Text of Lecture 9: Quarks II Quarks and the Baryon Multiplets Colour and Gluons Confinement & Asymptotic...
Lecture 9: Quarks II Quarks and the Baryon Multiplets Colour and Gluons Confinement & Asymptotic Freedom Quark Flow Diagrams Section 6.2, Section 6.3, Section 7.1 Useful Sections in Martin & Shaw:
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 So try building 3-quark states Start with 2: Building Baryons (note that m( ) m( + ) so they are not anti-particles, and similarly for the * group)
So try building 3-quark states Now add a 3rd: The baryon decuplet !! and the sealed the Nobel prize The Decuplet ddd ddu duu uuu dds uus dss uss sss uds 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)
1 I3I3 Y p (938 ) (1321) 0 (1315) n (940) (1197) 0 (1193) (1116) (1189) But what about the octet? It must have something to do with spin... (in the decuplet theyre 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 But why 2 states in the middle? Coping with the Octet ddd ddu duu uuu dds uus dss uss sss uds ways of getting spin 1/2: u d s u d s u d s u d s u d s u d s these ''look" pretty much the same as far as the strong force is concerned (Isospin) 00 J=1/2 J=3/2
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: q q q ''flux tube" * formally still just a hypothesis (calculation is highly non-perturbative) Flux Tubes (hence the analogy with ''colour", since white light can be decomposed into either red, green & blue or their opposites - cyan, magenta & yellow)
For this configuration, the field strength (flux of lines passing through a surface) does not fall off as 1/r 2 any more Can be stopped by terminating field line on another colour charge Ah! So only colourless states have finite energy ! ''Confinement" q q q q q q q qq q PoP ! ''fragmentation" Confinement The field energy will thus scale with the length of the string and so as L then E it will remain constant. Clearly we cant allow this!!
Need Colourless States... So what about qqqqqq states ? Sure thats basically the deuteron (np = uuuddd) How about qqqqq ? Pentaquarks
for q > 0.16e, the number of fractionally charged particles is less than 4x10 22 per nucleon (Halyo et al., PRL 2000) Search for Fractional Charge Search for Free Fractional Charges (M. Perl et al.) v x = qE/6 r v z = 2r 2 g/9
q q q Getting very close to a quark: q RGRG q RBRB q 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 ''Asymptotic Freedom" Asymptotic Freedom
the opposite of what happens with vacuum polarization in QED!) Note that asymptotic freedom means that the running coupling will decrease with higher momentum transfer This also means that perturbative QCD calculations will work at high energies! High Energy Limit
Where Are The Coupling Constants Running ???
G RBRB B u = qq annihilation R So how do we now interpret pion exchange?? duuduu duddud uduudu dduddu p p n n Pion Exchange Revisited = qq creation B d R GBGB G (ud) or (ud)
K + K + Quark Flow Diagrams p + p p + n + + ssss suussuus KK+KK+ uduuududuuud uddduuududdduuud pppp npnp udduuudduu udduuudduu +p+p +p+p ++ p + + ++ p + + Quark Flow Diagrams: