Multiple Interactions, Saturation, and Final States in pp Collisions and DIS

Transcription

1 Introduction Minimum bias and Underlying event ˇ Multiple Interactions, Saturation, and Final States in pp Collisions and DIS Gösta Gustafson Lund Univ. and Hamburg Univ. Epiphany 2009, Krakow 5-7 Jan. Dedicated to the memory of Jan Kwieciński Work done with Emil Avsar, Christoffer Flensburg, and Leif Lönnblad MI, saturation and final states 1 Gösta Gustafson LU,HU

2 Introduction Minimum bias and Underlying event ˇ Outline Introduction Minimum bias and Underlying event MI, saturation and final states 2 Gösta Gustafson LU,HU

3 Introduction Minimum bias and Underlying event ˇ Introduction Minijet cross section >> σ tot in high energy pp collisions Multiple subcollisions important feature Formulation in transverse coordinate space and eikonal approximation suitable for saturation and mult. coll. Successfully applied to γ p collisions: total and diffr. scatt. Final states: Best model PYTHIA. Extensive tunes to CDF data (R. Field) Problems: How to hadronize? Fit to data needs color reconnections. Correlations and fluctuations difficult in momentum space cascades New approach based on Mueller s dipole cascade MI, saturation and final states 3 Gösta Gustafson LU,HU

4 Introduction Minimum bias and Underlying event ˇ Minimum bias and Underlying event Inclusive parton scattering cross section diverges like dˆσ/dp 2 1/p4 for p Integrated cross section above ptmin for pp at 14 TeV jet cross section total cross section 1000 sigma (mb) Integrated cross section ptmin (GeV) Average pp collisions has several hard subcollisions MI, saturation and final states 4 Gösta Gustafson LU,HU

5 Introduction Minimum bias and Underlying event ˇ Direct observation: Four-jet events with pairwise back-to-back jets: AFS (ISR), UA2(Sp ps collider), CDF(Tevatron) CDF 3-jet + prompt photon analysis Yellow region = double parton scattering (DPS) The rest = PYTHIA showers MI, saturation and final states 5 Gösta Gustafson LU,HU

6 Introduction Minimum bias and Underlying event ˇ Early suggestion: Increasing cross setion driven by minijets. Minimum bias events dominated by (semi)hard parton subcollisions. Assumption behind the PYTHIA model (T. Sjöstrand - M. van Zijl - P. Skands) Cutoff needed for small p Hadrons are color neutral Coulomb potential screened for large impact parameters or small p. Fits to data cutoff 2 GeV. (Similar cutoff obtained in k -factorization formalism.) MI, saturation and final states 6 Gösta Gustafson LU,HU

7 Introduction Minimum bias and Underlying event ˇ Typically 2-3 interactions/event at the Tevatron, 4-5 at the LHC However: Subcollisions are correlated. Central collsions have many interactions Peripheral collisions have few interactions σ DPS = σ Aσ B σ eff for A B = σ eff 14.5 mb Strong enhancement MI, saturation and final states 7 Gösta Gustafson LU,HU

8 Introduction Minimum bias and Underlying event ˇ Associated Charge Density PYTHIA Tune A vs HERWIG PYTHIA tunes describe CDF data well (R. Field) PTmaxT > 2 GeV/cAssociated Particle Density: dn/d d Associated Particle Density CDF Preliminary data uncorrected theory + CDFSIM PTmaxT > 2.0 GeV/c PY Tune A Charged Particles ( <1.0, PT>0.5 GeV/c) PTmaxT not included PTmaxT Back-to-Back 30 < ET(jet#1) < 70 GeV "Jet#1" Region (degrees) But HERWIG (without multiple Data - Theory: Associated parton Particle interactions) Density dn/d d produces too few particles in the Back-to-Back CDF Preliminary PYTHIA Tune A direction opposite 30 < ET(jet#1) of PTmaxT! < 70 GeV data uncorrected theory + CDFSIM Associated Particle Density CDF Preliminary data uncorrected theory + CDFSIM Associated Particle Density: dn/d d PTmaxT > 2.0 GeV/c HERWIG Charged Particles ( <1.0, PT>0.5 GeV/c) PTmaxT not included PTmaxT (degrees) Back-to-Back 30 < ET(jet#1) < 70 GeV "Jet#1" Region Data - Theory: Associated Particle Density dn/d d CDF Preliminary data uncorrected theory + CDFSIM For PTmaxT > 2.0 GeV both PYTHIA and HERWIG produce slightly too many associated particles in the direction of PTmaxT! HERWIG Back-to-Back 30 < ET(jet#1) < 70 GeV Data - Theory 0.0 Data - Theory Charged Particles PTmaxT ( <1.0, PT>0.5 GeV/c) PTmaxT > 2.0 GeV/c (not included) "Jet#1" Region Charged Particles PTmaxT ( <1.0, PT>0.5 GeV/c) PTmaxT > 2.0 GeV/c (not included) "Jet#1" Region (degrees) (degrees) KITP Collider Workshop February 17, 2004 Rick Field - Florida/CDF Page 71 MI, saturation and final states 8 Gösta Gustafson LU,HU

