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Resummation in High Energy Scattering -- BFKL vs Sudakov

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. High energy scattering. k T. k T. x 0 >>…>>x n. k T. Un-integrated gluon distribution. BFKL:.

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Resummation in High Energy Scattering -- BFKL vs Sudakov

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  1. 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 kT kT x0>>…>>xn kT Un-integrated gluon distribution BFKL:

  3. Non-linear term at high density • Balitsky-Fadin-Lipatov-Kuraev, 1977-78 • Balitsky-Kovchegov: Non-linear term, 98

  4. Hard processes at small-x • Manifest dependence on un-integrated gluon distributions • Dominguiz-Marquet-Xiao-Yuan, 2010 kT kT x0>>…>>xn kT

  5. Additional dynamics comes in Soft gluon • BFKL vs Sudakov resummations (LL) kT kT x0>>…>>xn kT

  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 p H,MH WW-gluon distribution A

  7. Explicit one-loop calculations • 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

  9. Examples • Contributes to • Collinear gluon from the proton • Collinear gluon from nucleus • Soft gluon to Sudakov double logs

  10. Only contributes to small-x collinear gluon

  11. Final result • Double logs at one-loop order • Include both BFKL (BK) and Sudakov

  12. Photon-Jet correlation • Leading order Dipole gluon distribution

  13. One gluon radiation (real)

  14. BK-evolution These two do not Contribute to soft Gluon radiation

  15. Soft gluon radiation • A2 from (a,b) contribute to CF/2 (jet) • A2 from (c,d) contribute to CF • Interference contribute to 1/2Nc

  16. ggqq • |A1|2CA, |A2|2CF/2, |A3|2CF/2 • 2A1*(A2+A3)-Nc/2 • 2A2*A3, 1/Nc suppressed

  17. qgqg • |A1|2CF, |A2|2CF/2, |A3|2CA/2 • 2A3*(A1+A2)-Nc/2 • 2A1*A2, large Nc suppressed

  18. gggg • |A1|2CA, |A2|2CA/2, |A3|2CA/2 • 2A1*(A2+A3)+2A2*A3-Nc

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

  20. Phenomenological applications 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 Interference between Them, leads to energy Loss calculated in Liou-Mueller

  22. Next-to-leading-logarithms (NLL) • Matrix form in the Sudakovresummation • Sun,Yuan,Yuan,1405.1105 • Kidonakis-Sterman, NPB 1997 • Banfi-Dasgupta-Delenda, PLB2008 D0@Tevatron

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

  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

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