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EXAM 2 Results

EXAM 2 Results. Mean,  = 65.6 Std Dev,  = 14.4. 30 40 50 60 70 80 90 100. Breakdown : Problem 1 20 14-20 19.2 Problem 2 20 14-20 19.4 Problem 3a 20 2-20 7.5

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EXAM 2 Results

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  1. EXAM 2 Results Mean,  = 65.6 Std Dev,  = 14.4 30 40 50 60 70 80 90 100 Breakdown: Problem 1 20 14-20 19.2 Problem 2 20 14-20 19.4 Problem 3a 20 2-20 7.5 Problem 3b 12 0-12 8.2 Problem 4 16 0-16 7.0 Problem 5 12 0-12 3.2 Compilation of total scores past 4 PHYS926 sections  200 300 400 500 600

  2. The remaining octet states involve G3 and G8 which do not change color. We need 2 states ORHTOGONAL to the sterile singlet state. The possibilities are: and obviously only 2 are actually independent. We need to find two that are also orthogonal to each other, the convention is to use (see again how 3 and 8 were defined)

  3. QUANTUMCHROMO-DYNAMICSQ.C.D b b bg bg g g bg rg b b bg rb r r u u d u d p+ p

  4. But since the gluons are CHARGE CARRIERS themselves they also interact with ONE ANOTHER! interactions include: with coupling ~g 3-gluon vertex 4-gluon vertex with coupling ~g2

  5. This means all STRONG processes are much more complicated with many more Feynman diagrams contributing: Besides the “tree-level” and familiar “2nd-order” processes: we also have the likes of: and

  6. QED interactions respect the behavior of the Coulomb potential • infinite reach involves smallest • energy-momentum transfers • close single boson exchanges involve potentially • large energy-momentum transfers But something MUCH different happens with abelian theories

  7. Most distant reaching individual branches still involve the smallest momentum carriers The field lines are better represented (qualitatively) by color flux tubes: Since the exchanged gluons are attracted to one another the field is even more “confined” than an electric dipole!

  8. Further complications 1 137 In QED each vertex introduces a factor of  = to all calculations involving the process. That factor is so small, we need only deal with a limited number of vertices (“higher order” diagrams can often be neglected. Contributing sums CONVERGE. Calculations in the theory are PERTURBATIVE. But judging by the force between 2 protons: s > 137 ~ 1 With so many complicated, higher order diagrams HOW CAN ANYTHING BE CALCULATED?

  9. CHARGE IN A DI-ELECTRIC MEDIUM A charge imbedded in a di-electric can polarize the surrounding molecules into dipoles A halo of opposite charge partially cancels Q’s field. Q  qeff = Q dielectric constant but once within intermolecular distances you will observe the FULL charge Q Q/ r  ~molecular distances

  10. Vacuum Polarization In QED the vacuum can sprout virtual e+e-wink in and out of existencebut are polarized for their brief existence, partially screening the TRUE CHARGE by contributions from: e- e+ each “bubble” is polarized The TRUE or BARE charge on an electron is NOT what’s measured by e&M experiments and tabulated on the inside cover of nearly every physics text. e- e+ e- e+ e- e+ e- e+ e- e+ THAT would be the fully screened “effective charge”

  11. The corresponding “intermolecular” spacing that’s appropriate here would be the COMPTON WAVELENGTH of the electron (related to the spread of the electron’s own wavefunction) To get within THAT distance of another electron requires MeV electron beams to observe! Scattering experiments with 0.5 MeV electron beams (v = c/10) show the nominal electron charge requires a 6×10-6 = 0.0006% correction

  12. Vacuum Polarization In QED the vacuum can sprout virtual e+e-wink in and out of existencebut are polarized for their brief existence, partially screening the TRUE CHARGE by contributions from: The matrix element for the single loop process: m  X(p2)is a function of p2 in text: X(p2)=(/3) ln( | p2 |/me2 ) e- e+ e- e+ e- e+ effective= (1 + m + m2 + m3 + ...) e2/ħc e- e+ e- e+ e- e+ Notice:as mgoes upaeffectivegoes up and mgoes up as p2 goes up.

  13. Thus higher momentum virtual particles have a higher probability of creating these dipole pairs …and higher momentum virtual particles are “felt” by (exchanged between) only the closest of interacting charges. is the charge as seen “far” from the source, e The true charge is HIGHER.

  14. The Lamb Shift Relativistic corrections insufficient to explain hyperfine structure 2p½(n=2, ℓ= 1, j = ½) 2s½(n=2, ℓ= 0, j = ½) are expected to be perfectly degenerate 1947Lamb & Retherfordfound 2s½energy state > 2p½state • Bethe’s explanation: • Coulomb’s law inadequate • The field is quantized (into photons!) • and spontaneously produces e+e- pairs near • the nucleus…partially screening its charge • Corrects the magnetic dipole moment • of both electron and proton!

  15. What happens in Q.C.D. ?? q3 q4 ur Like e+e- pair production this always screens the quarks electric charge nflav q1 q2 ur ururis one example. This bubble can happen nflavor× ncolordifferent ways. 1 3 of the time shielding color charge driving s up at short distances, down at large distances. Obviously only the colorless G3, G8 exchanges can mediate this particular interaction This makes 2 × nflavor diagrams that result in sheilding color charge.

  16. But ALSO (completely UNlike QED) QCD includes diagrams like: r r b b ncolor ways g g Each of these anti-shield (drive s down at short distances, up at large distances) r b r r ncolor ways g g r each ncolor ways r b b b g g

  17. r b b g ncolor ways for this bubble to be formed but br bg doesn’t shieldat all in fact brings the color charges right up closer the to target enhances the sources color charge

  18. In short order we just found 2nflavor diagrams that SHIELD color 4ncolor diagrams that ANTI-SHIELD In fact there are even more diagrams contributing to ANTI-SHIELDING. = 12 SHIELD: 2nflavor ANTI-SHIELD:11ncolor = 33 QCD coupling DECREASES at short distances!!

  19. 2 important consequences: • at high energy collisions between hadrons • s 0 • for impacts that probe small distances • quarks are essentially free • at large separations the coupling between • color charges grow HUGE “asymptotic freedom” “confinement” All final states (even quark composites) carry no net color charge! Naturally occurring stable “particles” cannot carry COLOR Quarks are confined in color singlet packages of 2 (mesons) color/anticolor and 3 (baryons) all 3colors

  20. Variation of the QCD coupling parameter s with q2 s q2, GeV2/c2

  21. If try to separate quarks u u d d gr u u d d Gm3 d gr u u d d Gm8

  22. If try to separate quarks u u d d u gr u d rr d p+ u d d u d

  23. If try to separate quarks u u d p+ u d d u d p+ u d d u d

  24. If try to separate quarks u u d

  25. Hadrons _ g q _ q q q LEP (CERN) Geneva Hadrons

  26. e+e–  +–e+e– qqe+e– qqg OPAL Experiment

  27. _ e+e- q q g 3 jets JADE detector at PETRA e+e- collider (DESY, Hamburg, Germany)

  28. 2-jet event

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