Hadronization: Concepts and Models from Perturbative to Non-Perturbative QCD

Hadronization: Concepts and Models From Perturbative to Non-Perturbative QCD

Bryan Webber University of Cambridge Hadronization Workshop ECT*, Trento, 1-5 Sept 2008

Hadronization ECT* 08 1 Bryan Webber What is Hadronization? In practice, two rather distinct meanings: • General concepts/models for soft QCD – Local parton-hadron duality (LPHD) – Universal low-scale effective α S (ULSEA)

• Models for formation of individual hadrons – Monte Carlo models: string & cluster – Thermal/statistical models – AdS/QCD

Hadronization ECT* 08 2 Bryan Webber General Concepts • Local parton-hadron duality – Momentum & flavour follows parton flow – Predicts asymptotic spectra – Predicts two-particle correlations • Universal low-scale effective αS – Related to “tube” model – Regulates IR renormalons in PT – Predicts power corrections to event shapes – Predicts jet shapes and energy corrections

Hadronization ECT* 08 3 Bryan Webber Local parton-hadron duality • Evolution equation for fragmentation function has extra z2 due to soft gluon coherence ∂ 1 dz α t F (x, t) = S P (z)F (x/z, z2t) ∂t z 2π !x • Solution by moments t dt F˜(N, t) exp γ(N, α ) ! F˜(N, t ) ∼ S t 0 !"t0 ! # 1 αS N 1+2γ(N,α ) γ(N, α ) = z − S P (z) S 2π !0 • Anomalous dimension dominates asymptotically

Hadronization ECT* 08 4 Bryan Webber 1 αS N 1+2γ(N,α ) γ(N, α ) = z − S P (z) S 2π !0 CAαS 1 ∼ π N 1 + 2γ(N, α ) − S • This is regular at N=1

1 2 8CAαS γ(N, αS) = (N 1) + (N 1) 4 !" − π − − # C α 1 1 2π = A S (N 1) + (N 1)2 + 2π − 4 − 32 C α − · · · ! ! A S

Hadronization ECT* 08 5 Bryan Webber t αS (t) dt! γ(N, αS) γ(N, α (t!)) = dα S t β(α ) S ! ! ! S

where β ( α ) = b α 2 + . Hence S − S · · · ˜ 1 2CA 1 1 2π 2 F (N, t) exp (N 1) + 3 (N 1) + ∼ ! b παS − 4bαS − 48b#CAαS − · · · $ " αS =αS (t) Mean Position Width multiplicity of peak of peak • Gaussian in N Gaussian in ξ ln(1/x) ↔ ≡ • Mean multiplicity 1 n(s) = dx F (x, s) = F˜(1, s) ! " !0 1 2CA 2CA s exp exp ln 2 ∼ b !παS(s) ∼ πb Λ " # $

Hadronization ECT* 08 6 Bryan Webber Average Multiplicity Width of distribution Mean number of hadrons is N = 1 moment of fragmentation function: 1 2 1 1 2π 3 σ = (ln s)4 . n(s) = dx F (x, s) = F˜(1, s) 24b C α3(s) ∝ ! " s A S ! Z0 LPHD Predictions 1 2CA 2CA s exp exp ln 2 ∼ bsπαS(s) ∼ s πb Λ „ « + # 8 e e : • Good agreement with data LEP 206 GeV (plus NLL corrections) in good agreement with data. LEP 189 GeV 7 LEP 133 GeV LEP 91 GeV TOPAZ 58 GeV 6 TASSO 44 GeV TASSO 35 GeV 5 TASSO 22 GeV ! DIS: * 2 /d H1 100-8000 GeV " ZEUS* 80-160 GeV2 d 4 * 2

" ZEUS 40-80 GeV * 2 1/ H1 12-100 GeV 3 ZEUS* 10-20 GeV2

0 0 1 2 3 4 5 6 !=ln(1/xp)

6 9 Hadronization ECT* 08 7 Bryan Webber LPHD in pp dijets CDF Preliminary Mjj=82 GeV Mjj=105 GeV Mjj=140 GeV

CDF Preliminary !!!! !!!! !! !! !!!

