1 / 18

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

emiko
Download Presentation

Lecture 6: QCD at long distance

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related