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Lecture 6: QCD at long distance

Lecture 6: QCD at long distance. Last week:. We discussed ep scattering ( DIS) and the evidence of quarks QED interaction between the electron and the quark at short distance Point-like constituents deduced from the x-section measurements

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Lecture 6: QCD at long distance

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  1. Lecture 6: QCD at long distance

  2. Last week: • We discussed ep scattering ( DIS) and the evidence of quarks • QED interaction between the electron and the quark at short distance • Point-like constituents deduced from the x-section measurements • Sum rules: Integrals over the structure functions that basically express the conservation laws of the constituent quark quantum numbers • Breaking of the Bjorken sum rule - > evidence for partons other than the quarks present in the protons ( NOTE: direct evidence for gluons comes from 3-jet events in e+e- collisions) • Experimental determination of parton distribution functions (PDFs) for quarks, anti-quarks and gluons

  3. Last lecture: QCD at short distance • Proton-anti-proton scattering at high energy • Differential x-section for • Just like in Rutherford scattering! • We are able to calculate the scattering cross-section between 2 partons usinng perturbation theory due to the running of the coupling constant ( small at short distance)

  4. DIS and pQCD proton- anti-proton scattering -> 2 jets (QCD) Electron-proton Scattering (QED) PDFs (fa/A,,fb/B)

  5. At long distance • The theoretical description is much harder (as is large) • We have phenomenological models that describe certain aspects of the data • Some people say that “this is not even QCD”… • But 99% of the particles produced in pp collisions come from soft interactions => we need to deal with those • I’ll describe the classical string model of hadron production ( the pre-cursor of modern string theories) and will mention Regge theory and the dual parton model

  6. We start with the following observations: • At this point we have a picture of hadrons composed of elementary fermions that (accurately) specify the quantum number content of the baryons and mesons.  • quarks carry an extra quantum number, color, and the interactions that couple to this quantum number, QCD, are such as to “confine” quarks and anti-quarks to color singlets with volumes of order (1 fm)3 • We looked at some hadrons in their ground state – (handout 2 lectures ago) and how they decay • Not mentioned before: there are also excited states of hadrons ( just like in atoms) and they exhibit a remarkable systematic structure

  7. Excited hadrons and Regge trajectories • Examining these closely: hadrons occur along “trajectories” in J vs mass2 space • Constant slope

  8. Examples of Regge trajectories • Note: these are not the same hadrons as the tables on the previous page

  9. The rotating string • 2 massless quarks on the end of a string of gluons • Energy density per unit length : k • The ends rotate with velocity v=c • Local velocity at radius r, v=cr/R • Mass E=m • Angular mom J

  10. The string tension • Measure a’ from data = 0.93 GeV-2 • Then find k = 0.87 GeV/fm • This also comes from the mass ( ~ 1 GeV) and radius (~ 1 fm) of the hadrons

  11. Duality and strings S and t channel look the same if you stretch a string between the quarks

  12. Regge theory gives a clue on why the dual description works • X-sections for elastic and inelastic interactions are parameterized with a sqrt(s) dependence inspired by this model

  13. String fragmentation and particle production rate: the Lund string model Taken from a talk by Prof.

  14. Hadronization and decays: From a talk on Pythia: a Monte-Carlo generator based on Lund model Wit parameters tuned to data can describe both hard and soft particle production in pp collisions.

  15. Rapidity distributions • Lund model predicts a rapidity plateau • t0is the proper time

  16. Mt scaling predicted from most soft phenomenological models • The data exhibits approximate mT scaling at low mT in contrast to the power-law behavior at high-pT where hard scattering is expected to dominate

  17. Summary • We reviewed phenomenological models of soft hadron-hadron interactions • Classical string theory and linear term in the potential describe many features of the data • Rapidity distributions • mT scaling • Next we will move to AA collisions and see how the collective properties of the system show up in the observed quantities

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