1. Jet Fragmentation Ali Hanks JClub June 21, 2006 Ali Hanks - JClub

2. Motivation • Jets provide a connection between pQCD and non-pQCD • Jet fragmentation/structure is driven by soft QCD • Fragmentation functions are important for many theory calculations • Indentified particle multiplicities • Particle correlations • Jet fragmentation models are a key part of Monte Carlo event generators • Modification of fragmentation functions is a signature of medium effects in heavy ion collisions • Jet energy loss • Baryon/Meson suppression Ali Hanks - JClub

3. Intial parton distributuions: PDFs Long range = non-perturbitive Hard scattering of two partons Short range = perturbative Hadronization of scattered partons Long range = non-perturbative Hard Scattering in pp collisions Ali Hanks - JClub

4. Each step can be treated as independent of the others ab for any two partons, a and b, calculated from pQCD PDFs as functions of parton momentum fraction, x FFs for a parton to fragment to a hadron with momentum fraction z PDFs and FFs are independent of the process used to determine them (universality) Factorization Ali Hanks - JClub

5. Two partons collide (perturbative) Scattered parton emits a shower of quarks and gluons Parton Cascade (perturbative) Hadronization Partons pick up color matching partner from see of virtual quarks and gluons We can then observe these hadrons or there decays Jet Production Ali Hanks - JClub

6. FFs are independent of the process used to determine them  Scale independence ? No! Evolution is governed by the Dokshitzer-Gribov-Lipatov-Altarelli-Parisi (DGLAP) equation Scale Dependence - FF evolution • Pji = splitting function (more later) • This leads to a shift in the x distribution to lower values as the scale increases: • scaling violation Ali Hanks - JClub

7. This is the parton showering that occurs prior to hadronization Calculated perturbatively Dominated by collinear region z or (1-z)  1  log(Q2/2) Leading log approximation Requires the introduction of a cutoff scale Qcutoff (kT > Qcutoff) This usually means kT > 1 GeV Jets are a soft process  most interesting at kT < 1 GeV! Parton Splitting Ali Hanks - JClub

8. Gluon emission is coherent Strong interference Angular ordering of successive radiation Large cutoff is due to infrared divergences in the theory Add angular resolution to soft gluon emission (Msbar subtraction scheme) Analogous to energy resolution due to soft photon emission in QED Resume and find all IR divergences cancelled! Cutoff scale can be set as low as QCD ~ 200GeV Infrared Divergences and Coherence Ali Hanks - JClub

9. For inclusive hadron cross-sections there’s a sort of alternative to FFs  LPHD Local Parton Hadron Duality hypothesis Assumes hadronization occurs locally at the end of parton shower Hadrons “remember” parton distributions Nhadrons = KLPHD * Npartons Naively: as partons move away they drage a color-matching partner from sea of virtual quarks and gluons to become hadrons each parton becomes a hadron e.g. KLPHD(all hadrons) ~ 1 , KLPHD(+/-) ~ 1/2 - 2/3 Hadronization I Ali Hanks - JClub

10. We obtain our fragmentation functions by solving the DGLAP evolution equation  The normalization N, and parameters , , and  can be expressed as polynomials in a scaling variable  the initial energy scale 0 and QCD (or MS) taken as inputs This is then fit to data to obtain values for these parameters Hadronization II - Fragmentation Functions Ali Hanks - JClub

11. Hadronization II - Fragmentation Functions Ali Hanks - JClub

12. Three main models (with many variants and hybrids: Lund String Model Independent Fragmentation Models Cluster Fragmentation Models Goal of each is to represent existing data well and provide a framework or predicting future results while remaining internally consistent Partons from parton shower are transformed to colorless hadrons Use the Local parton-hadron duality hypothesis Hadron level momentum flow and quantum numbers follows the parton level The flavor of the quark initiating the jet is found in a hadron near the jet axis Fragmentation in Monte Carlo Hadronization Models Ali Hanks - JClub

13. Preconfinement of color (after parton shower) partons generated in the branching process tend to be arranged in confined color-singlet clusters The cluster mass is constrained by the infra-red cutoff used in the parton shower After the parton shower these clusters split non-perterbatively into quark anti-quark pairs enforced due to the small cutoff scale Does not require a fragmentation function to describe the transition or any free parameters Clusters typically decay into two hadrons depending on the mass of the cluster Cluster Fragmentation Model Ali Hanks - JClub

14. Models are probabilistic and iterative Process is described in terms of a few simple underlying branchings Color “string” stretched between q and q-bar moving apart The string is what is fragmenting rather than the partons Confinement with linearly increasing potential (1GeV/fm) String breaks to form 2 color singlet strings Process continues as long as the invariant mass of the string is greater than the on-shell mass of a hadron Lund String Model Ali Hanks - JClub

15. The simplest model is a color-singlet 2-jet event Energy stored in color dipole field increases linearly Related to presence of a triple-gluon vertex (self-interaction) Color flux tube formed as partons move apart Uniform along its length  confinement picture with linear potential Lund String Model (cont’d) • When the potential energy in the string gets large enough it breaks, producing a new quark antiquark pair • The system splits into two color-singlet systems • This will continue if either system has enough mass Ali Hanks - JClub

16. Pairs are generated according to the probability of a tunnelling process Leads to a flavor-independent gaussian spectrum for the pT of the pairs The string has now transverse excitations so the pT of the quark and antiquark pair must cancel in the string rest frame This tunnelling picture implies the suppression of heavy-quark production s quarks are produced with a suppression relative to the lighter quarks but there is still no mechanism for the production of charm and heavier quarks Lund String Model (cont’d) Ali Hanks - JClub

17. Meson production: choice between the possible multiplets for meson production Relative composition not given from first principles Spin counting suggests a 3:1 mixture of vector and pseudoscalar multiplets The mechanism follows naturally from idea that the meson is a short piece of string between two quark antiquark endpoints Baryon production: harder to generalize - two main scenarios are avaiable Diquark picture: any flavor q could be represented as an antidiquark Popcorn model: baryons appear from successive production of several qqbar pairs Lund String Model (cont’d) Ali Hanks - JClub

18. The hadron pT was determined from the pT of the new qqbar pair created Need to determine the energy and longitudinal momentum Momentum is constrained already In an iteration from the quark end, we then have We can now determine the fragmentation function, i.e. the probability that a given z is picked Note: result should be same if we start itereation with qbar = left-right symmetry Two free parameters remain that must be adjusted to fit the data Lund String Model (cont’d) Ali Hanks - JClub

19. Fragmentation of any system of partons is described by an incoherent sum of independent fragmentation procedures for each parton Carried out in c.m. frame of the jet system Uses an iteretative process: jet qq1 + jetremainder where the pair and the remainder jet are collinear The remainder jet is just a scaled version of the original Momentum sharing is given by a pdf f(z) where z is the momentum fraction of the hadron f(z) is assumed to be independent of the remaining energy Internal inconsistencies arrise within the details of this model so it is generally used just for special studies Independent Fragmentation Model Ali Hanks - JClub