Threshold resummation in hadronic scattering

Werner VogelsangUniv. Tübingen

Bloomington, 12/13/2013

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

Theoretical framework

pair mass2

One-particle inclusive (1PI) kinematics:

Pair-invariant mass (PIM) kinematics:

“like” Drell-Yan

with partonic variables

Define

PIM:

LO:

cf Drell-Yan

Beyond LO:

true to all orders!

at kth order: threshold logs

e.g. NLO:

1PI:

partonic variables:

mass2

LO:

Beyond LO:

at kth order:

not necessarily soft !

logs due to soft / collinear emission resummation

achieved in Mellin-moment space:

PIM:

Likewise, 1PI: moments

soft & coll. gluons

large-angle soft

like Drell-Yan

Kidonakis,Oderda,StermanBonciani,Catani,Mangano,NasonAlmeida,Sterman,WV

matrix problem in color space:

same structure for 1PI:

PIM:

1PI:

Compare leading logarithms (MS):

Resummation for pp h1 h2 X

L. Almeida, G.Sterman, WV

Resummation for p h X

(at COMPASS)

D.de Florian, M.Pfeuffer, A.Schäfer, WV

p h X:

Resummation for pp jet X

D.de Florian, P.Hinderer, A.Mukherjee, F.Ringer, WV

recall, 1PI: ?

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

Moch, Kumar (arXiv:1309.5311)

K

LHC

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

NNLO corrections in all-gluon channel:

Currie, Gehrmann-De Ridder, Glover, Pires, arXiv:1310.3993

Conclusions:

• significant resummation effects in hadronic scattering: PIM / 1PI kinematics

• predictions from resummation formalism as benchmark for full NNLO calculations

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

Eventually, inverse Mellin / Fourier transform:

“Matching” to NLO:

Catani,Mangano,Nason,Trentadue“Minimal prescription”