The High Energy Limit of QCD

1. The High Energy Limit of QCD The high energy limit is E -> infinity at fixed momentum transfer Not short distance limit which is E -> infinity at fixed angle Related Questions: How do gluons and quarks arise in hadrons? What are the possible forms of high density matter? Claim: The high energy limit is controlled by a universal, high energy density form of gluonic matter: The Color Glass Condensate In collisions, this matter produces a Glasma with interesting topolgical and dynamical properties Lecture I: The Color Glass Condensate Lecture II: The Glasma 1

2. How do we think about a high energy hadron? Work in fast moving frame: High Energy Limit is Small x Limit 2

3. The Gluon Wall: Wavefunction has: 3 quarks 3 quarks plus 1 gluon 3 quarks plus 2 gluon ……. 3 quarks plus many gluons Importantmatrixelements at high energies have lots of gluons in them 3

4. In RHIC Collisions Au-Au at 100GeV/Nucleon in each beam About 1000 slow moving (small x) particles are made in central collisions 4

5. Where do all the gluons go? Cross sections for hadrons rise very slowly with energy But the gluon density rises much more rapidly! The high energy limit is the high gluon density limit. Surely the density must saturate for fixed sizes of gluons at high energy. 5

6. What is the Color Glass Condensate? Glue at large x generates glue at small x Glue at small x is classical field Time dilation -> Classical field is glassy High phase space density -> Condensate Phase space density: Attractive potential Repulsive interactions Density as high as it can be Because the density is high is small is big 6

7. There must be a renormalization group The x which separates high x sources from small x fields is arbitrary Phobos multiplicity data High energy QCD “phase” diagram 7

8. Why is the Color Glass Condensate Important? It is a new universal form of matter: Matter: Carries energy; Separation of gluons is small compared to size of system; Number of gluons is large New: Can only be made and probed in high energy collsions Universal: Independent of hadron, renormalization group equations have a universal solution. Universality <=> Fundamental It is a theory of: Origin of glue and sea quarks in hadrons Cross sections Initial conditions for formation of Quark Gluon Plasma in heavy ion collisions 8

9. What does a sheet of Colored Glass look like? On the sheet is small Independent of big small Lienard-Wiechart potentials Random Color Density of gluons per unit area 9

10. The Color Glass Condensate Explains Growth of Gluons at Small x Renormalization group equation predicts: Gluon pile up at fixed size until gluons with strength act like a hard sphere Once one size scale is filled Move to smaller size scale Typical momentum scale grows 10

11. The CGC Explains Slow Growth of Total Cross Section Transverse distribution of gluons: Transverse profile set by initial conditions Size is determined when probe sees a fixed number of particles at some transverse distance 11

12. CGC Explains Qualitative Features of Electron-Hadron Scattering Q is resolution momentum of photon, x is that of struck quark • Function only of a particular combination of Q and x • Scaling relation Works for Can successfully describe quark and gluon distributions at small x and wide range of Q 12

13. CGC Gives Initial Conditions for QGP in Heavy Ion Collisions Two sheets of colored glass collide Glass melts into gluons and thermalize QGP is made which expands into a mixed phase of QGPand hadrons Mystery: The QGP is very strongly interacting: Arnold and Moore suggest heating may be due to instabilities in melting CGC 13

14. CGC predicted particle production at RHIC Proportionality constant can be computed. 14

15. CGC provides a theory of shadowing (modification of quark and gluon distributions in nuclei) Two effects: Multiple scattering: more particles at high pT CGC modification of evolution equations => less particles 15

16. Data from dA collisions at RHIC Consistent with CGC Look for fragments of deuteron since they measure them smallest x properties of the nucleus Back to back jet correlations seen in STAR? Detailed studies of x dependence? 16

17. Future studies of CGC at RHIC, LHC, and eRHIC At RHIC: Systematic pA studies; Many exciting possibilities Study and discover the QGP; Discover the CGC LHC: Can study at very small x with very high resolution Study the CGC eRHIC: Precision experiments and tests Careful and systematic study of CGC 17

18. Glasma Definition: The matter which is produced by the Color Glass Condensate immediately after the collision It is not a glass, evolving on a natural time scale It has components which are highly coherent, Components which are particle like Components of strength in between Initially it has large longitudinal color electric and color magnetic fields, and maximal topological charge density 18

19. Choose A = 0 in backward light cone. In left and right halves, pure gauge. Discontinuity across light cone to match color charge sources on light cone Field is not pure gauge in forward lightcone Physical motivation: Renormalization group description. In center of mass frame, degrees of freedom with are coherent fields. Larger y are sources 19

20. Before the collision, two sheets of mutually transverse color electric and color magnetic fields. Boosted Coulomb fields Random in color Thickness of sheets is 20

21. Initial fields: In radial gauge, the fields in the forward light cone are: Assume boost invariant solution 21

22. Boundary conditions are determined by solving equations across the light cone: Infinitesmally after the collision there are No transverse fields Longitudinal magnetic and electric fields 22

23. These fields have a local topological charge density Chern-Simons charge The Chern-Simons charge density is maximal! and has a transverse correlation length 23

24. How do the sources of color magnetic and color electric field arise? In forward light cone, the vector potential from one nucleus can multiply the CGC field from the other. Equal and opposite densities of charge 24

25. However: Glasma fields are initial conditions, not a solution to time independent equation of motion: Unlike the constant field where there is no magnetic field 25

26. The Glasma has three components: Coherent classical fields: Hard particles: Degrees of freedom which can be described as either hard particles or coherent fields The Glasma has mostly evaporated by a time During this time, scattering among the hard modes (parton cascade) is not important 26

27. Interactions in the coherent fields takes place on a scale of order 1/Qs Because of coherence, interactions of hard particles with the classical fields, g x 1/g ~ 1 Also take place on a time scale 1/Qs Very rapid strongly interacting system But boost invariance is a problem, as this does not allow longitudinal momentum to become thermalized Important for two reasons: Almost certainly instabilities of the hard-soft coupled system under boost non-invariant perturbations Can these instabilities generate either rapid thermalization or isotropization of momentum? 27

28. Consequence of nonzero Chern-Simons Charge: Vorticity Generation Positively charged particle accelerates along E, rotates in clockwise direction Negatively charged particle accelerates along -E, Rotates in anticlockwise direction Net vorticity generation Physical origin of t Hooft anomaly 28

29. Exciting times for theory: Beginning of a complete description of high energy limit of QCD Must understand the collective excitations of the CGC: pomerons, reggeons, odderons… Need to understand interactions of these collective excitations: ploops or Pomeron loops 29