9 Introduction Minimum bias and Underlying event ˇ Questions: Hadronization of many-parton system. Fit needs maximum color reconnection Correlations between impact parameter and momentum distributions expected, but not included MI, saturation and final states 9 Gösta Gustafson LU,HU

10 Eikonal formalism Transverse coordinate space suitable for rescattering and multple collisions Convolution in k -space Product in b-space S(b) = S 1 (b)s 2 (b)s 3 (b) S i = e η i(b) S = e P η i MI, saturation and final states 10 Gösta Gustafson LU,HU

11 Weizsäcker-Williams: Method of virtual quanta E g r r 2 short pulse I(t) E B g 2 1 r 2 δ(t) I(ω) g 2 d2 r r 2 1 dn g 2 d2 r r 2 dω ω g2 d 2 q dω q 2 ω MI, saturation and final states 11 Gösta Gustafson LU,HU

12 Coulomb field for r < 0.1 fm k > 2 GeV Gluon emission dipole field MI, saturation and final states 12 Gösta Gustafson LU,HU

13 Mueller Dipole model E 2 g 2 R2 r1 2r 2 2 ; dp 2 dy = ᾱd r 2π R 2 r 2 1 r 2 2 Cascade: Reproduces LL BFKL evolution MI, saturation and final states 13 Gösta Gustafson LU,HU

14 Dipole-dipole scattering ( ) f ij = α2 s 2 ln 2 r 13 r 24 r 14 r 23, Single gluon exhange Color reconnection MI, saturation and final states 14 Gösta Gustafson LU,HU

15 Eikonal approximation Unitarity Total, diffractive and elastic cross sections: σ tot d 2 b < 2(1 e P f ij ) > σ diff d 2 b < (1 e P f ij ) 2 > σ el d 2 b(< 1 e P f ij >) 2 (incl. elastic) The result is sensitive to fluctuations MI, saturation and final states 15 Gösta Gustafson LU,HU

16 Problems 1. LL BFKL not good enough 2. Non-linear effects 3. Massless gluon exchange violates the Froissart bound 4. Fluctuations and correlations. BK eq. mean field theory 5. Exclusive final states 6. Analytic calculations applicable at extreme energies MI, saturation and final states 16 Gösta Gustafson LU,HU

17 Monte Carlo Salam: Dipole splitting diverges for small r. Cross section finite but numerical difficulties New approach: Include NLL BFKL effects Include Nonlinear effects in evolution Remove virtual emissions Final states MI, saturation and final states 17 Gösta Gustafson LU,HU

18 NLL effects 3 major contributions: Running coupling Non-singular terms in splitting function (suppresses large z-values) Mostly included by energy conservation and the constraint that a daughter must not be faster than her recoiling parent Projectile-target symmetry (Energy-scale terms) Fixed by p -conservation (equivalent to consistency constraint) Includes effects beyond NLL: λ eff is not negative for large α s MI, saturation and final states 18 Gösta Gustafson LU,HU

19 Non-linear effects, Saturation Color suppressed relative to dipole splitting. Two dipoles with same color: Quadrupole. Better approximated by smaller dipoles Dipole swing MI, saturation and final states 19 Gösta Gustafson LU,HU

20 The swing Recoupling of the dipole chain Dipole loop Pomeron loop Similar recouling effect from gluon exchange MI, saturation and final states 20 Gösta Gustafson LU,HU

21 Almost frame independent result TeV 1.8 TeV 3.0 TeV no swing 1.8 TeV σ/σ δ Note: Number of dipoles not reduced. Saturation effect because smaller dipoles have smaller cross section. MI, saturation and final states 21 Gösta Gustafson LU,HU

22 Confinement Effective gluon mass 1 k 2 1 k 2 +m2 Dipole splitting: E r r 2 r r r max K 1 (r/r max ), r max = 1/m Dipole scattering: ln(1/r) K 0 (r max /r) Reduced spread to wider dipole distribution Froissart bound satisfied. (E. Avsar) MI, saturation and final states 22 Gösta Gustafson LU,HU

