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Lecture 9: Quarks II

Lecture 9: Quarks II. Quarks and the Baryon Multiplets Colour and Gluons Confinement & Asymptotic Freedom Quark Flow Diagrams. Useful Sections in Martin & Shaw:. Section 6.2, Section 6.3, Section 7.1. Building Baryons.

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Lecture 9: Quarks II

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  1. Lecture 9:Quarks II • Quarks and the Baryon Multiplets • Colour and Gluons • Confinement & Asymptotic Freedom • Quark Flow Diagrams Useful Sections in Martin & Shaw: Section 6.2, Section 6.3, Section 7.1

  2. Building Baryons Spin numbers of 1/2 and 3/2 suggest the superposition of 3 fermions Absence of anti-particles suggests there is not substantial anti-quark content Baryons: (note that m() ≠ m(+) so they are not anti-particles, and similarly for the * group)  So try building 3-quark states Start with 2:

  3. The Decuplet Baryons: Spin numbers of 1/2 and 3/2 suggest the superposition of 3 fermions Absence of anti-particles suggests there is not substantial anti-quark content (note that m() ≠ m(+) so they are not anti-particles, and similarly for the * group) ddd ddu duu uuu dds uus uds dss uss The baryon decuplet !! sss  So try building 3-quark states Now add a 3rd: and thesealed the Nobel prize 

  4. Coping with the Octet Y p (938) n (940) 1 0 (1193)  (1189) I3  (1197) (1116) 0 (1315)  (1321) -1 ddd ddu duu uuu ways of getting spin 1/2: dds uus uds 0 dss uss these ''look" pretty much the same as far as the strong force is concerned (Isospin)  sss But what about the octet? It must have something to do with spin... (in the decuplet they’re all parallel, here one quark points the other way) We can ''chop off the corners" by artificially demanding that 3 identical quarks must point in the same direction J=1/2 But why 2 states in the middle?  uds  uds  uds J=3/2

  5. Quark Questions Y So having 2 states in the centre isn’t strange... but why there aren’t more states elsewhere ?! p (938) n (940) 1  uus  u us ??? and i.e. why not 0 (1193)  (1189) I3  (1197) (1116) 0 (1315)  (1321) -1 The lowest energy state has them ddd ddu duu uuu ( ) Not so crazy  lowest energy states of simple, 2-particle systems tend to be ''s-wave" (symmetric under exchange) dds uus uds What happened to the Pauli Exclusion Principle ??? dss uss Why are there no groupings suggesting qq, qqq, qqqq, etc. ?? sss We can patch this up again by altering the previous artificial criterion to: J=1/2 ''Any pair of similar quarks must be in identical spin states" J=3/2 What holds these things together anyway ??

  6. Colour Call this new charge ''colour," and label the possible values as Red, Green and Blue call these ''gluons" Pauli Exclusion Principle there must be another quantum number which further distinguishes the quarks (perhaps a sort of ''charge") Perhaps, like charge, it also helps hold things together ! We see states containing up to 3 similar quarks  this ''charge" needs to have at least 3 values(unlike normal charge!) We need a new mediating boson to carry the force between colours (like the photon mediated the EM force between charges)

  7. Gluons R G the only way out is to attribute colour to the gluons as well. For the above case, the gluon would have to carry away RGquantum numbers In p-n scattering, u and d quarks appear to swap places. But their colours must also swap (via gluon interactions).  This suggests that an exchange-force is involved... But then we run into trouble while trying to conserve charge at an interaction vertex: (a quark-screw!)

  8. Non-Colour-Changing Gluons RG, RB, GR, GB, BR, BG So, for example, a gluon composed of the superpostion 1/2    RR BB would coupleredandbluequarks without changing their colours To handle all possible interchanges, we therefore need different gluons with colour quantum numbers But we currently have no reason to exclude exchanges which do not change the quark color as well!

  9. ''Better" Symmetry 1/ +   RR BB GG Since appropriate superpositions of this gluon with will yield the necessaryred-green andblue-greencouplings 1/2 RRBB To couple togreen as well, we just need one more gluon: Allowing these 2 additional gluons results in a higher degrees of symmetry since we are making use of all possible pair combinations ofRGB with the anti-colours Maybe this is a good thing to do... let’s try it and see !

  10. Another Way: SU(3) YC YC G R B IC IC R B G BG RG Central SU(3) states: 1/2 (  ) 1/6( ) 1/3(  ) RR BB RB BR RR BB GG BB GG RR GG BB RR GB GR In ''SU(3)-speak", the last state is actually a separate (singlet) representation of the group which is not realized in nature, so we end up with 8 gluons. Another way: ...starting to look familiar ?! The reason we get 9 states for the mesons is that the symmetry there is not perfect, so there is mixing. But, for colour, the symmetry is assumed to be perfect.

  11. Flux Tubes (hence the analogy with ''colour", since white light can be decomposed into eitherred, green&blueor their opposites -cyan, magenta&yellow) ''flux tube" q q q We could explain only having the quark combinations seen if we only allowed ''colourless" quark states involving either colour-anticolour, all 3 colours (RGB) , or all 3 anticolours. If the carriers of the force (the gluons) actually carry colour themselves, the field lines emanating from a single quark will interact: * formally still just a hypothesis (calculation is highly non-perturbative)

  12. Confinement Ah! So only colourless states have finite energy ! ''Confinement" PoP ! q q q q q q q q q q For this configuration, the field strength (flux of lines passing through a surface) does not fall off as 1/r2 any more  it will remain constant. The field energy will thus scale with the length of the string and so asL thenE  Clearly we can’t allow this!! Can be stopped by terminating field line on another colour charge ''fragmentation"

  13. How about qqqqq ? Pentaquarks Need Colourless States... So what about qqqqqq states ? Sure  that’s basically the deuteron (np = uuuddd)

  14. Search for Fractional Charge vz = 2r2g/9 vx = qE/6r for q > 0.16e, the number of fractionally charged particles is less than 4x1022 per nucleon (Halyo et al., PRL 2000) Search for Free Fractional Charges(M. Perl et al.)

  15. Asymptotic Freedom RB q q q q q RG q ''Asymptotic Freedom" Getting very close to a quark: So, on average, the colour is ''smeared" out into a sort of ''fuzzy ball" Thus, the closer you get, the less colour charge you see enclosed within a Gaussian surface. So, on distance scales of ~1 fm, quarks move around each other freely

  16. High Energy Limit This also means that perturbative QCD calculations will work at high energies! Note that asymptotic freedom means that the running coupling will decrease with higher momentum transfer the opposite of what happens with vacuum polarization in QED!)

  17. Where Are The Coupling Constants Running ???

  18. Pion Exchange Revisited d u u d u d n p RB R R B B u d   or = qq creation = qq annihilation (ud) (ud) G GB G d d u u d u n p So how do we now interpret pion exchange??

  19. Quark Flow Diagrams s u u s K K+ u d d d u u u d u d u u u d n  p p p s s  p + +++  p + + u d d u u u d d u u + p + p ++ Quark Flow Diagrams:  K + K+ p + p  p + n + +

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