Mjj=183 GeV Mjj=229 GeV Mjj=293 GeV

d dN

! ent v

e ximation 1 N

Mjj=378 GeV Mjj=488 GeV Mjj=628 GeV Leading Log Appro ragmentation without color coherence F MLLA Fit: (CDF Data only)

Qeff = 256 +_ 13 MeV

1 ! =log( _ ) Mjj sin x Hadronization ECT* 08 8 Bryan Webber where a is a constant that depends on the number of colors and the number of effectively where a is a constant that depends on the number of colors and the number of effectively masmslaesslsessqquuaarrkks.sT. hTe uhneknuownnktneromwOn(1)tiesremxpecOted(1to)biesinedxepeencdetnetdoftτo. Tbhee pirneddicetpedendent of τ. The predicted dependence of the inclusive momentum distribution on jet hardness is shown in Fig. 1. dependence of the inclusive mowmheernetaumis adciosntsrtiabnutttihoant doenpejnedts hoanrtdhne ensusmibsershofowconlorisnanFdigth. e1n.umber of effectively The two-parton momentum correlation function R(ξ1, ξ2) is defined to be the ratio of the massless quarks. The unknown term O(1) is expected to be independent of τ. The predicted Ttwhoe- atnwdoon-pe-paarrttoonnmmomoenmtuemndtiustmribuctioonrrfuenlcattioinosn: function R(ξ1, ξ2) is defined to be the ratio of the dependence of the inclusive momentum distribution on jet hardness is shown in Fig. 1. D(ξ1, ξ2) two- and one-parton momRe(nξ1t,uξ2m) = distribut,ion functions: (2) TDh(eξ1t)wDo(ξ-2p)arton momentum correlation function R(ξ1, ξ2) is defined to be the ratio of the

d2N two- and one-parton momentum distribution functions: where D(ξ1, ξ2) = dξ1dξ2 . The momentum distributions Dar(eξn1o,rξm2a)lized as follows: R(ξ1, ξ2) = , (2) D(ξ)dξ = n , where n is the average multiplicity of partons in a jet, and ! " ! " D(ξ1)D(ξ2) D(ξ1, ξ2) R(ξ1, ξ2) = , (2) ! D(ξ1, ξ2)dξ1dξ2 = n(n 1) for all pairs of partons in a jet. The average multiplicity ! − 2" D(ξ1)D(ξ2) d N o!f partons n is a function of the dijet mass Mjj and the size of the opening angle θc. For where D(ξ1, ξ2) = dξ1dξ2 . The momentum d2 istributions are normalized as follows: ! " where D(ξ , ξ ) = d N . The momentum distributions are normalized as follows: θ = 0.5, n varies from 6 to 12 for M in the r1ang2e 80–600dGξ1edVξ2/c2 [4]. D(ξc )dξ ! =" nT,wo-particlew∼ here∼ n jijs th eenergyaverage m correlationsultiplicity of partons in a jet, and The Fong-Webber approximation of EqD. ((ξ2)dfξor t=he twno-p,artwonhemreomentumiscortrheelatiaovnerage multiplicity of partons in a jet, and ! " ! " ! " ! " ) 1.6 )

2 1.6 2 1.4 CDF Run II 2 CDF Run II ! ! ! function [6] can1 be written as follows: ! ! " " D(ξ1, ξ2)dξ1dξ2 = n(n 1) fDo(rξ1a, ξll2)dpfitξ toa1 CDFdirξ datas2 =of np(anrto1n)s " fionr aalfitl toj pCDFea tdatai.rs oTf hpeartaovnesriangae jmet.ulTtihpeliacvietryage multiplicity , , 1 1.5 uncertainty of the fit 1 1.5 uncertainty of the fit ! ! − " ! " ! − " Fong/Webber Q =180 MeV " Fong/Webber Q =180 MeV 1.3 eff eff

