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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.
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High energy scattering 1/24/20162 kTkT kTkT kTkT x 0 >>…>>x n BFKL: Un-integrated gluon distribution
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Non-linear term at high density Balitsky-Fadin-Lipatov-Kuraev, 1977-78 Balitsky-Kovchegov: Non-linear term, 98 1/24/20163
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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
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Additional dynamics comes in BFKL vs Sudakov resummations (LL) 1/24/20165 kTkT kTkT kTkT x 0 >>…>>x n Soft gluon
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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
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Explicit one-loop calculations 1/24/20167 Collinear divergence DGLAP evolution Small-x divergence BK-type evolution Dominguiz-Mueller-Munier-Xiao, 2011
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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
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Examples Contributes to Collinear gluon from the proton Collinear gluon from nucleus Soft gluon to Sudakov double logs 1/24/20169
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Only contributes to small-x collinear gluon 1/24/201610
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Final result Double logs at one-loop order Include both BFKL (BK) and Sudakov 1/24/201611
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Photon-Jet correlation Leading order 1/24/201612 Dipole gluon distribution
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One gluon radiation (real) 1/24/201613
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BK-evolution 1/24/201614 These two do not Contribute to soft Gluon radiation
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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
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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
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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
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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
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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
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Phenomenological applications 1/24/201620 Di-hadron azimuthal Correlations at the Electron-ion Collider Zheng, Aschenauer,Lee,Xiao, Phys.Rev. D89 (2014) 074037
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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
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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
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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
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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
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