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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

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kT

kT

kT

x 0>

>…

>>

x n

BFKL: Un-integrated gluon distribution

Non-linear term at high density Balitsky-Fadin-Lipatov-Kuraev, 1977-

78

Balitsky-Kovchegov: Non-linear term, 98

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Hard processes at small-x

Manifest dependence on un-integrated gluon distributionsDominguiz-Marquet-Xiao-Yuan, 2010

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kT

kT

kT

x 0>

>…

>>

x n

Additional dynamics comes in

BFKL vs Sudakov resummations (LL)

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kT

kT

kT

x 0>

>…

>>

x n

Soft gluon

Sudakov resummation at small-x

Take massive scalar particle production p+A->H+X as an example to demonstrate the double logarithms, and resummation

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p H,MH

WW-gluon distribution

A

Explicit one-loop calculations

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Collinear divergence DGLAP evolution Small-x divergence BK-type evolution

Dominguiz-Mueller-Munier-Xiao, 2011

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,

α0Rapidity divergence

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Examples

Contributes toCollinear gluon from the protonCollinear gluon from nucleusSoft gluon to Sudakov double logs

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Only contributes to small-x collinear gluon

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Final result Double logs at one-loop order

Include both BFKL (BK) and Sudakov

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Photon-Jet correlation

Leading order

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Dipole gluon distribution

One gluon radiation (real)

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BK-evolution

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These two do notContribute to softGluon radiation

Soft gluon radiation

A2 from (a,b) contribute to CF/2 (jet)

A2 from (c,d) contribute to CF

Interference contribute to 1/2Nc

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ggqq

|A1|2CA, |A2|2CF/2, |A3|2CF/2

2A1*(A2+A3)-Nc/2

2A2*A3, 1/Nc suppressed

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qgqg

|A1|2CF, |A2|2CF/2, |A3|2CA/2

2A3*(A1+A2)-Nc/2

2A1*A2, large Nc suppressed

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gggg

|A1|2CA, |A2|2CA/2, |A3|2CA/2

2A1*(A2+A3)+2A2*A3-Nc

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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

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Sudakov

Phenomenological applications

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Di-hadron azimuthalCorrelations at theElectron-ion Collider

Zheng, Aschenauer,Lee,Xiao, Phys.Rev. D89 (2014) 074037

Beyond leading logs

Additional nuclear effects, such as energy loss will come inLiou-Mueller, 1402.1647

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Interference betweenThem, leads to energyLoss calculated in Liou-Mueller

Next-to-leading-logarithms (NLL) Matrix form in the Sudakov resummation

Sun,Yuan,Yuan,1405.1105

Kidonakis-Sterman, NPB 1997 Banfi-Dasgupta-Delenda,

PLB2008

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D0@Tevatron

Dijet with large rapidity gap

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Ducloue,Szymanowski,Wallon1309.3229, only take into account BFKL

Sudakov resummation will dominate Small angle distribution

CMS@LHC

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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