C( 1.4 R.Perez-Ramos Q =230 MeV C( 1.4 R.Perez-Ramos Q =230 MeV ! eff eff ! 0.5 of partons n is a functi2on of the dijet mass Mjj and the size of the opening angle θc. For of partons n isR(a∆ξfu, ∆nξct)i=onr !+2ofr (t∆hξe +d1.3∆ijξeQ=E)t+m# =100*0.5=50r a(∆ssξ M GeV∆ξ )a,nd t1.3he Q=Esiz# e=100*0.5=50(o3f) t hGeVe opening angle θ . For 1 2 0" 1 1 2 jet c 2 1 jj2 jet c c = 1.2 ! " ! 1 − ! " " 1.2 1.2 2 θc = 0.5, n varies from 6 to 12 for Mjj in the range 80–600 GeV/c [4]. 0 1.1 1.1 ! " ∼ 1.1∼ 2 θc =w0he.r5e,∆ξn= ξvaξr0i,easndftrhoemparame6tertsor0, r1,1a2ndfro2rdeMfinjejthiensttrehngethraofntgheeco8r0re–la6ti0on0 GeV/c [4]. − 1 1 ! " ∼ ∼1The Fong-Webber approximation of Eq. (2) for the two-parton momentum correlation " 0.9 0.9 and depend o-0.5n the variable τ =! ln(Q/Q ). Equation (3) is valid only for partons with ξ 1 =- eff " 0.8 0.8 The Fong-Webber appro! xima0.9tion of Eq. (2) for the two-parton momentum correlation 2 function [6] can be written as follows: around the peak of the inclusive parton mom0.7entum distribution, in the ran0.7ge ∆ξ 1. -1 ∼ ± 0.8 0.6 Text 0.6 function [6] can-1 be-0.5wri0tten0.5 as 1follows:-2 -1.5 -1 -0.5 0 0.5 1 1.5 2 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 The parameters r0, r1, and r2 are calc"u! lated separately for quark and g- luon jets from an + 1 "!1 "!2 "!1 "!2 2 R(∆ξ1, ∆ξ2) = r0 + r1(∆ξ1 + ∆ξ2) + r2(∆ξ1 ∆ξ2) , (3) expansion in powers of 1/√τ using the assumption that the number of effectiveCDFly m,a arXiv:0802.3182ssless − quarks N is 3. Keeping only terms controlled by theory, the parameters are: 2 f R(∆ξ1, ∆ξ2) w=herr0e +∆ξr=1(ξ∆ξ1ξ +, an∆dξt2h)e+para2m(∆eteξr1s r ,∆r ξ,2a)nd, r define the strength(3of)the correlation − 0 −0 1 2 q 0.64 q 1.6 q 2.25 r = 1.75 , anrd =depen,d onr t=he vari,able τ = ln(Q/Qe(ff4)). Equation (3) is valid only for partons with ξ 0 − √τ 1 τ 3/2 2 − τ 2 where ∆ξ = ξ ξ0, and the paarraomunedtethres pre0a,kro1f, tahnedinrcl2usdiveefipnaerttohnemsotmreenntgutmh doisftrtihbueticoon,rrienlathteiornange ∆ξ 1. − CP Fong & BW, ∼ ± g 0.28 Theg pa0r.a7metersg r , 1r.0, and r are cNPalc uB355(1991)54lated separately for quark and gluon jets from an and depend on ther0 =va1r.3i3able τ, =r1ln=(Q/,Qeffr2)=. 0 Eq1 u, ation2 (3) is v(a5l)id only for partons with ξ − √τ τ 3/2 − τ 2 Hadronization ECT* 08 expansion in pow9 ers of 1/√τ using the asBryansum pWtebberion that the number of effectively massless arouwnhderetqhaendpgesaupkersocrfiptshdeeniontectlhuesciovrreelaptiaonrtpoarnammeteorsmfoer npatrutomns indiqsutarkibjeutstaiondn, in the range ∆ξ 1. quarks N is 3. Keeping only terms controlled by theory, the parame∼ter±s are: gluon jets, respectively. f The parameters r0, r1, and r2 are calculated separately for quark and gluon jets from an The theoretical prediction of the shape of the two-parton momqentum correl0a.t6io4n distri-q 1.6 q 2.25 r0 = 1.75 , r1 = , r2 = , (4) expabnutsioinonfunicntiopn oiswsheorwsn oinf F1ig/. √2. τAlounsginthge ctehnteraladsisaguomnalp∆tiξon= th∆aξ−t, t√thheτeshanpue mof berτ 3o/2f effectiv−elyτ 2massless 1 − 2 the two-parton momentum correlation is parabolic with a maximum at ∆ξ1 = ∆ξ2. Along quarks Nf is 3. Keeping only terms controlled by theory, the parameters are: 0.28 0.7 1.0 rg = 1.33 , rg = , rg = , (5) 11 0 − √τ 1 τ 3/2 2 − τ 2 q 0.64 q 1.6 q 2.25 r0 = 1.75 , r1 = , r2 = , (4) −whe√reτq and g supersτcr3i/p2ts denote the −corrτel2ation parameters for partons in quark jets and gluon jets, respectively. T0h.2e8theoretical pred0i.c7tion of the shape1o.f0the two-parton momentum correlation distri- rg = 1.33 , rg = , rg = , (5) 0 bution function 1is show3n/2in Fig. 22. Along t2he central diagonal ∆ξ = ∆ξ , the shape of − √τ τ − τ 1 − 2 the two-parton momentum correlation is parabolic with a maximum at ∆ξ1 = ∆ξ2. Along where q and g superscripts denote the correlation parameters for partons in quark jets and gluon jets, respectively. 11 The theoretical prediction of the shape of the two-parton momentum correlation distribution function is shown in Fig. 2. Along the central diagonal ∆ξ = ∆ξ , the shape of 1 − 2 the two-parton momentum correlation is parabolic with a maximum at ∆ξ1 = ∆ξ2. Along

