(Non)Perturbative QCD At The Linear Collider

QCD@ILCAngularitiesHadronization for jets(Non)Perturbative QCDat the Linear ColliderLorenzo MagneaUniversità di Torino – INFN, Sezione di TorinoILC Physics in FlorenceGGI – 13/09/07Perspective

QCD@ILCAngularitiesHadronization for jetsOutlineQCD@ILCQCD for new physicsPrecision QCDAngularitiesA family of event shapesResummation for angularitiesScaling of power correctionsHadronization for jetsHadronization and jet areaMonteCarlo resultsPerspectivePerspective

QCD@ILCAngularitiesHadronization for jetsPerspectiveQCD@ILC Like LEP before it, ILC will be a wonderful machine forprecision QCD studies Precision meaurements of αsEvent shape distributions, jets.Hadronization effectsHeavy quarks Precision QCD is necessary for many new physics studies(and for precise determinations of mtop , mW ) Our understanding of QCD is incomplete, new studies andmore data are important LEP unfinished jobs GigaZ Hadronization beyond modelling Universality of power corrections, shape functions

QCD@ILCAngularitiesHadronization for jetsQCD for new physics: Grand Unification(from: P. Zerwas)Perspective

QCD@ILCAngularitiesHadronization for jetsPerspectiveControlling QCD effects for SM/BSM physics Multijet final states are commonplace Trilinear Higgs coupling via e e HHZ (up to 6 jets) Top Yukawa coupling via e e tt̄H SUSY final states (t̃t̄ jets missing energy) Understanding jet definition and dynamics is necessary Jet algorithm, size dependence, hadronization corrections. Flavor tagging crucial Define jet flavor (Banfi et al.) Precision observables require refined QCD analysis:resummations, effective theories Mtop from threshold scan (see A. Hoang) MW from W W production (see G. Zanderighi)

QCD@ILCAngularitiesHadronization for jetsPerspective(Non)Perturbative QCD after LEP/SLC Theoretical progress in QCD has continued after LEP/SLC. Achieved: NNLO event shape distributions, jet cross sections QCD models: non-perturbative corrections to event shapedistributions, shape functions Experimental analysis has almost stopped (LHC beckons .) Existing data not fully exploited More precise future data (GigaZ?) powerful constraints on hadronization models Do we need power corrections at ILC? 2 Λαs (500 GeV)' 0.00093 , 500QCDπGeV ' 0.0005. For permille accuracy: we do. Much larger impact in selected regions in phase space

QCD@ILCAngularitiesHadronization for jetsPerspective(Non)Perturbative QCD after LEP/SLC Theoretical progress in QCD has continued after LEP/SLC. Achieved: NNLO event shape distributions, jet cross sections QCD models: non-perturbative corrections to event shapedistributions, shape functions Experimental analysis has almost stopped (LHC beckons .) Existing data not fully exploited More precise future data (GigaZ?) powerful constraints on hadronization models Do we need power corrections at ILC? 2 Λαs (500 GeV)' 0.00093 , 500QCDπGeV ' 0.0005. For permille accuracy: we do. Much larger impact in selected regions in phase space

QCD@ILCAngularitiesHadronization for jetsPerspective(Non)Perturbative QCD after LEP/SLC Theoretical progress in QCD has continued after LEP/SLC. Achieved: NNLO event shape distributions, jet cross sections QCD models: non-perturbative corrections to event shapedistributions, shape functions Experimental analysis has almost stopped (LHC beckons .) Existing data not fully exploited More precise future data (GigaZ?) powerful constraints on hadronization models Do we need power corrections at ILC? 2 Λαs (500 GeV)' 0.00093 , 500QCDπGeV ' 0.0005. For permille accuracy: we do. Much larger impact in selected regions in phase space

QCD@ILCAngularitiesHadronization for jetsPerspective(Non)Perturbative QCD after LEP/SLC Theoretical progress in QCD has continued after LEP/SLC. Achieved: NNLO event shape distributions, jet cross sections QCD models: non-perturbative corrections to event shapedistributions, shape functions Experimental analysis has almost stopped (LHC beckons .) Existing data not fully exploited More precise future data (GigaZ?) powerful constraints on hadronization models Do we need power corrections at ILC? 2 Λαs (500 GeV)' 0.00093 , 500QCDπGeV ' 0.0005. For permille accuracy: we do. Much larger impact in selected regions in phase space

