1. Renormalization Group Evolution of Multi-gluon Correlators in High Energy QCD Jamal Jalilian-Marian Baruch College QCD Evolution Workshop 2012, JLAB

2. Gluon saturation “attractive” bremsstrahlung vs. “repulsive” recombination Gribov-Levin-Ryskin

3. Many-body dynamics of universal gluonic matter How does this happen ? How do correlation functions of these evolve ? Is there a universal fixed point for the RG evolution of d.o.f How does the coupling run ? How does saturation transition to chiral symmetry breaking and confinement

4. MV effective Action + RGE weight functional: probability distribution of color source at longitudinal scale invariance under change of RGE for Large x: color sourcesmall x: gluon field

5. The Classical Field saddle point of effective action-> Yang-Mills equations solutions are non-Abelian Weizsäcker-Williams fields pure (2d) gauge z color fields

6. JIMWLK evolution equation U is a Wilson line in adjoint representation virtualreal

7. QCD at low x: CGC (a high gluon density environment) CGC observables: with gluon distribution: with “multiple scatterings” evolution with ln (1/x) two main effects: pQCD with collinear factorization: single scattering evolution with ln Q 2

8. Observables DIS: structure functions particle production dilute-dense (pA, forward pp ) collisions: multiplicities p t spectra di-hadron angular correlations dense-dense (AA, pp) collisions: multiplicities, spectra long range rapidity correlations Spin

9. disappearance of back to back jets CGC fit from Albacete + Marquet, PRL (2010) Also by Tuchin, NPA846 (2010) and A. Stasto, B-W. Xiao, F. Yuan, arXiv:1109.1817 multiple scatterings de-correlate the hadrons

10. Di-jet production: pA recall DIS, single inclusive production in pA probe dipoles di-jet production in pA (and DIS) probe quadrupoles coordinate space: C. Marquet, NPA796 (2007) 41 including gluons in the projectile F. Dominguez,C. Marquet, B-W. Xiao, F. Yuan, PRD83 (2011) 105005 J. Jalilian-Marian, Y. Kovchegov, PRD70 (2004) 114017 momentum space:

11. Di-jet production: pA

12. di-jet production in pA F2 in DIS, single hadron in pA dipole quadrupole energy (rapidity) dependence from JIMWLK evolution of O's evolution of a dipole is well known: BK eq. how does a quadrupole evolve? calculations: classical how about quantum corrections (energy dependence) ?

13. Evolution of the 2-point function (dipole) BK equation (NLO)

14. Evolution of quadrupole from JIMWLK radiation kernels as in dipole

15. Evolution of quadrupole from JIMWLK with J. Jalilian-Marian, Y. Kovchegov: PRD70 (2004) 114017 Dominguez, Mueller, Munier, Xiao: PLB705 (2011) 106 J. Jalilian-Marian: Phys.Rev. D85 (2012) 014037

16. quadrupole evolution in the linear regime define re-write the evolution eq. for T Q rather than Q expand in powers of gauge fields (or color charges) ignore contribution of non-linear terms: T T and T Q T with quadrupole evolution reduces to a sum of BFKL evolution eqs Dominguez, Mueller, Munier, Xiao: PLB705 (2011) 106 J. Jalilian-Marian: Phys.Rev. D85 (2012) 014037 D. Triantafyllopoulos

17. di-hadron correlations in the high p t limit Dominguez, Marquet, Xiao, Yuan (2011) Dominguez, Xiao, Yuan (2011) factorization of target distribution functions and hard scattering matrix element partons are back to back

18. quadrupole evolution in the linear regime momentum space define assumesubject to an overall delta function quadrupole evolution eq. reduces to Bartels-Jaroszewicz- Kwiecinski-Praszalowicz (BJKP) eq. for evolution of 4-Reggeized gluons in a singlet state contribution only from linear term in expansion of Wilson lines (except for the z-dependent ones)

19. quadrupole evolution in the linear regime BJKP equation the color structure is identical on both sides of this eq. (independent of color averaging) 4-gluon exchange this will de-correlate the produced partons at high p t > Q s J. Jalilian-Marian, PRD85 (2012) 014037

20. color structure overall state is a singlet, how about pairwise? for N c = 3

21. the linear regime 3-gluon (odderon) exchange BJKP equation describes evolution of n-Reggeized gluons in a singlet state JIMWLK (linear) and BJKP eqs. agree for n=2,3,4 non-linear interactions: 1) MV action with JIMWLK evolution 2) Triple (and more?) pomeron vertices Chirilli, Szymanowski, Wallon (2010) BJKP equation Hatta, Iancu, Itakura, McLerran Dipole odderon: Kovchegov, Szymanowski, Wallon

22. QCD at high energy Two distinct approaches: 1) CGC M cLerran-Venugopalan effective action JIMWLK-BK evolution 2) Reggeized-gluon exchange BJKP equation triple,... pomeron vertex Conjecture: CGC contains BJKP + multi-pomeron vertices

23. line config.: square config.: Gaussian Gaussian + large N c “naive” Gaussian: can be calculated in a Gaussian model DMXY quadrupole evolution: limits

24. Gaussian Gaussian + large N c quadrupole evolution: limits

25. Dumitru-Jalilian-Marian-Lappi-Schenke-Venugopalan:PLB706 (2011) 219 quadrupole evolution on lattice a “random” (Gaussian) distribution of color charges (at initial rapidity y 0 ) construct the Wilson line evolve the Wilson line to a higher rapidity y compute ensemble average of any number of Wilson lines at y

26. comparing with “naive” Gaussian Quadrupole evolution

27. comparing with Gaussian + large N c Quadrupole evolution

28. comparing with Gaussian Quadrupole evolution

29. Geometric scaling also present in quadrupolesGrowth of the saturation scale Quadrupole evolution

30. The role of initial conditions McLerran-Venugopalan (93) how about higher order terms in  ? these higher order terms make the single inclusive spectra steeper and give leading N c correlations (ridge) Dumitru-Jalilian-Marian-Petreska, PRD84 (2011) 014018 Dumitru-Petreska,, arXiv:1112.4760 [hep-ph] with

31. The role of initial conditions Dumitru-Petreska, arXiv:1112.4760 [hep-ph] How important is the quartic action for di-hadron angular correlations?

32. A unique window to dynamics of high energy QCD Two-hadron angular correlations We have just started to scratch the surface: there is much more to be understood