11 Asymptotics of perturbation theory

It is expected that perturbation series will diverge at high order. There may even be signs of this already for some observables, e.g. the Gross–Llewellyn Smith sum rule:

1 1 α α 2 α 3 dx (F ν + F ν¯) = 1 S 3.6 S 19 S + Universal low-scale6 3 ef3fective− π − απ S− π · · · !0 One source of divergence is renorm"alon#chain g"rap#hs • Infrared renormalon Q dp F t α (p ) ∼ Q S t !0 Q dp Q2 n = α (Q) t bα (Q) ln S Q S p2 n "0 # t $ ! ∞ n n β0αS = α (Q) n![2bα (Q)] F αS n! S S ∼ 2πp n n=0 % & ! $ • Divergent series: truncate at smallest term 1 ! Quark loops β0 = 2Nf /3 ( n m = [ 2 b α S ( Q )] − ) uncertainty⇒ − ⇒p = 1, 2, . . . depends on observable F nm nm Λ δF nm![2bαS(Q)]Infrared ren−ormalo=n low momentum in loops ∼ ∼ ⇔Q ! Hadronization ECT* 08 10 “Naive non-Abelianization”Bryan: rep Wlaebberce

Nf Nf 33/2 , β 11 2Nf /3 → − 0 → −

– Typeset by FoilTEX – 8 Power Corrections • Renormalon is due to IR divergence of • Postulate universal IR-regular αS • Power corrections depend on 1 µI α (µ ) = α (p ) dp 0 I µ S t t I !0 • Match NP & PT at µ 2 GeV I ∼

Hadronization ECT* 08 11 Bryan Webber Power corrections to event shapes

• 1/Q renormalon present in C, absent in y3 $ $ 0.04 3 C y # 0.5 # 0.035 JADE JADE DELPHI L3 OPAL ALEPH SLD DELPHI 0.03 L3 0.4 OPAL SLD 0.025 0.3 0.02

0.2 0.015

2 O(%S)+Power Corr. 0.01 2 0.1 O(%S) only 0.005

0 0 0 20 40 60 80 100 120 140 160 180 200 0 20 40 60 80 100 120 140 160 180 200 "" "" !s [GeV] !s [GeV]

Hadronization ECT* 08 12 Bryan Webber ULSEA results from e+e Distributions Mean Values 1 a) 0.8 0.9 b) 0.7 0.8 0.6 0.7 ! 0 0 average 0.5 average 0.6 1-T 1-T M , M 2 M 2 0.5 H H 0.4 H BT BT BW BW 0.4 C 0.3 C 0.08 0.09 0.1 0.11 0.12 0.13 0.1 0.11 0.12 0.13 S(MZ) !S(MZ)

Movilla Fernandez, Bethke, Biebel & Kluth, EPJ C22(2001)1

Hadronization ECT* 08 13 Bryan Webber FRIF Workshop on First Principles Non-Perturbative QCD of Hadron Jets

8 8

10 10 0 107 107 /dC /d d d 105 105 1/ 1/

103 103

10 10

10-1 10-1 H1 H1 10-3 10-3 0.0 0.1ULSEA0.2 0.0 results0.5 1.0 from DIS 0 C

Figure 9: Normalised event shape distributions corrected to the hadron level for ρ0 and the C-parameteFr.RFIFor Wdeotarkilshsoepe tohne First Principles Non-Perturbative QCD of Hadron Jets caption of Fig. 8. + • Consistent with e e ZEUS

0 0.55 1 s.d. errors T " 95% confidence region ! NLO( 2)+NLL+PC Fits (stat. + exp. sys. errors) 0.60 s ZEUS (prel.) 98-00 to DISTRIBUTIONS stat. and exp. syst. errors 0.5 TT 2

=2 GeV) M I B

µ B ( 0.55 " 0

0.45 c 0.50 0 0.4 C 0.45 C 0.35 H1 0.40 0.3 0.110 0.115 0.120 0.125 0.130 0.11 0.115 0.12 0.125 0.13 (m ) ! s (M ) s Z Z

