Recent results on unintegrated parton distributions F. Hautmann I . - PowerPoint PPT Presentation

8th International Symposium on Radiative Corrections RADCOR2007 Galileo Galilei Institute, October 2007 Recent results on unintegrated parton distributions F. Hautmann I . Introduction II . Small-x final states from u-pdf’s in Monte-Carlo generators III . Progress towards precise operator definitions for u-pdf’s

I . Introduction Complex final states with multiple hard scales ↓ QCD methods based on parton distributions unintegrated in both longitudinal and transverse momentum (u-pdf’s) Classic examples: • Sudakov processes • small-x physics • simulation of fully exclusive final states See J.R. Andersen et al., hep-ph/0604189, Summary of 3rd Lund Workshop; S. Alekhin et al., hep-ph/0601012, “Hera and the LHC” Workshop Proceedings

♦ For small x, u-pdf’s can be introduced in a gauge-invariant manner via high-energy factorization ⇓ • resummation of ln x corrections to QCD evolution equations ֒ → including matching with collinear dynamics (ordinary pdf’s) [see talks by G. Altarelli and M. Ciafaloni] • Monte Carlo simulation of x → 0 parton showers ֒ → collinear matching yet to be developed ♦ To characterize u-pdf’s gauge-invariantly over the whole phase space is more difficult — full framework still missing, much ongoing work [see talk by T. Rogers]

Outline ⊲ Application of u-pdf’s to shower Monte-Carlo generators: • hadronic final states at x ≪ 1 • multi-jet production • angular correlations ⊲ Progress on unintegrated distributions beyond x ≪ 1 : • nonlocal operator matrix elements • endpoint divergences x → 1 • cut-off vs. subtractive regularization method

U-pdf’s and shower Monte-Carlo generators II.1 y 0 y ♦ All MC’s based on u-pdf’s rely on k ⊥ -factorization to n−1 e e’ y, Q² y n a) generate hard-scattering event } } Ξ Ξ x n x n k tn k tn b) couple it to initial-state gluon cascade q q p tn p tn n n x n−1 x n−1 k t n−1 q p tn−1 k tn−1 q p tn−1 n−1 n−1 p t q p t q x 0 1 x 0 1 n n k t 0 k t 0 p (a) (b) ♦ but differ by model for initial-state evolution ( BFKL , CCFM , LDC evolution equations) • with suitable constraints on angular ordering of gluon emission ⇒ correct leading ln x behavior • subleading contributions also important for final states

Implementations: H¨ oche, Krauss and Teubner, arXiv:0705.4577 ( BFKL ) Golec, Jadach, Placzek, Stephens, Skrzypek, hep-ph/0703317 ( CCFM ) L¨ onnblad & Sj¨ odahl, 2005; Gustafson, L¨ onnblad & Miu, 2002 ( LDC ) LDCMC Jung, 2004, 2002; Jung and Salam, 2001 ( CCFM ) CASCADE Marchesini & Webber, 1992 ( CCFM ) SMALLX Advantages over standard Monte-Carlo: • better treatment of high-energy logarithmic effects • likely more suitable for simulating underlying event’s k ⊥ Current limitations: • collinear radiation associated to x ∼ 1 not automatically included • procedure to correct for this not yet systematic ֒ → e.g.: LO-DGLAP in H¨ oche et al, 2007 • quark contributions in initial state yet to be implemented ֒ → k ⊥ kernel for sea-quark evolution [Catani & H, 1994] • limited knowledge of u-pdf’s [Jung et al., arXiv:0706.3793; J. R. Andersen et al., 2006]

Inclusive examples II.2 • inclusive data used to test model and determine unintegrated gluon [ ֒ → DIS, jets, heavy flavors] d 3 σ /dQ 2 dx d E T max (pb/GeV 2 ) 10 9 5 < Q 2 < 10 GeV 2 10 < Q 2 < 30 GeV 2 10 8 10 7 10 -4 ‹ x ‹ 1.7 10 -4 1.7 10 -4 ‹ x ‹ 3 10 -4 10 6 nb/GeV 10 8 10 5 K K K K K K K K K K K K K K K K K K K K K K K K K , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 , D = 0.7 CDF Data T T T T T T T T T T T T T T T T T T T T T T T T T 6 1.7 10 -4 ‹ x ‹ 3 10 -4 3 10 -4 ‹ x ‹ 5 10 -4 10 10 4 BFKL sum 10 3 2-jet 10 4 3-jet 10 2 3 10 -4 ‹ x ‹ 5 10 -4 5 10 -4 ‹ x ‹ 10 -3 jet 4-jet 10 dy 10 2 5 10 -4 ‹ x ‹ 10 -3 10 -3 ‹ x ‹ 3.3 10 -3 1 jet -1 / dk 1 10 -2 10 30 < Q 2 < 100 GeV 2 σ 10 -2 10 20 30 40 50 60 70 jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet |y |y |y |y |y |y |y |y |y |y |y |y |y |y |y |y |y |y |y |y |y |y |y |y |y |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 |<0.1 (x10 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 6 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) d 10 3 10 -4 H1 EPJC 33 (2004) 477 10 2 jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y 0.1<|y |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 |<0.7 (x10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) -6 10 Bg=0.025, µ =1.5 Bg=0.25, µ =1.5 10 5 10 -4 ‹ x ‹ 10 -3 -8 10 jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y 0.7<|y |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 |<1.1 Bg=0.25, µ =0 -10 10 jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet 1 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 -3 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y 1.1<|y |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 |<1.6 (x10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) -12 10 -1 10 -3 ‹ x ‹ 10 -2 parton level parton level parton level parton level parton level parton level parton level parton level parton level parton level parton level parton level parton level parton level parton level parton level parton level parton level parton level parton level parton level parton level parton level parton level parton level 10 SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA SHERPA jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet jet -6 -6 -6 -6 -6 -6 -6 -6 -6 -6 -6 -6 -6 -6 -6 -6 -6 -6 -6 -6 -6 -6 -6 -6 -6 -14 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y 1.6<|y |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 |<2.1 (x10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) 10 -2 10 3 2 10 10 10 20 30 40 50 60 70 jet k GeV E T max (GeV) (left) CASCADE (Jung, 2007) vs. H1 [hep-ex/0310019] jet E T distribution; (right) H¨ oche, Krauss and Teubner, 2007 vs. CDF [hep-ex/0701051] jet spectra ⊲ sensible results for evolved gluon ⊲ poorly constrained at low scales and low x