23 Applications pp Scattering Simple model for proton wave function: Triangle with 3 dipoles With swing With swing, Lab With swing, 1-pom. No swing No swing, Lab No swing, 1-pom. σ (mb) Tevatron AGASA s (GeV) MI, saturation and final states 23 Gösta Gustafson LU,HU

24 Elastic cross section d σ/dt e t (GeV 2 ) UA4 Tevatron MC LHC 546GeV (x100) 630GeV (x10) 14TeV (x0.1) 1.8TeV Energy variation of the dip fixed by the evolution MI, saturation and final states 24 Gösta Gustafson LU,HU

25 γ p scattering Geometric scaling 10 3 swing + quark masses H1, ZEUS 10 2 σ γ* p tot (µb) τ MI, saturation and final states 25 Gösta Gustafson LU,HU

26 Diffraction Sensitive to fluctuations and correlations Fluctuations within the cascade Less fluctuations needed in impact parameter profile. pp scattering more gray and less black/white. dσ tot /d 2 b Y= 9 Y=11 KT Y= 9 KT Y= b(gev -1 ) Diffractive excitation also reproduced. MI, saturation and final states 26 Gösta Gustafson LU,HU

27 DVCS and γ p Vp Quasi-elastic γ p γp scattering 10 H1 MC 10 H1 σ(pγ* pγ) (nb) 1 σ(pγ* pγ) (nb) 1 Q 2 =8GeV 2 Q 2 =15.5GeV 2 Q 2 =25GeV Q 2 (GeV 2 ) W (GeV) 100 MI, saturation and final states 27 Gösta Gustafson LU,HU

28 100 H1 σ(pγ* pγ) (nb/gev 2 ) Q 2 =15.5GeV 2 Q 2 =25GeV 2 (x0.1) Q 2 =8GeV 2 (x10) t (GeV 2 ) MI, saturation and final states 28 Gösta Gustafson LU,HU

29 γ p ρp σ(pγ* pρ) (nb) W=51GeV W=75GeV (x0.1) ZEUS H1 (x0.1) BG DGKP W=90GeV σ(pγ* pρ) (nb) Q 2 =4.8GeV 2 Q 2 =13.5GeV 2 H1 ZEUS BG DGKP Q 2 (GeV 2 ) W (GeV) Also t-dependence look good. As well as φ-production. Q 2 =32GeV 2 (BG = Boosted Gaussian wave function, DGKP = Dosch, Gousset, Kulzinger, Pirner) MI, saturation and final states 29 Gösta Gustafson LU,HU

30 Final States Dipoles which do not interact have to be treated as virtual and reabsorbed A C B r rapidity Total number of loops: Tevatron 3.5 ( ), LHC 5 FSR has to be added Work in progress MI, saturation and final states 30 Gösta Gustafson LU,HU

31 p n ch correlation Problem in present MCs. Fits to p -multiplicity correlation for hadrons need maximum color reconnection Dipole cascade adds contribution from p -multiplicity correlation for partons Cascade with many dipoles < r > small Stronger screening Smaller effective cutoff p 0 larger < p > in events with many hadrons MI, saturation and final states 31 Gösta Gustafson LU,HU

32 Toy model result (R. Corke) <p T > [GeV/c] CDF Run II Pythia No reconnection Pythia No reconnection + ES1 Pythia No reconnection + ES2 Pythia 8.114, RR * p 0 = 5.56 Pythia ES1, RR * p 0 = 4.35 Pythia ES2, RR * p 0 = Charged particle multiplicity MI, saturation and final states 32 Gösta Gustafson LU,HU

33 Dipole formulation of high energy collisions in transverse coordinate space Main ingredients: NLL contributions to BFKL Non-linear effects: Saturation and multiple subcollisions Confinement effects Includes momentum-impact parameter correlations Simple proton and photon model MC implementation Fair description of data: Total cross sections for pp and γ p (Quasi-) Elastic scattering in pp and γ p Diffractive excitation To come: Final states Wanted: Understanding the connection to t-channel picture of pomeron loops MI, saturation and final states 33 Gösta Gustafson LU,HU

34 Extras σ i /σ tot EL + SD L+R + DD EL SD R DD Y 0 /Y MI, saturation and final states 34 Gösta Gustafson LU,HU

35 σ γ* p tot (µb) swing no swing one pomeron swing + quark masses τ MI, saturation and final states 35 Gösta Gustafson LU,HU

36 Multiple Interactions, Saturation, and Final States in pp Collisions and DIS Gösta Gustafson Lund Univ. and Hamburg Univ. Epiphany 2009, Krakow 5-7 Jan. Dedicated to the memory of Jan Kwieciński Work done with Emil Avsar, Christoffer Flensburg, and Leif Lönnblad MI, saturation and final states 36 Gösta Gustafson LU,HU