Figure 10: Fit results to the differential distributions of τ, B, ρ0, τC and the C-parameter in the (αs, α0) plane [12]. The 2 2 Figure 11: Extracted parameter values for (αs,α0) from fits to differential distributions of shape variables [15]. The vertical 1σ contours correspond to χ = χmin + 1, including statistical and experimental systematic uncertainties. The value of αs (vertical line) and its uHadronizationncertainty (shaded ba nECT*d) are t a08ken from [16]. line and the shade14d area indicate the world average of αs(mZ ). Bryan Webber

R003 13

R003 14 In order to make an explicit connection with event shape studies [13], we can rewrite Eq. (3.18) in more detail as

1 β p K (µ ) = µ α (µ ) α (p ) 0 ln t + + 1 α2(p ) , (3.19) A I π I 0 I − s t − 2π µ β s t ! " I 0 # $ where α (1/µ ) µI α (k )dk is the average coupling over the infrared region, familiar 0 ≡ I 0 s t t from event shape studies, and we have carried out the subtraction of the perturbative % 67 π2 5 coupling, α (p ), to two-loop accuracy in the MS scheme, where K = C n . s t A 18 − 6 − 9 f Note that similar expressions in Ref. [13] are rescaled by the Milan facto&r, accoun'ting for gluon decays; this rescaling will be discussed below, in Section 3.5. The integral over the soft gluon direction can be evaluated by choosing polar coor- dinates in the η φ plane and expanding in powers of the radial variable. Discarding − the spurious collinear divergence arising when the gluon is emitted along the outgoing leg, which cancels against an identical one in the ‘global’ term, as shown in the Appendix, one ﬁnds

1 5 23 95 δp (1j) = C (µ ) + R R3 R5 + R7 . (3.20) # t$h 1j A I −R 16 − 3072 − 147456 O " # ( ) By symmetry, an identical result is obtained for the 2j dipole, formed by the trigger hard parton and the other incoming parton with momentum p2.

3.2 Dipole involving the trigger and recoil jets

In this case the transverse momentum of the soft gluon with respect to the dipole, which we label with (jr), is given by

κ2 = k2 e−η cosh2 η cos2 φ , (3.21) t,jr t − ( ) which leads to the integral

(jr) dφ cos φ δpt h = Cjr (µI ) dη . (3.22) # $ A 2 2 2 2π 2 2 3/2 *η +φ

In order to make an explicit connec1tion 1with ev1ent shap5e studies [13], we can rewrite δp (jr) = C (µ ) R + R3 R5 + R7 . (3.23) Eq. (3.18) in#mot$rhe detail jarsA I −R − 4 192 − 2304 O " # ( ) 3.3 Incoming dip1ole β p K (µ ) = µ α (µ ) α (p ) 0 ln t + + 1 α2(p ) , (3.19) A I π I 0 I − s t − 2π µ β s t The dipole involving the!two incoming partons, "labelleId as (012), i#s the sim$plest to compute, since in this case µκIt,12 = kt. For this dipole the integration over the interior of the jet does where α0 (1/µI ) 0 αPTs(k subtractiont)dkt is the average coupling over the infrared region, familiar not pr≡oduce a 1/R correction, since there is no collinear enhancement for radiation emitted from event shape studies, and we have carried out the subtraction of the perturbative % by the incoming partons as the jet becomes narrow. We expect radiatio6n7 fromπ2 this 5dipole coupling, α (p ), to two-loop accuracy in the MS scheme, where K = C n . s t A 18 − 6 − 9 f Note that similar expressions in Ref. [13] are rescaled by the Milan facto&r, accoun'ting for Dasgupta, Magnea & Salam, JHEP02(2008)055 gluon decays; this rescaling will be discussed below, in Section 3.5. The integral over the soft gluon direction can be evaluated by choosing polar coor- Hadronization ECT* 08 15 – 11 – Bryan Webber dinates in the η φ plane and expanding in powers of the radial variable. Discarding − the spurious collinear divergence arising when the gluon is emitted along the outgoing leg, which cancels against an identical one in the ‘global’ term, as shown in the Appendix, one ﬁnds

3.2 Dipole involving the trigger and recoil jets

In this case the transverse momentum of the soft gluon with respect to the dipole, which we label with (jr), is given by

κ2 = k2 e−η cosh2 η cos2 φ , (3.21) t,jr t − ( ) which leads to the integral

dφ cos φ δp (jr) = C (µ ) dη . (3.22) t h jr I 3/2 # $ A η2+φ2

1 1 1 5 δp (jr) = C (µ ) R + R3 R5 + R7 . (3.23) # t$h jr A I −R − 4 192 − 2304 O " # ( ) 3.3 Incoming dipole

