1. 1/24/20161 Resummation in High Energy Scattering -- BFKL vs Sudakov Feng Yuan Lawrence Berkeley National Laboratory Refs: Mueller, Xiao, Yuan, PRL110, 082301 (2013); Phys.Rev. D88 (2013) 114010.

2. High energy scattering 1/24/20162 kTkT kTkT kTkT x 0 >>…>>x n BFKL: Un-integrated gluon distribution

3. Non-linear term at high density Balitsky-Fadin-Lipatov-Kuraev, 1977-78 Balitsky-Kovchegov: Non-linear term, 98 1/24/20163

4. Hard processes at small-x Manifest dependence on un-integrated gluon distributions  Dominguiz-Marquet-Xiao-Yuan, 2010 1/24/20164 kTkT kTkT kTkT x 0 >>…>>x n

5. Additional dynamics comes in BFKL vs Sudakov resummations (LL) 1/24/20165 kTkT kTkT kTkT x 0 >>…>>x n Soft gluon

6. Sudakov resummation at small-x Take massive scalar particle production p+A->H+X as an example to demonstrate the double logarithms, and resummation 1/24/20166 pH,M H WW-gluon distribution A

7. Explicit one-loop calculations 1/24/20167 Collinear divergence  DGLAP evolution Small-x divergence  BK-type evolution Dominguiz-Mueller-Munier-Xiao, 2011

8. Soft vs Collinear gluons Radiated gluon momentum Soft gluon, α~β<<1 Collinear gluon, α~1, β<<1 Small-x collinear gluon, 1- β<<1, α  0  Rapidity divergence 1/24/20168

9. Examples Contributes to  Collinear gluon from the proton  Collinear gluon from nucleus  Soft gluon to Sudakov double logs 1/24/20169

10. Only contributes to small-x collinear gluon 1/24/201610

11. Final result Double logs at one-loop order Include both BFKL (BK) and Sudakov 1/24/201611

12. Photon-Jet correlation Leading order 1/24/201612 Dipole gluon distribution

13. One gluon radiation (real) 1/24/201613

14. BK-evolution 1/24/201614 These two do not Contribute to soft Gluon radiation

15. Soft gluon radiation A 2 from (a,b) contribute to C F /2 (jet) A 2 from (c,d) contribute to C F Interference contribute to 1/2Nc 1/24/201615

16. gg  qq |A 1 | 2  C A, |A 2 | 2  C F /2, |A 3 | 2  C F /2 2A 1 *(A 2 +A 3 )  -Nc/2 2A 2 *A 3, 1/Nc suppressed 1/24/201616

17. qg  qg |A 1 | 2  C F, |A 2 | 2  C F /2, |A 3 | 2  C A /2 2A 3 *(A 1 +A 2 )  -Nc/2 2A 1 *A 2, large Nc suppressed 1/24/201617

18. gg  gg |A 1 | 2  C A, |A 2 | 2  C A /2, |A 3 | 2  C A /2 2A 1 *(A 2 +A 3 )+2A 2 *A 3  -Nc 1/24/201618

19. Sudakov leading double logs Each incoming parton contributes to a half of the associated color factor  Initial gluon radiation, aka, TMDs 1/24/201619 Sudakov

20. Phenomenological applications 1/24/201620 Di-hadron azimuthal Correlations at the Electron-ion Collider Zheng, Aschenauer,Lee,Xiao, Phys.Rev. D89 (2014) 074037

21. Beyond leading logs Additional nuclear effects, such as energy loss will come in  Liou-Mueller, 1402.1647 1/24/201621 Interference between Them, leads to energy Loss calculated in Liou-Mueller

22. Next-to-leading-logarithms (NLL) Matrix form in the Sudakov resummation  Sun,Yuan,Yuan,1405.1105  Kidonakis-Sterman, NPB 1997  Banfi-Dasgupta-Delenda, PLB2008 1/24/201622 D0@Tevatron

23. Dijet with large rapidity gap 1/24/201623 Ducloue,Szymanowski,Wallon 1309.3229, only take into account BFKL Sudakov resummation will dominate Small angle distribution CMS@LHC

24. Conclusion Sudakov double logs can be re-summed in the small-x saturation formalism Soft gluon and collinear gluon radiation is well separated in phase space Shall provide arguments to apply the effective kt-factorization to describe dijet correlation in pA collisions 1/24/201624