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Threshold resummation in hadronic scattering Werner Vogelsang Univ. Tübingen Bloomington, 12/13/2013

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Daniele’s talk: Resummation in SIDIS & e + e - annihilation Color singlet hard LO scattering Natural connection to Drell-Yan and Now: processes with underlying QCD hard scattering: Insights into fragm. fcts. / nucleon structure Test / improve our understanding of QCD at high energies

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Theoretical framework

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pair mass 2 One-particle inclusive (1PI) kinematics: Pair-invariant mass (PIM) kinematics: “like” Drell-Yan

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with partonic variables Define PIM:

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LO: cf Drell-Yan

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Beyond LO: true to all orders! at k th order: threshold logs e.g. NLO:

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1PI: partonic variables: mass 2

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LO: Beyond LO: at k th order: not necessarily soft !

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logs due to soft / collinear emission resummation achieved in Mellin-moment space: PIM: Likewise, 1PI: moments

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soft & coll. gluons large-angle soft

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like Drell-Yan Kidonakis,Oderda,Sterman Bonciani,Catani,Mangano,Nason Almeida,Sterman,WV matrix problem in color space:

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same structure for 1PI:

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PIM: 1PI: Compare leading logarithms (MS):

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Resummation for pp h 1 h 2 X L. Almeida, G.Sterman, WV

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Resummation for p h X (at COMPASS) D.de Florian, M.Pfeuffer, A.Schäfer, WV

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p h X:

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Resummation for pp jet X D.de Florian, P.Hinderer, A.Mukherjee, F.Ringer, WV

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recall, 1PI: ?

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Threshold logarithms depend crucially on treatment of jet: Kidonakis, Sterman (1) keep jet massless at threshold: no dependence on R Kidonakis, Owens; Moch, Kumar (2) jet allowed to be massive at threshold: LO: jet massless

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Moch, Kumar (arXiv:1309.5311) K LHC

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Full (analytical) NLO calculation for “narrow jets” Jäger, Stratmann, WV; Mukherjee, WV …allows to pin down behavior near threshold: confirms that (2) is right de Florian, WV; de Florian, Hinderer, Mukherjee, Ringer, WV arXiv:1310.7192

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NNLO corrections in all-gluon channel: Currie, Gehrmann-De Ridder, Glover, Pires, arXiv:1310.3993

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Conclusions: significant resummation effects in hadronic scattering: PIM / 1PI kinematics predictions from resummation formalism as benchmark for full NNLO calculations

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Gehrmann-De Ridder, Gehrmann, Glover, Pires, arXiv:1301.7310

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Eventually, inverse Mellin / Fourier transform: “Matching” to NLO: Catani,Mangano,Nason,Trentadue “Minimal prescription ”

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