The dipole involving the two incoming partons, labelled as (12), is the simplest to compute, since in this case κt,12 = kt. For this dipole the integration over the interior of the jet does not produce a 1/R correction, since there is no collinear enhancement for radiation emitted by the incoming partons as the jet becomes narrow. We expect radiation from this dipole

– 11 – ULSEA jet energy correction

Tevatron LHC 4 10 9 Cambridge/Aachen 3 Cambridge/Aachen 8 LHC, gg gg 2 Tevatron, gg gg 7 UE 6 UE 1 5 4

eV] 0

eV] 3 G

G [ [

-1

t t

p 1 p

Had -2

0 Had -3 -1 Pythia tune A -2 -4 -3 Herwig + Jimmy Pythia tune A -5 -4 Herwig + Jimmy - 2 CA A(µI) /R -5 - 2 CA A(µI) /R -6 -6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 0 0.2 0.4 0.6 0.8 1 1.2 1.4 R R

Hadronization ECT* 08 16 Bryan Webber Monte Carlo Models

• “Tube” (longitudinal phase space) model • Independent fragmentation model • Confinement & Lund string model • Preconfinement & cluster model

Hadronization ECT* 08 17 Bryan Webber “Tube” Model for Jet Fragmentation • Precursor of MC models • Shows some features of ULSEA Experimentally, two jets: Flat rapidity plateau and limited

Hadronization ECT* 08 18 Bryan Webber Tube model gives simple estimates of hadronization corrections to perturbative quantities.

E.g. Jet energy and momentum:

with mean transverse momentum. Estimate from Fermi motion

Jet acquires non-perturbative mass: Large: ~ 10 GeV for 100 GeV jets.

Hadronization ECT* 08 19 Bryan Webber Independent Fragmentation Model (Field-Feynman) MC implementation of tube model.

Longitudinal momentum distribution = arbitrary fragmentation function: parameterization of data. Transverse momentum distribution = Gaussian.

Recursively apply Hook up remaining soft and

Strongly frame dependent. No obvious relation with perturbative emission. Not infrared safe. Not a model of confinement. Hadronization ECT* 08 20 Bryan Webber Confinement Asymptotic freedom: becomes increasingly QED-like at short distances.

QED: + – but at long distances, gluon self-interaction makes field lines attract each other:

QCD:

linear potential  confinement Event Generator Physics 3 Bryan Webber Interquark Potential

Can measure from or from lattice QCD: quarkonia spectra:

 String tension

Event Generator Physics 3 Bryan Webber 2-d String Model of Mesons Light quarks connected by string. L=0 mesons only have ‘yo-yo’ modes:

Obeys area law:

Hadronization ECT* 08 23 Bryan Webber The Lund String Model Start by ignoring gluon radiation: annihilation = pointlike source of pairs Intense chromomagnetic field within string  pairs created by tunnelling. Analogy with QED:

Expanding string breaks into mesons long before yo-yo point.

Hadronization ECT* 08 24 Bryan Webber Lund Symmetric Fragmentation Function

String picture  constraints on fragmentation function: • Lorentz invariance • Acausality • Left—right symmetry

adjustable parameters for quarks and

Fermi motion  Gaussian transverse momentum. Tunnelling probability becomes

and = main tunable parameters of model

Hadronization ECT* 08 25 Bryan Webber Baryon Production Baryon pictured as three quarks attached to a common centre:

At large separation, can consider two quarks tightly bound: diquark

 diquark treated like antiquark.

Two quarks can tunnel nearby in phase space: baryon—antibaryon pair Extra adjustable parameter for each diquark!

Alternative “popcorn” model:

Hadronization ECT* 08 26 Bryan Webber Three-Jet Events

So far: string model = motivated, constrained independent fragmentation! New feature: universal Gluon = kink on string  the string effect

Infrared safe matching with parton shower: gluons with inverse string width irrelevant. Hadronization ECT* 08 27 Bryan Webber String Model Summary

• String model strongly physically motivated. • Very successful fit to data. • Universal: fitted to , little freedom elsewhere.

• How does motivation translate to prediction? ~ one free parameter per hadron/effect!

• Blankets too much perturbative information?

• Can we get by with a simpler model?

Hadronization ECT* 08 28 Bryan Webber Cluster Model: Preconfinement

Planar approximation: gluon = colour—anticolour pair.

