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

2. 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

3. Theoretical framework

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

5. with partonic variables Define PIM:

6. LO: cf Drell-Yan

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

8. 1PI: partonic variables: mass 2

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

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

11. soft & coll. gluons large-angle soft

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

13.  same structure for 1PI:

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

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

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

19. p  h X:

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

23.  recall, 1PI: ?

24. 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

25. Moch, Kumar (arXiv:1309.5311) K LHC

26. 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

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

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

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

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