontrivial representation of SU(2)(isomporphic to rotation group SO(3))Generators Ji = 12σi with i = 1, 2, 3

σ1 =

(0 11 0

), σ2 =

(0 −ii 0

), σ3 =

(1 00 −1

)are traceless [S] and hermitian [U]

Basis conventionally as eigenvectors of σ3:(10

)and

(01

)describing a spin-12 particle, e.g. an electron





Application to Isospin

SU(2) symmetry with (n,p) as fundamental representationSU(2) algebra, defining the group:

[Ij , Ik ] = iεjkl IlGenerators Ii = 12τi with τi equal to Pauli matrices

Proton and neutron states represented by

p =(

10

)and n =

(01

)





The Group SU(3)

Special unitary group in 3 dimensions32 − 1 = 8 traceless and hermitian generatorsfundamental representation consisting of 3x3 matrices actingon triplet statesstandard choice for generators Fi = 12λi with Gell-Mannmatrices λi :

λ1 =

0 1 01 0 00 0 0

, λ2 = 0 −i 0i 0 0

0 0 0

,λ3 =

1 0 00 −1 00 0 0

, ... λ8 = 1√3

1 0 00 1 00 0 −2





The Group SU(3)

λ1, λ2, λ3 correspond to the Pauli matrices ⇒ SU(2) subgroupof SU(3)λ3 and λ8 are diagonal with simultaneous eigenvectors 10

0

, 01

0

, 00

1

Structure constants fijk define the SU(3) algebra:

[Fi ,Fj ] = ifijkFk





Color SU(3)

Eigenvectors connected to 3 color charges of a quark:

R =

100

, G = 01

0

, B = 00

1

Quarks interact via octet of vector bosons: the gluons





Flavour SU(3)

in 1960’s experimental evidence for a second additive quantumnumber called "strangeness"Isospin I3 → SU(2); together with strangeness S → SU(3)

Triplet |u〉 =

100

, |d〉 = 01

0

, |s〉 = 00

1

Hypercharge Y ≡ B + S (baryonnumber + strangeness) centersmultiplet at the originElectric charge Q = I3 + Y2





Flavour SU(3)

Analog antiquark multiplet:

but Flavour SU(3) symmetry explicitly broken⇒ different masses of u, d, s quarksnevertheless very useful symmetry





Mesons

Combination of quark and antiquark qqPutting the triplets together: 3⊗ 3 = 8⊕ 1Spin 0 octet (negative parity)

broken symmetry → different masses of hadronsChristopher Bauer Quark structure




Mesons





Baryons

Combination of 3 quarks qqq or antiquarks qqqPutting the triplets together: 3⊗ 3⊗ 3 = 10⊕ 8⊕ 8⊕ 1Spin 32 decuplet





Baryons





Baryons

Combination of 3 quarks qqq or antiquarks qqqPutting the triplets together: 3⊗ 3⊗ 3 = 10⊕ 8⊕ 8⊕ 1Spin 12 octet





Baryons




Summary

Quarks = elementary particles - building blocks of hadronscarry color chargeinteract by gluon exchangegluons as the exchange bosons of the strong force

Theoretical description by group theorySU(2) for isospinSU(3) for colors (R,G,B) or isospin and strangeness (u,d,s)Meson and baryon multiplets




Outlook

Next topic:Evidence for a fourth quark from weak interactions - The GIMmechanism




The End

Thank you for your attention!




Sources

F. Halzen and A. Martin, Quarks & Leptons, John Wiley &Sons (1984)Lecture notes by B. FrimanAitchison & Hey, Vol 2, eq. 15.51Figures: http://commons.wikimedia.org/wiki/Particle_physicsParticle Data Group(http://pdg.lbl.gov/2007/reviews/qcdrpp.pdf)Lecture notes by C. Fischer


Motivation - HistoryQuarks - the Elementary ParticlesOverview - the FlavorsColor - the Charge of the Strong InteractionGluons

Group Theory - the Symmetry of the QuarksSU(2) GroupsSU(3) Groups

Summary and Outlook

Seminar: Quarkonia-boundstatesofQCD,messengersofQGP … · 2007. 11. 5. · Motivation - History...

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