Follow colour structure of parton shower: colour-singlet pairs end up close in phase space

Mass spectrum of colour-singlet pairs asymptotically independent of energy, production mechanism, … Peaked at low mass

Hadronization ECT* 08 29 Bryan Webber Cluster mass distribution • Independent of shower scale Q – depends on Q 0 and Λ

Hadronization ECT* 08 30 Bryan Webber The Naïve Cluster Model Project colour singlets onto continuum of high-mass mesonic resonances (=clusters). Decay to lighter well- known resonances and stable hadrons.

Assume spin information washed out: decay = pure phase space.

 heavier hadrons suppressed  baryon & strangeness suppression ‘for free’ (i.e. untuneable). Hadron-level properties fully determined by cluster mass spectrum, i.e. by perturbative parameters. Shower cutoff becomes parameter of model.

Hadronization ECT* 08 31 Bryan Webber The Cluster Model

Although cluster mass spectrum peaked at small m, broad tail at high m. “Small fraction of clusters too heavy for isotropic two-body decay to be a good approximation”  Longitudinal cluster fission:

Rather string-like. Fission threshold becomes crucial parameter. ~15% of primary clusters get split but ~50% of hadrons come from them.

Hadronization ECT* 08 32 Bryan Webber The Cluster Model

“Leading hadrons are too soft”

 ‘perturbative’ quarks remember their direction somewhat

Rather string-like.

Extra adjustable parameter.

Hadronization ECT* 08 33 Bryan Webber Strings Clusters “Hadrons are produced by “Get the perturbative phase hadronization: you must right and any old get the non-perturbative hadronization model will dynamics right” be good enough” Improving data has meant Improving data has meant successively refining successively making non- perturbative phase of perturbative phase more evolution… string-like…

???

Hadronization ECT* 08 34 Bryan Webber Comparisons with LEP1/SLC: Spectra

Hadronization ECT* 08 Bryan Webber Comparisons with LEP1/SLC: Shapes

Hadronization ECT* 08 Bryan Webber LEP data (91GeV) thermal model 10 multiplicities

10-1

10-2

-3

10 - ’ + 0 0 - - - + 0 ± 0 + ± ± + 0 ’ 0 0 ± 0 2 2 ± 0 * ! ! K K " " f a # # $ % f f p & ' ' ' ' ( * ++ 2 K* K* ) K (1520) (1285) (1420) 1 1 (1385) (1385) (1385) (1530) f f & ' ' ' Thermal/Statistical Model ( + • AssumeFigure 1 . e C o me p− a r i s o n b 2 e t wjetseen t hiner mthermalal model p requilibriumedictions and experimental particle multiplicities for e+e− collis→ions at √s=91 GeV. – 3 parameters T, V, γ s Table 2 Values of fit parameters in e+e− collisions at different energies. 3 2 √s[GeV] T[MeV] V[fm ] γs χ /dof 10 152 1.7 20 1.5 0.82 0.02 333/21 ± ± ± 29-35 156 1.7 24 1.4 0.92 0.03 95/18 ± ± ± 91 154 0.50 40 1.0 0.76 0.007 631/30 ± ± ± 130-200 154 2.8 46 4.3 0.72 0.03 12/2 ± ± ± However, excluding those particles from the fit does not result in a significant improvement of the χ2 values, as is disAcu Andronicssed below et. al., arXiv:0804.4132

A further difficulty is visible if one inspects χ2 contour lines as shown in Fig. 3. One notices Hadronizationin ECT*this 08figure an anticorre37lation between the three Bryanfit p Waebberrameters which is particularly strong in (T,V) space. Closer inspection reveals, in addition, a series of local minima which indicates the difficulty in the determination of the fit parameters. Such local minima are typical for poor fits and imply that the true uncertainties in the fit parameters are likely much larger than the values obtained from the standard fit procedure employed here.

Despite these caveats about ﬁt quality and uncertainties it is noteworthy that the temper- ature parameters obtained from the data are close to 155 MeV and nearly independent of energy, similar to results of previous investigations. In contrast, the volume increases with Hadronization Volume

• dV/dy ~ 5 fm3

Hadronization ECT* 08 38 Bryan Webber Thermal model results

LEP data (91GeV) thermal model 10 multiplicities

10-1

10-2

-3

10 - ’ + 0 0 - - - + 0 ± 0 + ± ± + 0 ’ 0 0 ± 0 2 2 ± 0 * ! ! K K " " f a # # $ % f f p & ' ' ' ' ( * ++ 2 K* K* ) K (1520) (1285) (1420) 1 1 (1385) (1385) (1385) (1530) f f & ' ' ' ( Hadronization ECT* 08 39 Bryan Webber Figure 1. Comparison between thermal model predictions and experimental particle multiplicities for e+e− collisions at √s=91 GeV.