QCD@ILCAngularitiesHadronization for jetsPerspective(Non)Perturbative QCD after LEP/SLC Theoretical progress in QCD has continued after LEP/SLC. Achieved: NNLO event shape distributions, jet cross sections QCD models: non-perturbative corrections to event shapedistributions, shape functions Experimental analysis has almost stopped (LHC beckons .) Existing data not fully exploited More precise future data (GigaZ?) powerful constraints on hadronization models Do we need power corrections at ILC? 2 Λαs (500 GeV)' 0.00093 , 500QCDπGeV ' 0.0005. For permille accuracy: we do. Much larger impact in selected regions in phase space

QCD@ILCAngularitiesHadronization for jetsPerspective(Non)Perturbative QCD after LEP/SLC Theoretical progress in QCD has continued after LEP/SLC. Achieved: NNLO event shape distributions, jet cross sections QCD models: non-perturbative corrections to event shapedistributions, shape functions Experimental analysis has almost stopped (LHC beckons .) Existing data not fully exploited More precise future data (GigaZ?) powerful constraints on hadronization models Do we need power corrections at ILC? 2 Λαs (500 GeV)' 0.00093 , 500QCDπGeV ' 0.0005. For permille accuracy: we do. Much larger impact in selected regions in phase space

QCD@ILCAngularitiesHadronization for jetsPerspectiveNNLO event shape distributions(from: T. Gehrmann et al., arXiv:0709.1608)The perturbative thrust distribution vs. LEP dataThe perturbative thrust distribution at ILC

QCD@ILCAngularitiesHadronization for jetsPerspectiveResummation and power correction effectsA fit of LEP data for the heavy jet mass distribution with a shapefunction from thrust (Gardi, Rathsman).

QCD@ILCAngularitiesHadronization for jetsPerspectiveImpact of nonperturbative correctionsDifferent observables behave differently, understanding necessary(M. Dasgupta, G. Salam).#y3 ELPHIOPALSLDL3TOPAZTASSOPLUTO0.120.025CELLOMK 200.03520304050 6080 10020 40 60 80 100 120 140 160 180 200""!s [GeV]Q (GeV)Data for the average Durham jet resolutionData for the average thrust vs. QCD predictionsparameter y23 vs. NLO QCD

QCD@ILCAngularitiesHadronization for jetsOn event shape distributionsExamples Thrust: T maxn̂Ppi ·n̂ Pi pi i ;τ 1 T . n̂ is used to define several other shape variables.P(pi ·pj )2 C-parameter: C 3 32 i,j (p ·q)(pj ·q) .i does not require maximization procedures.P Broadening: B ,r i H ,r2Pi pi n̂ pi select or combine hemispheres.1 P ηi (1 a) . Angularity: τa Qi (p )i e recently introduced, one-parameter family.Perspective

QCD@ILCAngularitiesHadronization for jetsPerspectiveAngularities Definition: τa Also: τa 1QPi1QPi (p )i e ηi (1 a).ωi (sin θi )a (1 cos θi )1 a , Some properties τ0 1 T ; τ1 B . a 2 for IR safety. a 1 for simplicity of resummation (recoil negligible). For negative a, high rapidity particles (w.r.t. the thrust axis)are weighted less: better collinear behavior. At one loop, with the thrust axis given by particle i, 1 a/2 τa (1 xix)i(1 xj )1 a/2 (1 xk )a/2 (j k) .

QCD@ILCAngularitiesHadronization for jetsPerspectiveResumming Sudakov logarithmsInfrared and collinear emission dominates the two-jet limit Large double logarithms of the variable vanishing in thetwo-jet limit (L log τ ; L log C ; . . .) enhance finite orders need to resum. A pattern of exponentiation emergeshiP k P2kpp ckp L exp Lg1 (αs L) g2 (αs L) αs g3 (αs L) . . .k αs In general the Laplace transform exponentiates. For thrust"ZZ 1 du uν ντ 1 dσe 1 B αs uQ2dτ e expσ dτ00 u!#2Z uQ dq 22 2A αs (q ).2u2 Q2 q

QCD@ILCAngularitiesHadronization for jetsPerspectiveResummation for angularities Sudakov logs at one loop have simple scaling with a. (1)αs1dσ (1)dσ2 22ln Cdτa2 a τa F πτa 2 a dτ log .log Resummation is intricate. To NLL accuracy2( Z1" uQZ 1 aadudq 2σ̃a (ν) exp 2A αs (q 2 ) e u ν(q/Q) 12uq0u2 Q2 2/(2 a)1 1 B αs (u Q2 ) e u ν2#). General a-dependence of Sudakovlogs is nontrivial."(1)4 2 aA1 xg1 (x, a) ln (1 x)β0 1 a x2 a #xx 1 ln 1 .2 a2 a

