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Topical Seminar on Frontier of Particle Physics 2004: QCD and Light Hadrons Lecture 3

This seminar discusses the physics of small x, modified DGLAP equations, JIMWLK equation, phenomenology of saturation, and geometric nuclear effect in particle physics.

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Topical Seminar on Frontier of Particle Physics 2004: QCD and Light Hadrons Lecture 3

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  1. Topical Seminar on Frontier of Particle Physics 2004: QCD and Light Hadrons Lecture 3 Wei Zhu East China Normal University

  2. Outline of Lecture Three Small x Physics • Introduction • Modified DGLAP Equations • JIMWLK Equation • Phenomenology of Saturation • A Geometric Nuclear Effect

  3. DGLAP equations Modified DGLAP equations JIMWLK equations Beyond Impulse app. Impulse app. Saturation 1. Introduction Color Glass Condensation

  4. From saturation scale QS2, QCD evolution is stopped Saturation Scale DGLAP MD-DGLAP JIMWLK TRUE ? Qs2 ?

  5. 2. Modified DGLAP Equations

  6. Left: The solid (dotted) curves are the results of the MD-DGLAP equation with (without) antishadowing corrections. The dashed curves are the results of the DGLAP equation with the GRV98LO. Notice that the solid and dashed curves have opposite concavities. Right: As Left but for the sea quark distribution in the proton.

  7. Left:The Q2 dependence of the gluon distribution in proton at fixed values of x. The solid (dotted) curves correspond to with (without) antishadowing corrections. The dashed cuves are the results of the DGLAP equation with the GRV98LO. Right As Left but for the sea quark distribution function in proton.

  8. 3. JIMWLK Equation

  9. x z y Bare gluon Wilson line Multi pole Nuclear classical QCD field (W-W field)

  10. Unfortunately, nobody knows the correct solution of the JIMWLK equation except itszero-ordersolution.

  11. 4. Phenomenology of Saturation The distribution of partons in the transverse plane.

  12. R is the radius of the hadron and x the momentum fraction of the considered gluons. Saturation sets in when , or equivalently for: The recombination cross-section for gluon with transverse momentum Q is roughly given by the number of such gluons per unit of transverse area is given by

  13. is the probability that the dipole does not have an inelastic interaction as it passes through the nucleus

  14. quark saturation momentum gluon saturation momentum

  15. a maximum occupation number for quarks Some Predictions The CGC approach for nucleus - nucleus collision with the saturation of parton density.

  16. Geometrical scaling

  17. 5. A Geometric Nuclear Effect Twist-4, αs-order, tree approximation, FT

  18. Twist-4, αs-order, tree approximation, FL

  19. a time-space picture of FT

  20. Time-space pictures of FT

  21. Time-space pictures of FL

  22. Qiu-Vitev Resummation

  23. Scale for cold matter power corrections ~

  24. Factorization Saturation Nuclear Effect Evolution equation Structure Function

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