Table 2 Values of fit parameters in e+e− collisions at different energies. 3 2 √s[GeV] T[MeV] V[fm ] γs χ /dof 10 152 1.7 20 1.5 0.82 0.02 333/21 ± ± ± 29-35 156 1.7 24 1.4 0.92 0.03 95/18 ± ± ± 91 154 0.50 40 1.0 0.76 0.007 631/30 ± ± ± 130-200 154 2.8 46 4.3 0.72 0.03 12/2 ± ± ± However, excluding those particles from the fit does not result in a significant improvement of the χ2 values, as is discussed below.

A further difficulty is visible if one inspects χ2 contour lines as shown in Fig. 3. One notices in this figure an anticorrelation between the three fit parameters which is particularly strong in (T,V) space. Closer inspection reveals, in addition, a series of local minima which indicates the difficulty in the determination of the fit parameters. Such local minima are typical for poor fits and imply that the true uncertainties in the fit parameters are likely much larger than the values obtained from the standard fit procedure employed here.

• Strongly-coupled gauge theory dual to weakly-coupled 5D gravity – Promising approach to IR behaviour of QCD – Relative hadron multiplicities given by 5D radial wave function overlap with common Gaussian – 4 parameters (1 energy dependent)

N Evans & A Tedder, PRL100(2008)162003

Hadronization ECT* 08 40 Bryan Webber Hadron Yields at LEP1

Hadronization ECT* 08 41 Bryan Webber Conclusions? • General concepts (LPHD, ULSEA) successful at 20% level, but – No systematic scheme for improvement – Don’t say anything about hadrons • Monte Carlo models more successful – Complete final states – Matched to perturbation theory – But ad hoc parameters • Other models (thermal, holographic) – Fewer parameters but limited predictions – Match to perturbation theory at cluster/string level?

Hadronization ECT* 08 42 Bryan Webber The Underlying Event • Protons are extended objects • After a parton has been scattered out of each, what happens to the remnants?

• Only viable current model: multiple parton interactions

Hadronization ECT* 08 43 Bryan Webber Multiple Parton Interaction Model (PYTHIA/JIMMY)

For small pt min and high energy inclusive parton—parton cross section is larger than total proton—proton cross section.  More than one parton—parton scatter per proton— proton

Need a model of spatial distribution within proton  Perturbation theory gives n-scatter distributions

Hadronization ECT* 08 44 Bryan Webber Double Parton Scattering

• CDF Collaboration, PR D56 (1997) 3811

σγjσjj σDPS = σeﬀ

+1.7 σeﬀ = 14 1.7 2.3 mb ± −

Hadronization ECT* 08 45 Bryan Webber Tuning PYTHIA to the Underlying Event

• Rick Field (CDF): keep all parameters that can be fixed by LEP or HERA at their default values. What’s left? • Underlying event. Big uncertainties at LHC...

Hadronization ECT* 08 46 Bryan Webber <=>+A*'60B"0%15C+DE//F.@G+H2101:5+?+416+I+&5@+ JFH=E?K@,G.+L ?H,P

. JIMMY4.1 - Tuning A ,- + JIMMY4.1 - Tuning B * ( )*+ )

( PYTHIA6.214 - ATLAS Tuning %'

" 15 CDF data #$%&' " ! 10 !"$

!"# 5 !"%

0 10 20 30 40 50

/0 12'#34$-(5'0(4$(6'78 !"#$%&'(

?@+/@+/%*4'5 /010(2(3)045+416+"#'+716'*8901:+;&'1"+4"+"#'+<=> !"# $%&'()'*+,--.

Hadronization ECT* 08 47 Bryan Webber Optimal Jet Cone Size

9 1 Tevatron

] 8 2 quark jets 0.9 7 2 pt = 50 GeV [GeV pth

2 UE 6 0.8 t p

+ 0.7 2 h t

4 best R p 3 0.6 + Tevatron, gluon jets 2 pert

2 Tevatron, quark jets t

p 0.5

2 2 LHC, gluon jets 1 ptpert ptUE LHC, quark jets 0 0.4 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 50 100 500 1000

R pt [GeV]

Hadronization ECT* 08 48 Bryan Webber