QCD@ILCAngularitiesHadronization for jetsPerspectiveScaling for the shape functionAn analysis of power corrections for angularities using the shapefunction approach (Berger, Sterman) shows a remarkable scaling. As done for thrust, focus on small τa , large ν, set IRfactorization scale µ, expand in powers of ν/Q (soft),neglecting ν/Q2 (collinear). In this case(a)SNP (ν/Q, µ)µ2Z q/Q du u1 a ν(q/Q)adq 22 2Aα(q)e 1sq20q 2 /Q2 u n1 X 1ν 'λn (µ2 ) ,1 a n 1 n!QZ The full result suggested by the resummation can beexpressed in terms of two shape functionsσ̃a (ν) σ̃a,PT (ν, µ) f a,NP νQ, µg̃a,NP νQ2 a ,µ ,

QCD@ILCAngularitiesHadronization for jetsPerspective Leading power corrections are described by f a,NP and obey h i1/(1 a)ννf a,NP Q, µ f 0,NP Q,µ. Scaling can be traced to boost invariance in the eikonal limit.A renormalon calculation breaks boost invariance but scalingsurvives in the Sudakov limit. DGE (Berger, LM) yieldsBasoft (ν, u) 11 a 5u/32esin πuπuΓ( 2u) ν 2u 1 2 u Collinear contribution shows an intricate structure offractional power corrections in DGE, but they are suppressedby ν/Q2 a , consistent with resummation. Scaling is a testable prediction with existingLEP data. ILC, GigaZ provide lever arm, precision.

QCD@ILCAngularitiesHadronization for jetsPerspectiveTesting the scaling ruleThe scaling rule is a prediction waiting for data analysis . in themeantime, it can be compared with PYTHIA output (Berger).1.00.020RPY(!,a)/RPT(!,a)0.8(1-a) !"p0.0150.0100.005a -0.50.6a -0.25a 00.40.20.000-1.0-0.8-0.6-0.4-0.20.0aShift in the position of the peak of τa distribution,between NLL result and PYTHIA, after rescaling by1 a, vs. shift for a 0 computed from data.0.010203040506070!The leading shape function for different a, PYTHIAoutput (solid) vs. scaled result (dashed).

QCD@ILCAngularitiesHadronization for jetsPerspectiveHadronization for jets, in hadron collisionsM. Cacciari, M. Dasgupta, LM, G. Salam Consider the single inclusive distribution for a jet observablepO(y, pT , R), with an effective jet radius R ( y)2 ( φ)2 . Measure the effect on the distribution of single soft gluonemission by each hard dipole at power accuracy. Define R-dependent power correction Oij(R) Zdη dφZ µf2πµc(ij)dκT“”(ij)αs κTkT kT pi · p j δO (kT , η, φ) . (ij) κ pi · k pj · kT Express leading power R dependence in terms of (universal?)moment of coupling A A µf Z µf dk 0k αs (k ) · k Note: only the final state dipole would contribute in e e annihilation

QCD@ILCAngularitiesHadronization for jetsPerspectiveRadius dependence: pT distribution Let O ξT 1 2pT / S . In this case In-In dipole 4 ξT ,12 (R) SZdη dφ2παs (kt )dkt4kt cos φ A(µf )ktSR22 R416 R6384! . In-Jet dipoless ξT ,1j (R)3η2Z 2 A(µf )Sη 2 φ2 R2S„dηdφ2παs (κt )dκtκtκtcos φ e 2 Jet-Recoil dipole ξT ,jr (R) 2 A(µf )S“2R”1 R 1 R3 . . . 296 In-Recoil dipoles ξT ,1r (R) 2 A(µf )S3(cosh η cos φ) 2«52323 R R .R81536“1 R28”9 R4 73 R6 . . . 51224576.

QCD@ILCAngularitiesHadronization for jetsPerspectiveRadius dependence: mass distributionFor comparison, let O νJ MJ2 /S . Now only gluons recombinedwith the jet contribute, and one finds nonsingular R dependence. In-In dipole νJ,12 (R) 1 A(µf )S“1 R44“””1 R8 O R12 4608, In-Jet dipoles““””73 R3 125 R5 νJ,1j (R) 1 A(µf ) R 16R7 O R9,921616384S Jet-Recoil dipole“””“5 R5 O R9 νJ,jr (R) 1 A(µf ) R 576,S In-Recoil dipoles νJ,1r (R) 1 A(µf )S“1 R432“””3 R6 169 R8 O R10 256.589824